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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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