1

On the Optimum Packet Power Distribution forSpread Aloha Packet Detectors with Iterative

Successive Interference CancellationFlorian Collard, Riccardo De Gaudenzi

Eutelsat, Paris, France, European Space Agency, Keplerlaan 1, 2200 AG Noordwijk, The Netherlandse-mail: fcollard@eutelsat.com, rdegaude@xrsun0.estec.esa.nl

Abstract—Recent work [1], [2] has been stimulated by theneed to enhance the satellite networks Random Access (RA)performance. Results have shown that large performance im-provement is possible by exploiting Iterative Successive Inter-ference Cancellation (I-SIC) at the demodulator side. CodedSpread Spectrum Aloha (SSA) is a particularly suitable accesstechnique for RA satellite networks thanks to its inherentasynchronous access nature as well as its high multiple accessAchievable Sum Rate (ASR). Moreover, the adoption of I-SICallows to further boost the SSA sum rate and its robustnessto the packet power unbalance. In this paper, we derive ananalytical approach to the optimal packet power distributionthat maximizes the performance of SSA RA exploiting I-SIC atthe demodulator. The proposed approach takes into account thephysical layer coding and modulation together with the numberof demodulator iterations and the non-ideal cancellation effects.The analytical findings are successfully compared to simulationand measurement results. Finally, a practical algorithm thatapproximates the optimum incoming power packet distributionin a realistic multi-beam satellite broadband network with open-loop power control is proposed and validated in a study case.

Keywords: Satellite communication, SCADA systems,Multiaccess communication, Code division multiple access,Interference suppression.

I. INTRODUCTION AND PROBLEM OUTLINE

The last few years witnessed a growing interest for aspectsrelated to RA protocol enhancements for terrestrial and satel-lite applications. Emerging machine-to-machine [3], Internetof things [4] and beaconing [5] applications, require efficientRA-like communication protocols for supporting networkscomposed by a large number of sensors generating a low duty-cycle packet traffic. Until recently, RA adoption in satellitenetworks for bursty traffic support was penalized by the poorprotocol performance. This was mainly due to the satellitesystems’ inherent propagation delays, which also preclude theadoption of medium sensing techniques commonly used interrestrial networks. Recently, high performance RA mech-anism such as the Contention Resolution Diversity Aloha(CRDSA) [1] and the Enhanced-Spread Spectrum Aloha (E-SSA) [2] were proposed, demonstrated, and adopted in satellitecommunication standards [6], [7]. The key innovation in bothCRDSA and E-SSA, is the exploitation of I-SIC Multi UserDetection (MUD) to resolve destructive packet collisions. Theadvantage of I-SIC as a MUD technique is related to itsrobustness to power unbalance, its affordable implementationcomplexity [8], and its compatibility with long spreading

sequences (i.e. longer than one symbol). The specific I-SICtechnique adopted by CRDSA and E-SSA greatly extends themaximum RA load at which the system can operate with verylow Packet Loss Ratio (PLR) (e.g. < 10−3). Furthermore,I-SIC-based RA mechanisms show an almost on/off PLRdependency on the Medium Access Control (MAC) load. Thisfeature combined with a simple load-based congestion controlalgorithm such as the one described in [9], minimizes the needfor packet re-transmissions. Previous publications showed thatboth CRDSA and E-SSA performance can be further boostedexploiting the incoming packets power unbalance at the gate-way’s demodulator [2], [10]. This is a known result for MUDdemodulators that use Successive Interference Cancellation(SIC) [13], but less explored for memory-based I-SIC burstdemodulator such as the one adopted in E-SSA. This paperderives the optimum incoming packet power distribution forRA SSA burst packet detectors exploiting I-SIC. The focuson E-SSA is justified by its very good performance combinedwith an affordable demodulator complexity [10]. Althoughinitially derived for satellite networks, E-SSA RA techniquecan also be applied to terrestrial wireless networks [11], [12].For this reason, we keep the analysis quite generic withoutspecific references to the satellite application scenario exceptfor the study case discussed at the end of the paper. Theissue of user terminal power distribution optimization in aCode Division Multiple Access (CDMA) system with SIChas already been dealt with in the past. The Viterbi’s inves-tigation reported in [14] concluded that in case of a CDMAsystem with SIC the optimal received signals power profileis exponential. This approach, although optimum in terms ofASR, is somewhat impracticable as it requires coordinationamong terminals and does not take into account possibletransmitter power limits. Furthermore, results in [14] wereobtained under the assumption that the Synchronous CDMAsignals1 were continuously transmitting i.e., not bursty andasynchronous like in the packet RA systems of interest. Addi-tional information theoretic investigations on optimum powerdistribution for synchronous continuous CDMA transmissionhave been reported in [15], [16], and [18]. These papersderived the optimum incoming signals power distribution fora SIC-based MUD detector. Some key conclusions can beextracted from [15], and [16]: a) for heavily loaded CDMA

1This means that the start of the spreading sequence as well the symboltransitions are aligned among all signals.

2

systems the difference between optimum Belief PropagationMUD decoding and sub-optimum Minimum Mean SquareError SIC (MMSE-SIC) detector is modest; b) for an equal-rate system, when properly selecting the incoming power ofthe packets all points in the capacity region of the scalarGaussian multiple-access channel are achievable by successivesingle-user encoding, decoding, and interference cancellation(stripping); c) while in the power-constrained case capacityis achieved by Gaussian inputs, practical systems can usediscrete small-size modulation alphabets and low-rate For-ward Error Correcting code (FEC) with modest performancepenalty. The above findings are in line with the key E-SSAdesign drivers,2 and theoretically support the fact that E-SSArepresents a high performance RA scheme. The design ofoptimal closed-loop power control for cellular CDMA systemexploiting SIC is dealt with in [19]. In this case, imperfectinterference cancellation is considered and it is shown thatlarge ASR increase can also be obtained, provided that aproper closed-loop power control policy is adopted. AlthoughCDMA with physical layer coding and SIC are considered,the investigations reported in [15], [16], [18], [19] do nottake into account the following practical aspects relevant to aRA system: a) the transmission is bursty, i.e. not continuous;b) the packets are transmitted using DS-SS (not necessarilyCDMA) in a totally asynchronous fashion; c) the transmitterpower selection is decentralized i.e. each transmitter selectsthe transmit power without any coordination with the othertransmitters and without closed-loop power control mechanismthat may generate heavy signalling traffic.

The case of the optimal power distribution for an asyn-chronous packet CDMA system is briefly discussed in [11]where it is claimed that the same asymptotic sum rate of asynchronous (or non-packet based) system can be achievedwith equi-powered packets. The result is justified by means ofa specific example based on the partial packet overlap observedin an asynchronous system but not demonstrated in general.This statement is in contrast with a number of findings relatedto E-SSA [2] whereby the adoption of a lognormal powerdistribution provides a remarkable increase in the achievedRA ASR. So far, no attempt has been made to derive theoptimum packet power distribution maximizing the E-SSAASR. The aim of this paper is to fill the gap by investigatinghow to maximize the E-SSA demodulator ASR optimizing thereceived packets power distribution. Achievable performancefor practical coded modulation and ideal and non-ideal I-SICare compared to the relevant capacity bounds. A practical wayto achieve quasi-optimum power distribution for a satellitepacket RA network is provided showing substantial perfor-mance improvement. The following derivation represents anextension of [14] considering: a) the use of asynchronous(instead of synchronous) access; b) the bursty (instead ofcontinuous) nature of the transmission; c) the decentralized(instead of centralized) power control policy; d) the use ofpacket-oriented I-SIC (instead of conventional SIC); e) thetransmit power limitation; f) the fact that, in practical systems,

2Except for the use of an MMSE filter in front of the I-SIC detector whichis not included for complexity reasons.

bandwidth expansion is obtained not only through low rateFEC but also through direct-sequence spreading techniques.

The rest of the paper is organized as follows: Sect. II definesthe capacity bound applicable to a spread-spectrum RA systemoperating with non-equal packet powers and also consideringthe effect of modulation and coding. Sect. III derives theoptimum incoming packets power distribution for E-SSAexploiting two different models for the E-SSA demodulator.Sect. IV provides analytical and experimental results for theE-SSA RA scheme with optimized power distribution. Sect.V describes the possible RA ASR improvement obtainablethrough near-optimum open loop transmission packet powercontrol in a realistic multi-beam satellite study case. Finally,conclusions are presented in Sect. VI.

II. CAPACITY BOUNDS

In this section we report the applicable capacity boundstaking into account the key RA system parameters. Capac-ity expressed in bits/chip for CDMA systems using randomspreading sequences CR−CDMA has been derived in [20] as:

CR−CDMA = Ω

(K

Lw, γsys

)=

K

Lwlog2

[1 + γsys −

1

4ϕ

(γsys,

K

Lw

)]+ log2

[1 + γsys

K

Lw− 1

4ϕ

(γsys,

K

Lw

)]− log2 e

4γsysϕ

(γsys,

K

Lw

)with :

ϕ(x, z) =

[√x(1 +√z)2

+ 1−√x(1−√z)2

+ 1

]2

,

(1)

where K represents the number of active users, Lw is thespreading factor, γsys is the system signal-to-noise ratio (SNR)defined as γsys = 1

K

∑Kk=1 γk, γk being the individual user

SNR. For K/Lw →∞, CR−CDMA → CSU where CSU is thewell-known single user capacity bound (see (7) in [16]) givenby:

CSU = log2

(1 + CSU

[EbN0

]sys

), (2)

where [Eb/N0]sys is the so called system bit energy to noisepower spectral density (PSD) expressed as

[EbN0

]sys

= RsRbγsys,

where Rs is the symbol rate after coding and modulationand Rb the bit rate. If we assume that, before spreading,a FEC code with rate r is preceding an M -ary modulator,then Rs = Rb/(r log2M) and the chip rate Rc is givenby Rc = LwRs. The total CDMA random capacity canbe expressed as CR−CDMA = KRb/Rc = Kr log2M/Lw(bits/chip). Thus the RA capacity can be obtained solving thefollowing nonlinear equation for a given set of RA physicallayer parameters (M , r,

[EbN0

]sys

):

CR−CDMA = Ω

(CR−CDMA

r log2M, r log2M

[EbN0

]sys

). (3)

3

III. OPTIMUM PACKET POWER DISTRIBUTIONMAXIMIZING RA ACHIEVABLE SUM RATE

A detailed description of the E-SSA I-SIC burst demodula-tor processing is reported in Appendix A of [2]. It is importanthere to recall that the demodulator is iteratively operating ona sliding window encompassing W physical layer packets(typically W = 3). The whole content of the memory issequentially scanned Niter times looking for detectable packetswhich, once successfully decoded, are locally regenerated andcancelled from memory. This ”outer” iteration identified withthe index n (n = 1, 2, · · ·Niter) is on top of the memoryscan process searching for the K packets identified with theindex j (j = K, K − 1, · · · 1) in descending power orderas the decoding starts from the most powerful packet K).When the I-SIC process on the current memory windowis completed, a fraction of the oldest (rightmost) memorysamples is removed and the remaining samples are shiftedto the right and new memory samples added (sliding windowprocess). The complete I-SIC process on the memory windowis started again and so forth.

Let our RA system be modelled as a system whereby at agiven instant there are K colliding packets3 each characterizedby a received power Pj . In line with the E-SSA algorithm[2], we assume that the RA burst demodulator is rankingthe K packets initially present in the demodulator windowmemory so that P1 ≤ P2 . . . PK−1 ≤ PK . Recalling thatγj = Pj/(N0Rs) we introduce the Signal-to-Noise plusInterference (SNIR) ratio for packet j at iteration n as ρj(n) =Pj/[(N0 + [I0]j(n)Rs] where [I0]j(n) represents the MultipleAccess Interference (MAI) equivalent Power Spectral Density(PSD) seen by packet j at iteration n. The accuracy of theMAI approximation with an equivalent White Gaussian Noiseprocess has been confirmed in [2]. Due to the asynchronousRA nature each interfering packet has a partial overlap with thepacket of interest. We characterize the normalized interferencefactor between packets i and j with a random variable α(i, j)uniformly distributed in the interval [0, 1]. According to ourdefinition, α(i, j) = 1 means that there is full time overlapbetween the packet of interest and the interfering packet. Itfollows that α(i, i) = 0 as a packet is not interfering withitself.

Our E-SSA I-SIC modelling will proceed in two-steps: firsta simplified approach providing an approximate closed-formexpression for the optimized power distribution; second a moreaccurate recursive semi-analytic E-SSA model that is able tocompute the RA ASR for a given target PLR. Compared to [2]the proposed approach makes it possible to derive the wantedoptimal power distribution result with limited computationalcomplexity.

A. Simplified Iterative SIC Modelling

It is apparent that when starting an I-SIC overall cycle onthe current sliding memory window samples, only a subset ofpackets will be detectable, most likely the ones experiencing

3In practice assuming Poisson type of traffic the number of interferingpackets is slightly time variant. As shown in [21], for large spreading factorsthe fluctuation in the number of interferers is negligible.

the highest SNIR. But as soon as some packets are detectedand cancelled from memory, others will become detectable.The interest to repeat Niter times the memory scanning priorsliding the memory window, is mainly related to the burstyasynchronous interference nature. Removing some detectedpackets may increase the probability of detection for the pastones; thus the need to iterate back in the memory. Consid-ering the above, it is clear that E-SSA demodulator SNIRthreshold is different from a conventional SIC demodulatorwhereby at each SIC demodulation step the final target PLR(typically 10−3 or lower) shall be achieved. Instead for E-SSAa relatively high PLR value is sufficient to start the memory”cleaning-up” process while the target PLR value is attainedat the end of the iterative process.

Based on the above discussion, following the packet rankingaccording to their power described above (j = 1 correspondsto the lowest power packet), the E-SSA I-SIC convergencecondition at I-SIC iteration n can be described as:

ρj(n) ≥

[EsNt

]I−SIC

j

(n), (4)

where[

EsNt

]I−SIC

j

(n) represents the minimum SNIR at

iteration step n for the ranked packet j allowing the E-SSA I-SIC process to converge. The iteration n at which packet j isdecoded is not known a priori but dependent on the packetindex j. Thus in the following simplified model equations

we drop the dependency on n. In general[

EsNt

]I−SIC

j

is dependent on the current packet index j as there areless and less packets in memory moving from j = K to

j = 1. Following [17] it was found that[

EsNt

]I−SIC

j

gets larger when j is decreasing, asymptotically approachingthe value

[EsNt

]FEC

for j = 1. In order to progress in theE-SSA I-SIC analytical modelling, we assume that: a) ρ1 =[EsNt

]FEC

, where[EsNt

]FEC

represents the required FEC code

SNR to achieve the target PLR value; b)[

EsNt

]I−SIC

j

=[EsNt

]I−SIC

for j = K, K − 1, · · · 2. This corresponds to theassumption that the I-SIC SNIR convergence threshold is thesame for the first K − 1 packets while the weakest packetis supposed to achieve the target PLR at the end of the I-SIC process. Experimentally it has been found that a PLR of0.9 at the first I-SIC iteration for the most powerful K − 1packets is typically sufficient to achieve I-SIC convergence.Furthermore, we assume as a minimum convergence conditionthat the inequalities (4) are satisfied as equalities. By doing sothe E-SSA convergence condition given by (4) becomes:

ρj =

[EsNt

]FEC

if j = 1[EsNt

]I−SIC

if j 6= 1, (5)

where[EsNt

]I−SIC

corresponds to the SNIR for which PLR is0.9 as discussed before. The accuracy of this approximationwill be validated in Sect. III-B where the E-SSA model is

4

compared to simulation results. Following the E-SSA iterativedetector analysis reported in [2], the SNIR for the packet jcan be expressed as:

ρj =γj

1 + 1Lw

[∑j−1i=1 α(i, j)γi + β

∑Ki=j+1 α(i, j)γi

] , (6)

where 0 ≤ β ≤ 1 represents the normalized residual IC powerfactor; β = 0 corresponds to the ideal IC while β = 1 impliesno IC. By substituting (6) in (5) one gets a linear system of Kequations with K unknowns that can be numerically solvedto find the optimum E-SSA packet SNR distribution γi:

γ1 =[EsNt

]FEC

[1 + β

Lw

∑Ki=1 α(i, 1)γi

]γ2 =

[EsNt

]I−SIC

[1 + (1−β)

Lwα(1, 2)γ1

+ βLw

∑Ki=1 α(i, 2)γi

]...

γK =[EsNt

]I−SIC

[1 + 1

Lw

∑Ki=1 α(i,K)γi

],

with α(i, i) = 0 for i = 1, · · ·K as explained before. Thesolution of the above linear system of equations is conditionedto the actual realization of the packet overlap factors α(i, j).Assuming that the α(i, j) variables are known, then an exactcalculation of γj is possible. However, this is not feasible ina practical system as α(i, j) are time-varying and unknown apriori. In order to avoid the need to solve the linear systemof equations with time-varying coefficients, we will replaceα(i, j) with its average value i.e. α(i, j) ' E α(i, j) = 0.5for i 6= j. The accuracy of this approximation will be inves-tigated in Sect. IV-A. By introducing the auxiliary variable Υdefined as:

Υ = 1 +β

2Lw

K∑i=1

γi, (7)

then (7) becomes:

γ1 =[EsNt

]FEC

Υ

γ2 =[EsNt

]I−SIC

[Υ + (1−β)

2Lwγ1

]...

γK =[EsNt

]I−SIC

[Υ + (1−β)

2Lw

∑Ki=1 γi

].

(8)

From (8) one can get the following recursive expression forthe individual packets SNR:

γj =

[EsNt

]I−SIC

Υ

1 +

(1− β)

2Lw

[EsNt

]FEC

·

1 +

(1− β)

2Lw

[EsNt

]I−SIC

j−2

, for j > 1. (9)

Looking at (9) it is apparent that with the approximation madebefore, for the RA case of interest the optimum incomingpackets power profile is exponential (thus uniform in dB).This is a similar result to the one found by Viterbi in[20] although obtained with quite different assumptions onthe demodulator structure (continuous synchronous CDMAtransmission with SIC instead of bursty asynchronous with

I-SIC for E-SSA). According to this model the optimumpacket power distribution shall be uniformly distributed indB between 10 log10

[EsN0

]min

and 10 log10

[EsN0

]max

so thatfollowing (9) we get:[

EsN0

]min

=[EsNt

]I−SIC

Υ

1 + (1−β)2Lw

[EsNt

]FEC

'

[EsNt

]I−SIC

Υ,[EsN0

]max

=[EsN0

]min

1 + (1−β)

2Lw

[EsNt

]FEC

·

1 + (1−β)2Lw

[EsNt

]I−SIC

K−2

,

(10)

where in the first term of (10) we assumed (1−β)2Lw

[EsNt

]FEC

1. The most critical system parameter in (10) is cer-tainly the I-SIC demodulator threshold

[EsNt

]I−SIC

which isimplementation-dependent and not easy to determine since itis also related to the current E-SSA demodulator step. Therisk is that by using

[EsN0

]min

=[EsNt

]I−SIC

Υ as indicatedby (10), in certain cases the required target PLR may not beachieved due to the I-SIC process randomness. In order to beon the safe side one may assume a more conservative valuefor[EsN0

]min

i.e.[EsN0

]min

=[EsN0

]I−SIC

Υ '[EsNt

]FEC

Υ sothat (10) simplifies to:

[EsN0

]min

'[EsNt

]FEC

Υ[EsN0

]max

=[EsN0

]min

1 + (1−β)

2Lw

[EsNt

]FEC

·

1 + (1−β)2Lw

[EsNt

]I−SIC

K−2

.

(11)

The calculation of the term Υ is still following (7) butbeing the packet power distribution uniform in dB in therange 10

[log10

[EsN0

]min

, 10 log10

[EsN0

]max

]exploiting the

properties of geometric series for K 1 one gets:

K∑i=1

γi = Ψ

([EsN0

]min

,

[EsN0

]max

)

=

1 + (1−β)

2Lw

[[EsN0

]max

−[EsN0

]min

K−1

]K−1

− 1

(1−β)2Lw

[[EsN0

]max

−[EsN0

]min

K−1

] .

(12)

By using (12) the optimum packet power distribution range canbe derived by solving the following 3 by 3 nonlinear systemof equations:

[EsN0

]min

'[EsNt

]FEC

Υ[EsN0

]max

=[EsN0

]min

1 + (1−β)

2Lw

[EsNt

]FEC

·

1 + (1−β)2Lw

[EsNt

]I−SIC

K−2

Υ = 1 + β2Lw

Ψ([

EsN0

]min

,[EsN0

]max

).

(13)

The simplified analytical model developed in this section hasshown that for E-SSA the incoming packets uniform power

5

distribution in dB is very close to the optimal one. However,this simplified model can not provide accurate results in termsof E-SSA ASR for given target PLR. The current modelaccuracy weakness will be overcome in the next section.

B. Enhanced Iterative SIC Modelling

In this section we derive a more accurate modelling of theE-SSA I-SIC process taking into account the packet detec-tion error probability and avoiding the use of the parameter[EsNt

]I−SIC

which, as discussed before, is not easy to derive.The enhanced model can be obtained modifying (6) to includethe impact of the packet i probability of detection in the SNIRcalculation at iteration step n of the iterative E-SSA detectorthrough the variable σ(i, n) detailed in the equation below.Analytically, the enhanced I-SIC detector SNIR for the j-thpacket at iteration n, ρj(n) can be expressed as:

ρj(n) =γj

1 + 1Lw

[∑j−1

i=1α(i, j)σ(i, n)γi +

∑K

i=j+1α(i, j)σ(i, n − 1)γi

] ,(14)

σ(i, n)∆= β 1− Φ [ρi(n)]+ Φ [ρi(n)] , (15)

where Φ [ · ] represents the physical layer PLR as a functionof the current packet SNIR. The first term in the denominatorof (14) refers to the interference contribution by packets withlower SNIR than the current packet j. The second term in(14) corresponds to the interference contribution by the packetswith higher SNIR than packet j. Differently from (6), in (14)the impact of the PLR is accounted for by means of the termσ(i, n). In the expression of σ(i, n) the first term provides anestimation of the average normalized interference contributiontaking into account the probability of the i-th packet beingdetected and cancelled at iteration n. The second term insteadrepresents the average normalized interference contribution forthe i-th packet not being detected and cancelled at iterationn. Equation (14) reduces to (6) under the assumption that fori < j Φ[ρi(n)] ' 1 thus σ(i, n) ' 1 and that for i > jΦ[ρi(n)] ' 0, thus σ(i, n) ' β. Equation (14) can be itera-tively computed assuming Φ[ρi(0)] = 1 for i = 1, 2 · · ·K,as:

for n = 1 : Niter doI(n) = 0for j = 1 : K do

for i = 1 : K doif i == j then

σ(i, n) = 0else

σ(i, n) = β1− Φ[ρi(n− 1)]+ Φ[ρi(n− 1)]end ifI(n) = I(n) + σ(i, n)α(i, j)γi

end forρj(n) =

γj1+I(n)/(Lw)

end forend for

This approach is more accurate than the one described in Sect.III-A but has the disadvantage of necessitating a recursivesolution. This enhanced analytical modelling allows emulat-ing the E-SSA detector evolution for a given packet power

distribution assuming that the sliding window memory is longenough to avoid the impact of the memory edge effects. Withthe enhanced E-SSA I-SIC model, it is possible to analyticallyderive the E-SSA detector SNIR for all packets ρj(Niter)for j = 1, 2, · · ·K for an arbitrary power distribution. Ifthe condition ρj(Niter) ≥

[EsNt

]FEC

is satisfied, then we canconsider that for the current K packet load the detection of allthe packets has been possible with a PLR ≤ Φ

([EsNt

]FEC

).

This makes it possible evaluating the maximal E-SSA ASR,the associated PLR and the required number of detectoriterations for any arbitrary packet power distribution.

IV. OPTIMIZED RANDOM ACCESS ACHIEVABLE SUMRATE RESULTS

In this section we report the E-SSA ASR when using thepacket power distribution optimization methodology describedin Sect. III-A and Sect. III-B. Results are compared to thetheoretical bounds summarized in Sect. II. In particular, werecall that the E-SSA physical layer is closely derived fromthe terrestrial 3GPP Wideband CDMA standard [7]. Thus theturbo FEC coding rate is r = 1/3 and the modulation is binaryi.e. M = 2. Clearly Eb/N0 = [Es/N0]/(r log2M).

A. Optimized Packet Power Distribution Results

Fig. 1 shows the E-SSA demodulator incoming packetsoptimum power distribution using the exact solution of thesystem of equations (7) (straight line), the recursive solution of(9) (dashed line) and the one obtained by randomly generatingthe incoming packets power according to a uniform in dB dis-tribution (dashed-dot line) in the range

[[EbN0

]min

,[EbN0

]max

]according to (10). The practical approach, using randomindependent generation of packets, closely approximates theoptimum power distribution. This method has the advantageof not requiring any real-time coordination among terminalsfor setting their transmit power. The larger the number ofsimultaneously received packets is, the higher is the accuracyof approximating the overlap factors α(i, j) with their averagevalue. As the number of simultaneous incoming packets sup-ported is proportional to the spreading factor, the accuracy ofthe model depends on the spreading factor. For instance, forLw = 256 the standard deviation for the difference betweenthe optimum power distribution provided by (7) and (10) is0.05 dB. Reducing the spreading factor to Lw = 8 the standarddeviation of the difference grows to 0.3 dB. This type oferror causes fluctuations on PLR values which can preventthe I-SIC process to converge. At E-SSA maximum ASR, theprobability of I-SIC not converging is negligible for a packetpower distribution error standard deviation less than 0.1 dB. Iflarger than that, operations too close to the maximum E-SSAASR limits shall be avoided.

B. Achievable Sum Rate and Packet Loss Ratio Results

1) Without IC Residual Interference: In this section wereport the E-SSA ASR results for the optimized packet powerdistribution derived in Sect. III-A when no residual IC poweris present (i.e. β = 0). In order to verify the E-SSA I-SIC

6

demodulator analytical model accuracy, E-SSA demodulatorsimulations with the optimized uniform in dB packet powerdistribution have been compared to the iterative analyticalmodel described in Sect. III-B. In particular, Fig. 2 showsthe PLR versus the RA average MAC load assuming Poissontype of traffic, [Eb/N0]min = 2 dB and [Eb/N0]max =6, 9, 12, 20 dB. Fig. 2 results confirm the good matchbetween simulations and E-SSA I-SIC modelling describedin Sect. III-B. Note that the PLR shows a floor because weselected the FEC SNIR threshold

[EsNt

]FEC

to ensure that

for the worst-case packet detected Φ([

EsNt

]FEC

)= 10−3.

Looking at Fig. 2 we observe that the floor is always belowthe target PLR of 10−3 with a value dependent on theincoming packets power range randomization. Fluctuationsof the simulated floor results are due to the PLR statisticaluncertainty. The PLR floor level can be analytically predictedas:

PLRfloor

([EsN0

]min

,

[EsN0

]max

)=∫ [Es

N0

]max[

EsN0

]min

Φ (γ) pΓ(γ)dγ

pΓ(γ) =

1ζ γ for

[EsN0

]min≤ γ ≤

[EsN0

]max

0 elsewhere

ζ = ln

10 log10

[EsN0

]max

− 10 log10

[EsN0

]min

, (16)

where pΓ(γ) is the probability density function (PDF) of thereceived packets

[EsN0

](linear) when the received packets are

characterized by an uniform power distribution in dB in therange

(10 log10

[EsN0

]min

, 10 log10

[EsN0

]max

). It is remarked

that, although the packets have an exponential power profile,the linear PDF has a 1/γ dependency in the range of interest.Fig. 3 compares the E-SSA ASR versus the capacity boundsderived in Sect. II (unconstrained and R-CDMA constrainedto FEC code rate r = 1/3) as well as the CDMA SIC boundfrom (III.4) in [14] as a function of the [Eb/N0]sys whenthe packet power is randomized according to the approachdescribed in Sect. III-B. We notice a good match with an errorup to 10 % between the analytical ASR estimation based onthe Sect. III-B findings and the E-SSA Monte Carlo simulationresults. The performance using the simplified model describedin Sect. III-A is also shown in Fig. 3 but, as expected, resultsare less accurate. The E-SSA [Eb/N0]sys distance from ther = 1/3 CDMA with SIC capacity bound [14] is 4 dB at2 bits/chip ASR and it gets larger for higher values of ASR.This performance gap can be partially explained by the factthat the simulated, packet size is limited to 100 bits and afinite number of iterations (10) was adopted so as to avoidunduly long simulation run times. The impact of the E-SSAFEC code packet size on the RA ASR can be observed in Fig.4. For the FEC block size of 5100 bits at a ASR of 2 bits/chipthe E-SSA distance from the CDMA with SIC FEC rate 1/3constrained bound is reduced to less than 3 dB.

2) With IC Residual Interference: In this section we extendthe analytic model validation to the case where the E-SSA I-

SIC process is not ideal i.e. β 6= 0. For this purpose the E-SSA laboratory prototype described in [8] has been exploited.Experimentally it was found that the residual IC power cancel-lation factor β is slightly dependent on the actual Es/Nt. Forthe analytical results a value β = 0.008 has been chosen beingrepresentative of the worst-case implementation performance[8]. The other key system parameters are the spreading factorLw = 256 and the 3GPP FEC code rate r = 1/3 withblock size B = 1200 bits. The E-SSA demodulator measuredperformance has been compared to the iterative analyticalmodel defined by (14). In particular, Fig. 5 shows the PLRversus the RA average MAC load assuming Poisson type oftraffic, [Eb/N0]min = 2 dB and [Eb/N0]max = 6, 9, 12, 20dB. The PLR floor visible in this figure is appearing for similarreasons to the ones discussed in Sect. IV-B1. Fig. 6 shows theE-SSA ASR versus the Sect. II capacity bounds (unconstrainedand R-CDMA constrained to FEC code rate r = 1/3) and theCDMA with SIC one from (III.4) in [14] as a function of the[Eb/N0]sys when the packet power is randomized accordingto the approach described in Sect. III-B. We notice a prettygood match (error less than 6 %) between the analytical ASRestimation based on the Sect. III-B findings and the E-SSAlaboratory measurement results [8]. The semi-analytic E-SSAASR curve drops to zero when

[EbN0

]sys

is below the FEC

Eb/N0 threshold corresponding to the required PLR target.The simplified model described in Sect. III-A is also shownin Fig. 6 confirming the lower model’s accuracy (error up to13 %). The E-SSA ASR dependency on the residual IC powerfactor β is presented in Fig. 7. It is apparent that the ASRloss at [Eb/N0]sys = 10 dB is limited to 9 % for β ≤ 0.01.Finally, the required maximum number of E-SSA demodulatorI-SIC iterations Niter for achieving a PLR≤ 10−3 has beenanalytically derived following the model described in Sect.III-B for the case [Eb/N0]max = 10 dB. Looking at Fig. 8 itis remarked that for a packet size of 100 bits the number ofrequired iterations grows rapidly to 30 when approaching anaverage MAC load of 2 bits/chip.

C. Overall Packet Power Distribution Optimization Strategy

In this section we investigate the E-SSA RA performancedependency on some key system parameters exploiting thesemi-analytical methodology developed in Sect. III-B. Previ-ous results showed that when extra link margin is available,extra ASR may be achieved using the formerly developedpacket power distribution optimization. It is therefore interest-ing to understand how the RA ASR is affected by the choiceof the power randomization range. Fig. 9 illustrates the RAASR dependency on the [Eb/N0]max value when limiting thepackets’ power dynamic range below the optimum one. This istypically caused by the terminal radio frequency (RF) power orby the demodulator dynamic range limitations. The reductionof the packet power dynamic range generates an asymptote inthe E-SSA ASR when increasing [Eb/N0]max. This is origi-nated by the E-SSA demodulator I-SIC processing limitations.More complex joint MUD detection algorithms are expected toprovide higher ASR in the presence of equi-powered packetsat the expense of greater demodulator complexity.

7

We now investigate the RA ASR dependency on the[EbN0

]min

value when the[EbN0

]max

value is constrained bysystem design aspects. An example of such dependency isshown in Fig. 10 where

[EbN0

]max

= 15 dB has been assumed.More precisely Fig. 10-a refers to the case of β = 0. Inthis case the highest ASR is obtained for

[EbN0

]min

= 1 dBwhich corresponds to the FEC threshold for the target PLR of10−3. Reducing the packets dynamic range by increasing thevalue of

[EbN0

]min

the RA ASR monotonically decreases. Asshown in Fig. 10-b, when β = 0.05 the maximum RA ASRis obtained for

[EbN0

]min

= 5 dB which is well above the FECthreshold. Thus, differently from the β = 0 case, there is nota monotonic RA ASR dependency on the

[EbN0

]min

value. Theimportant conclusion of this analysis is that the region insidethe ASR polygon versus

[EbN0

]min

shown in Fig. 10 ensuresthat the target PLR will be achieved. However, to ensure astable system operation it is best to keep a certain distancefrom the polygon boundaries. Thus, for practical demodulatorsfor which β 6= 0, assuming a given value of

[EbN0

]max

by

the system design, the[EbN0

]min

value has to be adaptedaccording to the current MAC load. A possible pragmaticapproach for a given system operating ASR, is to select[EbN0

]min

as the numerical average between the values obtainedby the intersection of an horizontal line corresponding to thecurrent system ASR with the ASR polygon (continuous line)shown in Fig. 10-b

[EbN0

]min

curve; the resulting values arerepresented by the dashed line in Fig. 10-b. This approach willguarantee the maximum robustness of the system operationagainst possible packet power level errors (e.g. due to linkbudget uncertainties) or due to average traffic level variationfrom the expected one.

V. SATELLITE RANDOM ACCESS SYSTEM STUDY CASE

A. System Architecture

In order to assess the practical advantages of packet powerdistribution optimization the case of a Ka-band (30 GHz)geostationary multibeam satellite system has been investigated.The satellite has an European coverage obtained through 80beams with the antenna gain pattern shown in Fig. 11. Thekey RA parameters required to perform the system levelperformance assessment are listed in Table I. In particular, theE-SSA physical layer parameters representing an adaptationof the S-MIM ETSI standard [7] have been listed. The maindeviation from S-MIM is represented by the possibility toincrease the user bit rate Rb (80 kbps instead of 10 kbps) whilereducing the spreading factor Lw (16 instead of 256). Theterminal RF power has been limited to 100 mW to minimizethe RF front-end cost while making possible the support ofthe bit rate Rb. The associated antenna size dish is limited to75 cm to ease its installation. The satellite key parameters arelisted in Table I. The clear sky path loss has been computedfor each coverage area location.

B. Packet Power Transmission Control Algorithm

We assume a fixed satellite RA network with a largepopulation of terminals scattered across the coverage area.The proposed Uplink Packet Power Transmission Control(UPPTC) has the following features: a) it is approximatelyachieving the optimum power distribution derived in (13) atthe gateway demodulator input even in the presence of fading,non-uniform satellite antenna gain pattern and terminal RFpower limitations; b) it is based on open loop power control;c) it does not require information about the individual terminalpower settings; d) it can be easily extended to support differentclasses of services. A fixed satellite access system will facetime and location dependent attenuation due to atmosphericfading and to the variability of satellite receive antenna gainand geometrical path loss. As the user link has to be sized forthe worst case link attenuation (geometry dependent path loss,satellite antenna gain and atmospheric loss for the requiredlink availability), it is of interest to exploit the intrinsic linkmargin to enhance the RA system ASR as discussed in-depthin the previous sections. The terminal Equivalent IsotropicallyRadiated Power (EIRP) shall be adapted to the required targetvalue which takes into account the various system parameters.Examples are the geometry dependent path loss, satelliteantenna gain and atmospheric loss in addition to the E-SSA parameters including the optimum power randomizationrange. The latter will require some terminal EIRP ”headroom”allowing to approximate the optimum power randomizationdistribution previously derived. The terminal EIRP headroomchoice is a compromise among achievable packet bit rate, RAASR and the terminal cost. The maximum EIRP has typicallya strong impact on the terminal cost and, for this reason,an upper limit denoted as [PEIRP]max is typically imposed.Consequently, it may happen that not all the terminals haveenough available EIRP headroom to achieve the optimumtheoretical power randomization range. In this case a subsetof the terminal population will operate with a sub-optimumrandomized power range. It is assumed no packet transmissionoccurs with negative link margins. The terminal power controlis operating in open loop4 thus not causing any unwanted sig-nalling overhead. Analytically at time t the proposed UPPTCalgorithm for terminal k can be expressed as a function of theMAC load G as5 [22]:

PEIRP(G, t, k) =

[PEIRP]optmin (G, t, k) ·R(G, t, k)if [PEIRP]max ≥ [PEIRP]optmax (G, t, k)

[PEIRP]optmin (G, t, k) ·R∗(G, t, k)if [PEIRP]optmin (G, t, k) ≤ [PEIRP]max

< [PEIRP]optmax (G, t, k)0 if [PEIRP]max < [PEIRP]optmin (G, t, k),

4A part from some low-rate broadcast system information on the forwardlink common to all terminals.

5The algorithm is performing a reverse link budget to estimate the requiredmin/max terminal EIRP to achieve the optimum [Eb/N0]min,max at the E-SSA demodulator input through the randomization power variable R. If theoptimum EIRP is above the terminal capability, a terminal power soft limitingtakes place.

8

[PEIRP]optmin, max (G, t, k) =

KB

Rb

[EbN0

]opt

min, max

(G)

· Lup(t, k)

[G/T ]SAT(k), (17)

with KB is the Boltzmann constant, Rb is the terminalbit rate,

[EbN0

]opt

min(G) and

[EbN0

]opt

max(G) are the optimum

minimum E-SSA demodulator operating Eb/N0 derived asdescribed in Sect. IV-C and Lup(t, k) is the current uplinkattenuation for terminal k at time t estimated from the down-link received power and [G/T ]SAT(k) is the satellite receiveantenna G/T towards terminal k. The system parameters[EbN0

]opt

min(G),

[EbN0

]opt

max(G), Rb and [G/T ]SAT(k) are known

to the terminals (either stored or broadcasted in the forwardlink). Finally, the rv R(G, t, k) is uniformly distributed indB in the range

[0, 10 log10

[PEIRP]opt

max(G,t,k)

[PEIRP]optmin

(G,t,k)

]and the

rv R∗(G, t, k) is uniformly distributed in dB in the range[0, 10 log10

[PEIRP]max

[PEIRP]optmin

(G,t,k)

]. The system designer should

adapt the system parameters to ensure that the percentage ofterminals having a reduced power randomization range is smallenough (e.g. ≤ 20 %) not to cause significant impact on theoverall system ASR. If not the system can force all terminalsto work with a higher spreading factor by broadcasting thisparameter in the forward link. As a consequence, the individualterminal bit rate will be reduced at the advantage of anincreased system ASR.

C. Numerical Results

For the satellite system study case described before, Fig. 12-a shows the simulated PDF for the received packet Eb/N0

with and without (constant EIRP) UPPTC. The UPPTC furtherextends the power randomization range and, hence makes itcloser to the optimum (uniform in dB) received packet powerdistribution. Fig. 12-b shows the simulated PLR dependencyon the MAC average load G with or without optimized powercontrol according to the UPPTC algorithm described in (17).The system level simulations assumed a conservative β = 0.03

value,[EbN0

]opt

min, max= 2, 16 dB, and a uniform terminal

distribution in the coverage region. The advantage of theUPPTC algorithm optimizing the packet power distributionis evident as it brings a remarkable 85 % ASR improvement.Note that this improvement takes into account that withoutUPPTC there is already a 4 dB power spreading range due tothe difference in antenna gain and path loss for the differentlocations within the satellite coverage.

VI. CONCLUSIONS

In this paper we derived a semi-analytic approach for opti-mizing in a totally uncoordinated fashion the packet power dis-tribution of a E-SSA-based Random Access system. Analyticalfindings have been compared to simulation and experimentalresults. Optimized E-SSA RA ASR has been compared tothe relevant capacity bounds. Thanks to the proposed packetspower optimum randomization methodology, the theoretical

capacity bounds can be closely followed for a much widerrange of system signal-to-noise ratios compared to a systemnot exploiting this technique. The open-loop packet powerrandomization scheme can be easily implemented in practicalsystems without extra signalling that would be needed byclosed-loop power control schemes. The large system-leveladvantage of the proposed packet transmission technique hasbeen demonstrated in a broadband geostationary multi-beamsatellite study case.Acknowledgement: The authors would like to thank the Asso-ciated Editor, the anonymous reviewers, the colleagues AlbertoMengali, Pantelis-Daniel Arapoglou and Guray Acar for theirsuggestions on how to improve the manuscript.

REFERENCES

[1] E. Casini, R. De Gaudenzi and O. del Rıo Herrero,“Contention ResolutionDiversity Slotted Aloha (CRDSA): an Enhanced Random Access Schemefor Satellite Access Packet Networks,” IEEE Transactions on WirelessCommunications, vol. 6, no. 4, pp. 1408-1419, April 2007.

[2] O. del Rıo Herrero, R. De Gaudenzi,”High Efficiency Satellite MultipleAccess Scheme for Machine-to-Machine Communications,” IEEE Trans.on Aerospace and Electronic Systems, vol. 48, no. 4, October 2012, pp.2961-2989.

[3] “Machine-to-Machine Technologies & Architectures,” IEEE Communica-tions Surveys & Tutorials, vol. 16, no. 1, First Quarter 2014.

[4] L. Atzoria, A. Ierab, G. Morabito,“The Internet of Things: A Survey,”Elsevier Computer Networks, vol. 54, issue 15, 28 October 2010, pp.2787-2805.

[5] R. Lasowski and C. Linnhoff-Popien,“Beaconing as a Service: A NovelService-Oriented Beaconing Strategy for Vehicular ad-hoc Netowrks,”IEEE Communications Magazine, vol. 50, no. 10, October 2012, pp. 98-105.

[6] ETSI EN 301 545-2 V1.1.1 (2012-01) Digital Video Broadcasting (DVB);Second Generation DVB Interactive Satellite System (DVB-RCS2); Part2: Lower Layers for Satellite Standard.

[7] ETSI Technical Specifications, Air Interface for S-band Mobile InteractiveMultimedia (S-MIM), Part 1, 2, 3 TS 102 721-1, 2, 3.

[8] M. Andrenacci, G. Mendola, F. Collard, D. Finocchiaro, A. Recchia,“E-SSA Demodulator Implementation, Laboratory Tests and Satellite Vali-dation,” to appear on Wiley International Journal of Satellite Communi-cations and Networking, 2014.

[9] G.E. Corazza, S. Cioni, R. Padovani, “Application of Closed LoopResource Allocation for High Data Rate Packet Transmission,” IEEETransactions on Wireless Communications, vol. 6, no 11, November 2007,pp. 4049-4059.

[10] R. De Gaudenzi, O. Del Rıo Herrero,“Advances in Random Access Pro-tocols For Satellite Networks,” 2009 International Workshop on Satelliteand Space Communications (IWSSC 2009), Siena, Italy September 9-11,2009, pp. 331-336.

[11] J. Hou, J. E. Smee, H. D. Pfister and S. Tomasini,“ImplementingInterference Cancellation to Increase the EV-DO Rev. A Reverse LinkCapacity,” IEEE Comm. Magazine, February 2006, pp. 96-102.

[12] N. Franzen,“Comparison of Coordinated and Uncoordinated PHY/MACSchemes For Beaconing,” in Proc. 27th IET and AIAA Digital AvionicsSystem Conference (DASC), Williamsburg, VA, October 2012.

[13] P. Patel and J. Holtzman, “Analysis of a Simple Successive InteferenceCancellation Scheme in a DS/CDMA System,” IEEE Trans. on Sel. Areasin Comm., vol. 12, no. 5, June 1994, pp. 796-807.

[14] A. J. Viterbi, “Very Low Rate Convolutional Codes for MaximumTheoretical Performance of Spread-Spectrum Multiple-Access Channels,”IEEE Journal on Sel. Areas in Comm., vol. 8, no. 4, May 1990, pp. 641-649.

[15] G. Caire, S. Guemghar, A. Roumy, S. Verdu, “Maximizing the SpectralEfficiency of Coded CDMA Under Successive Decoding,” IEEE Trans.On Information Theory, vol. 50, no. 1, January 2004, pp. 152-164.

[16] G. Caire, R. R. Muller, T. Tanaka,“Iterative Multiuser Joint Decoding:Optimal Power Allocation and Low-complexity Implementation,” IEEETrans. On Information Theory, vol. 50, no. 9, Sept. 2004, pp. 1950-1973.

[17] F. Collard, “Study and Optimization of E-SSA Protocol, a High Ef-ficiency Multiple Access Scheme for Satellite Communication,” PhDThesis, Institut Superieur de l’ Aeronautique et de l’ Espace, Toulouse,September 2014.

9

[18] C. Schlegel, Z. Shi, M. Burnashev,“Optimal Power/rate Allocation andCode Selection for Iterative Joint Detection of Coded Random CDMA,”IEEE Trans. On Information Theory, vol. 52, no. 9, September 2006, pp.4286-4294.

[19] J. G. Andrews, and T. H. Meng,“Optimum Power Control for SuccessiveInterference Cancellation With Imperfect Channel Estimation,” IEEETrans. on Wireless Comm., vol. 2, no. 2, March 2003, pp. 375-383.

[20] S. Verdu and S. Shamai, “Spectral Efficiency of CDMA with RandomSpreading,” IEEE Transact. On Information Theory, vol. 45, no. 2, pp.622-640, March 1999.

[21] O. del Rıo Herrero, R. De Gaudenzi, J. L. Pijoan Vidal, “DesignGuidelines for Advanced Random Access Protocols,” In Proc. of the30th AIAA International Communications Satellite Systems Conference,September 24-27, 2012, Ottawa, Canada.

[22] R. De Gaudenzi, “Optimization of the Packets Power Distribution inSpread Aloha Random Access/Code Division Multiple Access SystemsExploiting Successive Interference Cancellation Detector,” PCT PatentFiling no. PCT/IB2013/00547, March 2013.

10

Physical layer parameters Symbol Unit ValueBit rate Rb kbps 80FEC coding rate r - 1/3Packet block size (info bits) bits 1200Symbol rate Rs kbaud 240Spreading factor Lw - 16Chip rate Rc Mcps 3.84Roll-off factor - 0.22Pilot/data power ratio dB -10Signal bandwidth MHz 4.68Terminal parameters Unit ValueTx Carrier frequency GHz 29.75High Power Amplifier saturated power W 0.1Antenna diameter m 0.75Antenna gain dBi 43Maximum Effective Isotropic Radiated Power dBW 33.0Antenna pointing losses dB 1.39Real Effective Isotropic Radiated Power dBW 31.6Satellite parameters Unit ValueOrbital location degrees E 9Antenna gain dBi see Fig. 11Receiver front-end equivalent noise temperature dBK 31

TABLE IMULTI-BEAM KA-BAND SYSTEM STUDY CASE PARAMETERS.

11

0 100 200 300 400 500 600 700 800 900 10002

2.5

3

3.5

4

4.5

5

5.5

6

Ranked packet number

Rec

eive

d pa

cket

s [E

b/N0] (

dB)

Optimal distribution: equation (7) Approximate distribution: equation (10)Uniform distribution in dB: equation (11)

(a) Lw = 256

0 5 10 15 20 25 30 35 40 45 501.5

2

2.5

3

3.5

4

4.5

5

Ranked packet number

Rec

eive

d pa

cket

s [E

b/N0] (

dB)

Optimal distribution: equation (7)Approximate distribution: equation (10)Uniform distribution in dB: equation (11)

(b) Lw = 16

Fig. 1. Comparison of optimum (7) and approximate (10-11) E-SSA incom-ing packets demodulator power distributions for β = 0.05: [Eb/Nt]FEC = 2dB, [Eb/Nt]I−SIC = 1 dB: a) Lw = 256, b) Lw = 16.

0 1 2 3 4 5 610

−5

10−4

10−3

10−2

10−1

100

Average MAC Load [bits/chip]

PLR

Eb/N

0]max

=6 dB analytical

[Eb/N

0]max

=9 dB analytical

[Eb/N

0]max

=12 dB analytical

[Eb/N

0]max

=20 dB analytical

[Eb/N

0]max

=6 dB simulation

[Eb/N

0]max

=9 dB simulation

[Eb/N

0]max

=12 dB simulation

[Eb/N

0]max

=20 dB simulation

Fig. 2. E-SSA analytical (enhanced I-SIC model) and simulated PLRvs average MAC load for Poisson type of traffic and various values of[Eb/N0]max: BPSK modulation, 3GPP FEC r = 1/3, packet block size100 bits, [Eb/N0]min = 2 dB, Niter = 10, β = 0.

−2 0 2 4 6 8 10 12 140

1

2

3

4

5

6

7

8

[Eb/N

0]sys

[dB]

Cap

acity

/ A

chie

vabl

e S

um R

ate

(AS

R)

[bits

/chi

p]

Capacity AWGN Shannon boundCapacity CDMA with SIC bound (r=1/3) from [14]ASR E−SSA enhanced I−SIC model (r=1/3, B=100 bits) ASR E−SSA simulation results (r=1/3, B=100 bits)ASR E−SSA simplified I−SIC model (r=1/3, B=100 bits)Capacity R−CDMA bound (r=1/3) from (3)

Fig. 3. Capacity bounds comparison with the E-SSA analytical (simplified andenhanced I-SIC models) and simulated achievable sum rate with optimizedpacket randomization range for Poisson type of traffic as a function of[Eb/N0]sys: BPSK modulation, 3GPP FEC r = 1/3, packet block size 100bits, Niter = 10, β = 0.

12

−2 0 2 4 6 8 10 12 140

1

2

3

4

5

6

7

8

[Eb/N

0]sys

[dB]

Cap

acity

/ A

chie

vabl

e S

um R

ate

(AS

R)

[bits

/chi

p]

Capacity AWGN Shannon boundCapacity CDMA with SIC bound (r=1/3) from [14]ASR E−SSA enhanced I−SIC model (r=1/3, B=100 bits)ASR E−SSA enhanced I−SIC model (r=1/3, B=1200 bits)ASR E−SSA enhanced I−SIC model (r=1/3, B=5100 bits)Capacity R−CDMA bound (r=1/3) from (3)

Fig. 4. Capacity bounds comparison with the E-SSA analytical (enhanced I-SIC model) achievable sum rate with optimized packet randomization rangefor Poisson type of traffic as a function of [Eb/N0]sys: BPSK modulation,3GPP FEC r = 1/3, for various packet block sizes, Niter = 10, β = 0.

0 1 2 3 4 5 6

10−4

10−3

10−2

10−1

100

Average MAC Load [bits/chip]

PLR

[Eb/N

0]max

=6 dB analytical

[Eb/N

0]max

=9 dB analytical

[Eb/N

0]max

=12 dB analytical

[Eb/N

0]max

=20 dB analytical

[Eb/N

0]max

=6 dB measurement

[Eb/N

0]max

=9 dB measurement

[Eb/N

0]max

=12 dB measurement

[Eb/N

0]max

=20 dB measurement

Fig. 5. E-SSA analytical (enhanced I-SIC model) and measured PLRvs average MAC load for Poisson type of traffic and various values of[Eb/N0]max: BPSK modulation, 3GPP FEC r = 1/3, packet block size100 bits, [Es/N0]min = 2 dB, Niter = 10, β 6= 0.

−2 0 2 4 6 8 10 12 140

1

2

3

4

5

6

7

8

[Eb/N

0]sys

[dB]

Cap

acity

/ A

chie

vabl

e S

um R

ate

(AS

R)

[bits

/chi

p]

Capacity CDMA with SIC (r=1/3, β=0.01) from [14]ASR E−SSA enhanced I−SIC model (r=1/3, B=1200 bits, β−0.01)ASR E−SSA demodulator measurements (r=1/3, B=1200 bits, β ∼ 0.01)Capacity AWGN Shannon boundCapacity CDMA with SIC bound (r=1/3, β=0) from [11]ASR E−SSA simplified I−SIC model (r=1/3, 1200 bits, β−0.01)Capacity R−CDMA bound (r=1/3) from (3)

Fig. 6. Capacity bounds comparison with the E-SSA analytical (simplified andenhanced I-SIC models) and measured achievable sum rate with optimizedpacket randomization range for Poisson type of traffic as a function of[Eb/N0]sys: BPSK modulation, 3GPP FEC r = 1/3, packet block size 1200bits, Niter = 10, β = 0.01.

0 5 10 150

1

2

3

4

5

6

7

8

[Eb/N

0]sys

[dB]

Cap

acity

/ A

chie

vabl

e S

um R

ate

(AS

R)

[bits

/chi

p]

ASR E−SSA enhanced I−SIC model (r=1/3, B=5114 bits, β=0)ASR E−SSA enhanced I−SIC model (r=1/3, B=5114 bits, β=0.008)ASR E−SSA enhanced I−SIC model (r=1/3, B=5114 bits, β=0.008)ASR E−SSA enhanced I−SIC model (r=1/3, B=5114 bits, β=0.05)Capacity AWGN Shannon boundCapacity CDMA with SIC bound (r=1/3, β=0) from [14]Capacity R−CDMA bound (r=1/3) from (3)

Fig. 7. Capacity bounds comparison with the E-SSA analytical (enhanced I-SIC model) achievable sum rate with optimized packet randomization rangefor Poisson type of traffic as a function of [Eb/N0]sys: BPSK modulation,3GPP FEC r = 1/3, for packet block size 5114 bits, Niter = 10, variousvalues of β.

13

0 0.5 1 1.5 2 2.510

0

101

102

MAC Average Channel Load [bits/chip]

Num

ber

of S

IC it

erat

ions

input block size 5100 bitsinput block size 100 bits

Fig. 8. E-SSA required number of iterations for achieving a PLR≤ 10−3

with optimized packet randomization range for Poisson type of traffic as afunction of the MAC average channel load G: BPSK modulation, 3GPP FECr = 1/3, for various packet block sizes, [Eb/N0]max = 10 dB. Resultsobtained using the enhanced I-SIC model.

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

[Eb/N

0]max

[dB]

Ach

ieva

ble

Sum

Rat

e (A

SR

) [b

its/c

hip]

Pmax

−Pmin

=0 dB

Pmax

−Pmin

=3 dB

Pmax

−Pmin

=6 dB

Pmax

−Pmin

=9 dB

Pmax

−Pmin

=12 dB

Fig. 9. E-SSA analytical achievable sum rate with optimized packet random-ization range as a function of the [Eb/N0]max: BPSK modulation, 3GPP FECr = 1/3, B = 100 bits for various values of Pmax − Pmin, Niter = 10,β = 0.05. Results obtained using the enhanced I-SIC model.

0 2 4 6 8 10 12 14 160

0.5

1

1.5

2

2.5

3

3.5

[Eb/N

0]min

[dB]

Ach

ieva

ble

Sum

Rat

e (A

SR

) [b

its/c

hip]

Proposed [Eb/N

0]min

versus E−SSA ASR

E−SSA operating region boundaries

(a) β = 0

0 2 4 6 8 10 12 14 160

0.5

1

1.5

2

2.5

Ach

ieva

ble

Sum

Rat

e (A

SR

) [b

its/c

hip]

[Eb/N

0]min

[dB]

E−SSA operating region boundariesProposed [E

b/N

0]min

versus E−SSA ASR

(b) β = 0.05

Fig. 10. E-SSA analytical achievable sum rate with optimized packetrandomization range as a function of the [Eb/N0]min: BPSK modulation,3GPP FEC r = 1/3, B = 100 bits, [Eb/N0]max = 15 dB, Niter = 10,different values of β. Results obtained using the enhanced I-SIC model.

14

Fig. 11. Satellite receive multibeam antenna gain (dBi) over the Europeancoverage.

0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

0.3

Received packets [Eb/N

0] [dB]

PD

F

With UPPTC algorithmWithout UPPTC algorithm

(a) Incoming packets Eb/N0 PDF

0 0.5 1 1.5 2 2.5 310

−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Pac

ket L

oss

Rat

io (

PLR

)

MAC Average Load (G) [bits/chips]

With UPPTC algorithmWithout UPPTC algorthm

(b) PLR versus Average MAC Load

Fig. 12. Multi-beam satellite system performance with or without the UPPTC:a) E-SSA incoming demodulator packets [Eb/N0] PDF with and without theUPPTC; b) E-SSA PLR dependency on the average MAC load with andwithout the UPPTC algorithm as per (17).