Cross-Layer Packet Scheduler Design of a ... - Semantic Scholar

248

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007

Cross-Layer Packet Scheduler Design of a Multibeam Broadband Satellite System with Adaptive Coding and Modulation M. Angeles Vázquez Castro, Member, IEEE, and Gonzalo Seco Granados, Member, IEEE

Abstract— This paper focuses on the broadcast channel of an interactive Multibeam Broadband Satellite (MBS) system with a transparent architecture. In particular, a cross-layer design is proposed for the packet scheduling on a forward link that implements Adaptive Coding and Modulation (ACM). A crosslayer approach is considered whereby the physical and Medium Access Control (MAC) layers share knowledge of the channel dynamics in presence of ACM. Transmission power and symbol rate are assumed to be constant, and hence the bit rate is time and space dependant according to the channel conditions. An architecture is proposed which relies on the physical characteristics of the Ka-band satellite propagation channel and the definition of “correlated areas”. The stable throughput region has been derived assuming full-queue traffic conditions. Moreover, the proposed architecture is simple but flexible enough to allow the implementation of different scheduling policies like the proportionally fair or opportunistic ones. Finally, a new timefair policy appropriate for wet seasons is proposed. It has the property of isolating users in clear-sky conditions from the effects of the reduced transmission rate experienced by users under a rain fade. Index Terms— Adaptive coding and modulation, cross-layer design, DVB-S2, fairness, rain fade, satellite communication scheduling.

I. I NTRODUCTION URRENT operational point-to-point multibeam satellite systems are designed for link closure in the worst-case propagation and location conditions. A fixed coding rate and modulation format are selected according to a given coverage and availability requirements. This worst-case approach implies the occurrence of high margins in the majority of the cases, when interference and propagation conditions result in a higher-than-required Signal to Interference plus Noise Ratio (SNIR). Modern satellite communication systems will avoid this inefficient use of power by adapting the modulation/coding scheme to the propagation conditions so that the spectral efficiency is as high as possible in all cases.

C

Manuscript received March 11, 2005; revised January 20, 2006; accepted March 12, 2006. The associate editor coordinating the review of this paper and approving it for publication was Q. Zhang. This work was supported in part by the European Commission through SatNEx Network of Excellence IST507052 and by the Spanish Ministry of Science and Education MEC through project ESP2005-03403. This work was partially done during the research fellowship of the first author at the European Space Agency. The authors are with the Dept. of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona, Escola Tècnica Superior d’Enginyeria, QC-1009 Bellaterra, Barcelona, Spain 08193 (email: [email protected]; [email protected]). Digital Object Identifier 10.1109/TWC.2007.05148

Conversely to terrestrial systems, the use of adaptive physical layer in satellite networks is still not operational. Existing solutions for resource allocation (packet scheduling) in satellite systems not implementing an adaptive physical layer will not fully exploit the particular features of such adaptation thus yielding poor performance. The standardization of the use of an adaptive physical layer (APL) over satellite has been recently completed by the DVB-S2 (Digital Video Broadcasting - Satellite, version 2) group (see [1], [2]), and therefore scarce literature is available. The standard informative part mentions the problem of resource allocation and outlines two possible approaches. However, such approaches are given in a very general way and do not actually provide technical solutions as discussed in [3]. In this paper, we address such a problem. We focus on the broadcast channel of a GEO (Geostationary Earth Orbit) Multibeam Broadband Satellite (MBS) system with transparent architecture that implements an APL for interactive applications where users are not mobile. The broadcast channel or forward link is defined as the communications link between the ground gateway (GW) and satellite terminal (ST). The gateway sends through the satellite transponder one carrier per beam to the multiple receivers located within each satellite beam and, therefore, a certain division of the power, bandwidth and/or time allocation is necessary. The channel capacity is the region containing the set of possible rates that can be maintained by all users simultaneously [4]; it is an intrinsic characteristic of the channel, independent of the possible channel allocation alternatives. In this paper, a crosslayer design is applied to the packet scheduling of the forward link, assuming the availability of Receiver and Transmitter Channel Side State Information (RCSI and TCSI), by means of a dynamic user-location- based packet queuing algorithm, which allows for implementing different scheduling policies, such as the proportionally fair or opportunistic ones. The paper is organized as follows. Sections II, III and IV present the system, physical layer and channel model, respectively. Section V analyzes the cross-layer design principles and presents the packet scheduler architecture. Section VI derives the broadcast throughput stable region. Section VII presents the numerical results, and finally Section VIII draws the conclusions. II. S YSTEM M ODEL The APL considered hereinafter on the forward link is based on adapting both the coding rate and the modulation format

c 2007 IEEE 1536-1276/07$20.00 

CASTRO AND GRANADOS: CROSS-LAYER PACKET SCHEDULER DESIGN OF A MULTIBEAM BROADBAND SATELLITE SYSTEM

(ACM) to best match the user SNIR, thus making the received data rate location and time dependent. Although APL technology is also applicable to regenerative satellite systems, in the rest of the paper we will consider a transparent satellite system architecture. In particular, a transparent payload with a hybrid Time Division Multiplexing/Frequency Division Multiplexing (TDM/FDM) scheme and a beam frequency plan designed according to a given frequency reuse is considered. Only one TDM downlink carrier per beam is assumed. The feeder link (or uplink, from the GW to the satellite) and the user link (or downlink, from the satellite to the ST) will be operating at Ka band (20GHz-30GHz). The total available power is distributed among the beams either evenly or not according to traffic and additional system requirements. In the following and without loss of generality in what concerns the scheduling, the beam power is pre-allocated and fixed since a second level of long-term resource management takes care of beam power allocation. Beam power management comes on top of the packet scheduling, which is the topic addressed here. Another important assumption is that the downlink carrier bandwidth is assumed constant, and therefore the symbol rate is constant independently of the transmitted coding rate and modulation format. Fig. 1 shows a general block diagram of an APL satellite forward link. It is composed by the GW - which includes the APL modulator, the packet scheduler and possibly additional resource management features- the Satellite and the ST. The ST can communicate with the GW via a return channel (terrestrial or satellite). The ST belongs to the k-th beam out of the total number of beams of the network, NB . The user channel is interfered by the transmission from the rest of the co-channel beams and by external systems. No particular characteristics for the return channel need to be assumed, since the procedure followed by the terminal to inform the GW and the format of such information are not relevant to this work. The only assumptions made hereinafter are that the GW keeps track of channel variations occurring at the terminals, and the physical layer configuration used in the forward transmission to each individual user are known by both the GW and the ST. These assumptions do not place any restriction into the rest of the development since they just imply a nominal operation of the system. It should be noted that in a GEO scenario, the delay resulting from the channel estimation algorithm and the large propagation delay leads to a holdup of the latest valid APL while the new update is not received at the GW. This loop delay may lead to a loss of transmission efficiency or packet loss, which has been analyzed in [5]. The total received signal power to noise plus interference ratio in beam k (SNIR) is a stochastic process denoted as k (t, x ¯), where t is the time and x ¯ is a two-dimensional ξtot ¯ beamk. variable modeling the receiver position such that ∈ Granularity of x ¯ is assumed to be on the order of several km to allow for both micro and macro climatic changes.  k −1 ¯) can be expressed as ξtot (t, x ¯) = ξ k (t, x  k tot −1  k −1 k ξup (t, x ¯) + ξdown (t, x ¯) , where ξup (t, x ¯) and k ξdown (t, x ¯) stand for the SNIR of the feeder and user links, respectively. The feeder link is typically designed for a low outage probability and high SNIR, so the first term can

249

Interference Beam #1 Interference Beam #2 Channel attenuation Interference Beam #N B

AWGN

External Interference

noise

SATELLITE TERMINAL

GW

Beam # k Return Channel

ACM

Channel estimation

Fig. 1. Generic block diagram of a APL link of a broadband satellite system.

be neglected. This can be easily achieved due to the large antenna size at the GWs and use of space diversity. Thus k k (t, x ¯) ≈ ξdown (t, x ¯) and1 ξtot ξ k (t, x ¯) =

¯) pkr (t, x , n (t, x ¯) + ikinterbeam (t, x ¯) + iexternal

(1)

¯) is the received power stochastic process; where pkr (t, x n (t, x ¯) is the thermal noise power stochastic process; ¯) is the stochastic process representing the interikinterbeam (t, x ference due to the signals transmitted to other beams; iexternal is the interference stochastic process due to other (external) systems. The total signal to noise plus interference in (1) can be expressed as follows ξ k (t, x¯) = υ k (¯ x) a2 (t, x ¯)  B k 2 RKTSY S (t, x¯) + υ (¯ x) a (t, x ¯) N n=1

n=k

gtn (¯ x) gtk (t,¯ x)

+ iexternal

, (2)

pk gk (t¯ x)g

where υ k (¯ x) = t tl(¯x) r is the received power in clear sky at location x¯ at beam k; pkt is the satellite transmitted power from beam k towards location x¯, gtk (¯ x) is the beam k transmitter antenna gain towards position x¯, gr is the ST antenna gain, a2 (t, x ¯) is the channel attenuation stochastic process; l (¯ x) is the free space losses; R is the symbol rate, which is constant and given by the bandwidth allocated to beam k, and K is the Boltzmann constant. Note that it has been assumed that the transmitted power of beams k and n are equal, which might not be the case if real time resource management optimizes beam powers. The noise power is affected by the channel 1 We omit hereinafter the subscript “tot” in the SNIR for the sake of notation simplicity.

250

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007

conditions as follows: TSY S (t, x ¯) =

  a2 (t, x ¯) + TRAIN 1 − a2 (t, x ¯)

TSKY

TGROUN D + Tf (lf − 1) + + T0 (fRX − 1) , lf (3) where TSKY and TRAIN are the noise temperatures of the sky and rain; TGROUN D is the contribution of the ground to the system noise; Tf and lf represent the temperature and losses of the wave guide connecting the antenna to the receiver, respectively; fRX is the noise factor of the receiver, and T0 = 290K. If numerator and denominator of (2) are divided by the channel attenuation, (2) becomes υ k (¯ x) , [RKTSY S (t, x ¯) + iexternal ] + υ k (¯ x) Gk (¯ x) (4) NB gtn (¯x) where Gk (t, x ¯) = n=1 is the parameter accounting gk (¯ x)

¯) = ξ k (t, x

1 a2 (t,¯ x)

n=k

t

for the interbeam interference.

III. A DAPTIVE P HYSICAL L AYER M ODEL In the multibeam satellite case, the adaptive transmission approach that it is considered here is the one given in [6], for which a continuous APL model can be developed as follows. Let us assume that the required symbol energyto-noise-plus-interference spectral density ratio Es /Nt for a given coding rate and modulation format in order to achieve a given BER (or PER − Bit or Packet Error Rate) is equal to δm , m = 1, 2, . . . , M , with M being the total number of available physical layers or ACM modes. If TDM transmission and constant transmitted power are assumed, then all the beam transmission power is allocated to one particular user at a time. The maximum allowed instantaneous bit rate when using m-th mode is ⎧ R ⎨ ¯) , if ξ (t, x ¯ ) ≤ δm ηm ξ (t, x ¯) = , (5) Rb,m (t, x δm ⎩ η R, if ξ (t, x ¯) > δ m

m

where ηm is the spectral efficiency (information bits per channel symbol) of the m-th physical layer. The first equation on the right hand side of (5) reflects the adaptation of the symbol rate, and hence of the bit rate as well, in order to achieve the given δm as well as the dependency of the bit rate with the total received signal power to noise plus interference ratio at a given beam (4) (the superscript k (beam k) has been omitted for convenience). The second equation shows that the maximum allowed symbol rate determines the maximum allowable bit rate when the required symbol energy-to-noiseplus-interference spectral density ratio for a given BER (or PER) is achieved. According to the system model described in Section II, ξ (t, x ¯) can be accurately estimated. In the case of ACM under consideration, the APL model becomes discrete by restricting the symbol rate to be always equal to its maximum value R , and then using the ACM mode with the highest possible spectral efficiency for a given value of

SNIR. This leads to ⎧ 0, if ξ (t, x ¯ ) < δ1 ⎪ ⎪ ⎨ ηm R, if δm ≤ ξ (t, x ¯) < δm+1 ¯) = Rb (t, x for 1 ≤ m ≤ M − 1 ⎪ ⎪ ⎩ ηM R, if ξ (t, x ¯ ) ≥ δM

,

(6)

where he have assumed that the spectral efficiencies, ηm , and Es /Nt thresholds, δm , are defined in increasing order. This quantization of the continuous model (5) results in a power/bandwidth inefficiency in case of coarse granularity. The finer the granularity, the better the performance since it will approach to the continuous case. In DVB-S2 [1] the granularity is chosen around 1 dB (i.e. 10 log (δm+1 /δm ) ≈ 1dB). In any case, the performance achievable with the APL is closely related to the temporal and spatial variation of the channel attenuation. IV. T IME AND S PACE VARIANT C HANNEL M ODEL In this section, we present a channel model that gathers both the time and space variability of the Ka-band real channel. The model provides both the first- and second-order statistical characterization, which are defined as follows. The first-order statistical characterization in time of the channel attenuation is given by the probability density function (pdf) of the attenuation for a given location x ¯ (i.e. the probability that the attenuation is within a certain range of value at that location). We can obtain from this function the percentage of time the attenuation exceeds a given value at x ¯. This pdf is easily available since there are a number of models providing empirical probability distributions of the rain attenuation for any latitude and longitude averaged over one year time. In general, the performance of the different models is rather similar, but [7]–[9] are generally considered as being the best ones. Other contributions besides the rain must be added, like the attenuation due to gasses and scintillation. It must be noted that scintillation also presents time variability, which is relatively fast [10]. Several models exist to combine all these contributions [11]. On the other hand, the first-order statistical characterization in space (i.e. the mean and standard deviation of the attenuation over a certain area) requires the assumption of a certain user distribution within the coverage area. The complete second-order statistical characterization in ¯) and a (t2 , x ¯). time would be given by the joint pdf of a (t1 , x However, such function is normally not available, and in practice the usual procedure consists in identifying some second-order statistics of the process and characterizing them using real measurements. The following second-order statistics have been identified in the literature: duration of the periods of time between fade events (i.e. inter-fade period), duration of fade events and fade slope. Their meaning is intuitively related to the temporal evolution of the rain events, namely: their frequency of occurrence, how long they are, and how long it takes since the rain event starts till it reaches its maximum intensity, respectively. Similarly to the temporal characterization, the second-order statistical characterization in space would be given by the ¯2 ). This characterization is joint pdf of a (t, x ¯1 ) and a (t, x related to the location of rain cells within the coverage area and it is given by the cloud spatial distribution. Models of

CASTRO AND GRANADOS: CROSS-LAYER PACKET SCHEDULER DESIGN OF A MULTIBEAM BROADBAND SATELLITE SYSTEM

rain cells structure exist already. However, existing physical models of attenuation based on the rain cell structure, such as [12], assume a randomly located population of rain cells throughout the coverage area, which does match the first-order statistical rain properties (over one year time). In any case, real channel conditions show a marked space correlation: the probability that very close locations undergo similar channel conditions is very high, and the probability decreases with the distance between the locations. This is the property underlying the following definition. Let us introduce the new concept of Correlated Area (CA), which will be fundamental from a system engineering and design perspective. It is defined as the geographical zone within which channel conditions are highly correlated at a given time; that is to say, users located within a CA undergo similar channel attenuations, and users located in different CAs experience channel attenuations that are virtually uncorrelated. The size of the CAs (typically on the order of a few dozens of kilometers) is relevant in order to assess the space variability of the channel within the coverage of one. Next, we explain our channel model, which reproduces the time and space variability taking into account the appropriate first- and second-order statistics. The time variability is reproduced with the stochastic dynamic channel model described in [13], which consists in generating a channel attenuation timeseries from a low-pass filtered Gaussian process with zero mean followed by a nonlinear memoryless transformation. The key equations relevant to our purposes have been summarized in the Appendix. This model can only be applied to generate fade events since no dynamic transition mechanism between clear-sky conditions and bad channel (i.e. cloudy sky or rain) conditions is present in the model. Note that the cut-off frequency of the filter should take on different values in case diurnal/seasonal variations are taken into consideration. However, in our model such variations have not been considered due to the lack of empirical values to define such cut-off frequencies; only different first-order statistics for different latitudes and longitudes have been included since they are widely available [14]. The space variability is introduced in the model by using ¯h belong the CAs defined above. Two users located at x ¯k and x to two different CAs at a given time t0 , if the following holds ¯i,k ) − ξ (t0 , x¯j,h )| < Δξ |ξ (t0 , x

k = h; i = 1, 2, . . . , Uk (t) ; j = 1, 2, . . . , Uh (t)

(7)

for some increment of SNIR, Δξ, where x¯i,j are the locations of the Uj (t) users within the j-th CA. Note that the variation depends also on the antenna interference pattern. It is possible then to assume an average SNIR for every CA as ξ¯j (t) = Uj 1 ¯i,j ). i=1 ξ (t, x Uj From the propagation point of view, the size the correlated areas is related to the spatial correlation of rain cells. Following an exponential model of the rain cell [12], cell radius ranges up to 30-50 km for Ka-band propagation. Nevertheless, the radius of the cell depends on the intensity; normally, the higher the intensity the smaller the radius. From the point of view of the practical design of the communication network, the

251

BEAM K CORRELATED AREA 1 Transmitted power Generate Channel Attenuation

w1(t ) white Gaussian noise

H (s) =

1 s+ β

x1(t )

Transmitted power Antennas pattern

ameσ a x1 (t )

a(t , x )

Antennas pattern Interbeam interf. power x

Received signal power

Thermal noise power External interference power (t)

÷

CORRELATED AREA Nmax H (s) =

1 xNmax (t ) (t ) σ x ame a Nmax s+ β

white Gaussian Transmitted power noise Antennas pattern

x ∈ CA1

Transmitted power

Generate Channel Attenuation

wNmax (t )

ξ (t, x )

a(t , x )

Received signal power

Antennas pattern

Interbeam interf. power x Thermal noise power External interference power (t)

÷

ξ (t, x ) x ∈ CA Nmax

Fig. 2. Channel and system model. The SNIR in each correlated area is computed according to (1)-(4).

location of correlated areas should be associated with centers of population, i.e. areas whose size is on the order of a typical rain cell and that are the main sources of traffic. As a result, each area would typically be associated to one of the main cities in the beam coverage and its surroundings. A block diagram of the overall channel model is shown in Fig. 2. wi (t) is a random white Gaussian process with mean 0 and standard deviation 1, which is the input of the model used to generate the channel attenuation in each correlated area (see the Appendix). The processes wi (t) and wl (t) are uncorrelated with each other for any i = l, which implies that the channel attenuation processes generated for each CA are also uncorrelated. Note that total interference is in general different for each user since it shows space and time variability due to the interbeam and external interference, respectively. The number of users associated to each correlated area varies with time, which in practice means that the number and location of CAs may be optimized by the GW in order to adapt the system architecture, as described in next section, to particular events, channel conditions, etc. In a real system implementation, the threshold Δξ should probably vary according to the intensity of the rain attenuation to track the changes of the attenuation profile within the beam, and this implies that the area associate to each CAs would also vary. This option is totally feasible because the GW has real-time information about each ST SNIR together with the corresponding MAC address, which can be related to the ST location using the database available for packet routing.

252

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007

ξ (t, x )

ξ (t, x )

Scheduler Queue 1

Buffer 1

Queue 2

Buffer 2

ACM COD&MOD

DCOD&DMOD

η1

η1

COD&MOD

η2

DCOD&DMOD

a (t , x ) interference

η2

Queue 3 1

2

noise Queue N

Buffer M

COD&MOD

ηM

DCOD&DMOD

ηM

Fig. 3. Block diagram of the architecture of the proposed packet scheduler.

V. PACKET S CHEDULER : C ROSS -L AYER D ESIGN P RINCIPLES AND A RCHITECTURE The packet scheduler we present here takes advantage of the concept of CA of the channel model explained above to classify users geographically. This classification allows packets from users associated with approximately similar channel characteristics to be independently queued from other (distant) users that will probably have different and uncorrelated channel characteristics. This allows for the possibility of maximizing throughput by allocating more transmission resources to the users with better channel conditions (i.e. opportunistic allocation) but also for the possibility of a fair treatment of users at the expense of a reduction in the total throughput. The block diagram of the architecture of the proposed packet scheduler is presented in Fig. 3. When each packet enters the scheduler, it is classified according to the CA to which its destination belongs, and sent to the first FIFO (first-in first-out) queuing module. This module has one FIFO queue for each of the CAs that have been defined at a given instant. The number of FIFO queues is N (t), and its maximum possible value is Nmax , which is determined by the hardware/software implementation of the GW. The packet is then queued in the FIFO corresponding to the destination CA of the packet. This type of classification allows for an as late as possible assignment of the corresponding physical layer within the transmitter, which is beneficial since channel conditions might vary during the processing and waiting time. Note that the packet data may come directly from the edge routers co-located at the common transmitter or might be preprocessed (e.g. encapsulated, encrypted, conditioned at traffic level to meet Service Level Agreements, SLAs). The first scheduling algorithm in the architecture (represented by block “1” in Fig. 3) takes the packets from the first N (t) queues and introduces them in the second queuing module, which consists of M buffers, M being the number of ACM modes. The size of each buffer is a fixed number of information bits, denoted as bm , m = 1, 2, . . . , M . Such number, which depends on the size of the block codes used for each physical layer, is chosen as small as possible in order to minimize the processing delay, i.e. is chosen equal

to the codeword size. It should be noted that this size may vary significantly for different ACM modes. In particular, in the DVB-S2 standard [1], bm ranges from 3072 up to 58320 information bits. These numbers are large compared to terrestrial standards, and is caused by the large coding blocks used to achieve the high reliability required for the satellite broadcast channel. The second scheduling algorithm (represented by block “2” in Fig. 3) is in charge of taking the information bits from one of the buffers and passing them to the corresponding coding and modulation unit that forms that signal to be transmitted. The presented architecture permits a simple implementation of the packed scheduler. Only a reduced number of FIFO queues and buffers are necessary. The number of queues is proportional to the number of correlated areas, which can be chosen according to the required complexity. In any case, compared to a queuing module with as many queues as number of active users, the complexity is reduced by about three orders of magnitude (in one beam of a broadband system, the number of users can be on the order of several tens of thousands, whereas typically less than 10 CAs should be defined). The first scheduling algorithm (block “1”) proposed is a pure Round Robin, RR, which simply consists of accessing the buffers, for instance in top-down direction, one after the other. The main virtue of RR scheduling is its simplicity. The only condition for such RR in the packet scheduler presented here is to operate at a much higher rate than the scheduling algorithm “2”. In this case, the scheduling algorithm “1” is a transparent algorithm in the sense that it allows buffers to be filled as soon as there are packets available on the queues, and the use of an algorithm different to RR for the scheduler “1” would not affect the performance of the system. On the other hand, the scheduling algorithm “2” is one of the elements determining the performance of the architecture proposed herein. This algorithm is an Adaptive Weighted Round Robin, AWRR. In a general case, AWRR scheduling is chosen to better handle “servers” with “timevariant processing” capacities. In our problem, the physical channel is the unique server, and its capacity is time-variant due to the fading. In the implementation of the Weighted Round Robin, WRR, a scheduling sequence is generated according to the weights assigned to the buffers, ωm . The sum of weights must be equal to one, and ωm represents the relative frequency with which the m-th buffer is accessed. Each time m-th buffer is accessed, bm information bits are passed to the corresponding codification and modulation unit, which generates a packet transmitted in a time slot of duration Tm = bm / (ηm R) = Lm /R, being Lm the number of symbols (the bm bits coded and modulated). Note that these weights are not equal to the time share of the channel available for each buffer due to the different duration of the time slots for different ACM modes. RR is a special instance of AWRR, in which all the weights are equal and constant with time (i.e. ωm = 1/M , m = 1, ..., M ). Weights adaptation with time is proposed in order to adapt the system to both the traffic and channel dynamics. At a given time, the AWRR of the proposed architecture may perform either a fair allocation in terms of equal through-

CASTRO AND GRANADOS: CROSS-LAYER PACKET SCHEDULER DESIGN OF A MULTIBEAM BROADBAND SATELLITE SYSTEM

put (rate of information bits) for all buffers, if the weights are ωm =

1 ηm Tm M 1 j=1 ηj Tj

,

m = 1, . . . , M ,

(8)

or an opportunistic allocation (more time share to users with better channel conditions), if the weights are ωm =

ηm Tm M 

,

m = 1, . . . , M .

(9)

ηj Tj

j=1

By allowing equal throughput, not only the overall throughput decreases but the users belonging to CAs having clear sky conditions will be affected by the bad weather conditions affecting other CAs by getting their throughput reduced proportionally to the number of users in bad weather conditions. Note that depending on the location and season it may be reasonable to assume a high percentage of users in bad weather conditions. A reverse policy is the opportunistic one, which favors the users with low-attenuation channels. In this case, for the likely scenario of having most of the CAs with good weather conditions, the few ones having bad weather conditions may suffer from starvation. Another well-known and accepted scheduling policy is the proportional fair or Nash solution by which all the users are equally satisfied if the rain burden is proportionally distributed among all of them. This criterion is reasonable if the burden is not much and/or it does not last much time as it the case in terrestrial mobile systems. However, in broadband satellite, the burden may last from few minutes up to some hours depending on the location and season. Therefore, it is realistic to assume that this solution is not the optimum one for broadband satellite systems, at least in wet seasons. We propose an intermediate solution, which will be extended in the following section. It pursues time fairness thus providing CAs isolation by distributing the scheduling cycle time equally between CAs in good and in bad channel conditions. Nevertheless the proposed architecture allows a variety of scheduling policies. VI. B ROADCAST T HROUGHPUT S TABLE R EGION This section presents which are the feasible vectors of bit rates as a function of the weights ωm introduced above. After a general derivation, the rationale underlying the choice of the weights is explained and an example with few physical layers is given. From Information Theory it is well known that any communication channel is characterized by a maximal information rate, namely the channel capacity developed by Claude Shannon, which provides the upper limit for reliable transmission [4] and is the following function of (4): ¯)), expressed in information bits C (t, x¯) = log2 (1 + ξ (t, x per transmission2 . If the previous formula is multiplied by the Nyquist channel symbol rate (i.e. channel bandwidth B), the capacity is then expressed in information bits per second. However, the Shannon´s capacity is given for single user communication in a Gaussian channel. In [15] it is shown that for 2 Note that the channel, a (t, x ¯), varies slowly enough (i.e. channel is constant during a slot time) so that the Shannon capacity formula is valid for each instant t.

253

a general flat-fading channel with arbitrary fading distribution (thus including our case of Ka broadband satellite transmission with directional antennas), when Channel State Information (CSI) is available both at the transmitter and the receiver, the ¯)) dξ. It is capacity is given by C = B ξ log2 (1 + ξ) p (ξ (t, x also shown that in case the transmission power is constant, such capacity can be approached using the ACM model presented in Section III. In order to gain further insight into our proposed packet scheduler (Fig. 3), let us consider without loss of generality the particular case of having only two output buffers (M = 2), i.e. an ACM model only with two physical layers. Channel is allocated to the first buffer during a fraction of time φ1 and to the second buffer the remainder of the scheduling cycle time (φ2 = 1 − φ1 ). Note that these weights are related to the ones defined above as follows φm =

ωm T m M 

ωj T j

j=1

ωm = Tm

φm , M  φj j=1

m = 1, . . . , M .

(10)

Tj

The average information transmission rate associated to each buffer3 is Rm = φm Cm , with Cm = ηm R being the actual information transmission rate associated to the m-th ACM mode as defined by (6). Since φ1 + φ2 = 1, the region of the 2+ plane containing the achievable vectors of throughput R2 1 (R1 , R2 ) is the area below the line R C1 + C2 = 1. It is very interesting to note that the Shannon capacity region for two users has exactly the same form [16], which can be also denoted as the rate pairs { (R1 = αC1 , R2 = (1 − α) C2 ) ; 0 ≤ α ≤ 1}. Therefore, it can be deduced that the buffering module at the output of the transmitter maps the complex structure of the capacity region onto a throughput region space of as many dimensions as physical layers are considered since the channel is not allocated to the users but to the buffers. In our case, each dimension no longer refers to a single user but to a large number of users (sharing the same channel conditions) since the system is broadband. Generalizing to M dimensions, the stable region S, which contains the possible combinations of throughputs for each physical layer in the output buffering system is given by S (C1 , C2 , . . . , CM ) = ⎧ ⎫ M  ⎨ ⎬ R j ¯ = (R1 , R2 , . . . , RM ) ∈ M  R ≤ 1 . + ⎩ ⎭ Cj

(11)

j=1

The frontier of the stable region is the hyperplane for which equality is achieved in (11). Sincethe weights φm of the AWRR algorithm are chosen M so that m=1 φm = 1, the actual vector of throughputs can be at any point inside S (C1 , C2 , . . . , CM ) (including its frontier) depending on the traffic conditions. The virtue of the algorithm is that a minimum throughput equal to Rm = φm Cm is 3 At

this point, we consider buffers to be full all the time.

254

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007

guaranteed for each buffer regardless of the traffic offered to other buffers. If stable conditions are assured by means of an appropriate Admission Control (AC) scheme, the size of the queues in the first queuing module will remain finite. If this is not the case and the system is under saturation conditions (i.e. the per-layer input traffic falls outside S), a throughput of Rm = φm Cm still achieved for each buffer, but in this case the average delay will increase as the queues are filled up. In any case, the actual throughput of a set of buffers can be increased beyond the guaranteed minimum when the traffic offered to other buffers is lower than their corresponding minimum values and the time share that is not used by these buffers is employed by the former ones. Weights however must be adaptive in time, φ¯ (t) = (φ1 (t) , . . . , φM (t)), since the number of active buffers (i.e. non empty buffers) is time variant according to the time variant channel conditions and the adaptive number of correlation regions. Such time variability results in a time variant channel capacity and the weights adaptation can be chosen either to maintain always the same throughput for each physical layer or to favor ones respect the others by applying for instance (8) or (9), and (10), only to the active buffers and assigning weights equal to zero to the inactive ones. Since each buffer corresponds to a physical layer, the higher the weight allocated to the most efficient ones, the higher the total throughput will be. In this case, the least efficient physical layers might suffer from starvation when a group of users experience high channel attenuation. Nevertheless, the most important benefit provided by the presented architecture is that groups of users with different channel conditions will belong to different CAs (by a proper selection of the CAs), and therefore their traffic will be routed to different queues (in the first queuing module) and to different buffers. Then, the AWRR scheduling algorithm guarantees a minimum throughput for each group of users in such a way that saturation in one group (e.g. users with bad channel conditions) does not affect the service provided to other groups (e.g. users with good channel conditions). Fig. 4 shows an example of weights adaptation. M = 3 physical layers are considered. At time t1 buffers 1 and 2 are active, with spectral efficiencies such that η2 > η1 . The working point is P1 , with coordinates R1 (t1 ) = φ1 (t1 ) η1 R1 and R2 (t1 ) = φ2 (t1 ) η2 R2 , which belongs to the frontier of S (C1 , C2 ). Since buffer 3 is inactive, φ3 (t1 ). At time t2 , as a consequence of channel improvement, buffer 2 becomes inactive while buffer 3 becomes active, with η3 > η2 . One solution is to maintain the same time proportions, that is to say φ1 (t2 ) = φ1 (t1 ), φ3 (t2 ) = φ2 (t1 ) with φ2 (t2 ) = 0. However, since the region of feasible throughputs has changed, it may be preferred to vary the proportions and choose the weights as shown in Fig. 4, where the new working point is P2 , which offers a much higher total throughput than P1 . VII. N UMERICAL R ESULTS A. System Assumptions The system parameters have been selected according to Table I. The spectral efficiencies are taken from the DVBS2 standard [1]. The bit rates achievable with each physical layer under the continuous model (5) and with the discrete

R 2 ,R3 C3

t1

t2

Buffer 1

Buffer 1

Buffer 2

Buffer 2

Buffer 3

Buffer 3

C2

φ (t2 )C3

P2

P1

φ (t1 ) C2

φ (t 2 )C1 φ (t1 )C1

C1

R1

Fig. 4. Stable throughput region for M = 2 and example of weights adaptation. TABLE I S YSTEM PARAMETERS System parameter

Value

Number of beams

43

Carrier frequency

20 GHz

Access

TDM

Symbol rate

30 Mbaud/s

Frequency reuse factor

3

Satellite saturated RF power per beam

16 dBW

Antenna peak gain

50 dB

Satellite terminal G/T

17.85 dB/K

Latitude of CAs (degrees)

CA1, CA3: 8.3 - 10.5 CA2, CA4: 10.5 - 12.3

Longitude of CAs (degrees)

CA1, CA2: 46.1 - 48.1 CA3, CA4: 43.4 - 46.1

ACM model under consideration (6) are represented in Fig. 5, where a comparison with the Shannon limit is also included, for two possible values of the maximum usable bandwidth4. 24 physical layers out of the 28 proposed by the standard have been considered in this plot. The 24 inclined and horizontal lines represent first part of (5), while the staircase-shaped line corresponds to (6). Note how both quantization and the use of realizable codes and modulations formats create a gap with respect to the Shannon limit. A model of the forward link of a GEO broadband multibeam satellite system with adaptive physical layer has been imple4 In Fig. 5, it is assumed without loss of generality that the maximum symbol rate R coincides with the maximum usable bandwidth.

CASTRO AND GRANADOS: CROSS-LAYER PACKET SCHEDULER DESIGN OF A MULTIBEAM BROADBAND SATELLITE SYSTEM

255

R with the AC M model for tw o va lues of the max imum allowe d bandwidth B b

0"

10

Shannon Capacity for B = 300MHz

3

Clear sky conditions

-1"

Rainy conditions

-2" -3"

B i t r a t e w i t h A C M model for B =300MHz

-4"

2

-5" -6"

R b (M bits/s)

10

A t t (dB )

-7" -8" -9"

Shannon Capacity for B =30MHz 10

-10"

1

-11"

Bit rate with ACM model for B = 30MHz

-12" 0"

10"

20"

30"

40

50"

60

70

80

90" 100

110" 120" 130

140

150" 160

170

180" 190" 200

Time (seconds) Possible bit rates with each physical layer 74

76

78

80

82 84 86 88 C /N = ξ (t,x) × R (dB-Hz )

90

92

94

96

t

Fig. 5. Comparison between the bit rate achieved with the ACM model, the bit rate with each individual physical layer and the Shannon capacity for two values of the maximum bandwidth.

R The models of the system, physical layer mented in OPNET. and channel, described in Sections II, III and IV, respectively have been implemented in detail. Simulation of such models is time-driven, while simulation of traffic injected into the system and the whole packet scheduling procedure are event-driven. Exponential inter-arrival times are considered. The following assumptions have been made. First, the input traffic does not saturate the system during clear sky conditions but it does so under rain conditions; no source bit rate control is implemented (since the paper focuses on the performance of the packet scheduler by itself), therefore packet delaying in the first FIFO queuing module is the only means to avoid packet losses during rain fading. Second, the beam size (with a diameter of about 200 km) is divided into four CAs. The overall fading attenuation considered for the users in bad channel conditions has the time evolution shown in Fig. 6 (note that the rain event has been low-pass filtered simulating the effect of the channel estimation algorithm). The bad channel conditions affect two out of the four defined CAs and, assuming that users are evenly distributed, 50% of users are in bad channel conditions while 50% are in clearsky conditions. Note that within each CA, the attenuation has a coherence time of about 1 second (rain fading decay rate is rarely above 0.5dB/sec). Since the system reacts to attenuation variations on the order of 1dB (given by the horizontal separation between two inclined lines in Fig. 5), the sampling time has been set to 0.5 seconds, which is a sufficiently conservative choice to track any channel variation. Without loss of generality, simulations focus on the scheduler performance of one particular beam (in particular the one covering the south of Europe and northern Italy) out of the 43 beams included and simultaneously simulated in system (see Table 1), which has coverage over around π2002 km2 . The four CAs are defined in Table I. A channel quality report is sent by the ST to the gateway any time a relevant change in the physical layer is detected. Therefore, the delay in the physical layer updating process is also modeled through this signaling packet, which is sent to the GW over the satellite channel. The data packet delay can be expressed as Td = Tprop + Tq ,

Fig. 6. Rain event for the system case considered. An attenuation equal to -2dB was chosen as clear sky conditions instead of 0 dB.

where Tprop is around 240-250ms, depending on the latitude and longitude of the user location, and Tq is the waiting time at the queues experienced across the system. For the sake of clarity, only plots assuming four output buffers (i.e. ACM modes, M = 4) will be shown in the following. The characteristics of these modes are (from [1]): mode 1: 8PSK, η1 = 2 and T1 = 0.738s, mode 2: 8PSK, η2 = 2.5 and T2 = 0.738s, mode 3: 8PSK, η3 = 3 and T3 = 0.738s, mode 4: 32APSK (Asymmetric Phase Shift Keying), η4 = 3.75 and T4 = 0.4428s. Obviously, the fading event affects more significantly in this situation than in the case of using 24 ACM modes since reducing the number of ACM modes decreases the adaptation capability of the physical layer, resulting in less protection against fading and lower average throughput.

B. Study Case I. Non Adaptive Scheduling Policy The first study case considers that the second scheduling algorithm is RR for the active buffers (i.e. WRR with weights ωi = 1/(number of active buffers) for each active buffer and ωi = 0 for the inactive ones). Fig. 7 shows the effect of increasing the system load. The different loads are given as percentage of the maximum possible (clear sky conditions) which is 30 · 106 × η4 = 112.5Mbits/s. It can be observed that the depleting throughput (i.e. throughput after the rain event) is the maximum one since a large number of packets are queued in the first FIFO module during the fading event. Also note that the recovering/depleting time becomes longer when increasing the system load. Fig. 8 shows the effect of the rain event on the packet delay. It can be observed that all users suffer a sharp increase in delay (and correspondingly a decrease in throughput) caused by the increase in the attenuation in only two of the four CAs. The effect that the presence of rain in some areas severely degrades the performance for users in other areas with clear sky is clearly undesirable. Such effect is due to the use of WRR with weights ωi = 1/(number of active buffers) because when buffers with lower spectral efficiency become active to serve the users in the rainy CAs (note that at the beginning only buffer 4 is active), the time share of users in bad channel conditions increases, and hence the delay of users with good channel conditions increases as well (while the throughput decreases).

256

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007

TABLE II W EIGHTS ADAPTATION FOR TIME FAIRNESS PROVISION FOR THE CASE OF Throughput bits/second

M=4 AND TWO CA S WITH A PROPORTION OF USERS IN CLEAR SKY AND RAINY CONDITION OF

70%

85% 80%

Weights ωm

Weights φm

#4

(ω1 , ω2 , ω3 , ω4 )

(φ1 , φ2 , φ3 , φ4 )

X

(0, 0, 0, 1)

(0, 0, 0, 1)

X

(0, 0, 3, 5) /8

(0, 0, 1/2, 1/2)

X

(0, 3, 0, 5) /8

(0, 1/2, 0, 1/2)

X

(3, 0, 0, 5) /8

(1/2, 0, 0, 1/2)

X

X

(0, 3, 3, 10) /16

(0, 1/4, 1/4, 1/2)

X

X

(3, 0, 3, 10) /16

(1/4, 0, 1/4, 1/2)

X

(3, 3, 0, 10) /16

(1/4, 1/4, 0, 1/2)

X

(3, 3, 3, 15) /24

(1/6, 1/6, 1/6, 1/2)

Buffers

75%

#1

#2

#3 X

X X X X

Fig. 7. Total beam throughput for N = 4 and M = 4 for system loads of 70%, 75%, 80% and 85% of the maximum capacity in clear sky. RR scheduling algorithm is used.

User in rainy conditions

X

X

X

X

X

User in rainy conditions User in clear sky conditions

Fig. 8. Average delay of packet scheduler when N = 4, M = 4, system load is 80% and the RR scheduling algorithm is used.

C. Study Case II. Proposed Adaptive Time-Fair Policy A second study case shows the effect of applying AWRR to perform the policy proposed in this paper. The scheduling weights are adapted according to the buffers that are active, as shown in Table II, in such a way that the same time share is granted to the buffer corresponding to good conditions (buffer 4) as to the other three buffers altogether, which allows for a adaptive time fairness instead of usual throughput fairness. This is an intermediate criterion compared to the proportionally fair: instead of proportionally sharing the rain burden (which may last a long period) users in good conditions are more favored, thus guaranteeing these users are not affected by the rain event and providing isolation between good and bad users, as shown in Fig. 9. This is regarded as a highly desirable feature for a broadband system. Certainly, in this case the flows transmitted to users through buffers 1 to 3 will be affected in more extent than in the case of applying RR, where all users share the “rain burden”, and this can be confirmed by comparing the delays experiencing by the users in rainy conditions for both algorithms (i.e. the delay of this type of users is larger in Fig. 9 than in Fig. 8). A reasonable long-term solution might be to switch from a proportionally fair policy for the dry seasons (where rain events are scarce and relatively short) to the proposed one. In the dry seasons, it would be more adequate to share the

User End-to-End Delay (seconds)

User End-to-End Delay (seconds)

50/50. ACTIVE BUFFERS ARE MARKED WITH AN “X”.

User in clear sky conditions

Fig. 9. Average delay of packet scheduler when N = 4, M = 4, system load is 80% and the AWRR scheduling algorithm with weights according to Table II is used.

rain burden among all users, while during the wet season the rain burden would be mostly absorbed by the affected users. Another example of the proposed scheduling algorithm is shown in Table III. In this case the weights adaptation rule is such that buffer 4 is guaranteed access to the channel during at least 3/4 of the time, which is equivalent to ensuring a minimum throughput of 84.375Mbits/s for that buffer. This adaptation rule is appropriate when an increased protection of users in clear sky conditions is sought and, for instance, this would be the case when the system is to be designed in such a way that the presence of rain in one CA does not affect the users in the other three CAs. VIII. C ONCLUSIONS A cross-layer design has been applied to propose a suitable architecture of a packet scheduler. The scheduler has been developed for the broadcast channel (forward link) of a MBS system channel using ACM. Under the assumptions that power and bandwidth are constant in each beam, the scheduler determines the fractions of time assigned to transmission by each physical layer. The architecture is based on the physical behavior of the Ka satellite propagation channel and the definition of “correlated area”, CA, which is a time-dependant geographical area where users undergo similar (correlated) channel conditions. This concept allows optimizing the sched-

CASTRO AND GRANADOS: CROSS-LAYER PACKET SCHEDULER DESIGN OF A MULTIBEAM BROADBAND SATELLITE SYSTEM

TABLE III W EIGHTS ADAPTATION FOR TIME FAIRNESS PROVISION FOR THE CASE OF M=4 AND TWO CA S WITH A PROPORTION OF USERS IN CLEAR SKY AND RAINY CONDITION OF

Buffers #1

#2

#3

X

X

X

(ω1 , ω2 , ω3 , ω4 )

(φ1 , φ2 , φ3 , φ4 )

(0, 0, 0, 1)

(0, 0, 0, 1) (0, 0, 1/4, 3/4)

X

(0, 1, 0, 5) /6

(0, 1/4, 0, 3/4)

X

(1, 0, 0, 5) /6

(1/4, 0, 0, 3/4)

X

X

(0, 1, 1, 10) /12

(0, 1/8, 1/8, 3/4)

X

X

(1, 0, 1, 10) /12

(1/8, 0, 1/8, 3/4)

X

(1, 1, 0, 10) /12

(1/8, 1/8, 0, 3/4)

X

(1, 1, 1, 10) /13

(1/12, 1/12, 1/12, 3/4)

X

uler architecture since packets are queued on a first stage independently of the physical layer required by the addressed user, but depending only on the location this user. The assignment of the physical layer occurs on the last stage of the scheduler, thus avoiding erroneous assignments since channel conditions may vary during the scheduling processing time. The stable throughput region has been derived yielding an area in a space of as many dimensions as output buffers, each one corresponding to a different physical layer. The proposed architecture is flexible enough to allow the implementation of different scheduling policies like the proportional fair or opportunistic ones. Moreover, it is realizable in practice with low complexity since the number of queues in the scheduler is rather limited (less than ten, i.e. the maximum number of CAs within the beam coverage), which differs from other approaches proposing the use of one queue for each user (note that such a system may provide service to several tens of thousands of active users). By making use of the grouping of users in CAs, a time-fairness-based adaptive algorithm, appropriate for wet seasons and offering user isolation, has been proposed and simulated using a model of the complete system. Future areas of research include the extension of the cross-layer design to the transport and application layers of the protocol stack, with the objective of developing an architecture capable of providing quality of service, as well as the adaptation of the architectures to regenerative systems. A PPENDIX The stochastic dynamic channel model follows the one described in [13]. The stationary probability distribution of the attenuation a (t) during a rain event is lognormal and it is described by two parameters, the median am and the standard deviation σa of ln (a (t)) . A third parameter β is needed in order to control the rate of change for the process modeled. The equation describing the stationary fluctuation of the attenuation may be written as da (t) = K1a (a) dt + dwa (t) ,

(14) (15)

The generation of a process fulfilling (12)-(15) is not straightforward. In order to find an alternative way for producing the attenuation time series, the following transformation is introduced:   a (t) 1 ln . (16) x (t) = σa am

(0, 0, 1, 5) /6

X

X

Weights φm

X

X X

Weights ωm X

X

X

#4

75/25. ACTIVE BUFFERS ARE MARKED WITH AN “X”.

where K1a (a), K2a (a) are defined as   a 2 K1a (a) = aβ σa − ln am K2a (a) = 2βa2 σa2 .

257

(12)

where dwa (t)) is a process with independent increments (i.e. a Wiener-Lévy process [17]) such that      2 E dwa a = 0 ; E |dwa | a = K2a (a) dt , (13)

It can be shown by using the Itô´s lemma that x (t) is an Ornstein and Uhlenbeck process, and therefore it fulfils the equation (17) dx (t) = −βx (t) dt + dwx (t) ,    where dwx (t) is a Wiener-Lévy process with E dwx x =  2  0 and E |dwx | x = 2βdt. Process x (t) can be easily generated since, according to (17), it can be obtained as the output of a filter with transfer function H (s) = 1/ (s + β) when its input is white Gaussian noise. Next, the attenuation is produced using the inverse of (16), a (t) = am exp (σa x (t)), as depicted in Fig. (2). ACKNOWLEDGMENT The first author wants to express her gratitude for the excellent technical discussions and scientific support received from the people with the Communications Section at ESTEC, ESA during her 2-year Fellowship, in particular to the Division Head, Dr. R. De Gaudenzi. These discussions allowed us to achieve the results presented in this paper. R EFERENCES [1] Digital Video Broadcasting (DVB); Second Generation Framing Structure, Channel Coding and Modulation Systems for Broadcasting, Interactive Services, News Gathering and other Broadband Satellite Applications (DVB-S2), ETSI EN 302 307 v1.1.1, Mar. 2005. [2] A. Morello and U. Reimers, “DVB-S2, the second generation standard for satellite broadcasting and unicasting,” International J. Satellite Commun. Networking, vol. 22, no. 3, pp. 249–268, May/June 2004. [3] R. Rinaldo, M. A. V. Castro, and A. Morello, “DVB-S2 ACM modes for IP and MPEG unicast applications,” International J. Satellite Commun. Networking, vol. 22, no. 3, pp. 367–399, May/June 2004. [4] T. Cover and J. A. Thomas, Elements of Information Theory. New York: John Wiley & Sons, 1991. [5] S. Cioni, R. de Gaudenzi, and R. Rinaldo, “Adaptive coding and modulation for the forward link of broadband satellite networks,” in Proc. IEEE Globecom, Dec. 2003, vol. 6, pp. 3311-3315. [6] R. Rinaldo and R. de Gaudenzi, “Capacity analysis and system optimization for the forward link of multi-beam satellite broadband systems exploiting adaptive coding and modulation,” International J. Satellite Commun. Networking, vol. 22, no. 3, pp. 401–423, May/June 2004. [7] Propagation Data and Prediction Methods Required for the Design of Earth-Space Telecommunications Systems, REC ITU-R P.618-7, International Telecommunication Union, 2001. [8] E. Matricciani, “Physical-mathematical model of the dynamics of rain attenuation based on rain rate time series and two layer vertical structure of precipitation,” Radio Science, vol. 31, no. 2, pp. 281–295, Apr. 1996. [9] C. Capsoni, F. Fedi, C. Magistroni, A. Paraboni, and A. Pawlina, “Data and theory for a new model of the horizontal structure of raincells for propagation applications,” Radio Science, vol. 22, no. 3, pp. 395–404, June 1987. [10] M. M. J. L. van de Kamp, “Climatic Radiowave Propagation Models for the Design Of Satellite Communications Systems.” Ph.D. diss., Eindhoven University of Technology, 1999.

258

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007

[11] L. Castanet, J. Lemorton, T. Konefal, A. K. Shukla, P. A. Watson, and C. L. Wrench, “Comparison of various methods for combining propagation effects and predicting loss in low-availability systems in the 20-50 GHz frequency range,” International J. Satellite Commun., vol. 19, no. 3, pp. 317–334, May/June 1991. [12] J. Goldhirsh, “Two-dimensional visualization of rain cell structures,” Radio Science, vol. 35, no. 3, pp. 713–729, June 2000. [13] T. Maseng and P. M. Bakken, “A stochastic-dynamic model of rain attenuation,” IEEE Trans. Commun., vol. 29, no. 5, pp. 660–669, May 1981. [14] Characteristics of Precipitation for Propagation Modeling, REC ITU-R P.837-3, International Telecommunication Union, 2001. [15] A. J. Goldsmith and P. Varaiya, “Capacity of fading channels side information,” IEEE Trans. Inform. Theory, vol. 43, no. 6, pp. 1986–1992, Nov. 1997. [16] L. Lifang and A. J. Goldsmith, “Capacity and optimal resource allocation for fading broadcast channels-Part I: Ergodic capacity,” IEEE Trans. Inform. Theory, vol. 47, no. 3, pp. 1083–1102, Mar. 2001. [17] A. Papoulis, Propability, Random Variables, and Stochastic Processes. New York: McGraw Hill, 1991. María Angeles Vázquez Castro (M’99) was born in Vigo, Spain. She received the M.Sc. degree in Telecommunications Engineering in 1994 and the Ph.D. degree (cum Laude) in 1998 from University of Vigo. She was an Assistant Professor at the University Carlos III de Madrid from 1998 to 2001. She was a guest researcher at University of Southern California in 2000. From 2002 to 2004 she was an internal Research Fellow at the European Space Research and Technology Center (ESTEC), European Space Agency, Noordwijk, The Netherlands, working on the development of DVB-S2 with the Communications Section. She is currently Associate Professor at the Department of Telecommunications and Systems Engineering of the Universitat Autònoma de Barcelona leading the Wireless Communications Research Group. This group is member of the European Network of Excellence on Satellite Communications SATNEX and has been recently awarded by the Catalonian Government the distinction of emergent research group. She has published more than 60 papers on international journals and conferences and holds one patent of a packet scheduler. Her current areas of interest are related to wireless communications, with particular interest in satellite communications networks cross-layer design and optimization.

Gonzalo Seco Granados (M’2002) was born in Barcelona, Spain, in 1972. He received the M.Sc. and Ph.D. degrees in Telecommunication Engineering in 1996 and 2000, respectively, from Universitat Politècnica de Catalunya (UPC), Barcelona, Spain. He also received an MBA from IESE-University of Navarra, Barcelona, in 2002. From 2002 to 2005, he was member of the technical staff at the Electrical Engineering Department, European Space Research and Technology Center (ESTEC), European Space Agency, Noordwijk, The Netherlands, involved in the Galileo project and in the development of radionavigation receivers. He led the activities concerning indoor positioning for GPS and Galileo. He has also worked in the design of antenna arrays for GNSS and synchronization of communication systems. Since the beginning of 2006, he is associate professor at the Department of Telecommunications and Systems Engineering of the Universitat Autònoma de Barcelona. Dr. Seco-Granados received two best Ph.D. thesis awards from UPC and the Spanish Association of Telecommunication Engineers as well as the best presentation award at the ION-GPS’2003 conference. He was co-guest editor for a special issue of the IEEE Signal Processing Magazine. His present research interests in the area of communications include cross-layer design, network optimization and resource management for fixed and mobile satellite communication systems.