near-far resistant detection of cdma signals via isolation bit insertion

8/11/2019 Near-Far Resistant Detection of CDMA Signals via Isolation Bit Insertion

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IEEE TRANSACTIONS ON COMMUNICATIONS,VOL. 43, NO. 2 / 3 / 4 , FEBRUARY/MARCH/APRIL 1995 1313

Near-Far Resistant Detection of CDMA Signalsvia Isolation Bit Insertion

Fu-Chun Zheng and StephenK. Barton,Senior Member, IEEE

Abstract-This paper presents a novel scheme for near-f arresistant CDMA detection: Isolation Bit Insertion (IBI). At thetransmitter, isolation bits are inserted into the information bitsequence before modulation, and a practical linear decorrelatingdetector (LDD) is obtained at the receiver. All the advantagesthat an LDD theoretically offers are retained and realised inpractice.

I. INTRODUCTION

CDMA, as an alternative to FDMA and TDMA,hasinterested more and more researchers in the commercial com-munications field over the last decade. The fundam ental limi-tation of the DS/CDMA systems currently in operationremains the so-called near-far effect.

Many techniques haveso far been proposed to combatthe near-far effect, including power control, successive sub-traction [l], optimum[2], and suboptimum[3]-[7] approaches.Among these techniques,a suboptimum detector,the lineardccorrelating detector (LDD), is emergingas an attractiveoption, owing to its following three advantages:1) optimumnear-far resistance; 2) computational complexity whichincreases linearly wilh respect to the number of users (assum-ing no parameter updating is needed); and3) bit-error-rate(BER) is independent of the interfering signal powers at thereceiver [41. However, since the LDD is a sequence detector,the direct use of the LDD would cause an unacceptably longdetection delay. To overcome this problem, severalapproaches have been reported, based either on the hard deci-sion measures [SI or on the edge correction method[ 6 ] .

The former makes the detection become power dependentagain, the latter is valid only fora specific channel codingscheme.

This paper presentsa novel scheme: Isolation Bit Inser-tion (IBI), in which neilhcr hard decision nor spccilic channelcoding scheme is involved. Asa result, all the above thcoreti-cal advantages of an LD D ar e retained and realised in practice.

11. ISOLA TION B IT INSER TION (IBI) BASEDDETECTION SCHEME

Consider the BPSK DS/SSMA system depicted in Fig.1. The received signal can be expressedas follows [3][4]:

Paper approved by Behnaarn Aazhang, the Editorfor SpreadSpectmm Networksof the IEEE Communicadons So~icty.Manuscriptreceived May 11, 1993; revised June1, 1994. h i s research was sup-ported by the UK Science and Engineering llescarch Council under re-search grantNo. GR/G53644.

This paper was presentedhi part at the IEE Colloquium onPer-sonal Communications: Circuits, Systems, and Tcchnology, London,UK, January22, 1993.

The authors are with the Departmentof Elcctronic and Elcctri.

N-1 K

r ( t ) = C k( i ) sk( t T k + v(t) (1)id k=l

where v(t) is AWGN with varianced the numbe r of trans-mitted information bits,K the number of active users in thechannel, T the duration of each information bit,rk the timedelay of theklh user, [bk(i) lbk(i) f l = O ... N ) thetransmitted information bit sequence, ands k t ) = d w u k ( t >os(o,t + ok . Here, is the spread-ing waveform for the kth user. Then , the matched filter out-puts y k ( l ) an be expressed [41 as

y ( l )= R(l)b'(l - 1) +R(O)b'(l) + R(-l)b'(l + 1) + ~ ( l ) 2)

where b'(l) = E(l)b(l) , E(l)=

d i a g ( m , . d m ) ,b(l) = [bi(l), * * b ~ ( l ) I ~ , andR(.) = [i-q(')]KxK represents the normalised cross-correlation

Y l) = [y i ( l ) , - K ( ~ ) ] ~ ,

cal Engin eering, Universityof Bradford. Bradford. UK.IEEE Log Number 9411593. 0090-6778/95$4.00 1995 IEEE

~

pig. 1 The modelof convent ional B P SU SM A systems.


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1314 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 43, NO. 2/3 /4 , FEBRUARY/MARCH/APRIL 1995

m

matrices: rV(m) = (EiE,)-f si(t q)s,(f + mT ;)dt. In

addition,v(l) is the matched filter output noise (G aussian) vec-tor with autocorrela tion matrixE [ ~ ( m ~ ) v ( m ~ ) ~ ]02R(ml m2). Witho ut loss of generality,it can be assumed that0 5 r1 r2 5 . r K T. In this case,

R ( l ) is an upper, and R(-1) a lower triangular matrix(R(1) = RT(-l)).The task of anLDD is to determineb(l) from (2). In

view of the situation described in Se ction1, a new scheme isproposed as follows.

At the transmitter,a zero bit, termedisolation bit inthis paper, is inserted into the information bit sequence forevery M bits (before modulation). The following segmentedsequen ce is then obtained:(&(i)] = { b k 0 ) , b k ( M ) , 0,

0,bk(nM) , bk (nM+ M ) , 0, -), where n is the segmentnumber. Notice that, bk(nM + m) = 6,(n(M + 1) + m). Theselection ofM is very flexible from th e point of view of com -putation , although it m ay be re stricted by other factors, suchas

channel bandwidth, codeword length, and detection delay.Then, according to(2), the following linear equation system(correspon ding o the nth s egmen t) holds at the receiver:

z n) = G(n)d(n) + u(n) (3). , (n (M + 1) + M 1)T3T,

00

b k ( M ) , * . > bk 2M 1 ) , 0 , ...

where z n) = [y(n(M+d(n) = [ b ' ( d O T, .. b'(nM + M - )TIT,. -

: n ( M + l ) ) T, ( n ( M + 1) + M )T]T, and0:(O) Rt(-l) 0 . . .

Here, R ,.) representsR(.) at time n(M + 1) + m. In the time-variant system,R(.) must be updated with the evolution ofnand m.

To reduce the comp utationa l burden of solving(3) to anaffordable level, the special block tridiagon al structure ofG ( n ) must be exploited. According to [8],d(n) = n) = G- ' (n )z (n) can be calculated in the followingfashion:

b'(nM + M 1) = x(M 1)b'(nM + m ) = x(m) F,b'(nM + m + 1)m = M 2, M 1, . . , 0

(4a)

x(0)= A;'y(n(M + 1))x(m)= A [y(n(M + 1) + m) - R,(l)x(m 1)lm = l , 2 , . . . , M - l

(4b)

A, = Rk(0) Rk(l)F,i

(5a) F, = A;'R;(-l) (5b)m = 1 , 2 , . - . , M - 2

(5c)

Then, the bk l) can be estimated as( n ~ m sign(b;(nM + m)).

The process in (5a-c) is referred toas actorisation, andthat in (4a-b) aselimination. The w hole sch eme is also illus-trated in Fig. 2a and Fig. 2b.

The received signals can thus be detected segment bysegment, and the detection delay is only one segment (M bits).Knowledge of signal powers is not needed.

Assuming that all system parameters are perfectlytracked, the BER for the IBI detector,i .e . , the probability that

0 = RG(0)F - ~ - 1 n

0 - 0 Ro(-1> 9

An.r-1 = R&-l(O) Rb-1(1)FM-2 .i

1O

I

?sK(t - T r K

Fig. 2a. The modcl of IBI bascd BPSWSSMA systems.


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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 43, NO. 2 / 3 / 4 , F E B R U A RY / M A R C H / A P R I L 1995

IBI

Con.

~

1315

Factorisation: Eq(2.5) L , = 1 - 1 / M ) ( 2 K 2- Kt2 + 3/2) + K / MElimination: Eq(2.4) L2 = 1 - 1 / M ) ( 5 K- + 1 / K )+ ( 2 K - 1)/M

Dccision L3 = 1Dccis ion L c = 1

from Samplcrs to Dccidcrs..............................................

L..............................................

Linear Decorrclator

Fig. 2b. The h e a r decorrelatorin Fig. 2a.

the (nM + m)th bit of the kth u ser is misdetected, canbe ascer-tained:

where Q(.) is the Gaussian Q-function:

Q ( x )= 4.5r2dt ,and (G-'(n)) +k, d + k denotes the

(mK+k)th diagonal element ofG- ' (n ) . It can be seen thatPk .) s independent of the interfering signal powers. From(6), the n ear-far resistance NFR) [4] f the IBI detector canreadily be derived:i j k = I / (G- ' (n ) )d+k , + k . Note that thisNFR s optimum[4].

The com putational details of the IBI detector are listedin Table I. Obviously, the total computational load

L , + L2 + L 3 ) s in the order of magnitude ofO ( K 2 ) , ut willbe reduced toO K) f the R(.)'s do not need to be updated;

Finally, the IBI schem e requires partial synchronisationof the transmitters,i e., the relative delay between two corre-sponding segments from any two different users should bemade less thanT . Also, for a given information bit rate, thetransmission rate is increased by1 / M . These two factors,however, can be considered as the penalty for the performanceimprovement achieved by the IBI scheme.

1 -

d z z

III. SCHEME SIMULATION

Three simulation examples have been generated, using511-chip Gold codes withM = 8 and a transmission rateof

The five waveforms depictedin Fig. 3a are digi-talised using an 8-bit linear analogue-to-digital converter(ADC) and transmitted using the IBI scheme. The values ofthe system parameters are recordedin Table 11. SNRl = 30dl3. The received signals are detected usingboth the conven-tional and the IBI detectors. The detection results are then putthrough an 8-bit linear DAC, an d the ou tput waveforms of theDAC a re shown in Fig. 3b and Fig. 3c, respectively. Clearly,the conventional detector fails for the weaker signals, whilethe IBI detector recoversall signals. This example illustratesthe substantial waveform quality improvement whichan IBIdetector alone can offer.

1 T = 32 kbps. SNRk 10 logE k / f f 2 .

TABLE I1SYSTEM PARAMETEIIS USED LV EXAMPLE 1

k 1 2 3 4 5rk (T) 0.0 0.1 0.3 0.6 0.7

0.0 0 . 8 ~ 0.31~ 1. 1~ 1 . 6 ~lOlg(EJE,)(dB) 0 60 50 30 10

0 wave1wave2wave3wave4wave5

-..---.....

0 200 400 600 800 1000t ime

Fig. 3a. The five waveforms transmittedin Example 1.

h'ote: In calcuialing the numberof Numerical OPeralionsNOPs), the spccialstruucturcsof A, (symnictric) andR;(+l) (triangular) hav e been assum ed.


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1316 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 43, NO. 2 / 3 / 4 , FEBRUARY/MARCH/APRIL 1995

--- wave1

wav e 5.....

0 200 400 600 800 1000time t

Fig. 3b. Example 1: the five waveforms obtainedby using the conv ention al detector.

0 wave1wave2wave3wavdwavd.....

0 200 400 600 800 1000tim t

Fig. 3c. Example 1: the ive waveforms obtained by using the LDD.

c2> Monte-Carlo testing.K = 10. The values of thesystem parameters are listed inTable 111. SNRl s progres-sively increased, and ten Mo nte-Carlo runs are carried out foreach SNRl oint. The corresponding BERsof the conven-tional detector and the L DD are plotted in Fig. 4a and Fig. 4b,respectively. The BER sof the two strong est users (i.e., User 4

0.0

-0.5

-1.0

% -3.5

4 . 0 14.5

IJserSL IJser6

. B . User7IJser8

User ?User10

--.-- ---..-

5 . 0 1 I I I , , I-10 -8 -6 4 -2 0 2 4 6 8 10

SNR of user I

Fig. 4a. Conventional detector: BERs of 10 users in Example 2.

Fig. 4b. LDD: BERs of 10 users in Example 2.

and 7) appear in neither Fig. 4a nor Fig. 4b, because they arezero in both cases. Fig. 4a shows that the weakest users'BERs never fall below104.5=31.6 , while Fig. 4b indicatesthat all users achieve the BERof 10-2=1 at SNRk f 7.5 dB.Thu s, in the IBI dete ctor, all users' BERs are determined onlyby theirSNRs.

TABLE 111SYSTEM PARAMETERS USED Ihr EXAMPLE 2

k 1 2 3 4 5 6 I 8 9 10rk fl 0.0 0.1 0.15 0.2 0.22 0.3 0.4 0.7 0.81 0.95

0.11~ 0 .51~ 0.91~ 0.61~ 1 . 1 1 ~ 1.51~ 1.21~ 1.61~ 1.41~ 1 . 1 1 1 ~lOlg E,/E,) dB) 0 20 10 50 10 5 45 3 1 2


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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 43, NO. 2/3/4, FEBRUARY/MARCH /APRIL 1995 1317

0.5

- a.- User2: con4 6 - Userl: dec

4 UserZ: dec

0.4

0 3

7 0.24

rr? l

U...

e-0.1

0.0

-0.1

-50 40 -30 -20 -10 0 10 20 30 40 50

IOlOg,dEJEi)

Fig. 5. Convention al detector and LDD:further comparison of BERs.

REFERENCESA. J. Viterbi, Very low rate convolutional codes for maximum theo-retical perfor man ce of spread -spectrum multiple-ac cess channels,IEEE J Select. Areas Commun. vol. SAC-8, pp. 641-649, May 1990.S . Verdu, M inimum probab ilityof error for asynchrono us Gaussianmultiple-access channels,IEEE Trans. Inform. Theory, vol. IT-32 , pp.

M. K. Varanashi and B. Aazhang, Multistage detection in asyn-chronous code-division multiple-access communications,IEEETrans. Commun. vol. COM-38, pp. 509-519, April 1990.R. Lupas and S . Verdu, Near-far resistance of multiuser detectors inasynchronous channels, IEEE Trans. C o m u n . vol. COM-38, pp.

Z. Xie, et al . A family of suboptimum detectors for coherentmul-tiuser communications, IEEE Trans. Comun . , vol. COM-8, pp.683-690, May 1990.

S . S . H. Wijayasuriya, et al . A near-far resistant sliding windowdecorrelating algorithm for m ulti-user detectorsin DS-CDMA sys-tems, Proc. ofIEEE Globecom,pp. 1331-1338,1992.

U. Madhow and M.Honig, Error probability and near-far resistanceof minimum mean squared error interference suppression schemes forCDMA, Proc. of IEEE Globecom, pp. 1339-1343.1992.

G. H. Golub and C. F. Van Loan,Matrix Computation,Oxford : N o hOxford Academic.1983.

85-96,Jan. 1986.

496-508, April. 1990.

near-far resistant detection of cdma signals via isolation bit insertion

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