High Efficiency Satellite Multiple Access Scheme for Machine-to ...

I. INTRODUCTION

High Efficiency Satellite Multiple Access Scheme for Machine-to-Machine Communications ´ HERRERO OSCAR DEL RIO RICCARDO DE GAUDENZI, Senior Member, IEEE European Space Agency

The work presented here describes the key design drivers and performance of a high efficiency satellite mobile messaging system well adapted to the machine-to-machine communication services targeting, in particular, the vehicular market. It is shown that the proposed return link multiple access solution is providing a random access channel (RACH) aggregated spectral efficiency around 2 bit/s/Hz in the presence of power unbalance with reliable packet delivery over typical land mobile satellite (LMS) channels.

Manuscript received October 16, 2010; revised February 26, May 31, October 6, and October 10, 2011; released for publication October 23, 2011. IEEE Log No. T-AES/48/4/944185. Refereeing of this contribution was handled by M. Rice. Authors’ address: European Space Agency, ESTEC TEC-ET, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands, E-mail: ([email protected]).

c 2012 IEEE 0018-9251/12/$26.00 °

Mobile satellite services are experiencing a new momentum thanks to the success of satellite-based digital broadcasting networks like Sirius, XM [1] in the United States, SDMB [2] in Korea, and the development of new bidirectional systems exploiting hybrid satellite/terrestrial networks (SkyTerra-MSV, Terrestar, ICO-G in the U.S., Eutelsat’s W2A S-band payload in Europe). The latter are exploiting the new S-band licensing rule based on the principle of ancillary terrestrial component (ATC) in the United States or complementary ground component (CGC) in Europe. ATC/CGC will allow complementing satellite coverage in satellite-unfriendly urban/suburban areas by a network of terrestrial repeaters, thus, achieving a more uniform quality of service over the system coverage area. Smart frequency reuse schemes between the satellite and the ATC/CGC will allow combining the good coverage with a high spectral efficiency. A new standard for satellite/terrestrial hybrid broadcasting of multimedia content dubbed Digital Video Broadcasting Satellite-to-Hand-held (DVB-SH) has been recently approved by the European Telecommunication Standards Insitute (ETSI) [3]. Broadcasting in the hybrid satellite/terrestrial networks is a natural application for the space-to-Earth link (forward link). A new range of applications can take advantage of the S-band assigned to Earth-to-space communication (return link) in addition to the space-to-Earth direction. Among them, the support of machine-to-machine communication services [4, 5] for the vehicular market represents a good opportunity. These services can make use of the return link capacity for the transmission of telemetry data, requiring only a small fraction of capacity in the forward direction. It is crucial to minimize the cost of the user terminals and the cost of the communications to render these services economically viable. This paper proposes an in-depth analysis of a return link multiple access scheme able to achieve the objectives of low terminal cost and high transmission efficiencies for large-scale vehicle satellite-based telemetry services. The proposed return link multiple access scheme employs asynchronous spread spectrum Aloha (SSA) techniques [6, 7] combined with low-rate forward error correction (FEC) [8] and downlink channel quality-based transmit on-off packet control at the user side. The proposed waveform for the return link is based on a modified version of the 3GPP Wideband Code Division Multiple Access (W-CDMA) Standard Random Access Channel (RACH) physical layer design [9]. Furthermore, we introduce novel processing techniques at the gateway demodulator side to maximize the system throughput while keeping low the packet error probability. The gateway demodulator

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 48, NO. 4

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Fig. 1. Hybrid satellite/terrestrial mobile system architecture.

employs successive interference cancelation (SIC) at packet level with a cyclic redundancy check (CRC) and a sliding memory several physical layer bursts long. The novel transmission control mechanism at the transmitter exploits a signal-to-noise ratio (SNR) estimator of the received signal in the forward link to dynamically identify the line-of-sight (LOS) conditions in a land mobile satellite (LMS) channel. Performance results of this scheme have been derived through an analytical model and Monte Carlo simulations and show that a normalized channel utilization close to 2 bit/s/Hz (total bit rate being transmitted by all terminals as a fraction of the total chip rate) with packet loss ratios (PLRs) in the 10¡3 —10¡4 region can be achieved with low power and low gain user terminals in an LMS environment. Analytical results are closely approximating the enhanced spread spectrum Aloha (E-SSA) simulated behavior both in terms of throughput and PLR. Following this Introduction, Section II outlines the main system and communication requirements. Section III describes the shortcomings of existing multiple access schemes and the key elements of the new return link multiple access scheme. Section IV describes the enhanced spread spectrum Aloha (E-SSA) detector and provides key performance results. Section V describes the proposed satellite return link waveform derived from the 3GPP W-CDMA standard physical layer design. Section VI describes the uplink packet transmission control 2962

and provides key performance results. Finally, the conclusions are drawn in Section VII. II.

SYSTEM REQUIREMENTS AND PROBLEM STATEMENT

The system under consideration is a GEO mobile satellite system operating in the mobile satellite systems (MSS) bands, i.e., L or S-band, aiming at the provision of machine-to-machine communication services to a large population of low-cost vehicular satellite terminals1 (STs). The system shall leverage as much as possible on existing broadcast and communication standards to minimize the cost of the user terminals, and the few MHz of band available for each satellite beam will be shared by a very large number of vehicles. It should be recalled that the satellite beam area is typically very large compared with the terrestrial networks cells, i.e., from several hundreds to a few thousands kilometers of diameter. In Fig. 1 we present an example system architecture for a hybrid satellite/terrestrial mobile system in S-band. All mobile terminals communicate in S-band either to the satellite or the CGC. The CGC will be placed within the satellite coverage, by exploiting smart frequency reuse schemes, in order to complement the system coverage in satellite-unfriendly urban and suburban areas. From 1 Application to different bands (e.g. Ku and Ka-bands), or to different type of services (e.g. aeronautical services, SCADA, sensor networks), although possible, are not discussed here.


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the set of machine-to-machine communication services [4, 5] we concentrate on services for the automotive market such as fleet management, automated asset tracking, stolen vehicle recovery system, pay as you drive (insurance, road tax, road tolling), and vehicle diagnostics. The system will integrate appropriate communication and positioning systems in a complete platform, including e.g. Geographic Information System (GIS), GEO-referenced database, and Global Navigation Satellite Systems (GNSS) receivers, in order to support situation awareness services. The key communication characteristics of these services are, to a large extent small packet size (few hundreds bits), low data rate (few kilobit/s), low duty cycle (few times monthly, weekly, daily, or event driven) and a potentially very large number of communicating terminals. This type of communication scenario poses several technical challenges to a GEO MSS, and in particular to the return link. Low cost, low directivity, and low EIRP satellite terminals are desired for the transmission of very small volumes of data (short messages). This requires the use of the CGC in urban and suburban environments. The sharing of the frequency band (few MHz) by a potentially very large number of terminals requires a very dynamic use of the capacity on the return link. An efficient use of the return link capacity (e.g. > 1 bit/s/Hz aggregate spectral efficiency) in such dynamic conditions calls for advanced multiple access schemes that minimize the amount of overhead and signalling for each transmitted information bit. The land vehicular satellite channel causes frequent signal level variations due to shadowing and multipath fading. This requires the use of an efficient transmission control scheme on the mobile terminals, that prevents unsuccessful transmissions in case of sizeable shadowing levels to avoid wasting resources or polluting the channel with multiple access interference (MAI). In the following sections we describe and assess the performance of a high efficiency satellite mobile multiple access scheme for the return link, well adapted to the above applications and fully integrated with existing broadcast and communication standards. III. RETURN LINK MULTIPLE ACCESS MESSAGING SCHEME Considering the low duty cycle, the small message size and the truly packet nature of the service, a pure random access (RA) solution is preferred for the return link to a reservation-based one, such as demand assignment multiple access (DAMA) [10, 11]. For bulkier data transmission applications, DAMA techniques are today widely used in satellite networks [12, 13], and they typically use an RA channel for network login and initial capacity requests. Using DAMA in conjunction with RA will result in a very

inefficient service scenario because of the capacity set-up time and associated signalling overhead. This is particularly true when the size of packets is very small and the transmission duty cycle is low as in our case. In addition, the performance of the DAMA scheme will be further degraded in an LMS channel as the capacity assignments granted by a gateway to the terminal cannot guarantee LOS conditions at the time of reception by the terminal. Thus, an important amount of assigned capacity will result in erroneous transmissions with the need of retransmissions. RA schemes have been widely investigated in the literature as well as their advantages and disadvantages [14]. RA techniques based on channel sensing [15, 16], commonly used in terrestrial networks, cannot be exploited in satellite networks because of the large round trip delay. Slotted Aloha (SA) [17—19] or an enhanced version of the scheme, such as diversity slotted Aloha (DSA) [20], are used today in satellite time division multiple access (TDMA) systems with low efficiency and reliability for transactional and supervisory control and data acquisition (SCADA) applications, and for network login procedures in broadband access satellite networks. Recently an enhanced version of DSA dubbed contention resolution diversity slotted Aloha (CRDSA) has been introduced [21] and its performance compared against that of SA and DSA. The medium access channel (MAC) throughput is quite poor for SA (normalized throughput T = 10¡3 packets/slot for a PLR of 10¡3 ). If we assume a waveform with quadrature phase shift keying (QPSK) modulation and FEC coding rate 1/2 it corresponds to a normalized throughput2 T = 10¡3 bit/s/Hz. Higher SA MAC throughput may be achieved by relaxing the PLR requirement and thus calling for frequent packet retransmissions. For the same PLR, DSA gets a higher yet modest throughput of T = 1:7 ¢ 10¡2 packets/slot (or bit/s/Hz under the previous waveform assumptions) while CRDSA throughput can be as high as T = 5 ¢ 10¡1 packets/slot (or bit/s/Hz) for a PLR of 10¡5 [22]. Slotted RA systems require terminals to keep the time slot synchronization. The resulting synchronization overhead greatly reduces the system efficiency, in particular for networks characterized by a large number of terminals with a very low transmission duty cycle like is the case in the envisaged application. Finally, for TDMA-based slotted RA the terminal EIRP requirement is related to the aggregated data rate of the TDMA multiple access scheme instead of the single terminal bit rate. Thus TDMA-based slotted RA is penalizing low-cost terminal solutions. 2 The

transmit square-root raised-cosine roll-off factor extra bandwidth has not been taken into account.

DEL RÍO HERRERO & E GAUDENZI: HIGH EFFICIENCY SATELLITE MULTIPLE ACCESS SCHEME

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Fig. 2. Overview of the proposed satellite communication system.

SSA proposed in [6] and adopted in Satellite Universal Mobile Telecommunication System (S-UMTS) Standard [47, 49], has potentially attractive features as it provides a higher throughput capability than SA for the same PLR target under equal power multiple access conditions when adopting powerful physical layer FEC (e.g. coding rates · 1=2). In [8] it is shown through simplified analysis that SSA throughput is critically dependent on the demodulator signal-to-noise plus interference (SNIR) threshold. Results reported in [8] indicate that differently from SA, SSA shows a steep PLR increase with MAC load. Thus SSA can be operated with low PLR close to the peak of the throughput characteristic. As an example, using turbo codes and relatively small packets, SSA can achieve throughput in the order of T = 0:5 b/s/Hz for a PLR of 10¡3 . Additionally, SSA allows operating in a truly asynchronous mode, with no overhead for terminal burst synchronization. Furthermore, SSA throughput is enhanced by using low FEC coding rates [8] and low order modulations which is not the case for slotted RA schemes. However, the SSA Achilles’ heel resides in its high sensitivity to multiple access carrier power unbalance. This phenomenon is disrupting the SSA scheme throughput. As shown in Section IV-D, SSA throughput is diminished by several orders of magnitude when received packets power is lognormally distributed with standard deviation of 2—3 dB. Thus, to achieve its full potential, SSA requires either tight power control or interference cancellation [23—25]. It is to be remarked that return link closed loop power control over LMS channels 2964

is having important performance limitations due to the propagation delay and requires an important signalling overhead in the forward link [26]. Finally, SSA terminal EIRP is closely related to the single user (and not aggregate as for TDMA) data rate. Thus also from this point SSA is advantageous compared with TDMA RA. The previous review of known RA techniques reveals that none of them is fully satisfying the system requirements outlined in Section II. Overall, truly asynchronous (unslotted) SSA scheme is to be preferred provided that its high near-far sensitivity can be mitigated. Interference cancellation for SSA has been proposed in the past in [27]—[33]. However, the detailed approach for implementing, analyzing, and optimizing the throughput performance of SIC in a satellite unslotted packet SSA system was not reported in the literature. In the present paper, we present and analytically derive the performance of the proposed SIC algorithm for unslotted packet SSA multiple access. The algorithm is dubbed E-SSA detector. References [34] and [35] contain early simulation results and high-level description of the E-SSA concept, which is here described in much greater detail, is now theoretically justified as well as complemented by new results. In Fig. 2 we provide a functional overview of the satellite communication system. In particular the blocks in grey represent the technical contributions from this paper that are analyzed in detail in the following sections. The forward link is based on DVB-SH [3] while the return link is based on E-SSA.


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Fig. 3. E-SSA algorithm description.

The transmissions on the terminal are governed by an open loop transmission control mechanism that continuously monitors the forward link signal reception in order to reduce the transmit packet power unbalance, to maximize the transmission success rate and to avoid unnecessary pollution of the channel with MAI. The channel in the return link is an LMS channel with thermal Gaussian noise and MAI from other users sharing the same channel. The gateway receiver implements the E-SSA packet demodulator.

overlap of packets on each window step. To reduce the detector complexity the window step ¢W, in symbols, is the largest possible yielding acceptable performance reduction. Normally, the window step ¢W is between 1=3 to 1=2 of the window length W depending on its size. At each window step, the following iterative detection process (see Appendix I) takes place. 1) Store in the detector memory the new baseband signal samples corresponding to the current window step. 2) Perform packets preamble detection and select the packet with highest SNIR value. 3) Perform data-aided channel estimation for the selected packet over the preamble. 4) Perform FEC decoding of the selected packet. 5) If the decoded FEC frame is considered correct after CRC check then: a) Perform enhanced data-aided channel estimation over the whole recovered packet (carrier frequency, phase, amplitude, timing) following the algorithm described in Appendix I4 ; b) Reconstruct at baseband the detected packet for the following cancellation step; c) Perform interference cancellation (see [36] for a preliminary analysis on the channel estimation error impact on SIC). 6) Repeat from step 2 until NitWmax iterations are performed. When the limit is reached, advance the observation window by ¢W.

IV. ENHANCED SPREAD SPECTRUM ALOHA DETECTOR The E-SSA detector located at the gateway is the heart of the system as it has to support a high throughput of incoming packets. A detailed analytical description of the E-SSA algorithm is provided in Appendix I. A high-level introductory description follows. The IF composite CDMA signal coming out from the gateway RF front-end is band-pass filtered, converted to digital samples through IF sampling,3 digitally down-converted to baseband with I-Q components separation and stored in a digital memory of 2 ¢ WNsc real samples (we assume that complex baseband samples are stored in I-Q format). Nsc corresponds to the number of chips per physical layer channel symbol and W corresponds to the memory window size in symbols for the gateway interference cancellation process. As shown later, the window size W is optimized to be the smallest possible value yielding good cancellation performance. Typically, W should be three times the physical layer packet length in symbols. The principle of the sliding window mechanism is illustrated in Fig. 3. The sliding window is shifted in time in discrete steps allowing some

In Section IV-D the parameter NitWmax is selected as a trade-off between the diminishing performance

3 Alternatively,

4 In

I-Q baseband conversion and digital sampling can also be implemented.

the following analysis the channel estimation is considered ideal.


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gain and the increasing processing complexity of the gateway detector. In any case, the gateway iterative processor capabilities are able to maintain real-time processing of the incoming signal samples. It is important to note that on each window position, assuming the system is stable and packets are being successfully decoded with a low PLR (e.g. PLR · 10¡3 ), a number of packets will have been already recovered on the previous window step. In the example given in Fig. 3, we can see that packets 3 to 7, that are partially or fully contained in the window step n¢W, have already been successfully decoded and cancelled at window step (n ¡ 1)¢W. Therefore, as the window is shifted the maximum number of decoding and interference cancellation attempts over a given packet Nitpkmax will be a function of NitWmax , W, ¢W, and the packet length in symbols Lp , and can be computed as Nitpkmax = intf((W ¡ Lp )=¢W) ¢ NitWmax g with intf¢g the integer part function. A. SSA and E-SSA Performance Analysis In this section, the SSA and E-SSA performance are derived based on a simplified yet accurate system modeling. In the following derivations, it is assumed that the chip synchronous collision event, whose probability is computed in Section IV-C, is made negligible compared with the target PLR probability, i.e., Pcoll ¿ PLR by proper sizing of the number of spreading sequences (see Section IV-C). 1) SSA Performance Analysis: To derive the SSA analytical performance we need first to derive the probability density function (pdf) for the number of packets colliding with the desired one. Taking a time window of plus or minus a packet around the desired packet p in Fig. 4, we observe that the total number kt of packets colliding with the desired one can be represented by the sum of two random variables (RVs) kt = kb + ka

(1)

where kb and ka represent, respectively, the number of colliding packets before and after the desired packet p. Assuming that packets are generated according to a Poisson distribution, kb and ka are two Poisson RV with intensity ¸p = GGp , while kt is a Poisson RV with intensity ¸t = 2¸p = 2GGp . We define G as the MAC load expressed in information bits/s/Hz. The CDMA processing gain Gp is defined as Gp = Rc =Rb = SF=(r log2 M) where Rc is the channel chip rate, Rb is information bit rate, r is the FEC scheme coding rate, M is the modulation cardinality and SF is the spreading factor. Therefore, ¸p represents the average number of packet arrivals over one packet duration and ¸t is the average number of packet arrivals over the §1 packet window (see Fig. 4) and 2966

Fig. 4. Example of interfering packets time distribution: ka = 5, kb = 4.

is exactly 2¸p . The Poisson RV discrete pdf is given by the following equation: pPoisson (k; ¸t ) =

¸kt exp(¡¸t ) : k!

(2)

As shown in Fig. 4, the interference is coming from asynchronous packets that might only partially overlap the packet of interest. In the general case, this will generate a time-dependent interference component that is a function of the number of interfering packets at each time instant. However, as we will see in Section IV-D, we consider very large values of Gp in our system scenario (e.g. Gp = 768), and consequently the values of ¸p will also be very large, ranging from 150 at low loads (e.g. G = 0:2) to 1500 at high loads (e.g. G = 2:0). Under these conditions the instantaneous number of interfering packets to the packet of interest will moderately fluctuate around its mean value ¹p = ¸p and the average number of interfering packets to the packet of interest is equal to ®k, where ® is the average overlapping factor of the interfering packets to the packet of interest, and is equal to 0.5. It is known that for large values of ¸p the Poisson distribution approximates a normal distribution with mean ¹p = ¸p and standard deviation p ¾p = ¸p . For the large values of ¸p typical of our system (e.g. ¸p = 384 for G = 0:5) the fluctuation of the number of interfering packets will be modest being distributed according to a narrow normal pdf


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p with ¾p =¹p = 1= ¸p = 5 ¢ 10¡2 . The goodness of this approximation has been proven empirically and is testified by the results of Appendix II. In Sections VI and VI-B, we see that the gateway received packet power fluctuation is caused by the uplink LMS channel fading/shadowing statistics and the satellite/user terminal antenna gain variations as a function of the mobile location conditioned to the packet transmission authorization by the packet control algorithm described in Section VI. Assuming it is true that the power of each received packet fluctuates around its LOS value [Eb =N0 ]LOS as [Eb =N0 ](a) = a2 [Eb =N0 ]LOS , each with independent lognormal distribution5 pA (a) characterized by a mean ¹ [dB] and a standard deviation ¾ [dB], the individual received packet amplitude a distribution around the LOS value is given by [37]: ¸ · 20 (20 log10 a ¡ ¹)2 pA (a) = p exp ¡ 2¾2 2¼ ln 10¾a for a > 0: (3) In order to simplify our model, we use a discrete amplitude distribution for the packets amplitude. For this purpose, we create a discrete lognormal pdf as follows: · ¸ Z Eb =N0 (i+1) Eb pEb=N0 (i) = a2 pA (a)da N0 LOS Eb =N0 (i) for i = 1, 2, : : : , 1

(4)

to which a specific value of Eb =N0 (i) is associated. The Eb =N0 bins are computed in a way that they are equally spaced in the logarithmic domain (e.g. in steps of 0.1 dB). We can now compute the SSA PLR as a weighted average of the probability P¯e (i) of erroneously detecting the desired packet p when its Eb =N0 is mapped to bin i: PLRSSA (G) =

1 X

P¯e (i)pEb=N0 (i):

(5)

i=1

It follows that P¯e (i) is given by P¯e (i) =

1 X k=0

Pe (i j k)pPoisson (k; ¸t )

(6)

where Pe (i j k) is the probability of error of the desired packet p when its Eb =N0 is mapped to bin i and conditioned to the case when there are k interfering packets over the §1 packet window. It can be computed as follows: ½· ¸¾ Eb Pe (i j k) = ¡ (i, k) (7) Nt where ¡FER (Eb =Nt ) is the function associating the FEC frame error rate (FER) to the energy per bit to 5 This

hypothesis is verified in Section VI-B.

noise plus interference density ratio (linear) Eb =Nt . For the specific 3GPP Turbo FEC code [38] used in this paper, a good match with the simulated FER is provided by the following best fit law: 8 (F0 +F1 ½+F2 ½2 +F3 ½3 +F4 ½4 +F5 +½5 +F6 ½6 +F7 ½7 +F8 ½8 ) < 10 if ½ ¸ ¡2 ¡FER f½g = : 1 if ½ < ¡2

(8) with ½ = 10 log10 [Eb =Nt ] and F0 = ¡0:21358, F1 = ¡0:37122, F2 = ¡0:224, F3 = ¡0:0418, F4 = 0:0039, F5 = 7:79 10¡4 , F6 = 6 10¡4 , F7 = 1:90 10¡4 , F8 = ¡7:5598 10¡5 . Assuming k interfering packets are falling in the §1 packet window around the pth desired packet, the corresponding Eb =(N0 + I0 ) = Eb =Nt value can be computed as 3 2 Eb · ¸ (i) 7 6 N0 Eb 7 (9) (i, k) = 6 5 4 I (k) Nt 0 1+ N0 being I0 (k) the average power spectral density of the k interfering packets overlapping with the desired packet p. The exact computation of (9) is cumbersome being the interferers lognormally distributed and each having a different overlapping factor with the desired packet. However in our system scenario, the equation can be greatly simplified by approximating the CDMA MAI as additive white Gaussian Noise (AWGN).6 This approximation, motivated by the central limit theorem (CLT) [39], is experimentally justified in Appendix II. According to Appendix II findings the MAI Gaussian approximation derived in the following (see (10)) already holds very well for G ¸ 0:1 b/s/Hz with a mean MAI power level equal to ®k times the mean power level of each interfering packet, with ® = 0:5 the average interfering packets overlapping factor previously defined. This result has been obtained assuming the worst case of phase coherent interfering packets with ¾ = 3 dB lognormal distributed power and asssuming that, according to (3), all packets have the same power distribution. Furthermore, in Appendix II it has been shown that the ratio of standard deviation over the mean value of the MAI instantaneous power is very small for G ¸ 0:2, and thus the MAI power can be considered constant over the packet of interest. We now split the power of the interfering packets in a discrete distribution of Eb =N0 (l) = P(l)=(Rb N0 ) with an associated bin probability pEb=N0 (l), in a similar way as it has been done for the desired packet in (4). As a result, applying the law of large numbers, 6 We do not make a difference for MAI if it is caused by a packet reusing the same spreading sequence as the desired one with different code phase or it is using a different spreading sequence.


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on each Eb =N0 (l) bin there will be an equivalent (real) number7 of interfering packets Np (l, k) = ®kpEb=N0 (l). In view of the above the k interferers MAI interference to AWGN power spectral density I0 (k)=N0 term in (9) can thus be approximated as 1

1

l=1

l=1

I0 (k) 1 X P(l) 1 X Eb ' Np (l, k) = (l)Np (l, k) N0 N0 Rc Gp N0 ½ ¾ 1 ®k Eb ®k X Eb (l)pEb =N0 (l) = E (l) = Gp N Gp N0 l=1 0 · ¸ ®k Eb 2 10[(¹+¾ =(20 log 10(e))=10] : (10) = Gp N0 LOS In deriving (10) the lognormal Eb =N0 (l) distribution from (3) and the Ef(Eb =N0 )(l)g = [Eb =N0 ]LOS Efa2 (l)g derivation from Appendix III have been accounted for. Finally, the MAC throughput in terms of b/s/Hz as a function of the normalized MAC channel load T(G) is simply given by T(G) = G[1 ¡ PLR(G)]:

(11)

2) E-SSA Analysis: The previous PLR result obtained for SSA can be extended to the E-SSA case. However, due to the recursive SIC processing we should now derive recursive equations for the PLR estimation. In the new model, we process the packets from highest to lowest Eb =N0 bins (i.e., decreasing values of i). This seems reasonable, as we normally process strongest packets first in E-SSA (see Section IV). In addition, the model will also support iterative processing within a window position, as described in Fig. 3. At each iteration m = 0, 1, 2, 3, : : : NitWmax we compute the E-SSA PLR similarly to the SSA case: PLR(m+1) E-SSA (G) =

1 X

P¯e(m+1) (i)pEb=N0 (i)

(12)

i=1

where P¯e(m+1) (i) represents the packet error probability of the desired packet p when its Eb =N0 is mapped to bin i and pEb=N0 is the discrete Eb =N0 pdf. It follows that P¯ (m+1) (i) is given by: e

P¯e(m+1) (i) =

1 X k=0

Pe(m+1) (i j k) = ¡ ·

Eb (i j k) Nt

7 It

¸(m+1)

Pe(m+1) (i j k)pPoisson (k; ¸t )

(·

2

6 6 =6 4

Eb (i j k) Nt Eb (i) N0

1+

¸(m+1) )

(13)

(14)

3

7 7 7 I0(m+1) (k, i) 5

(17) describes the residual equivalent where (real) number of colliding packets at iteration m + 1 in the Eb =N0 (l) bin of the discrete pdf pEb=N0 , ® = 0:5 as for the SSA case, and k is the total number of interfering packets occurring with probability pPoisson (k; ¸t ). For all values l · i, P¯e is a recursive function. Therefore, we initialize all values to 1 at iteration m = 0, i.e., P¯e(0) (l) = 1. In addition, for a given iteration, P¯e(m+1) (i) is a function of P¯e(m+1) (l) for all l > i. This implies that P¯e(m+1) (i) needs to be derived from the highest values to the lowest values of i, as previously described. It is to be remarked that the probability of erroneous packet reception follows an approach similar to the SSA case with two major differences: 1) the model is now iterative to reflect the iterative window processing as described in Fig. 3, 2) the equivalent number of colliding packets at a given iteration and at a given Eb =N0 bin accounts for the SIC effects of previous iterations and of higher Eb =N0 bins as shown in (17). Np(m+1) (l, k, i)

B. Link Margin Optimization for E-SSA Although it is known that SIC can take benefit from power unbalance by ranking the packets in descending order of power and starting the detection from the most powerful one [40], in our system we are also facing AWGN noise link limitations. Thus we should find an optimum trade-off between the potential SIC advantages provided by a noneven packet power distribution and the risk that the received packet will be undetectable even in the absence of cochannel interference because the SNR is too low. The packet probability to be incorrectly received in the MAI absence and in the presence of power fluctuations dubbed Pfloor , is simply obtained by averaging the FEC FER function ¡FER f g according to the received packet Eb =N0 lognormal distribution (3). Thus: ½ · ¸ ¾ E Pfloor ¹, ¾, b N0 LOS ½ μ · ¸ ¶¾ Z 1 E = ¡FER 10 log10 a2 b pA (a)da N0 LOS 0 (18)

(15)

N0

is noted that this is a mathematical model that computes average distributions rather than specific trials.

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1

I0(m+1) (k, i) 1 X Eb ' (l)Np(m+1) (l, k, i) (16) N0 Gp N0 l=1 ( if l · i ®kpEb=N0 (l)P¯e(m) (l) (m+1) (l, k, i) = Np (m+1) (l) if l > i ®kpEb=N0 (l)P¯e

where the function ¡FER (¢) describes the FEC FER function of the current [Eb =N0 ]LOS [dB] as described by (7) in Section IV-A. In (18) it is assumed that the FEC FER performance ¡FER (½) is independent from the user speed and the channel conditions. This assumption is reasonable assuming a proper


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Fig. 5. PLR floor probability ¹ = ¡3 dB and ¾ = 1, 2, 3, 4 dB as function of LOS Eb =N0 value.

functioning of the physical layer time interleaver, i.e., a not too low mobile user speed as well as considering that the channel is non-frequency-selective. This assumption has been experimentally validated for L- and S-band channels and holds true for signal bandwidth up to 5 MHz [51] which is the case of our system. Furthermore, thanks to the presence of pilot-aided channel estimation, the performance of the channel estimator is very close to ideal channel estimation for the vehicular user terminal conditions here considered [53]. Figure 5 shows the dependency of Pfloor on [Eb =N0 ]LOS for different values of ¾ and for ¹ = ¡3 dB. As expected, the required [Eb =N0 ]LOS for given Pfloor rapidly increases with the lognormal standard deviation ¾. C. Code Collision Probability The probability Pcoll (Ncodes ) of reusing the same spreading code among a family of Ncodes covering the full packet duration with the same code phase (code collision) can be computed as the probability of code collision is the sum of the product of the number of packet arrivals i within a chip duration (Poisson

distributed) by the probability that at least one of the i interfering packets chooses the same code sequence as the packet of interest. This latter term corresponds to 1 minus the probability that all i interfering packets choose a different code than the packet of interest. Taking into account the independence in the code selection process for the i packets and that 1 ¡ 1=Ncodes represents the probability that one interfering packet chooses a different code than the packet of interest, then one can find that: Pcoll (Ncodes ) =

+1 X

fPoisson (i, ¸c )

i=1

"

μ

£ 1¡ 1¡ fPoisson (k, ¸c ) =

¸kc exp(¡¸c ) , k!

1 Ncodes

¶i #

¸c =

(19) G Li

being G the MAC channel normalized load measured in information b/s/Hz, Li the packet length in information bits, and ¸c the packet arrival rate in packets/chip. For the derivation of ¸c , the transmit square-root raised-cosine roll-off factor has not been


2969

Fig. 6. Probability of code collision versus normalized load G for Li = 1000 and Ncodes as parameter.

taken into account and we have considered that the signal bandwidth and the chip rate Rc are equivalent. Therefore, the normalized channel load G can also be expressed in bits/chip. For the case where Ncodes = 1, (19) reduces to the probability that two or more packets are received at the gateway demodulator within a chip interval, i.e., Pcoll =

+1 X

fPoisson (i, ¸c ) =

i=1

+1 X i=1

= 1 ¡ exp(¡¸c ):

¸ic exp(¡¸c ) i! (20)

An example of probability of collision calculation for Li = 1000 bits can be found in Fig. 6. It should be remarked that the results contained in Fig. 6 provide a pessimistic view about the code collision impact in terms of performance. In reality even a code phase aligned colliding packet can make the packet decodable if the physical layer FEC is powerful enough to mitigate the effect of a chip synchronous interfering packet. This is particularly true for practical systems whereby the number of different code sequences can be minimized by exploiting the received packets power and carrier frequency diversity. This will mitigate the probability of destructive effects due to collisions between chip aligned sequences. The 2970

analysis of code collision probability in the presence of power and frequency errors requires a very detailed system modelling which goes beyond the scope of this paper. D. E-SSA MAC Performance Results A detailed system model according to the block diagram of Fig. 7 has been developed for the E-SSA MAC performance analysis. Traffic is generated with a time granularity of one symbol according to a Poisson distribution as described in Section IV-A. For each generated burst a random delay is added and the packet power is randomized according to a lognormal distribution as for (3). All the generated packets are summed up together with the AWGN demodulator and the resulting signal is entering the E-SSA burst demodulator. The system model adopted has a sufficient level of detail to faithfully represent the system behavior. However, it is remarked that some simplification in the system modeling has been required to achieve an acceptable simulation speed. For the following numerical results it is assumed that there are enough spreading sequences in the system to make the code collision probability negligible taking into account the preamble sequence sizing approach detailed in Section IV-C. In the model of


OCTOBER 2012

Fig. 7. Functional block diagram of MAC simulator.

the gateway received packet power is following a lognormal distribution representing the joint effect of return mobile link satellite shadowing, fading, and packet transmission control algorithms. This lognormal received power distribution assumption is demonstrated in Section VI-B.2. The lognormal RV is assumed to be decorrelated among all return link packets and to be constant over the packet duration. This configuration represents the worst case corresponding to mobile speed lower than than 20 Km/h for the system parameters of Table I and a packet size of 100 bits. For faster mobile speeds the interleaver is able to decorrelate the fading, thus the AWGN FER FEC characteristic ¡FER is replaced by the one obtained fitting simulated results obtained for the specific fading conditions and user speed. The performance of the RA scheme described in Section III and Appendix I has been analyzed by means of an RA computer-based simulator. The two techniques, i.e., SSA and E-SSA have been analyzed with and without power control errors. The simulated E-SSA technique includes interference cancellation of successful packets and performs iterative processing of the received signal within a

TABLE I Simulation Parameters Parameter

Value

Signal bandwidth Bw [Eb =N0 ]LOS Modulation FEC scheme Coding rate r Spreading factor LW Processing gain Gp

5 MHz 13.7 dB BPSK 3GPP Turbo Code 1/3 256 768

Chip rate Rc Packet payload size Coded packet payload size Lpa

3.84 Mchip/s 100 bits (for simulations only) 300 bits (for simulations only)

Shadowing lognormal process mean value ¹ (see (3)) Shadowing lognormal process standard deviation ¾ (see (3)) Sliding window size W Sliding window step ¢W Maximum number of SIC iterations NitWmax

¡3 dB 0, 1, 2 and 3 dB 3 frames 1 frame 5 (baseline)

given time window. When not stated differently, the parameters described in Table I have been used for the simulations.


2971

Fig. 8. Simulated versus analytical SSA performance with and without power unbalance. (a) SSA throughput with and without power unbalance. (b) SSA PLR with and without power unblance.

Simulation and semi-analytical performance results are shown in Figs. 8 and 9 for SSA and E-SSA, respectively. The semi-analytical results have been derived by using the model developed in Section IV-A and the parameters used are in line with the simulation ones reported in Table I. As we can see for the case of 2972

SSA, there is a significant performance degradation in the presence of power unbalance. In this case the MAC throughput reduces from 0.48 bit/s/Hz for ¾ = 0 dB down to 0.05 bit/s/Hz for ¾ = 3 dB at PLR = 10¡3 . Unfortunately this case is realistic because, as shown in Section VI-B, even exploiting


OCTOBER 2012

Fig. 9. Simulated versus analytical E-SSA performance with and without power unbalance. (a) E-SSA throughput with and without power unbalance. (b) E-SSA PLR with and without power unbalance.

packet transmission control techniques, the received packets power at the gateway will typically experience standard deviations in the order of 2 dB but can reach almost 3 dB in less favorable environments. On the contrary, the E-SSA scheme is very robust to power unbalance and actually benefits from it. As shown in Fig. 9(b) the introduction of the iterative SIC process leads to a kind of two-state behavior, i.e., the packets are correctly received until a critical level of system load is reached. At this point packets are lost. Consequently the E-SSA PLR curve becomes

very steep compared with the SSA one allowing error-free operations very close to the MAC peak throughput. The maximum achievable throughput goes from 1.2 bit/s/Hz for the case of ¾ = 0 dB up to 1.9 bit/s/Hz for the case of ¾ = 3 dB at PLR = 10¡3 . This corresponds to a forty-fold improvement compared with conventional SSA under power unbalance conditions. In addition it is possible to operate E-SSA close to the MAC peak throughput with little probability of retransmission. In fact a throughput of 1.9 bit/s/Hz can be achieved for a PLR = 10¡4 . This is


2973

Fig. 10. Evolution of E-SSA undetected packets Eb =N0 distribution during recursive interference cancellation process at G = 1:8 b/s/Hz.

a quite remarkable result for the proposed solution as it allows to obtain a very high MAC throughput (1.9 bit/s/Hz) with very low PLR and resilience to power unbalance. As it can be see in Fig. 8, for ¾ = 2 and 3 dB, at high loads (G = 1:0 ¡ 1:2), the SSA simulated throughput slightly diverges from the analytical curves. This is probably due to some limitations in the characterization of the interference in the model, but this small difference occurs in MAC loading regions well beyond the practical loading range of the system. In the E-SSA case, some bigger differences can be appreciated between the semi-analytical model and simulations as shown in Fig. 9. In this case, in addition to the interference model we have also introduced the SIC model. Therefore, in addition to the small variations for ¾ = 2 and 3 dB at high loads, as for the SSA model, we also have some variations near the saturation point. In any case, we can conclude that the analytical model matches quite well the simulation results despite its limited complexity. It is also important to note that as expected for the current study case with ¾ = 3 dB, a floor on the PLR appears. As discussed in Section IV-B, this is due to presence of lognormal8 packet power variations which causes a number of packets to be received at the gateway below the demodulator threshold even assuming perfect interference cancellation. When 8 In practice the assumption of lognormal received packet power distribution is pessimistic and is better modeled by a truncated tail distribution for which the PLR floor effect is mitigated.

2974

this event occurs with the probability derived in (18), there is no possibility to decode the received packet. If required, an increase of the return link [Eb =N0 ]LOS could reduce the PER floor by one order of magnitude (see Fig. 5). This example indicates the importance of having enough [Eb =N0 ]LOS to avoid that the weakest CDMA packets cannot be recovered because of the AWGN floor. For ¹ = ¡3 dB, ¾ = 3 dB, and [Eb =N0 ]LOS = 13:7 dB, the PLR error floor following (18) results in 2:7 ¢ 10¡4 which is in line with the PLR = 3 ¢ 10¡4 floor found by simulation in Fig. 9 for a similar MAC layer configuration. Alternatively, we can also increase the packet payload size to improve the coding gain and lower the PLR floor. We are currently using a value of 100 bits, but this has been chosen to speed up the simulations. In a real system, a larger packet size (e.g. around 500—1000 bits) can be used making the PLR floor lower. In addition, some sensitivity analysis of the key E-SSA SIC demodulator parameters have been performed. In Fig. 10 we illustrate the evolution of the Eb =N0 pdf corresponding to undetected packets during the interference cancelation process for the E-SSA detector and a normalized load G = 1:8 bit/s/Hz. The results are obtained using the semi-analytical model derived in Section IV-A as a function of the iteration Niter . As we can see, the asymptotic performance results are obtained after only three iterations, even at high loads as the one considered here. The packets that cannot be decoded after three iterations (continuous line) are those below the demodulator threshold as discussed above. Similarly, by using the simulator, we have also studied the sensitivity to the number of SIC iterations NitWmax for two different load values:


OCTOBER 2012

Fig. 11. E-SSA performance sensitivity to number of SIC iterations, ¾ = 3 dB.

G = 1:5 b/s/Hz and G = 1:9 bit/s/Hz. As we can see in Fig. 11, with NitWmax = 2 we already achieve a very good performance when G = 1:5. The same result has been previously found with the analytical model for G = 1:8 bit/s/Hz. However, when we approach the E-SSA saturation point with G = 1:9 b/s/Hz, we need 5 iterations to achieve the same performance. It is worth noting that the E-SSA performance improvement with the number of interference cancelation iterations does not go, in any case, below the PLR floor derived in (18). In summary, the optimal value for NitWmax appears to be 2 if we operate at loads below the saturation point (e.g. G · 1:8 bit/s/Hz), but then quickly increases when we reach the saturation point. Another aspect which has been investigated is the maximum window step size in the recursive SIC algorithm. Experimentally it has been found that the PLR performance remains practically unchanged up to a window step size of 1/3 of the window size (e.g. 1 packet step size for a 3 packets window). Increasing the step size further will cause a noticeable performance degradation. Clearly increasing the step size is also reducing the amount of processing required at the gateway side. The performance impact of a larger FEC block size (i.e., 1000 bits) cannot be simulated because of the prohibitive simulation time. A preliminary case has been simulated at G = 2:0 b/s/Hz with ¾ = 3 dB for two FEC block sizes: 100 and 500 information bits. In the first case we can achieve a PLR no lower than 10¡3 with NitWmax = 7, while in the second case we have achieved a PLR = 5 ¢ 10¡4 with NitWmax = 5. As we can see, increasing the FEC block size further improves the performance of the E-SSA scheme. In addition, increasing the FEC block size helps in reducing the

PLR floor. However, further experimental verifications are performed to better quantify the extent of the improvement. E. Preamble Receiver Operating Characteristic Performance Assessment As E-SSA is a spread Aloha RA system with no retransmissions, the preamble acquisition performance is very good (i.e., lower than the target PLR) in terms of the probability of missed detection Pmd and the probability of false alarm Pfa at the very high MAC operating load allowed by E-SSA. The preamble receiver operating characteristic (ROC) is obtained plotting Pmd versus the probability of false alarm Pfa as a function of the detector threshold normalized to the noise variance (named ¸). Naming as Tc the chip duration, LW the number of chips per symbol it follows that the symbol duration Ts is given by Ts = LW Tc . The Pmd and Pfa for a preamble detector coherently accumulating Nc symbols each followed by Nnc noncoherent postintegrations can be computed by simply extending the results of [41] to account for the carrier frequency offset ¢f and the finite number of samples per chip p: ³p p ´ Pmd (¸, ½) = QNnc

2½, 2¸

Nnc ¡1

Pfa (¸) =

X i=0

exp[i ln(¸) ¡ ln(i) ¡ ¸]

½ = Nc Nnc LW

QM (®, ¯) =

1 ®M¡1

Z

·

Ec N0 + I0

1 ¯

¸·

xM exp

sin(¼Nc LW ¢fTc ) Nc LW sin(¼¢fTc )

½ μ ¡


x2 + ®2 2

¶¾

¸2

sinc

³

(21) ´

1 2p

IM¡1 (®x)dx

2975

Fig. 12. Packet detector ROC characteristic for various coherent/noncoherent integration times Nc with Ec =(N0 + I0 ) = ¡30 dB, Np = 32768 chips preamble length, LW = 256 chips spreading factor, ¢f = 0, p = 2.

where QM (®, ¯) is the modified Marcum function. The preamble length in chips is Np with Np = Nc LW Nnc , being Nc the number of symbols (1 symbol is composed of LW chips) coherently accumulated, Nnc the number of noncoherent accumulations. A preliminary preamble detector ROC performance characteristic has been derived in Fig. 12 for various lengths of the correlator coherent integration for a preamble length of 128 symbols (corresponding to Np = 32768 chips for a spreading factor LW = 256). The preamble detector minimum operating Ec =(N0 + I0 ) for equi-powered received packets can be simply computed using the following simplified equation: Ec =N0 Ec · ¸ ' (22) GLW N0 + I0 1+ ¡ 1 Ec =N0 r log2 M being Ec =N0 = r log2 MEb =N0 =LW , M the modulation order, r the FEC coding rate and LW the spreading factor. In our 3GPP-like case M = 2, r = 1=3, LW = 256. Using Eb =N0 = 13:7 dB, G = 1:2 bit/s/Hz (see Fig. 9) we get Ec =(N0 + I0 ) ' ¡30 dB. In case of packets with unbalanced power (¹ = ¡3 dB and ¾ = 3 dB), G = 2 bit/s/Hz, the simulated SNIR pdf shows a SNIR distribution between ¡45 < Ec =(N0 + I0 ) < ¡22 dB. Considering that the E-SSA algorithm will start detecting the packet with the highest SNIR (i.e., ¡22 dB), in the following we consider as worst case the preamble detection at Ec =(N0 + I0 ) ' ¡30 dB to assess the ROC performance. Results obtained in the absence of frequency error showed that probability of miss detection and false alarm will be below 10¡3 . In practice, as 2976

discussed above, the coherent correlation is broken into smaller intervals due to the incoming packet residual frequency error. As shown in Fig. 12 the corresponding ROC performance are degraded compared with the full coherent integration approach. Using differential instead of noncoherent detection the loss can be contained, but most likely a preamble length of 128 symbols will be marginal [42]. Concerning the return frequency error it is considered that by using the downlink clock reference at the mobile terminal we can achieve a very good transmit frequency accuracy. Assuming that the satellite Doppler is precorrected at the gateway station, the main frequency error source will be due to the satellite frequency conversion errors and is estimated in the order of §1 KHz. The correlation loss computation of ¡ (¢fTc ) shows that for a §1 KHz return link frequency uncertainty, using 30 parallel correlators the coherent correlation loss will amount to 1.2 dB. The number of parallel correlators can be reduced using shorter coherent correlation time to increase the amount of maximum tolerable frequency error. In this case the ROC performance will degrade as shown in Fig. 12. Efficient ways to implement parallel frequency acquisition with reduced performance loss are described in [43] and [44]. V.

UPLINK RANDOM ACCESS PHYSICAL LAYER ADAPTATIONS OF 3GPP STANDARD

One of the system requirements is to reuse as much as possible existing wireless technologies. The decision to base the return link physical layer on the 3GPP W-CDMA [45, 38, 46] is supported by the following arguments: 1) well-known standard today is


OCTOBER 2012

commercially rolled-out throughout Europe and other countries; 2) it adopts a powerful turbo-based FEC with flexible block size and code rate; 3) it supports a CDMA RACH which can be largely reused for our application. In the following, we describe the main adaptations required by the 3GPP W-CDMA physical layer standard to support E-SSA. 1) PRACH Spreading and Modulation [46]: The 3GPP Physical Radio Access CHannel (PRACH) can be fully reused except for the transmission procedure. The latter, based on power ramping with fast feedback from the base station, can be easily modified to transmit single packets with longer duration as required by our satellite network. 2) PRACH Preamble Codes [46]: Although the PRACH preamble basic design appears to be compatible with our requirements, the preamble acquisition analysis reported in Section IV-E shows the need for a considerably longer preamble. These results indicate that an extended preamble (e.g. 32768 chips) is required to operate at the target Ec =(N0 + I0 ) = ¡30 dB.9 It is clear that such an extended preamble will represent a too high overhead compared with the useful information part of the 3GPP packet (300 symbols). It is therefore recommended to consider a bigger packet size (e.g. 1000 bits of useful information, corresponding to 3000 coded symbols or less than 5% overhead as proposed in S-UMTS Family A Standard [47]). 3) Physical Layer Procedures: Concerning the RACH procedures, it is proposed to replace document [48] with the corresponding document in the S-UMTS Family A Standard [49], as it can be easily adapted to the specific messaging systems needs. VI. UPLINK PACKET TRANSMISSION CONTROL The proposed solution for return link packet control dubbed SNIR driven uplink packet transmission control (SDUPTC) is based on the principle to transmit packets only when the downlink signal quality is good enough, i.e., the signal strength or better SNR is within a certain window representative of LOS conditions. If this is not the case the transmission is delayed until (quasi)-LOS conditions are verified. The proposed simple SDUPTC algorithm is intended to maximize the probability of packet successful transmission well as to limit the power unbalance among the packets received at the gateway side to improve the MAC performance. In addition, it will avoid creating MAI when not useful for packet transmission. It is recalled that the performance is related to the aggregated MAI and the large number of users interfering without desired packet transmission will reduce the system capacity. 9 We

expect to operate at loads that correspond to more than one thousand simultaneous CDMA packets on average.

As shown in Section IV-B, there is an optimum operating E-SSA point in terms of received packets power unbalance for a given link margin we should approach in the system operations. A. Uplink Packet Transmission Control Algorithm The downlink DVB-SH signal is used to perform a SNIR estimate which is then exploited to decide when the downlink channel conditions are good enough to transmit queued packets at the terminal side. Assuming the exploitation of the DVB-SH B (TDM) waveform [3] in the downlink, the pilot-aided SNIR estimate is available every TDM slot. According to the DVB-SH standard, two fields of Npil = 80 pilot symbols each are available in each TDM payload slot of Nslot = 2176 symbols. The data-aided (pilot-aided) version of the classical signal-to-noise ratio estimator (SNORE) algorithm [50] is proposed as it satisfies the following conditions: 1) SNIR estimate is robust against automatic gain control (AGC) imperfections; 2) SNIR estimate is accurate being a maximum likelihood estimator; 3) algorithm implementation is relatively simple. Assuming that the residual carrier frequency and phase error has already been recovered, the estimated pilot SNIR at time tk = Npil + kNslot =2 can be ˆ ˆ d generically expressed as SNIR(t k , Wav ) = PS (tk )=PNt (tk ), where Wav ¸ 1 represents the number of pilot fields coherently averaged by the SNORE algorithm, PˆS represents the estimated pilot sequence received power, and PˆNt represents the estimated noise plus interference received power. In the following, for notation simplicity we assume that SNIR = SNR. To adaptively estimate in a distributed manner the LOS SNR level for each mobile terminal one can simply store as LOS SNR the average of the best Nb SNR estimates over a sufficiently large observation time window Tobs . In analytical form this corresponds to d SNR LOS (t) = max

(

SNRref min ,

) Nb Nb 1 X d max fSNR(tk , Wav )g tk 2[t,t¡Tobs ] Nb l=1

(23) SNRref min

is a prestored minimum system where guaranteed LOS received signal power value. The d use of this minimum system value avoids SNR LOS estimation errors when the mobile terminal is under satellite link obstruction for too long (e.g. car parked in a garage or through a long tunnel). Packet transmission at time t = t¤ will then follow the following rule: ( d ¤ )] ¸ SNR (t¤ ) 1 if [SNR(t dB th ¤ PT (t ) = (24) 0 otherwise


2977

with PT the ST transmission flag and SNRth (t¤ ) the adaptive downlink SNR threshold used to drive the uplink packet transmission given by ¤ d SNRth (t¤ ) = [SNR LOS (t , Wav )]dB ¡ [¢SNIR]dB

where ¢SNIR

(25) is the allowed SNR fluctuation in dB.

B. SDUPTC Results The SDUPTC analysis reported in this section is intended to verify its correct functioning over typical LMS channels as well as to realistically estimate the gateway received packets power level fluctuations. This will allow consolidating the assumptions on received packet power statistics adopted for link MAC throughput simulations of Section IV-D. Although we assumed a constant mobile terminal transmit power, the received power at the gateway will be fluctuating because of the following reasons: 1) uncertainty in the mobile terminal downlink carrier SNIR estimate for return link packet transmission decision; 2) extra margin ¢SNIR in the SNIR estimation threshold; 3) return link shadowing/fading amplitude (no STs power control assumed); 4) difference in the terminal antenna EIRP (e.g. different antenna gain due to terminal orientation or satellite elevation, dispersion in the value of the effective RF power at the antenna input); 5) different satellite antenna gain relative to the terminals position. In the following we investigate the impact of points 1, 2, and 3 above. Points 4 and 5 are considered too system design dependent to be accounted for in this paper. 1) System Model: To assess the performance of the proposed SDUPTC scheme, a simplified DVB SH-B physical layer compliant simulator has been developed. As shown in Fig. 13, the simulator is composed of a DVB SH-B modulator inclusive of pilot insertion, mobile fading channel, TDM demodulator inclusive of phase estimation, SNIR estimator, and decision logic for the return link packet transmission. The channel simulator is in line with the 3-state LMS Markov model from Fontan, et al. [51, 52]. To ease the system analysis the LMS channel simulator is used on a per state basis, i.e., the LMS channel model Markov chain transitions have been artificially blocked. The three states considered in this work represent the following shadowing conditions: a) state 1: LOS events; b) state 2: moderate shadowing events; c) state 3: deep shadowing events. The time sharing among the different states for the different environments is reported in Table II. It appears that state 1 is present 40—50% of the time and it is where packet transmission will likely occur. The demodulator phase estimation algorithm adopted is the one described in the Appendix A of the DVB-SH d implementation guidelines [53]. For the SNR calculation we used as reference value 2978

LOS SNRref min , the

d result of SNR LOS from previous simulations in the same mobile environment. To assess the impact of the return link different fading amplitude we took the following realistic assumptions: a) the lognormal shadowing is assumed fully correlated between the forward and the return link; b) the Rician fading is assumed to be fully uncorrelated between the forward and the return link. 2) Simulation Results: A number of tests and parameters optimizations have been performed to achieve good performance of the proposed return packet transmission control scheme over a variety of mobile environments (open = OPE, suburban = SUB, and intermediate tree shadowing = ITS) and different mobile speeds adopted10 (70 and 170 Km/h). Table III reports the main parameters used for the simulations of the STDUPC algorithm. In the following, the simulated results for the particular case of ITS and a mobile speed of 170 Km/h are reported. Figure 14 shows the simulated time series for state 1 of the LMS ITS environment. Figure 14 shows the SNR time series (received SNR fading plus shadowing (green line), received SNR with shadowing only (black line), and estimated SNR (red line)) for the selected environment and mobile speed. It is apparent the good SNIR estimation capabilities of the SNORE algorithm are apparent in this difficult environment even at high mobile speed (170 Km/h). Figure 14 also shows the behavior of the return link packet transmission decision algorithm for the previous time series. The real and estimated SNR thresholds for transmitting packets are reported with blue and red dashed horizontal lines, respectively. The decision for each DVB-SH slot to allow return packet transmission is indicated by blue circles (gene-aided decision) and red stars (proposed algorithm decision). As expected, in ITS environment, the transmission of packets is allowed only for a limited percentage of time due to frequent link obstructions. The power fluctuations statistics at satellite antenna input level are summarized in Table IV. It can be remarked that the proposed algorithm performs reasonably well compared with the gene-aided one. Experimentally, it has been checked that the received packets power approximately follows a lognormal distribution as assumed for E-SSA MAC performance analysis in Section IV-D. As an example, we can see in Fig. 15 that the simulated pdf of received normalized power for ITS state 1 at 170 km/h fits quite well to a lognormal distribution with a standard deviation of 2 dB. This is a nontrivial result considering that the SDUPTC algorithm is limiting the return link packet transmission to “good” downlink channel quality conditions thus “distorting” the 10 Performance

at lower speeds will be better as the channel is less

dynamic.


OCTOBER 2012

Fig. 13. Block diagram of SDUPTC simulator.

return link LMS channel statistics. The Rx power fluctuations standard deviation amounts to 2.0 dB with the assumed LMS ITS channel characteristics. The state 2 and 3 statistics for received packet power are based on a limited set of transmissions and are with low probability of occurrence thus not very significant. If no transmit packet control is

implemented, the received packet power standard deviation for the LMS ITS channel will amount to 6.4 dB causing severe degradation of the E-SSA performance (see Section IV-D). Simulations have been also performed for the different environments, i.e., open and suburban. For an open environment, the algorithm works fine for


2979

Fig. 14. LMS ITS environment state 1 time series simulations for mobile speed of 170 km/h. TABLE II Fontan’s 3-State Markov Chain States Time Share at S-Band for 40 deg Satellite Elevation [52]

TABLE III Parameters for the Return Packet Transmission Control Parameter

Environment Type

% Time State 1

% Time State 2

% Time State 3

Open area Suburban area Intermediate tree shadowing area

50 45.4 39.3

37.5 45.4 35.7

12.5 9.2 25.9

the 3 channel states with received power fluctuation of about 1 dB rms and less than 10% of incorrect transmission decisions. In state 1, 96% of the time transmission is allowed, in state 2, 60% and in state 3, 4.5%. In the case of suburban environment, the transmission probability drops to 17% for state 1 and 2.5% for state 2. Incorrect transmission decisions are less than 18%.11 The received power fluctuation will go up to 2.7 dB in state 2. Therefore, we can conclude that the algorithm is able to cope with typical LMS channel environments even at high mobile speed. 11 It

shall be noted that incorrect transmission decisions do not necessarily imply a packet loss. In some cases the terminal erroneously decides not to transmit, which is not a loss. In other cases, the terminal erroneously decides to transmit, but as we will see in Section IV-D the proposed access scheme is very robust to power unbalance.

2980

Value

Unit/Symbol

Carrier frequency Waveform TDM baud rate Number of symbols/slot Number of pilots symbols/field

2.2 DVB-SH (TDM) 3.7 2176 80

GHz

Number of pilot field/slot LOS SNR Mobile channel model Mobile channel environments Satellite elevation angle Mobile terminal speed Number of averaged SNORE pilots fields Max number of SNIR averaged estimates Allowed SNIR est. fluctuation for Tx

2 10 3-state Markov OPE, SUB, ITS 40 70 and 170 2

Mbaud Nslot Npil dB blocked deg Kmph Wav

10

Nb

3

dB, [¢]dB

VII. CONCLUSIONS AND OUTLOOK In this paper, an E-SSA solution with packet-oriented SIC processing and uplink packet transmission control has been proposed and shown to efficiently cope with the mobile satellite messaging system requirements. The E-SSA RA scheme and its gateway processing has been analyzed in detail. The theoretical E-SSA performance has been analytically derived and successfully compared with simulation


OCTOBER 2012

Fig. 15. Received normalized packet power pdf for ITS state 1 at 170 km/h. TABLE IV Performance Statistics for the Return Packet Transmission Control: ITS LMS Channel, 170 km/h Mobile Speed

Parameter Tx slots allowed [gene-aided] Tx slots allowed [proposed algorithm] Tx slots with correct decision Tx slots with incorrect no Tx decision Tx slots with incorrect Tx decision Rx power standard deviation

State 1 State 2 State 3 Value Value Value

Unit

18.7 24.0

0.0 0.1

0.0 0.0

% %

89.6 2.6

99.9 0.0

100.0 0.0

% %

7.8

0.2

0.0

%

2.0

N/A

N/A

dB

results. Differently from conventional SSA that is very sensitive to packet power unbalance, E-SSA has been shown to provide enhanced performance in the presence of realistic levels of power unbalance. E-SSA performance sensitivity to key parameters has been investigated and a recommended configuration derived. It has been shown that the proposed RA MAC scheme provides truly remarkable performance in terms of throughput, PLR, and resilience to received signal power unbalance. Power unbalance is enhancing the SIC iterative processing performance allowing the achievement of a MAC throughput in the order of 2 bit/s/Hz over a satellite mobile channel which is about 40 times higher than conventional SSA under the same conditions. The design of the E-SSA burst preamble, able to operate under such high MAC load conditions, has been analytically derived. Finally a decentralized uplink packet transmission control algorithm capable of ensuring that the packets

are transmitted only if the satellite mobile channel conditions are good enough has been described and its performance assessed through detailed simulations. APPENDIX I. E-SSA ALGORITHM DETAILED ANALYTICAL DESCRIPTION In this section we describe analytically the E-SSA algorithm under the following assumptions: 1) chip integer delays for the different packets; 2) baseband complex signals are represented after the demodulator chip matched (CMF) filter at 1 sample/chip assuming optimum sampling instant for the CMF, i.e., effect of chip pulse shaping and related oversampling are not represented; 3) frequency offset among different packets is neglected, just the carrier phase offset is represented; 4) all packets reuse the same preamble sequence. These assumptions simplify the analytical description of the E-SSA algorithm without altering its validity. Extension of the analytical treatment to the more general case is straightforward. We introduce the following notation for describing the E-SSA algorithm with Tc r˜ (l)

Lp Lpr Lpa = Lp ¡ Lpr Npm W = Npm Lp

chip duration complex baseband gateway demodulator sample received at time tl = lTc packet length in symbols packet preamble length in symbols packet payload length in symbols number of packets spanned by the memory memory window size in symbols


2981

M ¢W = W=M Nsc n NitWmax NitW

memory window size in window steps ¢W memory window step size in symbols number of chips per symbol sliding window shift index maximum number of SIC iterations on a given window position current inner loop iteration counter

The E-SSA algorithm is based on a memory-based ¯ processing. The complex samples memory array m content is modified during the E-SSA processing as a function of the current indexes n and NitW thus: W

W

W

˜ n,Nit (1), m ˜ n,Nit (2), : : : , m ˜ n,Nit (WNsc )]: ¯ NitW ) = [m m(n,

baseband sample generated by the transmitter for the packet number k. The relation between p˜ k (l) and the gateway received samples r˜ (l) is simply given by r˜ (l) =

k=1

p¯ pr = [p˜ pr (1), : : : , p˜ pr (Lpr Nsc )]

(27)

W

˜ n,Nit (m¢WNsc )] for m = 1, : : : , M: m Initialization phase: Before starting the double loop iteration described in the following the gateway ¯ is initialized as processor memory m ¯¯ (0, N W ) = [r˜ ((m ¡ 2)¢WN c ) + 1), : : : , r˜ ((m ¡ 1)¢WN c )] m m it max s s

(28)

Iterative E-SSA Processing: Each time the index n is incremented the outer loop is shifting by ¢W symbols content of the gateway demodulator memory thus adding ¢WNsc new samples to the memory content. The following steps are performed for n running from 1 to 1. Memory Window Update Step: At every sliding window step the memory is updated according to the following equation: ¯ m (n, 0) = [m ¯¯ 2 (n ¡ 1, NitWmax ), : : : m ¯¯ M (n ¡ 1, NitWmax ), m r˜ ((M + n ¡ 2)¢WNsc ) + 1), : : : ,

where p¯ kpa are the chip samples corresponding to the modulated and spread packet payload. Since the preamble is common to all packets, there is no dependence on the packet number k for p¯ pr elements. Channel Estimation for Detection Step: Having detected the packet location, the chip samples have to be corrected in carrier phase as well as normalized in amplitude. For estimating the channel (amplitude and phase) for a hypothetical received packet at location q + 1 in memory, a maximum likelihood preamble data-aided estimator is adopted. Let us now introduce the following array of size WNsc which contains the known preamble sequence p¯ pr shifted by q chips with q 2 [0, (W ¡ Lp )Nsc ]: 3 2 7 6 : : : : , 0, p¯ pr , 0, : : : , 0 7 p¯ Epr (q) = 6 40, | {z } |{z} | {z } 5 q

(33)

c Lpr Nsc (W¡Lpr )Ns ¡q

ˆ n, N W ), Thus the packet complex phasor dubbed C(q, it assuming there is a packet starting at location q + 1 in memory,12 is given by

(29)

The inner loop iterates NitW from 1 to NitWmax within the current sliding window location to decode packets and cancel them. Thus the index NitW is running from 1 to NitWmax . Let name p¯ k be the kth packet array of length Np samples received at time t0 (k) = f(k)Tc where f(k) is an integer function univocally mapping the packet identification k to the time domain. Thus: p p¯ k = 2Pk exp(|Ák )[p˜ k (f(k)), p˜ k (f(k) + 1), : : : ,

ˆ n, N W ) = C(q, it

1 ¯ NitW ) ¢ [p¯ Epr (q)]† m(n, Lpr Nsc

(34)

with † the transpose and conjugate array operator. Packet SNIR Ranking and Detection Step: To ¯ content is correlated perform this step, the memory m with all possible shifted versions of the preamble falling in the current signal observation window. For each possible packet preamble location q within the current memory, the SNIR-based quality factor is

(30)

with Pk the power associated to the received packet p¯ k , Ák its carrier phase, p˜ k (l) the lth complex unit power 2982

(32)

p¯ kpa = [p˜ kpa (1), : : : , p˜ kpa (Lpa Nsc )]

¯¯ (n, N W ), : : : , m ¯¯ (n, N W )] ¯ NitW ) = [m m(n, 1 M it it

p˜ k (f(k) + Lp Nsc )]

2Pk exp(|Ák )p˜ k (f(k)) + n˜ (l)

p¯ k = [p¯ pr , p¯ kpa ]

The memory array is broken down into M components each of length ¢WNsc as

r˜ ((M + n ¡ 1)¢WNsc )]:

p

where ±(l) is the Kronecker delta function ±(l) = 1 for l = 0, 0 otherwise; n˜ (l) corresponds to complex AWGN noise p RV with zero mean and standard deviation N0 Tc . The packet array p¯ k can be decomposed in the preamble p¯ pr and payload p¯ kpa subarrays of size Lpr and Lpa , respectively. Thus (30) can be rewritten as

(26)

for m = 2, : : : , M:

±(f(k) ¡ l)

(31)

¯ NitW ) m(n,

W ¯¯ (n, N W ) = [m ˜ n,Nit (((m ¡ 1)¢WNsc ) + 1), : : : , m m it

1 X

12 The

presence of the packet will be verified later through verification that the correlation value exceeds a minimum threshold.


OCTOBER 2012

computed as ¡ (q, n, NitW ) =

The FEC decoder represented by the ¸(¢) function, operates on the s¯sk (q¤ , n, NitW ) complex packet symbols array of size Lpa samples and exploits the SNIR estimation ¡ (q¤ , n, NitW ) to provide after (recursive) decoding the packet information bits array:

ˆ n, N W )j2 jC(q, it

1 ¯¯ ˆ n, N W )j2 ¯ (n, NitW )j2 ¡ jC(q, jm it Np2 q (35) ˆ n, N W )j2 jC(q, it

with j ¢ j the Euclidean norm operator, the estimated received kth packet signal power, and ¯¯ ¯ q (n, NitW ) a complex array containing the Lp memory m samples corresponding to the kth packet location, i.e., ¯¯ ¯ q (n, NitW ) m W

W

W

˜ n,Nit (2 + q), : : : , m ˜ n,Nit (Lp Nsc + q)]: ˜ n,Nit (1 + q), m = [m (36) ¯¯ ¯ q (n, NitW )j2 (1=Np2 )jm

represents an estimate of Clearly the signal plus interference power for the kth packet. The potential packet with the highest SNIR has the location q¤ within the current memory observation window n at iteration NitW that is derived as ¡ (q¤ , n, NitW ) =

max

q2[0,(W¡Lpr )Nsc ]

f¡ (q, n, NitW )g: ¤

(37)

, n, NitW )

¸° The packet presence is declared if ¡ (q where ° is the packet detection threshold [54]. If no packet presence is declared, the inner loop is completed and a new window shift is implemented exiting the current inner loop. Packet Demodulation Step: After packet presence detection and the start of packet sample identification it is now possible to remove the unknown carrier phase and to normalize its amplitude exploiting the ˆ ¤ , n, N W ). At this point it is also possible to phasor C(q it isolate from the demodulator memory the subarray of size Lpa Nsc containing the useful samples at chip rate required for the identified packet demodulation as s¯ck (q¤ , n, NitW ) 1 ˆ ¤ , n, N W ) C(q it

˜ [m

n,NitW

W ˜ n,Nit

m

Packet Cancellation Step: If the CRC check is not successful, the next packet with the highest SNIR and above the packet detection threshold is processed. Once all detected packets have been processed the inner loop is terminated. Instead if the CRC check is successful then the packet is reencoded, modulated, and spread to obtain the following array of Lpa Nsc samples: k k k p¯ˆ (q¤ , n, NitW ) = [p˜ˆ (q¤ + 1 + Lpr Nsc ), : : : , p˜ˆ (q¤ + Lp Nsc )]:

(41) The preamble is then added and the array is extended to an array of size WNsc as E p¯ˆ (q¤ , n, NitW ) 2

3

6 7 k =6 : : : , 0, p¯ pr , p¯ˆ (q¤ , n, NitW ), 0, : : : , 0 7 40, 5: {z } | {z } |{z} | {z } | q¤

Lpr

Lpa

(W¡Lp )Nsc ¡q¤

(42) Now it is possible to refine the channel estimation using a maximum likelihood complex phasor estimate based on the knowledge of the preamble and the payload complex symbols (regenerated at the previous step) thus: ˆˆ ¤ , n, NitW ) = C(q

E 1 ¯ NitW ) ¢ [p¯ˆ (q¤ , n, NitW )]† m(n, Lp Nsc

and finally the detected packet is removed from gateway demodulator memory by the following step:

(q¤ + 1 + Lpr Nsc ), : : : , (q

¤

+ Lp Nsc )]:

(38)

The packet payload complex symbol samples can be obtained by multiplying the packet payload samples by the conjugate of the known payload spreading sequence samples c˜ pa (l) and coherently accumulating over the Nsc samples corresponding to the symbol duration. The resulting array composed of the individual Npa correlator outputs is obtained as s¯sk (q¤ , n, NitW ) = [s˜sk (1), s˜sk (2), : : : , s˜sk (Lpa )] c

1 s˜sk (v) = c Ns

(40)

(43)

= [s˜ck (1), s˜ck (2), : : : , s˜ck (Lpa Nsc )] =

pˆ ki (q¤ , n, NitW ) = ¸fs¯sk (q¤ , n, NitW ), ¡ (q¤ , n, NitW )g:

vNs X

l=(v¡1)Nsc +1

¤ (l) s˜ck (l)c˜ pa

(39) for v = 1, : : : , Lpa :

E ˆˆ ¤ ¯ NitW ) ¡ C(q ¯ NitW + 1) = m(n, , n, NitW )p¯ˆ (q¤ , n, NitW ): m(n,

(44) The packet demodulation and cancellation steps are repeated successively with the remaining packets detected in the SNIR ranking and detection step. Once all packets detected above the packet detection threshold have been processed following the order of the SNIR ranking process, we increase NitW and we repeat all the previous steps until the maximum number of iterations within the current sliding window is reached, i.e., NitW = NitWmax . At this point the window shift index n from the outer loop is incremented and the inner loop repeated NitWmax times and so on.


2983

¯ = 75. Fig. 16. Spread Aloha MAI amplitude pdf: G = 0:1 and N p

APPENDIX II. ON THE CENTRAL LIMIT THEOREM APPLICABILITY To provide more quantitative evidence of the goodness of the CLT application to justify the spread Aloha interference Gaussian approximation, the MAI key statistics have first been derived by simulation. The resulting interference amplitude distribution has been compared with the one obtained using the analytical Gaussian approximation. For this purpose a physical layer simulator has been built to emulate the asynchronous CDMA interference seen by the packet of interest burst demodulator according to the model described in Section IV-A. The arrival time of the interfering packets is following a Poisson distribution as for (2) with a chip level time granularity. The interfering CDMA packets are assumed to be binary modulated with pseudorandom sequences and carrier phase coherent. As for Section IV-D assumptions, each packet is composed of 300 binary equi-probable coded symbols and each symbol contains 256 chips. Each generated packet is multiplied in amplitude by the square root of an independent lognormal in power RVs (see (3)) with constant amplitude over the whole packet duration. The generated DS/CDMA interfering packets are then summed together and the resulting signal X(t) amplitude distribution pdf is derived by Monte Carlo simulation. In doing so the MAI ergodicity assumption [56] has been made. The validity of this hypothesis for the interference process X(t) has been rigourously demonstrated by showing 2984

that: 1 T!1 T lim

Z

2T 0

μ

1¡

¸ 2T

¶

(EfX 2 (t + ¸)X 2 (t)g ¡ E 2 fX 2 (t)g)d¸

(45)

= 0:

The detailed derivation of (45) is not reported for conciseness. Simulation results are compared with the zero mean Gaussian pdf with standard deviation ¾X derived from (46) below assuming the applicability of the CLT. For the interference amplitude X(t) Gaussian approximation we used the standard deviation value ¾X of the aggregate interfering signal amplitude defined as ¯ PEfa2 g ¾2 = EfX 2 (t)g ' N X

p

¯ P10[(¹+¾ =N p

2

=(20 log 10(e))=10]

(46)

¯ is the equivalent average number of where N p ¯ =¸®= interfering packets over the desired packet (N p t GGp ; see Section IV-A), P is the nominal received packed power in the absence of the multiplicative lognormal RV a, Efa2 g is derived in Appendix III and ¹, ¾ are the lognormal packet power mean and standard deviation expressed in dB (see (3) for the parameters definition). As from Fig. 16 we can see that for ¹ = ¡3 dB and ¾ = 3 dB already for a very low load e.g. G = 0:1 b/s/Hz (corresponding to ¯ = 75) the MAI amplitude Gaussian approximation N p holds very well down to very low pdf probabilities.


OCTOBER 2012

Fig. 17. Simulated standard deviation over mean statistics for resulting MAI power as function of MAC load when ¹ = ¡3 dB and standard deviation ¾ = 3 dB.

The goodness of the CLT applicability for the MAI interference is further supported by the derivation by analysis and simulation of the standard deviation and the mean of the instantaneous MAI power X 2 (t) as a function of the MAC load. First, the MAI power mean and standard deviation have been analytically derived. It is know from literature that the sum of N lognormal RVs can be approximated with a lognormal RV. Particularizing the result of the Wilkinson’s method reported in [57] to the case of N independent lognormal RVs each with mean ¹ and standard deviation ¾ (both expressed in dB) it can be found that the sum of these N RVs is well approximated by a lognormal RV having mean ¹§ and standard deviation ¾§ (both expressed in dB) provided by ¶ μ 1 1 2 ln u1 (N, ¹, ¾) ¡ ln u2 (N, ¹, ¾) ¹§ (N, ¹, ¾) = ° 2 p 1 ¾§ (N, ¹, ¾) = ln u2 (N, ¹, ¾) ¡ 2 ln u1 (N, ¹, ¾) ° ¶ μ °2 u1 (N, ¹, ¾) = N exp °¹ + ¾ 2 2 (47) u2 (N, ¹, ¾) = N exp(2°¹ + 2° 2 ¾2 ) +2

N¡1 X i=1

(N ¡ i) exp(2°¹ + ° 2 ¾2 )

° = ln 10=10: For the derivation of the theoretical curve we have ¯ . The results corresponding to (47) assumed N = N p

for ¹ ¡ 3 dB and ¾ = 3 dB is reported in Fig. 17 as a continuous line. The MAI power statistics simulations have been obtained for two cases. A first case indicated as zero delay in Fig. 17, corresponding ¯ interfering packets perfectly aligned to the to N p packet of interest as assumed when deriving (47). A second case indicated as Poisson in Fig. 17 with asynchronous interfering packet arrivals following a Poisson packet arrival process as defined in (2). Observing Fig. 17 it appears that the (47) result is well in line with the zero delay simulations (circles) while the simulated Poisson ¾§ =¹§ ratio is slightly above the zero delay case. In both cases it was found that ¾§ reduces while ¹§ increases as a function of the load. Thus as shown in Fig. 17, the ratio of the standard deviation over the mean rapidly decreases and for G = 0:2 is already around 2 ¢ 10¡2 . Consequently, the power of the interference can be considered constant over the packet of interest as assumed for the Gaussian MAI applicability in (10). APPENDIX III. LOGNORMAL RV SECOND ORDER MOMENT Let a be a lognormally distributed RV according to (3). By lognormal distribution it follows that: a = 10°=20

(48)

with ° a Gaussian RV with mean ¹ and standard definition ¾ as defined for (3) in Section IV-A. Thus: ¸ · 1 (° ¡ ¹)2 : (49) f¡ (°) = p exp ¡ 2¾ 2 2¼¾


2985

Taking into account (48) the nth order moment of the RV a is ½ μ ¶¾ ln 10 Efan g = Ef10n°=20 g = E exp n ° : (50) 20

[7]

Recalling now the definition of the characteristic function Ã¡ (¢) [55] of the RV °:

[8]

Ã¡ (º) = Efexp(|º°)g

(51)

and taking into account that ° is a Gaussian RV it follows that: μ 2 2¶ º ¾ Ã¡ (º) = exp ¡ exp(|º¹): (52) 2

[9]

[10]

Comparing (50) and (51) it follows that: Efan g = Ã¡ (º)jº=n ln 10=|20 " # μ ¶ n2 ln2 10¾2 n ln 10¹ = exp exp 2 ¢ 400 20 2

= 10[(ln 10=2)(n¾=20) ] 10(n¹=20) :

[11]

(53)

[12]

(54)

[13]

The authors would like to thank A. Arcidiacono and D. Finocchiaro from Eutelsat S.A.S. (F) for inspiring and supporting the current work. The constructive comments to the initial work provided by the Associate Editor Professor Rice, the anonymous reviewers, G. Gallinaro from Space Engineering (I) and Professor Giannetti from University of Pisa (I) are also acknowledged.

[14]

For the case n = 2 from (50) we get Efa2 g = 10(¹+¾

2

=[20 log 10(e)])=10

:

ACKNOWLEDGMENTS

[16]

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 48, NO. 4 OCTOBER 2012

Oscar del Río Herrero was born in Barcelona, Spain, in 1971. He received the B.E. degree in telecommunications and the M.E. degree in electronics from the University Ramon Llull, Barcelona, Spain, in 1992 and 1994, respectively. He received a post-graduate degree in space science and technology with emphasis in satellite communications from the Space Studies Institute of Catalonia (IEEC), Barcelona, Spain, in 1995. He joined ESA's Research and Technology Center (ESTEC), Noordwijk, The Netherlands, in 1996. In 1996 and 1997 he worked as a radio-navigation system engineer in the preparation of the Galileo programme. From 1998 to 2009, he worked as a communications systems engineer in the Electrical Systems Department. His research interests include high-performance on-board processors, packet access and resource management schemes and IP inter-working for future broadband satellite systems. Since 2010 he has worked as system engineer for the Iris project in the ESA’s Telecommunication Directorate, aiming at the development of a new satellite-based air-ground communication system for air traffic management.

Riccardo De Gaudenzi (SM’98) was born in Italy in 1960. He received his Doctor Engineer degree (cum Laude) in electronic engineering from the University of Pisa, Italy in 1985 and the PhD from the Technical University of Delft, The Netherlands in 1999. From 1986 to 1988 he was with the European Space Agency (ESA), Stations and Communications Engineering Department, Darmstadt, Germany, where he was involved in satellite telecommunication ground systems design and testing. In particular, he followed the development of two new ESA satellite tracking systems. In 1988, he joined ESA’s Research and Technology Centre (ESTEC), Noordwijk, The Netherlands where in 2000 he was appointed head of the Communication Systems Section and since 2005 he is Head of the Radio Frequency Systems, Payload and Technology Division. The division is responsible for supporting the definition and development of advanced satellite system, subsystems and related technologies for telecommunications, navigation and earth observation applications. In 1996 he spent one year with Qualcomm Inc., San Diego, CA, in the Globalstar LEO project system group under an ESA fellowship. His current interest is mainly related with efficient digital modulation and multiple access techniques for fixed and mobile satellite services, synchronization topics, adaptive interference mitigation techniques and communication systems simulation techniques. He actively contributed to the development and the demonstration of the ETSI S-UMTS Family A, DVB-S2 and DVB-SH standards. From 2001 to 2005 he served as associate editor for CDMA and Synchronization for IEEE Transactions on Communications. He is corecipient of the 2003 and 2008 Jack Neubauer Memorial Award Best Paper from the IEEE Vehicular Technology Society. DEL RÍO HERRERO & E GAUDENZI: HIGH EFFICIENCY SATELLITE MULTIPLE ACCESS SCHEME

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