Blind RAKE receiver with joint diversity combining and code tracking for DS/SS communication



1.43 %. Using linear interpolation for fading estimation, the BER performances with L = 70, 40 and 10 are shown in the same Fig- ure for comparison. It can be seen that, with L = 70 and 40, irre- ducible error floors occur at BER


5 x 1 k 2 and 5 x l t 3 , respectively, whereas the proposed technique can reduce the BER to 2 x 10-4, achieving substantially better performance improve- ments. With L = 10, linear interpolation seems to perform better than the proposed technique, but the required bandwidth redun- dancy is now lo%, instead of 1.43%.

With a faster normalised fading rate of f D T = lo-*, the BER per- formances of the signal with L = 35, 20 and 5 are shown in Fig. 2. It can be seen that the performances are slightly worse than in the slow fading environment of Fig. 1. Here again, no error floor occurs under the conditions tested. The results obtained using lin- ear interpolation are also shown for comparison. It can be seen that, with linear interpolation and L = 35 and 20, the error floors occur at BER = 5 x 1C2 and 5 x lo", respectively. If the proposed technique is used, the BERs are substantially lower. Both the results in Figs. 1 and 2 indicate that the proposed technique is a bandwidth-efficient method. In a bandwidth limited system, the proposed PSA technique is obviously better for fading estimation.

Conclusions: A bandwidth-efficient technique for use in PSA sys- tems has been described and studied. The technique employs both data and pilot symbols to reduce the square of the estimation error. Computer simulation results have shown that, in frequency non-selective Rayleigh fading channels corrupted with AWGN, the technique requires a minimal bandwidth redundancy to trans- mit the pilot symbols. In a slow fading environment with


= 5 x 1C3, the bandwidth redundancy required to transmit the pilot symbols can be reduced to as low as 1.43%. Moreover, the pro- posed technique achieves substantially lower error floors.

In fact, only when both multipath diversity combining and code tracking are optimised simultaneously for frequency-selective fad- ing effects can overall receiver performance be improved. In this Letter, a technique achieving joint blind multipath diversity com- bining and a code tracking loop is proposed. Based on this tech- nique, a multipath diversity combiner with the improved known modulas adaptive (KMA) algorithm operates with the modified PN code timing recovery to achieve simultaneous improvement of overall receiver performance with very low computation load. In the modified PN code timing recovery, the timing error signals are independently extracted and then effectively combined in the same fashion as that exploited in the multipath diversity combiner to achieve improved code tracking performance as well.

rece sig


0 IEE 1998

Electronics Letters Online No: 19981088

M.H. Ng and S.W. Cheung (Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kond

Corresponding author: S.W. Cheung E-mail:

I June 1998


1 MOHER, M.L., and LODGE, J.H : 'TCMP-A modulation and coding strategy for Rician fading channels', IEEE J. Sel. Areas Conzmun.,

2 SAMPEI, s., and SUNAGA, T : 'Rayleigh fading compensation for QAM in land mobile radio communications', IEEE Trans. Veh. Technol., 1993, 42, (2), pp. 137-147

3 LAU, H.K., and CHEUNG, s.w.: 'A pilot symbol-aided technique used for digital signal in multipath environments'. Proc. IEEE Int. Conf. Commun., New Orleans, USA, May 1994, pp. 1126-1 130 1989, 7, (9), pp. 1347-1355



receiver with joint diversity

combining and code tracking for





A RAKE receiver achieving joint blind multipath diversity combining and code tracking is proposed. An improved known modulus adaptive algorithm is exploited to perform multipath diversity combining and to support the modified code tracking in the blind mode. Computer simulation results have indicated very attractive behaviour of the proposed technique.

Introduction: Frequency-selective f a l n g can often lead to severe performance degradation in wideband communication systems. Substantial efforts have been made in adaptive equalisation and diversity combining (RAKE) techniques in order to improve receiver performance, but little work has been devoted to optimis- ing code synchronisation systems, although the conventional code tracking loop


is vulnerable to multipath fading effects [I].

code timing recovery 163211 Fig. 1 RAKE receiver based on proposed technique

Proposed RAKE receiver: A complete block diagram of the RAKE receiver based on the proposed technique is shown in Fig. 1. The complex representation of the baseband signal at the output of the chip matched filter is


T ( t ) = a,(t)s(t -



n ( t ) (1) n=O

where s(t) = C


d, C &I cg(t-lTc-iTb) is the data-modulated PN

sequence with raised cosine chip shaping, d, is the ith information- bearing symbol, e, is the lth c h ~ p value of the PN sequence, Tb and T, are the symbol interval and the chip duration, respectively, M =

TJT, is the processing gain, g(t) i s the overall chip shape. The sig- nal r"(t) is sampled at twice the chip rate, i.e. sampled at the instants tk = (k


&JTC and t,-; = (k


- i ) T c , where E~ is the kth normalised chip timing error, to produce the two parallel sequences: integer-instant or on-time samples Y"k = Y"(tk), and

half-integer-instant samples


k-; =



Multipath diversity combining technique based on improved KMA algorithm: The integer-instant sample stream


T k = an(kTc)s(kTc - nTc


E ~ T , )


nk (2)


IS fed into the multipath diversity combiner based on tne improved KMA algorithm. Assume fist that the code acquisition process has been achieved. On each arm of the multipath diversity com- biner, the input samples r",-,, m = 0, 1, ..., L - 1, are cross-corre-

lated with the local PN sequence ck-(L-I), which has been code- acquired, and then passed through the arm filter, hk, which is a

lowpass fiter with bandwidth Bb comparable with the symbol rate, UTb, in order to reject effectively the PN self-noise, multiple access interference, and noise outside the bandwidth of the information- bearing symbols. The input samples x r , m = 0, 1, ..., L - 1, of the

improved KMA algorithm proposed here are taken from the out- put of the mth arm fiter h, and given as


where x and


denote the correlation and convolution operators, respectively.

To achieve multipath diversity combining, a multipath diversity combiner with coefficient vector W, = [wj, w,', ..., w:?]' is employed. The multipath diversity combiner output is

Y k = W T X k (4)

where X, = [x! , x; , ..., x,"'] T is the input vector of the improved

KMA algorithm and x: , m = 0, 1,


L ~ 1 are taken from the

outputs of the arm filters as shown in eqn. 3. Based on the deriva- tion and discussion presented previously [3], the update procedure can be rewritten as



= -- CL


+ j S L ] ( 5 )

I l X k l l 2

and the error signal [gkR


jg;], can thus be approximated as


2: and Z,I are the variable confidence zones of the real and imag- inary parts, respectively, and j k r and

j ;

are the real and imagi- nary parts, respectively, of the decision result of the multipath diversity combiner output.

P N code trucking loop: Here, we describe the operations in the modified PN code tracking loop. The early-late structure is replaced by the very simple digital correlator with the half-integer- instant stream and the code difference stream as its inputs. The incommg delayed (one symbol interval, Tb = MT,, delayed) half- integer-instant samples


m = 0, 1,


L - 1, are cross-cor-

related with the code difference stream,


= c ~ - ( ~ ~ ) - ~ c ~ - ~ ~ After passing through the arm filter, h,, the arm error signal z:

on the mth arm is generated in the following form: :z = Y"k-&,-m

x c k M


h,. The arm error signal z r on the mth arm has the same error characteristics as those of the conventional delay locked loop (DLL) operated on a single-path channel with AWGN, but here it is corrupted by the corresponding channel tap weight and the information-bearing symbol. The compound error signal, e,, can be obtained by combining the arm error signals, z p V m , with the tap weights, w:


which are the same as those exploited in the multipath diversity combiner; then, the data modulation effect on z

: compensated for by the decision-directed method:

The effects of channel multipath fading, the carrier phase error and data modulation on the arm timing error signal, zp , can be simultaneously overcome by exploiting multipath diversity com- bining. 1 5 1 0 0 5 r $ 0 c g-0 5 -1 .o -1 5


-1 5 -1 0 -0.5 0 0.5 1.0 151 5 -1.0 -0.5 0 0.5 1 .O 1.5

a real part b real part

63212 Fig. 2 Signal constellations after multipath diversity combiner with EKF-based estimator [2] and proposed technique

a EKF when SNR = -5dB

b MKMA when SNR = -5dB


August 1998

Vol. 34

Simulation results: Computer simulation results illustrating the performance of the proposed technique are presented in this Sec- tion. Fig. 2 shows the signal constellations obtained by a multip- ath diversity combiner with the EKF-based estimator [2] and the proposed technique, in the case of a frequency offset AJ(l/T,) = 1W and SNR = -5dB. The multipath diversity combiner, aided by the EKF-based estimator [2], and with the proposed technique, can track the carrier frequency offset and cluster the output signal constellation at the right position. It is also obvious that the mul- tipath diversity combiner with the proposed technique can cluster the output signals at the right position much better than can one aided by the EKF-based estimator [2].

Conclusion: A technique of joint blind multipath diversity combin- ing and code tracking is proposed in this Letter. It has been shown that this technique can accomplish multipath diversity combining in the blind mode. The simulation results show that such a tech- nique can certainly achieve simultaneous improvement of multip- ath diversity combining and code tracking on frequency-selective fading channels.

0 IEE 1998

Electronics Letters Online No: 19981040

Jia-Chin Lin (Department of Electrical Engineering, Room 531, National Taiwan University, 106-1 7 Taipei, Taiwan, Republic of China)


26 May 1998


1 SHEEN, w.-H., and STUBER, G.L.: 'Effects of multipath fading on delay-locked loops for spread spectrum systems', IEEE Trans. Commun., 1994,42, pp. 1947-1956

2 ILTIS, R.A.: 'An EKF-based joint estimator for interference multipath, and code delay in a DS spread-spectrum receiver', IEEE

Trans. Commun., 1994,42, pp. 1288-1299

3 LIN, J.-c., and LEE, L.-s.: 'A modified blind equalization technique based on a constant modulus algorithm'. ICC'98, 1998 (accepted) 4 OH, K.N., and CHIN, Y.o.: 'Modified constant modulus algorithm:

Blind equalization and carrier phase recovery algorithm'. Proc. ICC'95, Seattle, WA, June 1995, pp. 498-502



error rate performance of




Nakagami-lognormal channels

C. Tellambura

A convergent infinite series has been presented for the bit error performance of W4 DQPSK for Nakagami-lognormal channels if the fading figure m is an integer. The authors show that this infinite series can be replaced by a finite series. A convergent series for the BER is also derived when the fading figure, m, is real.

Introduction: In a recent Letter [l], Tjhung and Chai have derived an infinite series for the bit error rate (BER) of 7d4 DQPSK for Nakagami-lognormal (NLN) channels provided the Nakagami fading figure is constrained to be an integer. This modulation scheme, differential quadrature phase shift keying, has been adopted for several practical mobile systems. Therefore, evalua- tion of its performance under general fading and shadowing con- ditions is useful. The purpose of this Letter is to suggest some improvements to the infinite-series solution.

Theory: The conditional BER, P,(els), derived in [l] utilises a BER expression from [2] which involves the generalised Marcum's Q function and an infinite series of modified Bessel functions. Conse- quently, eqn. 8 in [l] is an infinite series. However, it possible to replace this by a finite series. From [3], the conditional BER can be written as