~ Simulutiun: The BER performance against the parametcr L i s simulated and shown iii Fig. 2. It is noted that when L i s infinitc, thc BER curve with the proposed algorithm is identical to that with coherent demodulation. As L = 30, the performance closely approaches that of coherent dcmodulation. When I, = IO, the proposed algorithm exhibits Icss than O.3dB degradation compared with coherent demodulation. We also notc that the algorithm prcscntcd in [3] is excellent, although its perfoimance can be furthcr improved by the usc of ow ncw algorithm, even with a value of L as small as 10. Fig. 3 dcmonstl-ates the performance or the proposed algorithm undcr thc condition of carrier frequency offsets. In this siniulation, L has a value of 10. It is shown that, cvcn with a small value OS L, the algorithm pcrfornis reasonably well under small frequency offSCtS. Chclusion: We present a new Viterbi-type algorithm for thc burst detection of QAM with unknown carricr phase. This algorithm employs thc innst rcccnt L symbols of the received sequence, leading to a rcasonably good performance even with small values of L. Specifically, we found by siniulation that, as L = IO, a reasonable trade-off can he found between thc implcmenlation complexily and the systcm pcrformancc undcr the condition of unknown phase andlor carricr frcqucncy offscts. Bvuluution model,for C-BI'SK: When two or more packets arrivc at about thc sanic timc, a practical coherent narrow-band rcccivcr is likcly to lock its carricr onto the strongest sigiial rather than onc that is randomly selected [4] or arrives firs1 [5]. The carrier lock will, however, not be stable unless lhe carricr-to-intcrference ratio (Cil) is suflicienlly high. Thus successful capture by a receiver can be defined as the reception of the strongest packcl without bit crror whilc tlic carrier-sync remains stable. pr&tically :, howcvcr, thcrc is no sharp bordcr of C/1 above which thc carricr-sync will rcmain stable and below which it will not. It is assumcd hcrc that the carrier-sync can bc acquircd and rcmain stablc with ii probability of P y ( s i ) for a givcii sj = W,/Z,, &., where U; is the power of lhe locked source, 4,&.the power sum of [lie other sources, and xj is referred to as the effective C/I for the.jth source. The bit error probability determined by thc bit dccision proccss fluctuates from bil lo bil because of the arbitrariness of the modulating data, cven if the amplitudes and phase offsets remain unchanged over a packet period (referred to 8s slow-fading assumption). Let P,,<,?(n)dcnotc thc probability (rcferred to a s capture probability) that any one of ;packets in collision is decoded without bil error after maintaining carrier lock. Assuming a common power dislributioii of sources, we may write Acknowlcdgment: This work was supported by the National Fundamental Rcscarch Projecl (G1998010410). 0 IEE I999 I October 1999 El<mronir,sLetters Onihie Nm 19991422 Dol: IO. I04Y/el:I99P1422 Jin Zhtmg, Shuoliang Mei, Jianhua Lu and Jun Gu (Dcpnrlinenr nf Elcecrrowic Enp;incering, Triii&a Univer,sily, Beiji,ig, 101~084,l'eoplc'~~ Republic of C l h a ) References over the Gaossian chamcl with unknown CBI tier phase', IEEE Tron.~.Conzn~u,~., 1987, COM-35, pp. 764-767 DIVSALAR, D., and SIMON. M.K.: 'Multiple-symhol differelllial detection of MPSK, IEEE Trotis. Cu,n,nun., 1990, 38, p p 300-308 COI,AVOI.I'F, c;., and RARTLI. R.: 'On iioncohcrcnt scqucncc detection of coded OAM', IEEE Cornmin. Lclf., 1998, 2, .PP. . 211-213 I'ROAKIS, J 'Digital communicalions' (McCraw-Hill, Ncw York, 1993). 3rd edn. ~ whcrc PI,[/<]is thc crror probability of thc /Mi bit, Ph tlic bit error rale, L the packet size (bits), and f()the probabilily density funclion of the effective C/I. D~terminutionof PI,: If the slrongesl signal rcmaiiis in phase and the others have a uniform distributed random phase offset 8, (0 5 Bra < 2n), then the sum of these signals is, aftcr the integrator of a C-BPSK dctector where d,, (= d,[k])denoles llie Iclh modulating bit (+1 for BPSK) of thc ith signal, and Ajk is thc kth amplitude of the ith signal. The last item of equ 2 is a Gaussian pi-ocess with a bandwidth of 2/T,, (wherc 7; is bit duration) and a powcr spcctrum dcusity oC Nd2. Using the slow-fading assumption and assuming that the iiilerrering signals have a wiform-distributed random bit-sync offset a, (0 < aj 5 I), we have a sampled value p; = A , d ~ ^ k + C A r ( d , ( k ~ ] ) ~ i + d , -8U( % I ) ) cos H,+ac cospc if3 (3) and modelling for coherent Assuming an equal probability of the data schcme, we can identify W. Ren, J.W. Ward, S. Hodgart aiid M.N. Sweeling An evaluation model of the capture effccl is proposcd Cor coherent BPSK (C-UPSK) demoddatian. by which the capture effect is investigated in the low carth orbit (LEO) v~tellitechannel imd thc resulting incrcasc in thrauglrput of slotted ALOHA for C-BPSK dcniodnlation, whcrc y cqiials A, i#j proLocols is dcrnonstratcd. Y= Introduction: When data packcts compcting for access to a radio receiver arrivc with diffcrenl power levels, the strongest packet may be able to capture a discriminating receiver. This capture efrecl can generate a much higher throiighpul for random access protocols, c.g. slotted ALOHA protocols, lhan suggcsted by tlic classical analysis in ideal channels [l]. This rcsult is of significance to the research in land niobilc channcls [Z 61. In this Leller, we address the capturc cffcct dcdicdtcd to C-BPSK demodulation. We realistically account for this aspect of B coherent radio recciver rather than make an ideal assumption [4 61, and cousequeutly dcrive a morc accurate evaluation model. The modcl is iiscd to examine the capture effecl in a specific LEO satcllitc channel wherc thc slow-fading assumplion applies. 1 + CAi(d,(p-,)(~,+d,8(l-c~i))co~H, (ZNol7i) (6) Averaging eqn. 4 over one packet will result in PI,, which is conditioned upon A,, A. Elj aiid a,. ~ ~ ELECTRONICS LETTERS 25th November 1999 Vol. 35 No. 24 2079 Result uiid di,.rcm.rion:We examine the capture cffcct in an LEO satcllitc channel using the proposcd model. In order to modcl .fl.), the propagalion model of LEO channcl proposcd by Coram ef U/. [7] is adopted, along with the link loss variation obtained from a UoSAT satellite [8].This model assumcs the signal amplitude to be Rice distributed, along wilh lognormal shadowing supcrimposed on both direct and difusc components. The filding and shadowing stalislics vary with elevation angle, cxpressed with three empirical formulae. The complexity of thc propagation model and inon-closed foim of the link loss pattcrn prevent an analytical solution. Thus Montc Carlo simulalion is execotcd to generate A,, A , 9 . aiand &. The in eqn. 1 is presumably assumed to havc thc shapc 0.9 0.8 .$ 0.7 3 0.6 0 h 0.5 ' e a 0.4 0.3 0.2 0.1 0 P,(z) = 1 2 3 4 5 6 7 8 simultaneously transmined packets 10 9 a 0.7 1 0.6 0.5 5, Y c 0.4 E 0.3 0.2 {: (z z ~ ~ a)/(b - a ) a 5 % a 5 I, (9) x>o The number of pilckets offcrcd to a receiver is assumed to bc Poisson dislributed with mean G pcr time slol. If slotted ALOHA protocols are considered, thc throughput with capture is Fig. 2 plots P,tt,c(n)iis a funclion of 11, and Fig. 3 shows the resulting throughput of slolted ALOHA. In thc Figures, SNR is defined tis A,,?/(ZA'd?iJ, where A,, is the rcccivcd amplitude of lhe sigiiill coming from an elevation angle of 10" rcgardlcss ol' signal rading. lncrcasing thc SNR generally improves the cilpturc probability. A relatively large link margin can result in a considerably enhanced capture probability, and conscqucntly bcnefil slotted ALOHA pi-otocols with a substantial throughput improvement. The simplified model generatcs a lower estimate l o the performancc, since the sum of the intcrfcring signals is actually neither Gaussian nor independent from bit lo bit when ii is not Iargc. But when n + 4,thc central limit theorem holds, i.e. the sum agrees with Gauss-(listribiition. 0.1 U- 0 1 2 3 4 5 6 7 6 mean olfered load, packetlslot 9 10 Fig. 3 Re,wlting throughput qf.slorlcd AI.OHA pro1ocol.s no ci,ptore A SNR = 20 dB + SNR = I5 dL1 SNR = 12 d B X. SNR = 10 d B X ~ sirnolified mudel References Simplifed model: The ith interfcring packet has a peak powcr of ( A ; ~ o s B , ) ~a1/ 2the input to sampling/holding (SIH) (see Pig. I). If 0, is uniform distributcd, this peak power is statistically I AIIRAMSON, N.: 'The throughput of packel broadcasting channe16', InEE Trnnr., 1977, COM-25, pp. 117-128 2 ICUPBRUS, r., and AMIIAK. I.: 'Packcl radio EIWIYOB.Lpit.. 1982, pp. 506 ~507 3 is, AMIIAK, I.C., and BLITTPRSWIJK, W , : in ii Raylcigh channel', 'Gtpilcily of slotled ALOHA in Raylcigh-fading ohannels', [ERE .I Se/. Arerrs Sincc bit-sync offset results in ia random sampling instant within 4,the power aftcr thc SIH is statistically estimated as Adding up all the interfering packets and approximately considering the sum as a Gaussian process that is independent from bit to bit, wc have an eslitnated signal-to-noisc ? a h This resull may be used instcad of lhe detailed analysis in cyn. 5. 2080 Conmitm 1987, SAC-5, pg. 261-269 4 %HANG, K., alld PAIILAVAN, K.: 'Relation between tiiinsilliSSion and throughpit of slatted ALOHA lotiill-packet radio networks', I,?.%% Truiis. C,~mmun.,1992, pp. 577-583 5 HAIIHAII, I.M.~,: 'ALOHA with Captiisc over slow and fils1 Cading radio channels wilh coding and divcrsity', IEEE J , Se/. Arem C ~ W M . , IRXL), SAC-7,pp. 79-aa 6 WIDIPANUESnJ, I.: 'Capture probability and throughput antilysis of slotted ALOHA and onslolled np-ISMA in a RicianiRayleigh environment', IEEn T~tms.Veh. 7BrlinoI.. 1994, pp. 457~465 7 C O K A Z A , O.I., and VATALARO, F.: 'A statistical model for land mobile satellitc chiumcls and its application to nongeostalionary orbit systems', IEEE Twz.s. Veh. Tcch,tol.. 1994, pp. 738-742 8 VALliNZlJCLA. A.: 'UaSAT telemetry &ita laboratory'. Tcchnical mport, Surrey Space Cenlrc, Univmdly of Surrcy, Guildford, UK, May I99X ELECTRONIC:S LETTERS 25th November 1999 !lo/. 35 No. 24

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