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Exploiting Code Division Multiplexing with Decentralized Multi User Detection in the Satellite Multibeam Forward Link Riccardo De Gaudenzi, Nader Alagha, Martina Angelone and Gennaro Gallinaro
Abstract In recent years the need for increased satellite throughput has been tackled by extending the number of satellite beams thus allowing a higher spectrum reuse and peak throughput. However, the satellite antenna size and the number of simultaneous beams which can be generated on-board over a given coverage region can not grow beyond certain limits due to payload accommodation constraints. The next step being pursued to increase the system throughput resides in extending the frequency reuse among the loaded beams and to mitigate the effects of the increased co-channel interference through more advanced digital signal processing. This can be achieved in two different ways. The first one, which received a large attention in recent years, is to centrally mitigate the multi-beam channel cross-talk by exploiting pre-coding techniques at the gateway. The second approach, less investigated in the past, is to put in place decentralized multi-user detection (MUD) at the user terminal side. The pre-coding approach has the advantage of concentrating the extra processing complexity at the gateway but it requires non standard payloads or accurate payload calibration techniques and periodic channel estimation reporting from the user terminal. Instead, the decentralized approach can operate in combination with existing payloads and does not require any terminal’s periodic channel estimate reporting to the gateway. Only the signal-to-noise plus interference variations due to possible fading as for conventional Adaptive Coding and Modulation (ACM) shall be reported. One of the main barriers to the decentralized MUD approach so far was the demodulator complexity. Some simplified approach for conventional Frequency/Time Division Multiplexing schemes has been recently published and its applicability to the forward link investigated. In this paper we investigate the possible advantages deriving from the adoption of DirectSequence Code Division Multiplexing (DS-CDM) associated with affordable complexity of the MUD at the user terminal side. It is shown that the proposed MUD scheme can be practically implemented and provides sizeable advantages compared to current state-of-the art when the traffic is not evenly distributed among the beams i.e. when a subset of beams has a higher load than the others. European Space Agency, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands. e-mail: {
[email protected]}
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Keywords: Multiuser Detection, Multiaccess communication, Code Division Multiple Access. I. I NTRODUCTION AND P ROBLEM O UTLINE The search for higher satellite networks throughput and flexible accommodation of geographically uneven traffic requirements calls for (locally) increasing the throughput. The concept of full frequency reuse in multi-beam satellite networks is not new as the Globalstar Low Earth Orbiting (LEO) global personal mobile communication system implemented it back in the nineties [1]. To achieve that the Globalstar system air interface, derived from the terrestrial digital mobile standard IS-95 [2], is exploiting DS-CDM in the forward link and Code Division Multiple Access (CDMA) in the return link. In the forward link the high level of co-channel interference caused by the full frequency reuse is counteracted by the DS-CDM signal bandwidth expansion (inter-beam interference) and the use of beam orthogonal CDM Walsh-Hadamard channelization sequences (intra-beam interference) [3]. The use of orthogonal CDM mitigates the intra-beam but not the inter-beam interference. Further physical layer enhancements to mitigate the cochannel interference effects were investigated in [4] exploiting CDMA blind linear multi-user detectors [5], [6]. The throughput advantages of more advanced interference mitigation linear detector schemes were investigated in [7] and practically demonstrated in [4] and [8]. Although showing attractive and feasible performance improvements, the path of forward link decentralized interference mitigation was not further pursued possibly due to the lack of commercial success of CDMA-based mobile LEO satellite constellations. It should be remarked that the vast majority of the MUD literature is dedicated to the (terrestrial) return link. While for terrestrial networks the return link is largely affected by the near-far effect [3], this is not really the case for satellite. Often, the real throughput bottleneck resides in the forward link which represents a more challenging problem, in particular, when considering the practical implementation aspects. More recently, the interest for interference mitigation in multi-beam satellite networks has been revamping. This is because pre-coding potentially allows to achieve the capacity of the information theoretical broadcast channel. Quite some research results have been published related to the adaptation of centralized pre-coding techniques to multi-beam satellite networks [9]–[15]. Pre-coding adoption in satellite networks requires a remarkable technological step in terms of both ground and space segments. In the ground segment the pre-coding implementation needs an increased computational complexity at the gateway for large multi-beam networks and
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novel resource allocation techniques. Furthermore, pre-coding demands for a quasi-real time reporting to the gateway of the individual terminals channel estimates but has minimum impact on their complexity. This generates a considerable amount of return signalling proportional to the network terminal population. To support pre-coding techniques, the system has to ensure a high level of phase coherency and group delay alignment among the payload transponders and feeder link carriers [10]. This implies a number of practical constraints to be applied to the ground and space segment or requires the implementation of accurate calibration techniques. Another practical aspect reducing the pre-coding gain is related to the fact that typically the physical layer frame is filled by packets belonging to different users of the same beam. Thus the pre-coding coefficients applied to the same physical layer frame are averaged over several beam locations. This phenomenon called multicasting pre-coding can be partly alleviated by proper techniques described in [10]. In spite of the required higher system complexity, [10] reports pre-coding gains that range from 40% up to 140%, even after considering different practical impairments. Finally, for high throughput satellite (HTS) broadband networks the required wide feeder link bandwidth is generally obtained by splitting the link among a number (tens) of gateway stations spatially separated among them to allow the feeder link bandwidth reuse. This common HTS architecture largely reduces the pre-coding benefits [9], as each gateway can only mitigate the interference corresponding to the subset of the satellite beams. This practical limitation can be circumvented by interconnecting at baseband level the gateways modulators and performing a centralized multi-gateway resource management. This solution requires a higher interconnection speed between each gateway and the central processing facility. Alternatively, one can resort to the adoption of a frequency plan which maximizes the number of beams seen by a single gateway for a given feeder link bandwidth. Finally, it is remarked that to exploit the pre-coding advantages the beam frequency reuse has to be increased and correspondingly the feeder link bandwidth. Although this issue is common to MUD, the increased number of gateways further disadvantage the pre-coding performance unless at least one of the techniques mentioned before or in [14] is adopted. The issue of providing solutions to support non uniform traffic loading across the coverage area is not limited to broadband HTS systems. Satellite mobile networks operating at L or Sband are also looking for ways to locally increase hot traffic spots throughput. In this case, the local adoption of full frequency reuse is potentially achievable today exploiting for example the
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Inmarsat geostationary or Globalstar Low Earth Orbiting (LEO) satellite fleet. This is because Inmarsat latest satellites [16] are embarking a powerful transparent digital processor capable to flexibly allocate frequency and power resources per beam. Instead, as mentioned before, Globalstar has been designed to permanently operate with full frequency reuse among the satellite beams [1]. The above issues affecting the exploitation of pre-coding techniques motivate the exploration of decentralized interference mitigation techniques for the forward link of a multi-beam satellite network. Some recent publications have investigated the exploitation of soft iterative MUD in the forward link of a Frequency/Time Division Multiplexing (FDM/TDM) multi-beam mobile satellite network [17], [18]. The MUD gains are obtained at the expense of exponential demodulator complexity dependency on the number of relevant interferers. Instead, [17], [18] considers a reduced complexity soft MUD detector [19]. In this case, moderate throughput gains are possible in certain coverage locations despite the relatively simple soft-MUD scheme adopted. However, to obtain Frame Error Rate (FER) of 10−2 or less, a relatively high signal-to-noise ratio is required due to the combination of the Land Mobile Satellite Channel (LMS) fading considered and likely MUD algorithm convergence issues. In this paper we aim at further exploring the path initiated in exploiting DS-CDMA for the forward link of a multi-beam satellite combined with aggressive frequency reuse and affordable complexity decentralized MUD. Compared to past work [7], the idea pursued in this paper is to combine linear and nonlinear interference mitigation schemes e.g. Minimum Mean Square Error (MMSE) and Successive Interference Cancellation (SIC). This combination has been shown to be capacity achieving [20]. This finding, associated with the fact that MMSE-SIC detector can be practically implemented, makes MMSE-SIC an attractive solution to be investigated for the satellite multi-beam forward link case. In tackling the forward link design with decentralized CDM MUD two important concepts are exploited. The first one is that for all the beams where high throughput is requested, full frequency reuse will be adopted to increase the available user link bandwidth. The higher level of interference seen at the user side will be mitigated by the decentralized MUD. The second concept is that, in common with [18], the central system resource manager can seamlessly shift throughput from the cold adjacent beams to the hot beam. This is easily achievable thanks to the full frequency reuse scheme combined with multi-beam MUD capable user terminal and allows
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to adapt to the uneven traffic request in the various satellite beams. The resource management aspects of the system are not investigated in detail in this paper. The main difference compared to [18] is that we exploit a CDM physical layer which allows to operate with a single colour instead of two as for the TDM/FDM scheme adopted in [18]. Also, the proposed CDM MUD is able to simultaneously demodulate up to three beams instead of two as it is the case for [18]. The paper is organized as follows. The physical layer design, resource allocation and decentralized MUD implementation aspects are discussed in Sect. II. Physical layer simulation results are illustrated in Section III. In Section IV the system throughput calculation methodology is derived for a high throughput multi-beam satellite system configuration. The proposed CDM with distributed MUD system level performance results are reported in Sect. V and compared to the more classical FDM/TDM solution with and without MUD or pre-coding. Finally, Sect. VI summarizes the main findings of the paper. II. D ISTRIBUTED M ULTI -U SER D ETECTOR D ESIGN AND I MPLEMENTATION A SPECTS A. Physical Layer Design Aspects Dealing with practical MUD schemes it is important to design the CDM signals in a way to maximize the detector performance. Differently from the reverse link, in the forward link the signals transmitted by each satellite beam are generated by the same gateway. Therefore, they can be easily orthogonally multiplexed using the well known Walsh Hadamard (WH) sequences [21] covered by a common complex scrambling sequence to better randomize the spreading sequence. This approach is in line with the one adopted by the 3rd Generation Partnership Program (3GPP) Wideband Code Division Multiple Access (W-CDMA) [22]. The WH sequences have the property that, if aligned at chip level as it is the case here, they provide zero crosscorrelation for the CDM signals within the beam b when the number of active CDM signal tot components Kbeam (b) is less than the spreading factor SF, which is defined as the ratio between tot the chip rate and the symbol rate. Instead if SF < Kbeam (b) ≤ 2 · SF, one extra complex tot scrambling sequence has to be used within the same beam b to cover the remaining Kbeam (b)−SF
CDM signals. This case corresponds to a beam loading factor β(b) defined as 4
β(b) =
tot Kbeam (b) , 1 < β(b) ≤ 2. SF
(1)
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The key advantage of this approach is that there will be no intra-beam co-channel interference if there are no more than SF CDM signals multiplexed in the same beam. Using orthogonal WH channelization sequences within the beam reduces the amount of non orthogonal interference seen by the SIC detector. Instead, the MMSE detector present in front of the SIC, will see the signal space dimensions occupied by all the CDM sequences (orthogonal or not), thus it will not benefit from their orthogonality as it is the case for the SIC. Another aspect to be considered is the modulation format before spreading. Release 99 of the 3GPP W-CDMA forward link physical layer adopted QPSK modulation, WH channelization/spreading and complex scrambling [22]. The input binary symbols were serially to parallel converted and then each I-Q component X-ored with a common WH sequence and then the I-Q resulting components stream multiplied by a complex scrambling sequence [22]. In [6], [23], it has been shown that the use of QPSK modulation with single WH channelization sequence and complex spreading outperforms other physical layer solutions when coupled with an MMSE type of detector. The main reason for this finding is that, by using QPSK instead of BPSK modulated symbols, we double the signal space dimensionality (and SF) in which the MMSE detector operates. Furthermore, the use of a single WH channelization sequence for both I-Q signal components maximizes the number (SF) of orthogonal channelization sequences available in the beam. In the proposed forward link signal design a more general Amplitude Phase Shift Keying (APSK) modulation is adopted and the same chip rate is adopted for the WH channelization and the complex spreading/scrambling sequence. The reason is to maximize the possible number of CDM signals present in each beam to minimize the bit rate/beam allocation granularity. Analytically, the k-th baseband CDM signal for the satellite beam b can be written as s ∞ SF P (b) X ˜b X b d [i] c˜ [i, n] gTx [t − (n − 1)Tc − (i − 1)Ts ], sbk (t) = tot Kbeam (b) i=1 k n=1 k d˜bk [i] = dbp,k [i] + dbq,k [i], n o r(b,k) r(b,k) b SF c˜k [i, n] = w|k|SF [n] cp,k [|(i − 1)SF + n|SF·Lf ] + cq,k [|(i − 1)SF + n|SF·Lf ] , r(b, k) = 2b − 1 + bkcSF , where
(2)
p P (b) is the power associated to the satellite beam b, Lf indicates the number of symbols
per frame each having duration Ts , |k|SF represents the k modulo SF operation, bkcSF is the truncation to the lowest integer of k/SF, d˜b [i] is the complex baseband APSK i-th symbol, c˜b [l] k
k
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represents the l-th chip of the composite complex spreading/channelization sequence with period SF · Lf and chip duration Tc , wkSF [n] is the n-th chip of the k-th Walsh-Hadamard sequence and gTx (t) is the transmission chip pulse shaping filter response. We assume that the p, q √ components of the r-th complex scrambling sequence have amplitude crp,k [l] ∈ {±1/ SF} and √ crq,k [l] ∈ {±1/ SF}. The expression of r(b, k) takes into account the fact that the WH codebook tot (b), will not size is limited to SF and that the maximum number of codes for the beam b, Kbeam
exceed 2 · SF. Thus, as explained before, different beam scrambling sequences have to be used in case the number of active CDMs for beam b exceeds SF. The beam b CDM multiplex is then given by sb (t) =
tot (b) Kbeam
tot (b) Kbeam
X
X
sbk (t) =
k=1
s
k=1
∞ SF P (b) X ˜b X b d [i] c˜ [i, n] gTx [t − (n − 1)Tc − (i − 1)Ts ]. tot Kbeam (b) i=1 k n=1 k (3)
Figure 1 shows a functional block diagram of the gateway beam modulator. The input bit stream is digitally demultiplexed into a number of parallel streams each feeding the CDM components of the different beams served by the gateway. The orthogonal beam CDM components are then added together in a CDM beam multiplex prior scrambling by means of the complex beam scrambling sequence multiplication. The use of two different complex scrambling sequences for a specific beam is required when the number of active channels/beam exceeds SF. This is the reason why a second CDM multiplex generator is present. The different beams are then uplinked to the satellite payload using a different feeder link frequency and then converted to the common beams’user link carrier frequency. The signal received at the user location (x, y) in beam l can be expressed as sR (t|x, y) =
Nb X
hb (x, y) sb (t − ∆τb − τp ) exp { [(2π∆fb (t − ∆τb − τp ) + θb ]} + v(t) (4)
b=1
where hb (x, y) is the satellite beam b to receiver overall link gain coefficient, ∆τb , ∆fb and θb are the b-th beam carrier group delay, frequency and phase offset respectively caused by the different beams Radio Frequency (RF) chains (satellite payload and gateway uplink)1 , τp (x, y) is the satellite to terminal link propagation delay and v(t) is the complex AWGN process with Power Spectral Density (PSD) N0 . We now introduce the concept of the number of dominant 1
For notation simplicity we do not report their potential “slow” time dependence.
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dom beams Nbeam (l) representing the maximum number of beams that the MUD demodulator is able
to simultaneously demodulate in beam l. For notation simplicity, in the following we assume that dom Nbeam (l) is independent of the user location in the beam l. However, the dominant beams actual dom index b ensemble of size Nbeam (l), is location dependent and will be identified by Bdom (l, x, y). dom Clearly 1 ≤ b ≤ Nb . We now treat the co-channel interference coming from the Nb − Nbeam (l)
non-dominant beams as an AWGN process iob (t) with PSD I0 . Thus (4) can be rewritten as tot (b) s Kbeam ∞ SF X X P (b) X ˜b X b b d [i] c˜ [i, n] sR (t|x, y) = h (x, y) tot (b) i=1 k n=1 k Kbeam k=1 b∈Bdom (l,x,y)
·
gTx [t − τp − ∆τb − (n − 1)Tc − (i − 1)Ts ]
·
exp { [(2π∆fb (t − τp (x, y) − ∆τb ) + θb ]} + v(t) + iob (t).
CRC INCLUSION/ CODE BLOCK SEGMENTAT
FEC ENCODER
S/P
APSK MODULATOR
CHANNELIZATION SEQUENCES GENERATOR
CRC INCLUSION/ CODE BLOCK SEGMENTAT
FEC ENCODER
S/P
SUM
APSK MODULATOR
BEAM INFORMATION BIT STREAM DIGITAL DEMUX
COMPLEX SCRAMBLING SEQUENCES GENERATOR CRC INCLUSION/ CODE BLOCK SEGMENTAT
FEC ENCODER
S/P
Fig. 1.
FEC ENCODER
S/P
SUM
APSK MODULATOR
CHANNELIZATION SEQUENCES GENERATOR
CRC INCLUSION/ CODE BLOCK SEGMENTAT
(5)
SUM
APSK MODULATOR
Functional block diagram of gateway beam CDM modulator.
Similarly to the approach followed in Wideband CDMA Satellite Universal Mobile Telecommunication Standard (S-UMTS W-CDMA) [4], each beam may have a dedicated Walsh sequence, dedicated to the beam code epoch acquisition, chip tracking as well as frequency and carrier
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phase estimation. Another sequence may be devoted to the beam signalling information common to all users in the beam. B. Physical Layer Design Impact on Satellite Resource Allocation Following the previous CDM physical layer design, in this section we outline the potential resource allocation flexibility provided by the selected scheme for the multi-beam satellite communication system scenario. As mentioned in Section I, one very interesting practical scenario is when we are in the presence of one or few hot spots surrounded by cold ones. This is exemplified in Fig. 2. Users in the hot spot like ST2 and ST3 can (also) be served by adjacent beams. More detailed discussion about hot spot resource management can be found in Sect. IV-B.
Fig. 2.
Example of multi-beam hot spot scenario.
Modern Geostationary (GEO) Mobile Satellite Services (MSS) satellites such as Inmarsat IV, Alphasat and Thuraya are equipped with semi-active multi-beam antennas and very powerful on-board transparent digital processors which can provide a high level of flexibility in terms
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of: a) frequency allocation/beam, b) frequency reuse scheme, c) power allocation/beam2 . The proposed CDM scheme is able to fully exploit such payload flexibility. First of all the satellite payload can allocate a full frequency reuse scheme around the hot spot(s) while keeping more conventional four colours frequency reuse scheme in other parts of the coverage region. Thus the feeder link bandwidth increase can be kept within acceptable limits if, as it is normally the case, the number of hot spots is bounded. Second, the MSS type of payload allows to unevenly allocate the beam power thanks to the presence of Multiport Power Amplifiers (MPA) on-board [24]. Thus the system resource management can optimize the beam power and active CDM components allocation depending on the traffic demand. For example, the hot beam can exploit the increased bandwidth and power allocated to this beam while adjacent beams can still provide the required level of traffic reusing the same frequency but less power and/or CDM components thanks to the MUD interference mitigation capabilities. The overall optimization of power, CDM codes and physical layer modulation and coding parameters (MODCOD) allocation in a real system will be shortly discussed in Sect. V-B. Let now introduce some definition which will be extensively used in the following. The dominant beams introduced in Sect. II-A, are the ones which are attempted to be demodulated by the MUD. A dominant beam becomes a serving beam if it is carrying useful information for the current user location. Thus serving beam resources are shared with other served locations. The decision if a dominant beam is a serving beam at a given terminal location is based on the current estimated Signal-to-Noise plus Interference ratio (SNIR). If the SNIR falls below a certain threshold known to the demodulator through gateway signalling information, then the dominant beam is not used as serving beam. More details on the serving beam assignment logic can be found in Appendix A. C. MUD Implementation Aspects A functional block diagram of the iterative MMSE-SIC (iMMSE-SIC) demodulator is presented in Fig. 3. For simplicity, the MMSE-SIC demodulator shown in the figure refers to a single CDM (WH) component processing. 2
The beam extra power allocation is subject to payload implementation limitations. Typically only few extra dBs of power
can be allocated to a specific beam.
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USEFUL PAYLOAD BITS
FEC DECODER
ADC
CDM FRAME COMPLEX SAMPLES MEMORY
MMSE DETECTOR
CRC CHECK
CDM DEMODULATOR FEC ENCODING
REFINED FRAME CHANNEL ESTIMATION
CARRIER LOCAL OSCILLATOR FRAME CANCELLATION PROCESSOR
DETECTED FRAME REGENERATION
PILOT-AIDED CHANNEL ESTIMATION
DEMODULATOR CONTROLLER
Fig. 3.
Functional block diagram of the iterative MMSE-SIC CDM demodulator.
In our investigation, we use an iterative version of the well known MMSE-SIC detector with hard decisions described in [25]. Similar to the return link Enhanced Spread-Spectrum ALOHA packet detector described in [26], we first store the frame baseband complex samples in the demodulator memory. The boundaries of the frame are known to the terminal demodulator once the forward link signal has been acquired. As mentioned before, we assume that the timing of all the satellite beams are aligned with a good accuracy. The alignment of the CDM signal components within the same beam is typically perfect as the multiplex is generated at the same gateway station and goes through the same RF uplink and satellite chains. Some group delay offset is typically present among different beams as the CDM multiplexes go through different RF payload chains. This inter beam differential delay has practically no impact on the performance of the MMSE-SIC demodulator. The beams carrier frequency is also assumed to be similar although, strictly speaking, there is no need to have a tight carrier frequency synchronization for the CDM multiplex coming from different beams (see (5)). Following Sect. II-A, we could assume that users already know, from gateway signalling, the number of codes currently on air. Also the users can be assumed to be already synchronized to a common beam
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pilot component, which also provides an estimate of the received beam power. The MMSE operates on the CDM components of the dominant beams. The MMSE outputs are then fed to a bank of demodulators attempting to demodulate and decode the CDM frames. The Cyclic Redundancy Check (CRC) validity is performed at the FEC decoders bank output. If any of the FEC CRC is found to be correct, the corresponding CDM physical layer signal component will be reconstructed at the chip level (with the same sampling rate as the frame memory) using the full payload symbol knowledge to enhance the pilot-based channel estimation used for initial frame detection. The reconstructed CDM multiplex component will then be subtracted from the demodulator frame memory and the whole MMSE-SIC process is repeated. Normally the MMSESIC process stops here, instead following [25], we perform further MMSE-SIC detector iterations. Thus the whole process described above is repeated Niter times. The reason for repeating the MMSE-SIC process is that some of the frames that initially were not decodable may become decodable once other CDM components have been detected and cancelled from memory. The iterative nature of the proposed MMSE-SIC detector is benefiting from the large number of active CDM signal components. For example, assuming there is an equi-powered interfering (adjacent) beam, and β(b)SF active CDM components/beam with β(b) ≥ 1 and SF 1, even with a FER at the first iteration close to 1, say FER[1] = 0.6, the iMMSE-SIC is likely to converge. This is because in average there will be FER[1] · 2β(b)SF decodable frames at the first iteration. Thus the memory cleaning process can start and at the second iteration new frames will become decodable. Although the MMSE-SIC is an attractive MUD scheme, the canonical MMSE implementation is cumbersome as it requires real-time matrix inversion. Considering the target single user terminal decentralized MUD implementation, simpler algorithmic solutions as the ones reviewed in the following are required to limit detector complexity. There are several possible practical approaches to implement the proposed decentralized MUD MMSE-SIC scheme. The first one which has already been shown to be implementable in ASIC technology is the so called Blind Minimum Output Energy detector (B-MOE). Originally proposed for CDMA applications by Honig [5] it has been extended in [6] to support interferers carrier frequency error and asynchronous interference. The LMS approach for B-MOE is very attractive for the forward link where the CDM carriers are continuously transmitted. The main drawback of this solution is related to the fact it requires spreading sequences which are as long as the symbol (i.e.
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Lf 1), thus there is less cross-correlation averaging effect than in the case of frame long spreading sequences [3]. An alternative approach to full MMSE implementation is represented by the so called Multistage Detector approach introduced by Moshavi [30] and further elaborated in [31]. Using a multi-stage MMSE detector allows exploiting long spreading sequences (i.e. as long as the frame duration), thus allowing a better CDM interference averaging. Furthermore, the multistage detector approach adopted in this paper greatly simplifies the MMSE implementation and has a complexity almost linear with the spreading factor. However, the multi-stage approach requires an off-line computation of weighting coefficients. An example of Multistage Detector application on top of SIC for the reverse link of packet CDMA is reported in [25]. III. P HYSICAL L AYER S IMULATION R ESULTS This section describes the methodology adopted for analyzing the physical layer simulations for the proposed forward link decentralized interference mitigation scheme. We also investigate the physical layer sensitivity to key system parameters. A. Physical Layer Simulator Description For the physical layer simulator it is important to achieve a high degree of accuracy while allowing a reasonable simulation run time. Leveraging on the past experience related to the simulation of reverse link Enhanced Spread-Spectrum ALOHA (E-SSA) random access [26], the physical layer modelling has been implemented with an hybrid symbol/chip level approach. In [26] it has been shown that, emulating the co-channel interference by means of an equivalent Gaussian process for the iSIC the CDM(A) demodulator provides very accurate results. Instead, for the MMSE pre-SIC processing, a chip level simulation is required. To efficiently combine the two approaches the overall simulator runs at non spread symbol level while the MMSE stage is emulated in terms of detector SNIR estimation at each iteration step. To compute the SNIR at each MMSE+SIC iteration a chip level modelling of the satellite multi-beam CDM true physical layer model described in Sect. II-A is required. The physical layer model shall include modulation, WH channelization/spreading and beam unique complex scrambling sequences. To emulate the CDM sequences cross-correlation averaging effect taking place over the physical layer FEC block covered by the frame long scrambling sequence, the MMSE SNIR output is computed averaging different realizations of the symbol long spreading sequence chunks. Experimentally,
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it has been found that by averaging over twenty independent symbols long scrambling sequence realizations is sufficient to get accurate results. For deriving the SNIR at the MMSE output in the presence of an arbitrary CDM interference we exploited the semi-analytic approach described in Appendix B. The model, initially devised for the random access return link analysis, has been adapted to account for the fact that in the forward link the CDM interferers are chip synchronous and some of them (intra-beam interfers) are orthogonal. Instead, for the SIC processing, the multi-beam signal generation is performed at symbol level without channelization and scrambling sequences. This approach does not allow to sum together the signals which will instead be kept separated in the demodulator frame memory. For each CDM signal present in the demodulator memory and for each iMMSE-SIC demodulator iteration, once the MMSE output SNIR has been computed following the approach described in Appendix B, then a zero mean Gaussian process with equivalent MMSE output detector SNIR is applied at the APSK demodulator input. It is important to remark that during the iMMSE-SIC iterations the equivalent noise plus interference process samples generated at the first iteration are maintained in memory and scaled down in amplitude to account for the SNIR increase taking place during the iSIC demodulation process. This approach represents a slight worst-case approximation, as the interfering frames canceling process will modify part of the interference signature present in the frame memory while the thermal noise AWGN component will remain the same. The goodness of this approximation has been evaluated in Sect. IV-B where accurate physical layer simulation results have been successfully compared to the MMSE-SIC analytical model described in Appendix B. A very important element for the physical layer simulation corresponds to the inclusion of an accurate FEC modelling. We preferred to simulate a real FEC decoder at the user terminal rather than resorting to best fit of the decoder frame error rate as a function of the SNIR as successfully adopted in [27]. Unless stated otherwise, the selected FEC for the physical layer simulations is the 3GPP turbo decoder with coding rate r = 1/3 and B = 1000 information bits per frame. When the physical layer frame is declared to be successfully decoded following CRC verification, the frame content is used to regenerate the corresponding CDM signal component using the full frame information bits to perform a refined channel estimation (amplitude and carrier phase). The regenerated physical layer frame baseband signal is then cancelled from the current demodulator frame memory. In our initial simulations the channel estimation is assumed to be perfect which is
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a realistic assumption considering that experimentally it has been found that channel estimation error is typically below 1 % in AWGN channels not affected by significant non-linearity or phase noise [28]. Finally, as the frame memory in the simulator operates at symbol level there is no need to spread the regenerated baseband complex signal but it is sufficient to remove it at symbol level from the frame memory. A full physical layer simulator inclusive of the multistage MMSE detector and channel estimation algorithms is described and analyzed in Sect. III-B7. The following physical layer results are using a fixed modulation and coding format (i.e. QPSK, r = 1/3 FEC 3GPP turbo code) and given Eb /N0 value for each CDM code component. As a consequence, they are not meant to be representative of a forward link scenario exploiting ACM and fixed average power limit on each beam. This case will be investigated in Sect. IV-B.
B. Physical Layer Simulations 1) Channel Load Dependency: We have first simulated the performance of the proposed multiplexing scheme in a specific beam location (x, y) for three different specific interference configurations derived from typical multi-beam system level scenarios described in Sect. V-B. However, in the following physical layer simulation the single CDM component Eb /N0 value is kept constant independently from the number of active codes per beam. Furthermore, the physical layer coding rate and modulation format is independent from the actual SNIR. These initial simplifications will be overcome in the system level simulations reported in Sect. IV-B where the beam power constraints and adaptive physical layer will be accounted for. The selected interference scenarios are: a) first a case corresponding to a 2 beams cluster with one reference dom beam and one interfering beam i.e. Nbeam = 2 with C/I = 0 dB; b) second a case corresponding dom to a 3 beams cluster with one reference beam and two interfering beams i.e. Nbeam = 3 with C/I
respectively of 0 and 4 dB; c) third a case corresponding to a 4 beams cluster with one reference dom beam and three interfering beams i.e. Nbeam = 4 with C/I respectively of 0, 4 and 8 dB. Full
frequency reuse among the beams is assumed in all cases. In the physical layer simulations there was no attempt to optimize the individual CDM physical layer coding rate (or modulation scheme) to optimize the throughput. To reduce the number of possible configurations, all CDMs were using the same 3GPP turbo code FEC with code rate r = 1/3 and QPSK modulation.
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Sect. IV-B and V-B show the advantages deriving from using ACM for the CDM case. Let now introduce the normalized aggregated information load G and the normalized effective aggregate throughput3 Te both measured in bits/chip defined as G = βtot r log2 Mmod , where βtot =
dom PNbeam
b=1
Te = G(1 − FER),
(6)
β(b) = K tot /SF is the total CDM load factor and Mmod represents the
modulation cardinality. The normalized effective throughput Te represents the effective spectral efficiency of the physical layer in terms of correctly received bits/chip. Clearly in case of no frame in errors FER = 0, then Te = G. Figure 4 shows the simulated total normalized effective throughput Te and FER performance as a function of the total normalized information load for SF = 16 and main beam energy per bit to noise PSD Eb /N0 = 13.7 dB4 for 1-2 interfering beams, Eb /N0 = 17.7 dB5 for 3 interfering beams, FEC block frame size B = 1000 information bits. It is remarked the steep Packet Loss Ratio (PLR) versus βtot characteristic allowing to achieve at FER=10−4 2 bits/chip (3 beams cluster) or Te = 1.4 bits/chip (2 beams cluster). For the second case corresponding to a 3 beams cluster, it is interesting to observe that, thanks to the sizeable AWGN link margin (more than 10 dB), it is possible to decode the third cluster beam multiplex despite the 4 dB lower power of the third beam. This is boosting the total throughput by more than 40 %. For the the third case (4 beams cluster), Eb /N0 was increased to 17.7 dB to allow the detection of the third interfering beam 8 dB lower in power compared to the reference beam. In this case exploiting the four dominant beams, we gain another 25 % total throughput compared to the second case (three dominant beams) at the expenses of 4 dB higher SNR requirement. It is remarked that while the SIC performance improves with interference power unbalance and it is not sensitive to the total CDM load factor βtot , the MMSE is quite sensitive to βtot [32]. The optimum value of βtot for MMSE detector is around 0.7, which explains the reduction of the MMSE performance when operating with β > 2. 3
In the following physical layer performance evaluation we do not consider the impact of sharing resources among adjacent
beams which is dealt with in Sect. V. 4
It is recalled the relation for the energy per chip to noise PSD Ec /N0 = [Eb /N0 ]r log2 (Mmod )/SF.
5
This value is selected to support the current simplified analysis not exploiting physical layer adaptation. More realistic Eb /N0
values will be considered in Sect. V dealing with system level analysis.
17
3
2 beams C/I=[0] dB, Eb/N0=13.7 dB 3 beams C/I=[0, 4] dB, Eb/N0=13.7 dB
2.5 Normalized Effective Throughput, Te [bits/chip]
4 beams C/I=[0, 4, 8] dB, Eb/N0=17.7 dB
2
1.5
1
0.5
0
0
0.5
1 1.5 2 2.5 Total Normalized Information Load, G [bits/chip]
3
3.5
(a) Total Throughput 0
10
−1
FER
10
−2
10
−3
10
2 beams C/I=[0] dB, Eb/N0=13.7 dB 3 beams C/I=[0, 4] dB, Eb/N0=13.7 dB 4 beams C/I=[0, 4, 8] dB, Eb/N0=17.7 dB −4
10
0
0.5
1 1.5 2 2.5 Total Normalized nformation Load, G [bits/chip]
3
3.5
(b) Packet Loss Ratio Fig. 4.
Simulated iMMSE-SIC CDM detector performance as a function of the total normalized load for the case of: a) 2
beams cluster (1 interfering beam) with C/I =0 dB; b) 3 beams cluster (2 interfering beams) with C/I =[0, 4] dB; c) 4 beams cluster (3 interfering beams) with C/I =[0, 4, 8] dB, Eb /N0 = 13.7 dB for 1 and 2 beams, Eb /N0 = 17.7 dB for 3 beams, B = 1000 bits, SF = 16.
18
2) C/I dependency: Figure 5 shows the simulated FER for fixed MODCOD as a function of the third beam C/I when 3 beams are active with the second interfering beam characterized by a fixed C/I = 0 dB. Clearly the third beam C/I increase causes a reduction of the interference seen in the cluster as well as a reduction of the third beam received Eb /N0 . The two contrasting effects are clearly visible in Fig. 5 simulated results showing that for given load and reference beam Eb /N0 value there is an optimum C/I value for the third beam which minimizes the FER of the multiplex. This results can be explained as follows. The FER measured corresponds to the aggregate FER from the three serving beam ”pipes”. Initially increasing the third beam C/I we reduce the interference seen by the MUD while keeping the third pipe operating at an SNIR allowing decoding. Increasing the C/I beyond 6 dB the third pipe Eb /N0 gets smaller than 6.7 dB as the Eb /N0 = 13.7 dB value corresponds to the first serving beam. Thus the third serving beam pipe starts to experience a non negligible FER affecting the combined pipes FER performance. Clearly, the result will be different if a flexible ACM physical layer MODOCOD configuration is adopted. In this case, according to Sect. IV discussion, the radio resource manager (RRM) will decide whether to use a cluster’s beam, depending on the quality of the received signal or the user location inside the beam. The RRM will also jointly assign the modulation and coding of contributing beams according to receivers feedback on the estimated SNIR values. See Sect. IV-B and Appendix D.
19
0
10
−1
FER
10
−2
10
−3
10
−4
10
0
2
4 3
Fig. 5.
rd
6
8
10
beam C/I [dB]
Simulated FER as a function of the third beam C/I: 3 active beams (2 interfering beams) with variable third beam
tot C/I and second beam C/I = 0 dB, Kbeam = 17, SF = 16, β tot = 3.19, G = 2.13 bits/chip, Eb /N0 =13.7 dB, B = 1000
bits.
3) Spreading factor dependency: Figure 6 shows very little dependence of the demodulator FER on the CDM spreading factor SF in the range 4 to 32. By reducing the spreading factor the demodulator complexity is reduced at the expenses of a larger granularity in the resource allocation (bit rate/CDM code).
20
−2
10
−3
FER
10
−4
10
0
Fig. 6.
5
10
15 20 25 Spreading factor [SF]
30
35
40
Simulated iMMSE-SIC CDM detector performance as a function of the spreading factor SF for the case of 3 active
beams (2 interfering beams) with C/I =[0, 4] dB, G = 2.0 bits/chip, Eb /N0 = 13.7 dB, B = 1000 bits.
4) MMSE-SIC detector dependency on the number of iterations: The simulation results reported in Fig. 7 shows the slight FER improvement achieved when increasing the number of i-MMSE-SIC iterations from 1 to 10. It seems that there is a diminishing return in performance when increasing the number of i-MMSE-SIC iterations beyond 5. The result is dependent on the beam power unbalance thus, it will depend on the terminal location in the coverage region. In general, being the interference synchronous, it is found that the required number of MMSE-SIC iterations is less compared to the case where interference is asynchronous.
21
−1
FER
10
−2
10
−3
10
0
2
4 6 Number of IC iterations [N iter]
8
10
Fig. 7. Simulated FER as a function of the iSIC number of iterations: 3 active beams (2 interfering beams) with C/I =[0, 4] tot dB, Kbeam = 17, SF = 16, βtot = 2.12, G = 1.42 bits/chip, Eb /N0 =13.7 dB, B = 1000 bits.
5) FEC block size dependency: Figure 8 reports the FER dependence on the FEC information bits block size is investigated for the single interfering beam case. It is apparent that using too small FEC blocks has a negative impact on the FER performance.
22
0
10
−1
FER
10
−2
10
−3
10
−4
10
0
1000
2000 3000 FEC block size [bits]
4000
5000
tot Fig. 8. Simulated FER as a function of the FEC information bits block size: 1 interfering beam with C/I =[0] dB, Kbeam = 19,
SF = 16, βtot = 2.37, G = 1.58 bits/chip, Eb /N0 =13.7 dB.
6) CDM Multiplex Power Randomization Impact: Taking into account the results reported in [25], one can consider the possibility to artificially generate a power randomization of the CDM beam components to enhance the MMSE-SIC detector performance. In fact, it is known that the power randomization is enhancing the SIC performance [29]. What is less evident is the CDM power randomization impact on the MMSE-SIC detector in particular under high load conditions. The physical layer simulator has been modified to include the possibility to apply a uniform in dB power distribution on each CDM beam component. To make a fair comparison the average power of the CDM beam multiplex has been kept constant. Recalling the Probability Density Function (PDF) pρ (ρ) corresponding to a random power ρ with a uniform distribution in dB scale for the CDM components 1 for P min ≤ ρ ≤ Pmax , ζρ pρ (ρ) = 0 elsewhere
23
ζ =
10 , ∆P (dB) = 10 log10 [Pmax ] − 10 log10 [Pmin ] . ln(10) ∆P (dB)
(7)
The average power of the CDM multiplex with the randomized power following the above PDF can be computed as Z ∞ i h ∆P (dB) 10 [Pmax − Pmin ] 10 P = ρ pρ (ρ) dρ = = Pmin 10 10 − 1 , ln(10) ∆P (dB) ln(10) ∆P (dB) 0
(8)
having observed that: h
Pmax = Pmin 10
∆P (dB) 10
i
.
(9)
Exploiting (8) we can derive Pmin as a function of ∆P (dB) as Pmin =
P ∆P (dB) ln(10) i, h ∆P (dB) 10 10 10 − 1
(10)
and Pmax can be derived replacing Pmin in (9). Simulation results for 1 (C/I = [0] dB) and 2 (C/I = [0, 4] dB)interfering beams, Eb /N0 = 13.7 dB, SF=16 as a function of the parameter ∆P (dB) are reported in Fig. 9. It is remarked that increasing the CDM beam multiplex power randomization range has a negative impact on the FER for the same average beam power. This is probably due to the very large loading factor at which the MMSE detector is operating (βtot > 3). The same figure shows the FER dependency on ∆P (dB) when only the SIC is used (the MMSE detector in front of the SIC is de-activated). In this case the FER is minimized using ∆P = 6 dB as the SIC is benefiting from the CDM power unbalance. Increasing the power randomization range beyond 6 dB, the FER is increasing again as the lowest interfering beam, the one with C/I = 4 dB, starts to be AWGN limited. Overall the MMSE-SIC detector with ∆P = 0 dB provides the best performance. Taking into account this section findings, in the following we will not exploit any CDM multiplex power randomization.
24
0
10
−1
10
−2
FER
10
−3
10
MMSE−SIC 1 interfering beam C/I=[0] dB, G=1.41 bits/chip MMSE−SIC 2 interfering beams C/I=[0, 4] dB, G=1.99 bits/chip SIC ONLY 2 interfering beams C/I=[0, 4] dB, G=1.99 bits/chip
−4
10
0
1
2
3 4 5 Power randomization range ∆ P [dB]
6
7
8
Fig. 9. Simulated FER as a function of the CDM multiplex power randomization range ∆P (dB) with SF = 16, Eb /N0 =13.7 tot dB, B = 1000 bits for: a) 2 active beams (1 interfering beam with C/I =[0] dB), Kbeam = 17, βtot = 2.12, G = 1.41 tot bits/chip; b) 3 active beams (2 interfering beams with C/I =[0, 4] dB), Kbeam = 16, βtot = 3.0, G = 1.99 bits/chip.
7) Multistage MMSE-SIC CDM Demodulator with Channel Estimation Performance Assessment: In this section performance results related to some full CDM multiplex waveform simulations of the MMSE-SIC demodulator inclusive of the multi-stage detector and key channel estimation sub-systems are presented. The MMSE multistage implemented is following the approach described in [30], [31]. As mentioned in Sect. II, the multistage detector implementation is particularly convenient in the present scenario as it is featuring affordable complexity, it is compatible with long spreading codes and does not require an adaptive implementation like the ones described in [5], [6]. Following [31], weight coefficients of the detector can be computed off-line as all the information required to compute such coefficients are available at the terminal based on gateway signalling (e.g. number of carriers in the multiplex) or locally measurable (e.g. noise floor, relative CDM components power). In the following physical layer simulations we assume that the initial CDM multiplex is
25
already acquired in terms of carrier frequency and chip timing. Considering that the forward link carrier is a continuous transmission, its initial acquisition is not a critical issue for the system performance. What has been implemented in the CDM demodulator is the accurate carrier phase and amplitude estimation exploiting the presence of pilot symbols time interleaved in the multiplex6 (1 pilot every 10 data symbols). After chip-level correlation with the beam unique scrambling sequence X-ored with the WH sequence and accumulation over the pilot symbol duration, pilot symbols wipe-out takes place. The resulting unmodulated pilot complex phasor estimation for the demodulation step is based on a sliding window covering 40 pilot symbols. Recalling the pilot symbol periodicity, it follows that the channel estimation window extends in time for 440 symbols (400 payload and 40 pilot symbols). The same channel estimation approach is followed for the SIC detector cancellation step, following successful frame decoding. However, this time also the full payload symbols symbols are known in addition to the pilot ones. In this case the refined channel estimation for Interference Cancellation (IC) is using a 200 symbols window. Figure 10 shows the throughput and PLR achievable for a scenario with all equally powered carriers for Nbdom = 2, 3, 4. Such a scenario is comparable with the results of Fig. 4. For Nbdom = 2 the agreement is quite good with PLR below 10−3 at a throughput of 1.5 bits/chip. An overhead of 11.03 % for pilots and preamble was included in each physical layer FEC frame. Instead for Nbdom = 3, 4 some performance degradation compared to the ideal channel estimation results of Fig. 4 is caused by the weaker power associated to the other beams. 6
In alternative to this time division pilot symbols multiplexing one can envisage a dedicate WH sequence for continuous pilot
transmission in the CDM multiplex.
26
Normalized Effective Throughput, Te [bits/chip]
2.5
2 Ndom =4 b
1.5 Ndom =3 b
1 Ndom =2 b
0.5
0
0
0.5
1 1.5 Total Normalized Information Load, G [bits/chip]
2
2.5
(a) Multistage MMSE-SIC 0
10
Ndom =2 b
−1
10
Ndom=3 b
−2
FER
10
Ndom =4 b
−3
10
−4
10
0
0.5
1 1.5 Total Normalized Information Load, G [bits/chip]
2
2.5
(b) SUD-SIC Fig. 10.
Simulated multistage iMMSE-SIC CDM detector performance as a function of the total normalized load for the case
of: a) 2 beams cluster (1 interfering beam) with C/I =0 dB; b) 3 beams cluster (2 interfering beams) with C/I =[0, 4] dB; c) 4 beams cluster (3 interfering beams) with C/I =[0, 4, 8] dB, Eb /N0 = 13.7 dB for 1 and 2 beams, Eb /N0 = 17.7 dB for 3 beams, B = 1000 bits, SF = 16. A frame overhead of 11.0 % for preamble and pilots was included.
27
IV. S YSTEM T HROUGHPUT A NALYSIS The study case considered in the following section corresponds to the forward link of a multi-beam satellite network. The following analytical derivations are generic, thus applicable to any frequency band including the MSS L/S-bands when neglecting the effects of fading. As discussed before, the satellite is assumed to have Nb beams with a fixed and equal power per beam assignment. A frequency reuse scheme corresponding to Nc colours is considered. For simplicity a single satellite antenna polarization is assumed. Thus, the allocated bandwidth per beam is simply given by Butot , Bb = Nc
(11)
where the overall available user downlink spectrum allocation is Butot and the overall system tot = Nb Bb . To achieve accurate performance results, we consider a multibandwidth is Bsys
dimensional throughput assessment allowing for the derivation of an average beam throughput. For the benchmark FDM/TDM configuration a conventional NcFDM -colour (typically 4) frequency reuse scheme along with a single user detector (SUD) at the receiver is adopted. Each TDM carrier will be characterized by a baud rate Rs . In this case at the generic terminal location (x, y) in the beam of interest l the other beams Co-channel Interference (COI) will be assimilated to an AWGN process with PSD [I0 ]COI (x, y|l, NcFDM ) = [I]COI (x, y|l, NcFDM )/Rs where Pbeam (x, y|l) [I]COI (x, y|l, NcFDM ) = C , (12) FDM ) (x, y|l, N c I where Pbeam (x, y) is the l-th beam received carrier power and CI (x, y|l, NcFDM ) represents the multi-beam antenna C/I at location (x, y) in beam l. For the challenger CDM case we assume a more aggressive frequency reuse characterized by NcCDM colours and a fixed equal power per beam allocation. Each CDM carrier is spread at chip rate Rc . Typically, a full frequency reuse is considered (NcCDM = 1). In beam b, the tot carrier is composed of Kbeam (b) CDM multiplexed signal components. Following (1), this can
be expressed as tot Kbeam (b) = βbeam (b)SF.
(13)
Recalling Sect. II-A, within the footprint of the beam of interest l, there are Nbdom (l) dominant beams with 1 ≤ Nbdom (l) ≤ Nb whose beam indexes ensemble at each terminal location (x, y) is identified by BD (x, y|l). Then the aggregated dominant interference from the other beams at
28
terminal location (x, y) served by beam l that will be processed as useful signal by the MUD corresponds to I dom (x, y|l, NcCDM ) =
X
Ib (x, y|NcCDM ) =
b∈BD (x,y|l)
where
C I
X b∈BD (x,y|l)
P (x, y|l) C beam , (x, y|b, NcCDM ) I
(14)
(x, y|b, NcCDM ) represents the C/I component at location (x, y) generated by the b-th
dominant beam. Thus the aggregate C/I due to the dominant interfering beams considered by the MUD scheme at terminal location (x, y) served by beam l is given by −1 −1 X C C . (x, y|l, NcCDM ) = (x, y|b, NcCDM ) I dom I
(15)
b∈BD (x,y|l)
In a similar way the unresolved interference aggregate power can be computed as X X P (x, y|l) C beam I unr (x, y|l, NcCDM ) = Ib (x, y|NcCDM ) = . CDM ) (x, y|b, N c I b3B (x,y|l) b3B (x,y|l) D
(16)
D
The unresolved interference C/I at terminal location (x, y) in beam l can be computed as −1 −1 X C C (x, y|l, NcCDM ) = (x, y|b, NcCDM ) . (17) I unr I b3BD (x,y|l)
This unresolved co-channel interference is treated as additional AWGN with PSD [I0 ]unr (x, y|l, NcCDM ) = C(x, y)/ CI unr (x, y|l, NcCDM )/Rs on top of the thermal noise at the demodulator. For comparing the two multiplexing schemes we will compute the normalized l-th beam throughput (spectral efficiency expressed in bits/symbol for FDM/TDM or bits/chip for CDM) defined as Tbeam (l) =
[Rb ]beam (l) , Bntot
where [Rb ]beam (l) the aggregated beam CDM or TDM multiplex bit rate7 and Bntot =
(18) tot Bu 1+α
the
normalized total system bandwidth, 0 ≤ α ≤ 1 being the roll-off factor of transmit square-root raised-cosine filter. The normalized total system bandwidth can be computed as N FDM R for the FDM benchmark s c tot Bn = . N CDM Rc for the CDM benchmark
(19)
c
7
tot For CDM the [Rb ]beam (l) corresponds to the sum of the bit rates of the Kbeam (l) CDM components, while for the FDM/TDM
case it is equal to the l TDM beam carrier bit rate.
29
In the following, we assume that in the more general case, the terminals are not uniformly distributed across the beam coverage. For the generic l-th beam of interest, the terminal spatial (l)
joint bi-dimensional distribution Probability Density Function (PDF) is pX,Y (x, y). Naming with B(l) the area covered by beam l, by PDF definition we have Z Z (l) pX,Y (x, y)dxdy = 1.
(20)
(x,y)∈B(l)
A. FDM Case Let us now compute the unconstrained (UC) normalized average throughput for the FDM benchmark case. The satellite beam l normalized throughput is given by Z Z h UC i UC T FDM (l) = TFDM (x, y|l)pX,Y (x, y)dxdy,
(21)
(x,y)∈Bl
where
Pbeam (x, y|l) log2 1 + . (22) NcFDM Rs {N0 + [I0 ]COI (x, y|l, NcFDM )} h MC ibeam For the MODCOD constrained FDM normalized throughput calculation T FDM (l) we UC TFDM (x, y|l) =
1
exploit the methodology described in [35]. B. CDM Case For the CDM challenger case, we compute the normalized throughput in two distinct cases: the first one corresponds to a uniform distribution (UD) of traffic loading over the satellite beams; the second one corresponds to the extreme case of a hot spot (HS) beam surrounded by six completely empty (cold) beams. The HS beam will be exploiting all the throughput generated by the six surrounding beams in addition to the throughout of the central beam. Clearly, the system is capable of coping with intermediate non-uniform traffic conditions thanks to the physical layer flexibility. The decentralized MUD allows to demodulate not only the nominal serving beam l, but also the strongest Nbdom − 1 adjacent co-frequency beams while offering the flexibly to redirect resources as needed. It should be noted that while in the UD case the resources shall be (evenly) distributed over the whole coverage area, in the HS case the system can exploit the strongest contributions of the adjacent cold beams to increase its throughput. As explained in detail in Appendix A, it is advantageous to have the number of dominant beams dependent on the user location as
30
shown in Fig. 2 where terminal ST1 is only served by the central beam while terminal ST2 and ST3 are served by 2 and 3 contributing (dominant) beams. An extension of the normalized throughput formula presented in [32] for the non equal power CDMA interfering signals in a simple cellular network return link case, has been derived in [33] for different types of detectors, e.g. SUD, optimum detector, MMSE, and the MMSE cascaded to the Successive Interference Cancellation one (MMSE-SIC). Unfortunately, the one-dimensional terrestrial multi-cell cellular network results of [32] are not applicable to our case. Furthermore, the possibility to exploit MMSE-SIC detector to mitigate the other cells interference is neglected in [32]. On the contrary, in CDM case, we want to process Nbdom − 1 adjacent co-frequency beams exploiting not only the MMSE filter but also the SIC processing. Finally we would like to remark several fundamental differences between the system model and constraints applicable to the CDM with decentralized approach versus classical multiuser schemes, particularly the Multiple Access Channel (MAC) of the return link and the Broadcasting Channel (BC) of the forward link. In particular: a) unlike the degraded broadcast channel where all channel state information is assumed to be known at the transmitter, the CDM decentralized approach requires only the knowledge at the transmitter of second-order statistics such as signal and interference power ratios measured at the receiver; b) Unlike the BC channel where the construction of signals of all transmitters is centralized, in the CDM case the transmitter only coordinates the information rates (or Modulation and Coding) assigned to each beam. As a result, the upper bounds of achievable rates of BC channels are not applicable to the CDM decentralized case; c) Unlike the MAC channel where power constraint is applied to individual uplink terminals,in the CDM case there is a power constraint applicable to the aggregate components per downlink beam. In summary, the capacity region and the strategy to reach the capacity of the decentralized MUD system and that of BC and MAC channel are fundamentally different. It should be noted that in the decentralized MUD approach, we intentionally introduce a constraint on the level of coordination among the beams that prevent a full joint signal construction for multiple beams. In the presence of such constraint, the upper bound of BC downlink channel [34] is no longer applicable to this channel. The use of CDM is a pragmatic approach to allow for multiple beam reception and flexible resource sharing among the beams. However, as shown in Appendix C, the CDM approach with MMSE-SIC receiver can only reach the upper rate of MAC channel which may not be the ultimate capacity of the
31
downlink channel. 1) Even Traffic Distribution Across the Beams Over the Whole Coverage Area: In this section we derive the l-th beam spatially averaged normalized throughput under the assumption of all (l)
beams having the same traffic request (i.e. pX,Y (x, y) = pX,Y (x, y) ∀ l) (UD case). Three different cases will be considered for the punctual and beam averaged normalized throughput derivation: a) unconstrained modulation and coding (UC); b) modulation constrained (MOD); c) MODCOD constrained (MC). Unconstrained Normalized Throughput: We first derive the the MUD total punctual UC nor UD−UC malized throughput TCDM (x, y|l) achievable at the generic location (x, y) in the beam of interest l. Following [33] with adaptations to the specific multi-beam forward link case, we get beam q CDM throughput contribution
z
}|
tot (q) Kbeam
{
A(Bl ) 1 X UC · η (x, y|l) , Nbserv (q) A(Bq,l ) SF k=1 k,q q∈Bs (x,y|l) UC ∗ ηk,q (x, y|l) = log2 1 + ζk,q (x, y|l) , ζ (x, y|l) if q 6= l or q = l and N dom (x, y|l) = 1 k,q b ∗ ζk,q (x, y|l) = outer dom ζ (l) if q = l and N (x, y|l) > 1,
UD−UC TCDM (x, y|l) =
X
1
·
k,l
b
outer
ζ k,l (l) = E(x,y)∈Bo (l) {ζk,l (x, y|l)}.
(23)
where Nbserv (q) represents the number of served beams by beam q, Bs (x, y|l) corresponds to the ensemble of Nbdom (x, y|l) dominant beams serving the user at location (x, y) in beam l (see UC Appendix A for their derivation), ηk,q (x, y|l) means the punctual MUD unconstrained spectral
efficiency and ζk,q (x, y|l) is the MMSE-SIC detector resulting SNIR for the k-th component of the CDM multiplex coming from the dominant beam q for an user located in beam l at the coordinates (x, y). The way to compute ζk,q (x, y|l) for the target MMSE-SIC detector is detailed in Appendix B. The capacity computation in our formulation is constrained by the average power limit at the beam level. It is noted that in (23) the sum of CDM power components tot [1, · · · , Kbeam (q)] is subject to an average beam power constraint. ∗ When q = l and Nbdom (x, y|l) > 1, the modified MMSE-SIC SNIR ζk,q (x, y|l) is obtained by
taking the average of ζk,q (x, y|l) over the outer region of beam l, dubbed Bo (l). As explained ∗ in Appendix A, the reason for using the MMSE-SIC modified value ζk,q (x, y|l) is that the inner
part of the beam will be solely served by the dominant beam l. However, the the information bits
32
destined for the inner region of beam l shall also be decodable in the outer region of the beam that is served by other dominant beam(s). This allows to remove the inner beam interference effect on the outer beam(s) carrying the useful information bits. Thus, we compute the reference beam l average throughput over the outer region and we exploit it in the inner part of the beam. In this way we choose the reference beam l MODCODs to be decodable over the outer region of the beam but the associated throughput is instead used in the inner beam l region. To avoid outage events the minimum MMSE-SIC SNIR for the reference beam l over the outer region shall be greater or equal than the minimum SNIR in the inner part of the beam. The quantity A(Bl ) represents the surface area of the beam of interest l while A(Bq,l ) indicates the surface sub-area of beam l served by the dominant beam q. The ratio ΥAq,l = A(Bl )/A(Bq,l ) ≥ 1 is introduced to account for the fact that the dominant beam q contributes to the throughput of the beam l only for a subset of the beam area. The average throughput in (23) is computed based on entire beam coverage area. Thus the “boosting” factor ΥAq,l provides a proper normalization of the effective beam q contribution to the punctual normalized throughput of the user located in (x, y). The factor
1 Nbserv (q)
appearing in (23) also deserves some explanation. In the UD case, thanks
to the FFR, each beam is serving itself and the Nbserv (q) − 1 adjacent beams. Thus to support the ACM operations with carriers serving multiple beams, the CDM multiplex is partitioned in Nbserv (q) time slots each dedicated at given time to one of the served beams. This allows to select the optimum ACM MODCOD for the coverage location served at given time. For simplicity, this time sharing is assumed equal, thus in (23) we divide the total normalized serving beams throughput by Nbserv (q). The Nbserv numerical derivation for the different cases of interest is provided in Sect. V-B. The normalized unconstrained beam average throughput is obtained averaging punctual normalized throughput (23) over the Bl beam area as Z Z h UD−UC i UD−UC (x, y|l)pX,Y (x, y)dxdy. T CDM (l) = TCDM
(24)
(x,y)∈Bl
Modulation Constrained Normalized Throughput: Let now derive the MOD constrained normal UD−MOD ized punctual throughput TCDM (x, y|l) achievable at the generic location (x, y) in the
33
beam of interest l. In this case, following [38], and similarly to (23), we get
UD−MOD TCDM
(x, y|l) =
X q∈Bs (x,y|l)
MOD ηk,q (x, y|l)
A(Bl ) 1 · · serv Nb (q) A(Bq,l ) SF
Mmod 1 X E = log2 Mmod − Mmod i=1
1
( log2
"M mod X j=1
tot (q) Kbeam
X
MOD ηk,q (x, y|l),
k=1
|ai − aj + w|2 − |w|2 exp − 2 (x, y|l) 2σk,q
!#) , (25)
MOD (x, y|l) where E {·} denotes statistical expectation performed over random variable w and ηk,q
represents the punctual MUD unconstrained spectral efficiency for the k-th component of the CDM multiplex coming from the dominant beam q for an user located in beam l at the coordinates (x, y), ai is the i-th complex symbol of the physical layer (unspread) signal constellation, w are 2 ∗ realization of the AWGN complex samples with σk,q (x, y|l) = 1/ζk,q (x, y|l). Similarly to (24)
the unconstrained average throughput over the Bl beam area is obtained as Z Z h UD−MOD i UD−MOD T CDM (l) = TCDM (x, y|l)pX,Y (x, y)dxdy
(26)
(x,y)∈Bl
MODCOD Constrained Normalized Throughput: Finally, to obtain more realistic results for a system adopting ACM, we compute the normalized throughput MC constrained. The MC normalized throughput is constrained to a specific set of NMC practical coded modulation8 schemes (MODCODs). In this case for each terminal geographical location (x, y) there are P tot (q) distinct SNIR values obtained at the MMSE-SIC terminal deKtot (l) = q∈B(x,y|l) Kbeam modulator (one for each CDM components for all dominant beams) reported at the gateway station one for each active CDM component. It is assumed that the gateway selects the best MODCODs configuration for each of the serving beam q at location (x, y). To be remarked that, differently from conventional TDM/FDM ACM scheme [35], in case of CDM an array of Ktot (l) distinct MODCODs have to be allocated for each terminal. We call this adaptive physical layer scheme multi-dimensional ACM. To be remarked that although at each MMSESIC step the orthogonal CDM beam components may have a similar SNIR value, only one 8
In practice, the simplest way to implement different MODCODs in the CDM scheme described in Sect. II-A is to keep the
chip rate, spreading factor and thus the symbol rate constant. The different MODCODs can be implemented simply modifying the FEC coding rate and/or the modulation format thus varying the input bit rate.
34
will be used for cancellation from frame memory. Then the MMSE filter will be re-computed and the SNIR will grow at each iterative detection step. Thus the MODCODs associated to the CDM components belonging to the same beam are in general different. We define with η MC and MC
ξ th the MODCODs set spectral efficiency in bits/symbol and the corresponding unspread SNR demodulation threshold. The MODCODs set is numerically described as two NMC -dimensional arrays composed by η MC = MC
ξ th
η MC (1) · · · η MC (NMC ) MC MC (NMC ) . (1) · · · ξth = ξth
(27) (28)
UD−MC The MODCODs constrained normalized punctual throughput TCDM (x, y|l) achievable at the generic location (x, y) in the beam of interest lcan be computed as
UD−MC
TCDM
(x, y|l) =
X q∈Bs (x,y|l)
A(Bl ) 1 · · serv Nb (q) A(Bq,l ) SF 1
tot (q) Kbeam
X
∗ MC ηk,q ζk,q (x, y|l) ,
(29)
k=1
where 0 η MC (m∗ ) MC ∗ ηk,q [ζk (x, y|l)] = MC η (NMC )
∗ MC if ζk,q (x, y|l) < ξth (1) ∗ MC if ζk,q (x, y|l) ≥ ξth (m∗ ) and ∗ MC ζk,q (x, y|l) < ξth (m∗ + 1) if m∗ < NMC
.
(30)
∗ MC if ζk,q (x, y|l) ≥ ξth (NMC ).
Similarly to (24) the unconstrained average throughput over the Bl beam area is obtained as Z Z h UD−MC i UD−MC T CDM (l) = TCDM (x, y|l)pX,Y (x, y)dxdy. (31) (x,y)∈Bl
2) Hot Spot Beam Case: In the HS case we consider the extreme hot spot configuration in which the throughput of all the 6 iso-frequency beams surrounding the central hot spot is exploited in addition to the throughput of the central beam, to satisfy the hot spot traffic demand. This means that there is no traffic demand for the six beams around the hot spot. In practice there are many intermediate situations whereby the system RRM can allocate some throughput to the 6 cold beams around the hot spot according to the needs. Consequently, the following results provide the hot spot normalized throughput upper limit achievable transferring the adjacent beams throughput to the hot spot. In this case the equations derived in Sect. IV-B1 are applicable with the simple adaptation that Nbserv (q) = 1 in (25), (24), (25), (26), (29), (31), as there is no sharing of beam q resources other than for the beam l of interest.
35
V. S YSTEM L EVEL P ERFORMANCE A NALYSIS A. System Level Simulator Description To perform a system level assessment of the proposed distributed MUD technique a multibeam forward link satellite simulator has been built. Three different system configurations have been considered (see Table I for details): •
Configuration 1 [CF1]: 40 active beams with four colours and conventional DVB-S2X TDM/FDM physical layer benchmark;
•
Configuration 2 [CF2]: 40 active beams with single colour and CDM physical layer with decentralized MUD;
•
Configuration 3 [CF3]: 7 active beams single colour hot spots cluster CDM physical layer with decentralized MUD.
The payload is able to activate up to 40 beams simultaneously. To achieve the required level of resource allocation and coverage flexibility a payload with an analogue or digital Beam Forming Network (BFN) and active Direct Radiating Antenna (DRA) is assumed. Each antenna feed is connected to a Solid-State Power Amplifier (SSPA) operating in multi-carrier mode. The use of Gallium Nitride SSPA allow to achieve the required RF power levels in addition to a relative high power conversion efficiency and linearity. Based on internal SSPA design information we assumed an SSPA Noise Power Ratio (NPR) of 17 dB at 2.3 dB compression point. In the antenna far-field an NPR of 19 dB is assumed accounting for the intrinsic DRA linearization effect described in [40]. The first configuration [CF1] corresponds to a conventional broadband multi-beam satellite network using four colours, FDM multiplexing and DVB-S2X physical layer [39]. The user link frequency band is Ka-band while the feeder link is assumed to be at Q/V-band. The second configuration [CF2] corresponds to the same [CF1] multi-beam antenna pattern but exploiting CDM with full frequency reuse. Finally, in the third configuration [CF3], we assume that only the central cluster composed by 7 out of the 40 beams is exploiting CDM with full frequency reuse. The remaining beams are not active or the ones active are not interfering with the hot spot cluster. In the following for fairness we assume that the satellite beam Effective Isotropic Radiated Power (EIRP) is kept constant in all configurations to 63 dBW under multi-carrier SSPA operating
36
conditions. This means that the transmitted PSD per beam will be inversely proportional to the number of antenna colours. The forward link satellite system parameters for the three above configurations are summarized in Table I. It is apparent the four-fold feeder link bandwidth requirement for [CF2] compared to [CF1]. This is simply due to the single versus four colour frequency reuse scheme adopted. Configuration Parameter
[CF1]
[CF2]
[CF3]
5
20
3.5
User link bandwidth [MHz]
500
500
500
Beam bandwidth [MHz]
125
500
500
Carrier baud rate [Mbaud]
104
NA
NA
Carrier chip rate [Mcps]
NA
416
416
RHCP
RHCP
RHCP
Number of colours
4
1
1
Number of active beams
40
40
7
EIRP/beam (dBW)
63
63
63
Far field NPR (dB)
19
19
19
Feeder link total bandwidth [GHz]
Polarization
TABLE I [CF1, CF2, CF3] M ULTIBEAM FORWARD LINK SATELLITE SYSTEM PARAMETERS . NA
STANDS FOR
N OT A PPLICABLE .
The user terminal parameters selected are reported in Table II. They are representative of current commercial Ka-band broadband user terminal’s capabilities. User terminal antenna diameter
0.6 m
User terminal antenna efficiency
65 %
User terminal front-end noise figure
2 dB
TABLE II M ULTIBEAM SATELLITE USER TERMINAL PARAMETERS .
The satellite coverage region is divided in 441 × 561 grid points and for each grid point (x, y) the C/N (x, y|l) and the [C/I](x, y|l) quantities are computed. For FDM the normalized
37
throughput calculation approach is the one described in Sect. IV-A. For CDM the results of Sect. IV-B, allow to estimate respectively the unconstrained, modulation and MODCOD constrained normalized punctual and beam average throughput. For [CF1] the normalized throughput has been estimated for the whole 40 beams set. For the configurations [CF2-CF3] only the central beam (number 120) normalized throughput was investigated to save calculation time, as it is representative of a typical beam performance. In general, the normalized throughput will be similar in the other beams of the satellite except for the ones at the edge of coverage experiencing less interference. Concerning the physical layer, three different assumptions have been made: a) For [CF1] ACM with the DVB-S2X MODCODs summarized in Tables X and XI of Appendix D have been adopted; b) For [CF2] and [CF3] multi-dimensional ACM the DVB-S2X BPSK and QPSK MODCODs summarized in Table X have been used. Differently from Sect. IV results, when exploiting CDM in [CF2] and [CF3] we have extended the DVB-S2X QPSK SNIR range by including the three DVB-S2X unspread BPSK MODCODs shown in Table X to minimize the link outage probability. For all the system level availability simulations it is assumed that the link shall be closed for 100% of the time at least in 99 % of the coverage locations. B. System Level Simulation Results 1) Satellite Antenna Isolation: Figures 11, 12, 13 show the satellite antenna C/I threedimensional plots for the [CF1], [CF2] and [CF3] configurations. For the [CF2] and [CF3] only the [C/I]1 and [C/I]2 components used by the MUD (see (15) for their definition) are shown in two distinct sub-plots.
38
Fig. 11.
Satellite antenna C/I for the configuration [CF1].
39
(a) First strongest interferer C/I
(b) Second strongest interferer C/I Fig. 12.
Satellite antenna C/I for the configuration [CF2]: a) [C/I]1 ; b) [C/I]2 .
40
(a) First strongest interferer C/I
(b) Second strongest interferer C/I Fig. 13.
Satellite antenna C/I for the 7 beams cluster configuration [CF3]: a) [C/I]1 ; b) [C/I]2 .
41
2) FDM/TDM [CF1] Results: The benchmark [CF1] FDM normalized throughput simulation results exploiting DVB-S2X MODCODs listed in Appendix D, are reported in Table III. The throughput is initially computed over the bandwidth allocated to the beam, which for a 4 colours scheme represents a quarter of the total beam bandwidth (i.e. 125 MHz). The throughput is then recomputed in the last column normalizing it to the available full beam bandwidth (500 MHz). The three-dimensional normalized [CF1] throughput is shown in Fig. 14.
Fig. 14.
Simulated [CF1] normalized throughput - FDM with four colours frequency reuse.
42
h
Case
MC
T FDM
ibeam
in the beam
h
MC
T FDM
ibeam
in the beam
Availability
sub-band [bits/symbol]
overall band [bits/symbol]
99 % coverage
Best beam
4.26
1.07
100 %
Worst beam
3.87
0.97
100 %
Beams average
4.06
1.02
100 %
TABLE III [CF1]
AVERAGE , WORST AND BEST BEAM NORMALIZED THROUGHPUT RESULTS .
3) CDM [CF2-CF3] Results: The general expression of the average throughput for [CF2] and [CF3] is based on the system throughput analysis of Section IV. Resource allocation is derived based on SNIR computation at the receiver (that is assumed to be fed back to the transmitter for the rate adjustment and coordination among the beams). Each user is served by 1 to 3 beams depending on the link quality observations. A detailed expression of the dominant and serving beams is provided in Appendix A. Table IV shows the number of served beams (Nbserv ) values for the different beam locations for UD and HS traffic distributions assuming a regular lattice beam pattern. The computation is based on simple geometrical considerations and differs for inner and outer FFR region beams. For [CF3] the UD configuration has not been extensively investigated as the resource allocation methodology described in Appendix A was found sub-optimum for this special 7-beams cluster case. Case
UD
HS
Inner beams
7
1
Outer beams
NA
1
TABLE IV N UMBER OF SERVED BEAMS (Nbserv ) VALUES FOR THE DIFFERENT BEAM LOCATIONS FOR DISTRIBUTIONS FOR BOTH
FFR AND PFR
UD
AND
HS TRAFFIC
CONFIGURATIONS .
Before discussing the CDM system level throughput results, we summarize the results related to the numerical computation of the service area dominant beam ratio parameter ΥAb,l = A(Bl )/A(Bb,l ) introduced in Sect. IV-B1. The ΥAb,l results are reported in Table V. In case
43
of [Nbdom ]max = 2, only the first strongest interferer (CDM multiplex) on top of beam 120 will be processed by the MUD. Fig. 15 depicts the beams 101, 102, 119, 121, 138, 139 serving areas when [Nbdom ]max = 2. In case of [Nbdom ]max = 3 the MUD will demodulate up to the two strongest outer beam interferers (CDM multiplexes) on top of beam 120. Thus it is more difficult to predict the served area. Fig. 16 depicts the beams 101, 102, 119, 121, 138, 139 serving areas when [Nbdom ]max = 3 for the first and second strongest interferers on reference beam 120. [Nbdom ]max
Serving beam ΥAb,l q=1
q=2
q=3
q=4
q=5
q=6
q=7
2
2.90
9.55
9.55
8.85
9.81
8.85
8.44
3
3.00
4.91
5.19
4.71
5.04
4.48
4.43
TABLE V N UMERICAL RESULTS FOR THE SERVICE AREA DOMINANT BEAM RATIO PARAMETER ΥAb,l l = 120,
[Nbdom ]max
= 2, 3,
ADJACENT SERVING BEAMS
FOR
(b) ARE 101, 102, 119, 121, 138, 139, D B.
[CF3]
REFERENCE BEAM
tot Kbeam
= 30, ρmin = −4
44
(a) Dominant beam 1 serving area {120=green}
(b) Dominant beams 2 serving areas {101=dark+ blue, 102=dark- blue, 119=green-, 121=green +, 138=red-, 139=red+} Fig. 15.
tot Serving beams areas on beam 120 for [CF2] with [Nbdom ]max = 2, Kbeam = 30, ρmin = −4 dB.
45
(a) Dominant beam 1 serving area {120=green}
(b) Dominant beam 2 serving areas {101=dark+ blue, 102=darkblue, 119=green-, 121=green +, 138=red-, 139=red+}
(c) Dominant beam 3 serving areas {101=dark+ blue, 102=darkblue, 119=green-, 121=green +, 138=red-, 139=red+} Fig. 16.
tot Serving beams areas on beam 120 for [CF2] with [Nbdom ]max = 3, Kbeam = 28, ρmin = −4 dB.
46
The punctual normalized throughput system simulation results for the [CF2] UD/HS and [CF3] HS configurations and [Nb ]max = 2 or [Nb ]max = 3 are reported in Fig. 17, 18, 19. For each simulated configuration the ρmin value has been optimized jointly with the number of CDM tot codes/beam (Kbeam ) to maximize the throughput while keeping the availability at the target
value. It is remarked that the lowest normalized punctual throughput location corresponds to the inner part of the beam, where, as explained in Sect. IV-B, a SUD is used. The very high punctual normalized throughput for the HS case is due to the fact that, as reported in Table V, the dominant beams around beam 120 are only serving about 1/ΥAb,l = A(Bb,l )/A(Bl ) of the beam 120 surface. As a consequence, the normalized throughput in (29) is boosted by the factor ΥAb,l . The beam averaged unconstrained, modulation constrained and MODCOD constrained normalized throughput for the beam of interest (beam 120 for [CF2] UD and HS cases and beams 101, 102, 119, 120, 121, 138, 139 for [CF3] UD case and 120 for [CF3] HS case) are reported in Table VI for Nbdom = 2 and Table VII for Nbdom = 3. These simulation results are including satellite nonlinearity intermodulation effects which, as explained before, are simply modelled as an extra AWGN contribution due to the satellite NPR seen in the far field. The results reported in Table VI for SF=16 show that for [Nbdom ]max = 2 the highest value for HS−MC
both T CDM
UD−MC
and T CDM
tot is obtained for Kbeam = 30 for the [CF2] configuration. Beyond this
CDM multiplex load the availability is below 100%. For Nbdom = 3, Table VII indicates that the maximum number of codes/beam achieving the required availability target, corresponds to tot tot Kbeam = 28 for [CF2] and Kbeam = 30 for [CF3]. The [CF3] configuration achieves even a higher
normalized throughput than that of the [CF2] for HS case. The HS performance improvement is due to the reduction of co-channel interference for the [CF3] case whereby only 7 of the 40 satellite beams are active. Using a simpler MUD with [Nbdom ]max = 2, causes a drop in throughput of 17-20 % compared to [Nbdom ]max = 3. Looking at the ”raw” punctual normalized throughput plots shown Fig. 17, 18, 19, it is apparent their spatial dependency. However, the RRM can re-balance the physical layer resources to have a more uniform throughput distribution over the required coverage area. The cost of such rebalancing is the reduction of the overall beam throughput. Thanks to the exploitation of the first ring of beams around the hot spot, with [Nb ]max = 3 it is possible to achieve unconstrained normalized throughput values in excess of 8.96 bits/chip for
47
[CF-2] and 9.48 bits/chips for [CF-3]. It should be reminded that thanks to the FFR, these normalized throughput are referring to the whole system bandwidth. The results is slightly reduced (i.e. 1-3 %) for the QPSK MOD constrained case. Instead, when exploiting the DVBS2X MODCODs, a 30-35 % throughput reduction compared to UC case is observed. This is because, following Fig. 20 results, the MMSE-SIC output SNIR range is quite low (i.e −3 ÷ +1 dB). In this SNIR range DVB-S2X MODCODs results to be quite sub-optimum in performance. Consequently, a better FEC will be required to fully exploit the MMSE-SIC potential. In the MC case the MUD throughput advantage compared to the conventional FDM/TDM 4 colour system (see Table III) is reduced to 6.7-fold from the 9.3-fold value obtained for the UC case. This hot spot throughput boost is obtained without requiring any beam power allocation flexibility. The UD normalized punctual throughput is instead reduced by the factor 1/Nbserv compared to the HS case because the resources of the serving beam are shared with the other Nbserv beams (see (23) and Table V for details). This is not the case for HS when the serving beam is fully dedicated to beam 120, thus its higher punctual and beam average normalized throughput. Finally, it is of interest to compare the punctual throughput simulation results with the simple bound derived in Appendix C. Figure 21 obtained for [CF3] shows that for both [Nbdom ]max = 2 and 3 the MMSE-SIC is closely following the MUD bound for each grid point belonging to beam 120. The only exception is in the inner part of the beam where the throughput is driven by the outer beam region link closure condition (see detailed explanation in Sect. IV-B and in Appendix A), causing the clipping effect on the achievable throughput. Figure 22 provides a visual mapping of the beam grid points mapping on the two-dimensional beam projection on Earth.
48
(a) Uniform beam traffic distribution (UD) case
(b) Hot spot traffic distribution (HS) case tot Fig. 17. Simulated [CF2] unconstrained normalized throughput - CDM with full frequency reuse, [Nbdom ]max = 2, Kbeam = 30,
SF = 16, ρmin = −4 dB, Reference beam 120: a) Uniform beam traffic distribution (UD) case; b) Hot spot traffic distribution (HS) case.
49
(a) Uniform beam traffic distribution (UD) case
(b) Hot spot traffic distribution (HS) case tot Fig. 18. Simulated [CF2] unconstrained normalized throughput - CDM with full frequency reuse, [Nbdom ]max = 3, Kbeam = 28,
SF = 16, ρmin = −4 dB, Reference beam 120: a) Uniform beam traffic distribution (UD) case; b) Hot spot traffic distribution (HS) case.
50
Fig. 19.
Nbdom
Nbdom
(a)
(b)
max
max
=2
=3
Simulated [CF3] central beam Hot spot traffic distribution (HS) unconstrained normalized throughput - CDM with
tot full frequency reuse, [Nbdom ]max = 2, 3, Kbeam = 30, SF = 16, ρmin = −4 dB, Reference cluster beams: 101, 102, 119, 120,
121, 138, 139: a) Uniform beam traffic distribution (UD) case; b) Hot spot (HS) traffic distribution (UD) case.
51
Fig. 20.
Nbdom
(a)
(b)
dom Nb = 3 case max
max
= 2 case
tot Simulated [CF3] central cluster MMSE-SIC output SNIR - CDM with full frequency reuse, Kbeam = 30, SF = 16,
ρmin = −4 dB, Reference cluster beams: 101, 102, 119, 120, 121, 138, 139: a) [Nbdom ]max = 2 case; b) [Nbdom ]max = 3.
Unconstrained punctual normalized throughput [bits/chip]
52
16 14 12 10 8 6 4 2 0
Bound MMSE−SIC 0
50
100
150 200 250 Beam grid index
Unconstrained punctual normalized throughput [bits/chip]
(a)
Nbdom
max
300
350
400
= 2 case
22 Bound MMSE−SIC
20 18 16 14 12 10 8 6 4 2
0
50
100
150 200 250 Beam grid index (b)
300
350
400
dom Nb = 3 case max
Fig. 21. Simulated [CF3] central cluster unconstrained Hot Spot (HS) normalized throughput versus Appendix C bound - CDM tot with full frequency reuse, Kbeam = 30, SF = 16, ρmin = −4 dB, Reference cluster beams: 101, 102, 119, 120, 121, 138, 139:
a) [Nbdom ]max = 2 case; b) [Nbdom ]max = 3 case.
53
50 49.5 P200
latitude (deg)
49
P8
48.5 48 P1 P363 47.5 47 46.5 46
7
8 9 longtitude (deg)
10
Fig. 22. Grid points in beam 120, illustrating the location of each grid points within the beam. The outer points are served by adjacent beams while the inner points are only served by beam 120.
HS−UC
HS−MOD
HS−MC
UD−UC
UD−MOD
UD−MC
tot Kbeam
T CDM
T CDM
T CDM
T CDM
T CDM
T CDM
Codes
[bits/chip]
[bits/chip]
[bits/chip]
[bits/chip]
[bits/chip]
[bits/chip]
%
2
28
7.64
7.56
5.13
1.09
1.03
0.78
100
2
30
7.89
7.81
5.20
1.13
1.07
0.79
100
2
32
8.09
8.02
5.37
1.16
1.10
0.81
98.35
3
28
7.78
7.69
5.28
NA
NA
NA
NA
3
30
7.96
7.88
5.27
NA
NA
NA
NA
3
32
8.24
8.13
5.40
NA
NA
NA
NA
Config
Availability
TABLE VI [CF2]
AND
[CF3] AVERAGE BEAM NORMALIZED THROUGHPUT SYSTEM STUDY FOR HOT SPOT (HS) AND UNIFORM USER
DISTRIBUTION
(UD)
CASES RESULTS FOR BEST
UC
BPSK, QPSK DVB-S2X MODCOD S , [Nbdom ]max = 2, SF = 16. I N BOLD THE
THROUGHPUT ACHIEVABLE FOR
100 % AVAILABILITY.
54
HS−UC
HS−MOD
HS−MC
UD−UC
UD−MOD
UD−MC
tot Kbeam
T CDM
T CDM
T CDM
T CDM
T CDM
T CDM
Codes
[bits/chip]
[bits/chip]
[bits/chip]
[bits/chip]
[bits/chip]
[bits/chip]
%
2
26
8.78
8.55
6.38
1.25
1.18
0.96
100
2
28
8.96
8.75
6.39
1.28
1.20
0.96
100
2
30
9.00
8.81
6.25
1.29
1.21
0.94
99.72
3
28
9.37
9.08
6.75
NA
NA
NA
NA
3
30
9.48
9.21
6.69
NA
NA
NA
NA
3
32
9.53
9.30
6.61
NA
NA
NA
NA
Config
Availability
TABLE VII [CF2]
AND
[CF3] AVERAGE BEAM NORMALIZED THROUGHPUT SYSTEM STUDY FOR HOT SPOT (HS) AND UNIFORM USER
DISTRIBUTION
(UD)
CASES RESULTS FOR BEST
UC
BPSK, QPSK DVB-S2X MODCOD S , [Nbdom ]max = 3, SF = 16. I N BOLD THE
THROUGHPUT ACHIEVABLE FOR
100 % AVAILABILITY.
C. Comparison with Other Techniques 1) FDM/TDM MUD and precoding Techniques: It is interesting to compare the CDM MMSESIC results with the ones obtained in [18]. In this reference a decentralized TDM/FDM MUD is presented based on soft IC, as opposed to the CDM MUD MMSE-SIC with hard decisions. The frequency reuse is based on a two-colour scheme instead of a single colour for CDM. Only the strongest co-channel interfering beam is processed by the MUD, instead of one or two co-channel beams in the CDM case previously analyzed. For completeness, we also compare the MUD results with the specific FFR precoding methodology described in [42] which is covering the case of hot spot traffic normally not covered in precoding literature. The aim is to give a first comparison of MUD and precoding in an hot spot scenario leaving to future work further optimization of the precoding and MUD schemes. In the uniform traffic distribution case only 8 beams are precoded as this is the typical number of beams seen by a single gateway. In the hot spot case we assume that 7 beams (hot spot plus 6 surrounding beams are precoded together and resources given to the hot spot as described in [42]. The satellite DC power consumption, the 200 beams antenna pattern as well as other system parameters considered in the following are the same as the one reported in Table 1 of [18]. By repeating the CDM MUD and the precoding simulations for the 200 active beams study case
55
made possible direct results comparison with [18] findings. When assuming an even traffic distribution among the beams the MUD reported in [18] achieves a normalized beam throughput of 1.11 bits/symbol (as defined in (18)) over the full user bandwidth of 500 MHz. The CDM scheme achieves an average normalized beam throughput of 0.89 bits/chip (see Table VIII). The precoding scheme performance is depending on the number of users multiplexed in the same DVB-S2X frame. Table VIII minimum of 0.77 bits/symbol and maximum of 1.18 bits/symbol values corresponds to 10 or 1 users/frame respectively. The benchmark FDM/TDM DVB-S2X with a conventional Single User Matched Filter (SUMF) achieves an average normalized beam throughput of 1.02 bits/symbol (see Table III). The performance improvement versus the benchmark for the FDM/TDM MUD is 9 % while the proposed CDM MUD has a loss of 15 % compared to the benchmark performance. As explained in Sect. IV-B, this poor CDM MUDbehavior is mainly due to the sub-optimum DVB-S2X MODCODs performance in the low SNR range at which the FEC is operating. The precoding results for 1 users/frame are better than the two other schemes. In particular, for uniform traffic distribution, 8 beams precoding shows 6 and 33 % throughput advantage compared to FDM/TDM MUD and CDM MUD respectively. The precoding gain is transformed in a loss compared to the other schemes when 10 users/frame multiplexing is adopted. Removing the 8 precoded beams/gateway constraint the uniform traffic case throughput can go up to 2.21 bits/symbol. In the hot spot case the conventional FDM/TDM with standard SUMF and using a payload providing on-board frequency flexibility (see [18] for detailed explanations) can achieve up to 2.0 bits/symbol i.e. doubling the performance compared to the uniform beam loading case. In the same conditions the FDM/TDM MUD allows to increase the normalized average hot beam throughput up to 2.22 bits/symbol i.e. 100 % improvement compared to the corresponding throughput achievable with even traffic distribution but only 11 % better than FDM/TDM SUMF with frequency flexibility. Instead, for the same hot spot case, the CDM MUD scheme achieves a normalized beam average hot beam MC throughput up to 5.86 bits/chip, thus 575 % larger than the benchmark system performance with even traffic distribution. This corresponds to a 293 % to 264 % performance improvement compared to the FDM/TDM SUMF and FDM/TDM MUD schemes, respectively. A more efficient FEC for the low MMSE-SIC SNIR operating range is expected to further improve the CDM performance probably by another 20 %. The CDM advantage is explained due to the full-frequency reuse scheme compared to the FDM/TDM two
56
colors (double bandwidth) and the fact that up to 2 interfering beams (3 in total) are used by the CMD MUD instead of up to 1 (2 in total) for FDM/TDM. Precoding results for 1 users/frame in the hot spot case are also better than the other schemes. In particular, for uniform traffic distribution, 8 beams precoding shows 288 % and 9 % throughput advantage compared to FDM/TDM MUD and CDM MUD respectively. The precoding gain is transformed in a loss compared to the other schemes when 10 users/frame multiplexing is adopted. It is apparent that for different reasons, the DVB-S2X physical layer is not best matched to both the CDM MUD and TDM precoding schemes. Number of
Beam throughput in Butot
Beam throughput Butot
colours
uniform traffic distribution
hot spot
4
1.02
2.0
[bits/symbol]
FDM/TDM with soft IC MUD
2
1.11
2.22
[bits/symbol]
CDM with MMSE-SIC MUD
1
0.89
5.86
[bits/chip]
1
0.77-1.18
4.34-6.40
[bits/symbol]
Case
FDM/TDM SUMF (with freq. flexibility)
(SF = 16,
tot Kbeam
= 28)
TDM with precoding (10-1 users/frame)
TABLE VIII S UMMARY OF NORMALIZED THROUGHPUT RESULTS FOR THE DIFFERENT TECHNIQUES .
It is concluded that compared to TDM/FDM decentralized MUD scheme reported in [18] the proposed CDM decentralized MUD scheme is effective mainly when a high level of resource assignment flexibility is required to cope with uneven traffic conditions. 2) Adjacent Beam FDM Resource Sharing with SUD: Reference [45] introduced a simple technique which we refer to as “Adjacent Beam FDM Resource Sharing” (AB-FDM-RS) to cope with the HS case exploiting conventional frequency reuse scheme and SUD at the receiver. Details are provided in Appendix E, particularly for [CF3] configuration of Sect. V-B3. Surprisingly, results show that for a classical 4-colour frequency reuse scheme, AB-FDM-RS provides an unconstrained upper bound throughput of 8.25 bits/symbol. Compared to conventional use of 4-colour scheme and no sharing of adjacent beam resources, this corresponds to 544 % boost in the HS offered throughput i.e. only 13 % lower than that of the CDM MUD scheme (as
57
shown in Table VII). Adopting three colours frequency reuse, the AB-FDM-RS unconstrained throughput upper bound amounts to 9.92 bits/symbol which is 655 % higher than the offered throughput by a conventional 3-colour system. This amount to a slight improvement (only 5%) compared to that of the CDM MUD scheme. These excellent results show that there are simpler solutions to tackle the HS case, not requiring the MUD adoption and not calling for a feeder link bandwidth increase. VI. C ONCLUSIONS In this paper the possible exploitation of CDM with decentralized MMSE-SIC MUD detector in the forward link of satellite system has been investigated. The MMSE-SIC detector allows the exploitation of full frequency reuse among the beams and can be practically implemented using a relatively simple multi-stage MMSE implementation and hard decision SIC. Compared to precoding techniques there is no need for satellite RF chains tight synchronization and frequent channel reporting. The proposed CDM physical layer exploiting orthogonal channelization sequences within each beam (up to the spreading factor value) allows to reduce the co-channel interference experienced by the SIC. The proposed MMSE-SIC physical layer performance dependency on a number of key system parameters have been assessed by simulation. It was also found that the demodulator channel estimation errors and multi-stage MMSE simplified architecture have negligible performance impact compared to the more complex full MMSE implementation for the cases of practical interest. Simulation results at physical layer level have been successfully compared to more abstract physical layer modelling which was subsequently used to derive the system level normalized throughput. Following beam assignment optimization algorithm derivation, extensive system level simulations have been performed aiming at deriving the proposed physical layer performance in the context of a multi-beam satellite study case. Except for the inner part of the beam where a single user detector is used for the reasons explained in the paper, the simulated MMSE-SIC detector unconstrained throughput is very close to the relevant theoretical capacity bound. Results have also been compared to a state-of-the-art FDM/TDM DVB-S2X benchmark system with real MODCODs and ACM. It was found that for the case of even traffic distribution among the 40 beams CDM with distributed MUD is in fact loosing 6 % in average beam throughput compared to the FDM benchmark. But when the traffic is not uniform, as it is often the case,
58
the use of the iso-frequency beams, processing of just one additional CDM beam multiplex in each user location, allows to flexibly increase the hot beam average beam throughput up to 626 % compared to the benchmark FDM/TDM system. It has also been shown that in the different system scenario described in [18] the proposed CDM MMSE hard SIC MUD solution is outperforming recently proposed TDM MUD soft SIC alternative by 264 % in the hot spot case. Instead, for the case of uniform beam loading the CDM MUD is under performing the TDM/FDM MUD solution by 15 %. This is mainly caused by the sub-optimum spectral efficiency of the low SNR DVB-S2X MODCODs for CDM resulting in a loss of about 30 % in throughput. In the particular HS case where all the throughput request is concentrated in a (central) beam, we found that a simpler SUD solution with three colours and smart adjacent beam assignment to the hot spot can outperform the CDM MMSE-SIC MUD by 5 %. Instead with more conventional four colour scheme the CDM MMSE-SIC MUD shows 14 % gain in the aggregate throughput while reaching similar offered capacity variation among the users. The exploitation of FFR implies an increased feeder link bandwidth. Furthermore, in case of conventional single feed per beam payloads, it requires a number of TWTAs on-board the satellite proportional to the number of beams on which full frequency reuse is envisaged. Thus, flexible assignment of FFR clusters is particularly suitable to be implemented in payloads based on active or semi-active antennas and with flexible bandwidth per beam allocation. This is the case for the last generation of MSS Geostationary satellites or the future generation of flexible HTS. Further work is required to investigate the RRM aspects for the proposed CDM physical layer exploiting multi-dimensional ACM as well as optimum flexible payload architectures capable to provide FFR over highly loaded areas. ACKNOWLEDGEMENTS The authors would like to acknowledge the fruitful discussion with Dr. A. Ginesi, Dr. E. Re, Dr. A. Modenini. Dr. D. P. Arapoglou from ESA-ESTEC. A special thank to V. Icolari from University of Bologna and Dr. D. P. Arapoglou from ESA-ESTEC for providing the Sect. V-C1 precoding results.
59
A PPENDIX A. Punctual Evaluation of the number of Dominant and Serving Beams Initial system performance analysis reported in [41] were assuming full frequency reuse and a fixed number for the dominant/serving beams9 providing service to the user located in the position (x, y) of beam l. Two distinct cases were considered i.e. Nbdom (l) = 2 and 3. The dominant beam identity was dependent on the user location. For each user location (x, y), in addition to the reference dominant beam l, the strongest adjacent interfering beam(s) (i1 (x, y|l) for Nbdom (l) = 2 and i1 (x, y|l), i2 (x, y|l) for Nbdom (l) = 3) were selected. All selected Nbdom (l) dominant beams were serving each location. Although this approach was simple to handle in terms of system analysis, results reported in [41] showed some important drawbacks. First, it requires that the the outer beam(s) should be decodable also within the inner zone of the reference dominant beam l. As the adjacent beam antenna gain is rapidly decaying approaching the center of beam l, the associated SNIR is also becoming very low. As a consequence, the neighboring beams bring low throughput to the inner part of the reference beam and eventually become not decodable even when exploiting the most protected MODCOD. Recalling that the neighboring beams resources have to be time shared among the served locations, it is apparent that allocating beam resources to low spectral efficiency locations, such as the inner part of the beam, reduces the overall spectral efficiency and/or system availability. The approach proposed here represents an evolution of the basic scheme proposed in [41]. We define at system level the maximum number of dominant beams [Nbdom ]max which can be demodulated by the MUD. We now assume the number of dominant beams Nbdom (x, y|l) ≤ [Nbdom ]max as location dependent. For a given beam user location (x, y) an adjacent beam is considered dominant and serving, thus belonging to BD and BS , if the corresponding MMSESIC SNIR is higher than a given system parameter ρmin . Instead, if the SNIR falls below ρmin the dominant adjacent beam is not exploited by the MUD and the corresponding interference treated as extra AWGN. The reference beam l is always treated as dominant and considered as serving beam only in the inner part of the beam when the SNIR corresponding to all other adjacent beams is below ρmin . The logic followed for assigning the ensemble of dominant beams BD (x, y|l) and 9
60
the serving beams BS (x, y|l) during the pre-run phase is synthetically described in Table IX. Once the for each coverage location the dominant/serving beams for [Nbdom ]max = 1, 2, 3 have been identified, the throughput is computed following the approach described in Sect. IV-B. [Nbdom ]max Case
1
2
3
[C0 ]
Nbdom (x, y|l) = 1
Nbdom (x, y|l) = 1
Nbdom (x, y|l) = 1
ρ(q) < ρmin ∀ q
BD (x, y|l) = {l}
BD (x, y|l) = {l}
BD (x, y|l) = {l}
q ∈ {l, i1 (x, y|l), i2 (x, y|l)}
BS (x, y|l) = {l}
BS (x, y|l) = {l}
BS (x, y|l) = {l}
[C1 ]
Nbdom (x, y|l) = 1
Nbdom (x, y|l) = 1
Nbdom (x, y|l) = 1
ρ(l) ≥ ρmin
BD (x, y|l) = {l}
BD (x, y|l) = {l}
BD (x, y|l) = {l}
ρ(q) < ρmin ∀ q 6= l
BS (x, y|l) = {l}
BS (x, y|l) = {l}
BS (x, y|l) = {l}
Nbdom (x, y|l) = 2
Nbdom (x, y|l) = 2
BD (x, y|l) = {l, i1 (x, y|l)}
BD (x, y|l) = {l, i1 (x, y|l)}
BS (x, y|l) = {i1 (x, y|l)}
BS (x, y|l) = {i1 (x, y|l)}
[C2 ] ρ(i1 (x, y|l)) ≥ ρmin
NA
ρ(i2 ) < ρmin
Nbdom (x, y|l) = 2
[C3 ] ρ(i1 (x, y|l)) < ρmin
NA
BD (x, y|l) = {l, i2 (x, y|l)}
NA
ρ(i2 ) ≥ ρmin
BS (x, y|l) = {i2 (x, y|l)}
[C4 ]
Nbdom (x, y|l) = 3
ρ(i1 (x, y|l)) ≥ ρmin
NA
NA
ρ(i2 (x, y|l)) ≥ ρmin
BD (x, y|l) = {l, i1 (x, y|l), i2 (x, y|l)} BS (x, y|l) = {i1 (x, y|l), i2 (x, y|l)}
TABLE IX D OMINANT AND SERVING BEAM ASSIGNMENT LOGIC .
61
B. Evaluation of the MMSE SNIR Taking into account the CDM signal introduced in the section II-A, in the following we customize its formulation to allow the derivation of the SNIR at the MMSE detector output at each step of the SIC. The beams signal multiplex is generated according to details of the coding, modulation and channelization/scrambling previously described. Let us now define as K tot the overall number of active CDM components for the satellite dominant beams. It easily follows dom Nbeam
K tot =
X
tot Kbeam (b).
(32)
b=1
As discussed in Sect. II-C, assuming successful signal component detection, at each MMSE-SIC step s the detector will see a reducing number of interferers K(s) = K tot − s + 1. For our current analysis we focus on a single-shot iMMSE-SIC detector iteration i.e. Niter =1. Following (4) the received signal at the terminal chip matched filter (CMF) output of the reference user terminal location (x, y) is given by y(t|x, y) = sR (t|x, y) ⊗ gRx (t).
(33)
Assuming that all the CDM components are time aligned10 (i.e. ∆τb = 0) and that the CMF sampling takes place at the optimum sampling time instant tm,n = τp (x, y) + nTc + mTs we get the following filter output sample value yn [m] =
dom Nbeam
tot (b) Kbeam
X
X
b=1
·
hb (x, y)
k=1
s
P (b) ˜b dk [m]˜ cbk [m, n] tot Kbeam (b)
exp { [(2π∆fb (nTc + mTs + θb ]} + wn [m],
(34)
where wn [m] = [(v(t) + iob (t)) ⊗ gRx (t)]|t=tm,n ∼ NC (0, σw2 ),
(35)
with σw2 = (N0 + I0 )/Tc . We can now derive the following N -th dimensional memory samples array y[m] to be initially processed to recover the K tot -dimensional information symbols vector d[m] y[m] = A1 d[m] + w[m], 10
(36)
The extension to the case of asynchronous (or quasi-synchronous) beam interference is straightforward but more complex
in terms of notation.
62
where y[m] = (y1 [m], · · · yN [m]) , d[m] = (d1 [m], · · · dK tot [m]) , w[m] = (w1 [m], · · · wN [m]) , ,
(37)
and A1 = Ψ1 · H1 · P1 , with the complex spreading matrix given by c˜ [1] · · · c˜K tot [1] 1 .. .. .. Ψ1 = . . . c˜1 [N ] · · · c˜K tot [N ]
(38)
.
(39)
The channel coefficient matrix is diagonal and assumed to be time invariant thus H1 = diag (h1 , · · · hK tot ) ,
(40)
and the CDM multiplex individual components transmit amplitude diagonal matrix is given by p p P1 = diag (41) P1 , · · · PK tot . We can now extend the previous notation for the signal samples to be processed by the MMSE-SIC detector step s as ys [m] = As ds [m] + ws [m],
(42)
with ys [m] = (ys [m], · · · yN [m]) , ds [m] = (ds [m], · · · dK tot [m]) , ws [m] = (ws [m], · · · wN [m]) , As = Ψ s · H s · P s ,
(43)
63
with the complex spreading matrix given by c˜ [1] · · · c˜K tot [1] s . .. ... Ψs = .. . c˜s [N ] · · · c˜K tot [N ]
,
(44)
where the channel coefficient matrix is diagonal and assumed to be time invariant thus Hs = diag (hs , · · · hK tot ) ,
(45)
and the CDM multiplex individual components transmit amplitude diagonal matrix is given by p p Ps = diag Ps , · · · PK tot . (46) The SNIR for the generic k-th CDM stream (k = 1, . . . , K max ) at the MMSE output is given by ζk =
1 − 1, Qk,k
(47)
with Qk,k denoting the the k-th element of the k × k-dimensional diagonal matrix Qk iteratively obtained as [36], [37]
−1 AH k Ak , Qk = IK−k+1 + γK tr (Ak Ak )
(48)
where γ the average SNR after despreading of the received CDM components. The information rates assigned to CDM components is decided by the transmitter that is assumed to have the knowledge of the SNIR values observed at each receiver. The information rate selection (i.e. modulation and coding assignment) by the transmitter is done in such a way that each component can be decoded reliably and removed at the receiver. The change of information rate assignment by the transmitter can change the order to reliable decoding and cancellation at the receiver. This can also impact the overall system throughput. Ultimately, different radio resource management strategies may lead the system to operate at different point on the rate region. For the average throughput (upper bound) assessment, we assumed a perfect cancellation of each decoded component. The rate assignment is also carried out according to the SNIR per component (after the cancellation of previously decoded components).
64
C. MUD Sum Rate Capacity Bounds It is known that CDMA with MMSE-SIC receiver can achieve the capacity bounds of an AWGN multiple access channel [43]. This is obtained combining sufficient statistics of linear MMSE estimates and the successive cancellation of decoded streams that allow for the implementation of the chain rule of mutual information [44]. In Appendix B, we outlined the computation of the SNIR at the output of the MMSE filter after each iteration of SIC as shown in (47). The SNIR values are used to compute the normalized throughput at each receiving node, as per (23). Here, we compare the MMSE-SIC throughput with the sum rate capacity bounds of simultaneous reception of multiple beams . This allows us to verify the optimality of the proposed CDM with MMSE-SIC receivers against the theoretical bounds of uncoordinated reception of multiple beams at each receiving node (satellite user terminals). For the AWGN Multiple Access Channel, the sum rate of information received from multiple sources (in our scenario, multiple beams) is bounded by the following inequality ( P[Nbdom ]max ) [Nbdom ]max X Pb Rb ≤ log2 1 + b=1 Nt + Iunr b=1 P[Nbdom ]max C −1 1 + b=2 (x, y|l) I b = log2 1 + . (49) −1 (x, y|l) SNR−1 + NPR−1 + C I unr
This corresponds to the case in which the MUD is able to only process [Nbdom ]max dominant beams. The average power received from beam b at the receiver is denoted by Pb which is shared among all CDM components passing through beam b. In (49), Nt denotes the contribution of thermal noise and other noise like impairments such as NPR. The contribution of unresolved cochannel interference from adjacent beams is accounted for as Iunr . The sum rate can equivalently be computed based on signal to noise ratio, NPR and the power ratio of the incumbent and adjacent beams CI b and CI unr , as shown in (49). The sum rate capacity bound in (49) assumes equal weighted sum of different contributing beams. In general, as shown in (23), the weighting factors of different beams could be different depending the number of regions served by each beam as well as the resource sharing policies. The use of sum rate capacity bound provides a simple and effective way to validate the system aggregate throughput. Using the chain rule, it is possible to separate the sum rate capacity bound into two or more components, each corresponding to one contributing beam. Similar to
65
the weighted sum of MMSE-SIC capacity in (23), the unconstrained capacity of the forward HS−UC link multi-beam channels can be written in terms of the individual contributions Tmax,b that
can be analytically expressed as [Nbdom ]max
HS−UC Tmax (x, y|l) =
X b=1
A(Bl ) · T HS−UC (x, y|l). A(Bb,l ) max,b
(50)
HS−UC For [Nbdom ]max = 2, the UC throughput components Tmax,b (x, y|l) are ( ) 1 HS−UC (x, y|l) = log2 1 + Tmax,1 −1 −1 SNR−1 + NPR−1 + CI unr (x, y|l) + CI b1 (x, y|l) ( ) C −1 (x, y|l) I b1 HS−UC Tmax,2 (x, y|l) = log2 1 + , (51) −1 −1 SNR + NPR−1 + CI unr (x, y|l) −1 −1 where CI unr (x, y|l) is computed from (17) and CI b1 (x, y|l) is the CI corresponding to the
first outer beam demodulated by the MUD. The first term in (51) corresponds to capacity of link when all adjacent beams are treated as noise and only the signal from the incumbent beam is decoded. This would only be possible if the information rate of the incumbent beam is selected to be lower than the capacity bound shown in this equation. Once the transmitted signal from the incumbent beam is successfully decoded and removed using the SIC process, then the signal from adjacent beam can be decoded. The throughput of this link is bounded by the the second equation in (51). It should be noted that using a simple mathematical manipulation, it can be shown that the sum of two terms in (51) is equal to the sum rate capacity bound in (49). Similar separation of terms can be performed for [Nbdom ]max = 3: ) ( 1 HS−UC Tmax,1 (x, y|l) = log2 1 + C −1 C −1 C −1 −1 −1 SNR + NPR + I unr + I b1 + I b2 ) ( C −1 HS−UC Tmax,2 (x, y|l) = log2
I b1
1+ SNR
−1
SNR
−1
( HS−UC Tmax,3 (x, y|l) = log2
where
C −1 I b2
1+
−1
+ NPR + C −1 I b2 −1
+ NPR
+
C −1 I unr
C −1
+ )
C −1 I b2
,
(52)
I unr
is the C/I corresponding to the second outer beam demodulated by the MUD.
Simulation results and the punctual system unconstrained throughput for MMSE-SIC receiver is computed and compared to that of unconstrained weighed sum rate for system throughput assessment. As shown in Fig. 21, the MMSE-SIC unconstrained capacity computations are very
66
close to weighed sum rate capacity bounds as described above. This observation is consistent with the known results that MMSE-SIC receivers are capacity achieving in AWGN MAC Channel [43] as long as the average power constraint per beam is respected. D. MODCOD Parameters Tables X and XI summarize the MODCODs adopted for system level simulations for the FDM benchmark and the CDM challenger physical layer configurations.
67
Mmod
r
MC ξth (dB)
η MC (bits/symbol)
Use Cases
2
0.20
-6.85
0.194
[CF1, CF2, CF3]
2
0.24
-5.50
0.237
[CF1, CF2, CF3]
2
0.33
-4.00
0.323
[CF1, CF2, CF3]
4
0.22
-2.85
0.435
[CF1, CF2, CF3]
4
0.25
-2.35
0.500
[CF1, CF2, CF3]
4
0.29
-2.03
0.568
[CF1, CF2, CF3]
4
0.33
-1.24
0.666
[CF1, CF2, CF3]
4
0.40
-0.30
0.800
[CF1, CF2, CF3]
4
0.45
0.22
0.889
[CF1, CF2, CF3]
4
0.50
1.00
1.000
[CF1, CF2, CF3]
4
0.55
1.45
1.089
[CF1, CF2, CF3]
4
0.60
2.23
1.200
[CF1, CF2, CF3]
4
0.67
3.1
1.334
[CF1, CF2, CF3]
4
0.75
4.03
1.500
[CF1, CF2, CF3]
4
0.80
4.68
1.600
[CF1, CF2, CF3]
4
0.83
5.18
1.666
[CF1, CF2, CF3]
4
0.89
6.2
1.778
[CF1, CF2, CF3]
4
0.90
6.42
1.800
[CF1, CF2, CF3]
8
0.56
4.73
1.647
[CF1, CF2, CF3]
8
0.58
5.13
1.714
[CF1, CF2, CF3]
8
0.60
5.50
1.779
[CF1, CF2, CF3]
8
0.64
6.12
1.90
[CF1, CF2, CF3]
8
0.67
6.62
2.001
[CF1]
8
0.69
7.02
2.062
[CF1]
8
0.72
7.49
2.145
[CF1]
8
0.75
7.91
2.250
[CF1]
8
0.83
9.35
2.499
[CF1]
8
0.89
10.69
2.667
[CF1]
8
0.90
10.98
2.700
[CF1]
TABLE X MODCOD PARAMETERS - PART I.
68
Mmod
r
MC ξth (dB)
η MC (bits/symbol)
Use Cases
16
0.50
5.97
1.972
[CF1]
16
0.53
6.55
2.105
[CF1]
16
0.56
6.84
2.193
[CF1]
16
0.60
7.41
2.370
[CF1]
16
0.58
7.51
2.282
[CF1]
16
0.64
8.38
2.525
[CF1]
16
0.67
8.43
2.635
[CF1]
16
0.67
8.97
2.668
[CF1]
16
0.69
9.27
2.746
[CF1]
16
0.72
9.71
2.856
[CF1]
16
0.75
10.21
3.000
[CF1]
16
0.78
10.75
3.077
[CF1]
16
0.80
11.03
3.200
[CF1]
16
0.83
11.61
3.332
[CF1]
16
0.86
11.99
3.387
[CF1]
16
0.89
12.89
3.556
[CF1]
16
0.90
13.13
3.600
[CF1]
32
0.67
11.10
3.290
[CF1]
32
0.71
11.75
3.510
[CF1]
32
0.73
12.17
3.621
[CF1]
32
0.75
12.73
3.750
[CF1]
32
0.78
13.05
3.841
[CF1]
32
0.80
13.64
4.000
[CF1]
32
0.83
14.28
4.165
[CF1]
32
0.89
15.69
4.445
[CF1]
32
0.90
16.05
4.500
[CF1]
64
0.71
13.98
4.206
[CF1]
64
0.73
14.81
4.339
[CF1]
64
0.78
15.47
4.603
[CF1]
64
0.80
15.87
4.735
[CF1]
64
0.83
16.55
4.934
[CF1]
128
0.75
17.73
5.163
[CF1]
128
0.78
18.53
5.356
[CF1]
256
0.64
16.98
5.066
[CF1]
256
0.67
17.24
5.242
[CF1]
256
0.69
18.10
5.417
[CF1]
256
0.71
18.59
5.593
[CF1]
256
0.73
18.84
5.769
[CF1]
256
0.75
19.57
5.901
[CF1]
TABLE XI MODCOD PARAMETERS - PART II.
69
E. Adjacent Beam FDM Resource Sharing with SUD for Hot Spot In this Appendix, the use of conventional FDM scheme and SUD to serve a hot spot central region by pulling resources of 6 adjacent beams is investigated. The system scenario is similar to [CF3] of Section V-A. However, instead of full frequency reuse among 7 adjacent beams, we consider orthogonal frequency division among beams based on either 3 or 4 colour frequency reuse scheme. Since orthogonal frequency division multiplexing and conventional SUD receivers are considered, the throughput evaluation for each user is based on conventional FDM case described in Sect. IV-A. The concept of sharing resources of adjacent beams to serve a hot spot in a conventional 4colour multi beam system was introduced in [45]. It was shown that central beam can be divided into 7 non-overlapping zones where the users at the central zone are served by the central beam and each outer zone is served by one adjacent beam. Although the signal strength of the adjacent beams are somewhat degraded (compared to adjacent beam centres), the link quality would still allow for a decent information delivery to the outer zones of the central beam. For a three-colour frequency reuse scheme, Fig. 23 shows the SNIR values at central zone served by the central beam as well as the outer zones that are served by an adjacent beam operating at different frequency colours. The co-channel interference of adjacent beams is taken into account in the SNIR computation. The assignment of a receiver to each zone is decided based on the link quality of the signals received from the central beam and adjacent beams. If the SNIR of the receiving signal from the central beam is above a threshold, the receiver is assigned to the central zone and is served by the incumbent (central) beam. The SNIR threshold value is selected as a system parameter and controls the number of receivers served by the central beam. Other receivers are assigned to an adjacent beam with the strongest received signal (detected at the receiver). The change of the threshold will change the number of users served by the central beam and adjacent beams. Compared to a conventional system where all users are served by one beam, the proposed approach serves the central beam users with 7 adjacent beams which leads to a significant increase in the aggregate throughput of the hot spot. Simulations were carried out to quantify the aggregate throughput for the same system scenario [CF3] of Section V-A based on 3 and 4 colour frequency reuse.
70
Punctual SNIR 16 20 14
12 10 10
5
0 11
8 10
50 49
9
48
8 Y (deg)
Fig. 23.
SNIR [dB]
SNIR [dB]
15
6
47 7
46
X (deg)
Beam 120 SNIR values for 3-colour FDM scheme using resources of the six adjacent beams.
Results are presented in Fig. 24. The aggregate throughput offered to the central beam is computed as a function of the relative SNIR threshold (instead absolute value of the threshold, the difference between the threshold and the maximum value of SNIR at the central of the beam is shown). The change of this relative threshold will increase the number of users assigned to the central beam. As a result the adjacent beams will only serve a smaller number of users closer to the edge of the beam leading to a higher aggregate throughput. However, this will also lead to a larger variation in the offered capacity among users within the beam. The variation of offered capacity is quantified using the standard deviation of offered capacity as shown in Fig. 24-(b). To have a fair distribution of the capacity, the threshold value corresponding to the minimum standard deviation should be selected. The resulting aggregate throughput in this case would be 9.25 bit/symbol. However, to compare similar situation to the results reported for the CDM scheme, we have highlighted the same level of standard deviation (5.39 bits/chip). The corresponding aggregate throughput for three-colour scheme reaches 9.92 bits/symbol that is 5% higher than that reached by the CDM as reported in Table VII. As for 4-colour scheme, it reaches 8.25 bits/symbol that is 13% lower than what is achievable by CDM MUD scheme.
Aggregate Throughput Capacity (bits/symbol)
71
10
3−colour 4−colour
9.5
9
8.5
8
7.5
7 0.1
0.2
0.3 0.4 0.5 0.6 SNIRmax −SNIRthreshold [dB])
0.7
0.8
0.7
0.8
Aggregate Throughput Standard Deviation (bits/symbol)
(a) Aggregate Throughput 8 7
3−colour 4−colour
6 5 4 3 2 1 0 0.1
0.2
0.3
0.4 0.5 0.6 SNIRmax −SNIRthreshold [dB]
(b) standard deviation Fig. 24. Figures of merit for serving Hot Spot [CF3] configuration using 3-colour and 4-colour frequency reuse scheme together with conventional SUD.
72
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