An adaptive channel estimator for CDMA systems in multipath fading channels

ABSTRACT CDMA systems in multipath fading channels need to estimate channel parameters for coherent detection of the transmitted signals. In this paper we present a simple but effective channel estimation algorithm that can be incorporated into most types of multiuser receivers to obtain good detection performance. This technique uses a set of correlation filters to independently estimate each of the channel parameters. One advantage our method has over subspace-based algorithms for channel estimation is that it can estimate the channel parameters without phase or amplitude ambiguity. Simulation results demonstrating that our channel estimator is capable of tracking reasonably fast fading channels are also presented in the paper.

AN ADAPTIVE CHANNEL ESTIMATOR FOR CDMA SYSTEMS IN MULTIPATH FADING CHANNELS ShanMo American Microsystems, Inc. 2300 Buckskin Road Pocatello, Idaho 83201 ABSTRACT CDMA systems in multipath fading channels need to estimate chan­nel parameters for coherent detection of the transmitted signals. In this paper we present a simple but effective channel estima­tion algorithm that can be incorporated into most types of mul­tiuser receivers to obtain good detection performance. This tech­nique .uses a set of correlation filters to independently estimate each of the channel parameters. One advantage our method has over subspace-based algorithms for channel estimation is that it can estimate the channel parameters without phase or amplitude ambiguity. Simulation results demonstrating that our channel es­timator is capable of tracking reasonably fast fading channels are also presented in the paper. 1. INTRODUCTION Multipath fading effects in CDMA communication channels of­ten cause severe detection problems at the receiving end. These non-ideal conditions necessitate channel estimation in practical wireless communication systems. Distortions due to channel im­perfections are in addition to and independent of the interference from the other users in the network. However, a multiuser receiver cannot correctly cancel interference caused by other users without knowing the channel channel characteristics. Since the parameters of channels are in general time-varying and must be tracked over time, adaptive algorithms are required for satisfactory mitigation of multipath fading effects. This paper presents a simple but effec­tive adaptive channel estimation scheme that mitigates intersymbol interference (lSI) in CDMA systems. Unlike the bank of matched filters (RAKE receivers) that are used in IS-95 systems [I], this technique uses a set of correlation filters to independently estimate each of the channel parameters. Unlike the subspace based ap­proaches in [2] and [3], our channel estimation results in no phase ambiguity and amplitude ambiguity. 2. DATA FORMULATION We consider a K -user CDMA system whose processing gain is N. Let us define dj [i] as the data symbol of the jth user at symbol in­dex i and we assume that the symbols are independent and equally likely to be -lor + 1. We also define an N-dimensional vector Cj [i] as the spreading code associated with the jth user at symbol index i. For fixed code CDMA, Cj [i] repeats itself in every symbol period. For long code CDMA, Cj [i] varies. Our channel estimator can deal with both fixed code or long code CDMA. In this pa­per, we consider fixed code CDMA, and drop the symbol index 0-7803-7041-4/01/$10.00 ©2001 IEEE 2205 V John Mathews Department of Electrical Engineering University of Utah Salt Lake City, Utah 84112 for Cj [i] in the following representations. Finally, we assume that each channel is linear but time-varying. Forney showed in [4] that a finite impulse response (FIR) filter can represent the discrete­time channel model that combines the effects of the transmitter filtering, the physical channel, the receiver filtering, and symbol sampling. Hoeher [5] applied the Monte Carlo-based analog chan­nel model in [6] to develop a discrete-time representation [4, 7] and proposed a slowly time-varying multipath fading channel model. Let an L-element vector given by represent the discrete-time response of a multipath fading channel for the jth user at the symbol time index i. For simplicity of pre­sentation, we assume that sampling is done at the chip rate. In (I), each element of hj [i] is usually modeled as a complex Gaussian process. The phase of a complex Gaussian process is uniformly distributed. The amplitude of a complex Gaussian process is Rice­distributed when thereis a line of sight between the transmitter and the receiver. Otherwise, the amplitude of the process is Rayleigh­distributed [7]. In the experiments described later in the paper, we do not assume any line of sight and hence the channel response hj [i] is modeled as Rayleigh distributed in its amplitude and uni­formly distributed in its phase [5]. Let us define c;ml as the spreading code of the pilot channel delayedbymchips,i.e.,ifcj = [Cj(O) cj(l) ... Cj (N - l)f, then Mathematically, the signal at the CDMA receiver input can be ex­pressed in the form T~-1 K r[i] = L L hj,i(m)dj[i]c;m) + 1J[i]' (3) m=O j=1 where 1J[i] denotes an N-dimensional vector of additive noise sam­ples. We assume that this noise sequence has zero mean value and has a covariance matrix given by a 2IN, where IN represents an identity matrix containing N x N elements. We further assume that the noise sequence is uncorrelated with the transmitted data sequence and the channel parameters. 3. THE ADAPTIVE CHANNEL ESTIMATOR For the purpose of developing the channel estimation method, let us start by considering a CDMA system that has a pilot channel. The derivations in this section have been extended to the case when pilot signals are not available using decision feedback approaches in [8], and described briefly later in the paper. Without loss of gen­erality, let us assume that the pilot user is indexed by one. RAKE receivers similar to those employed in the IS-95 standard estimate the channel parameters as a moving average of the product of the received signal, the pilot signal, and the matched filter with unit impulse response. That is, the mth coefficient of the channel is estimated at the ith instant as AI", hl,i(m) = P + 1 L k=i-P (4) This approach assumes that the spreading sequence is normalized such that II elm) 112= 1. An alternate approach for tracking the coefficients is to use a recursive estimate of the channel parameters given by A A ) ( 1'[']d [.] (m)) hl,i(m) = oohl,i-I(m) + (1- a r ~ I Z e l , (5) where the forgetting factor a is a small positive value close to but less than one. Assuming that the delayed versions of el are uncor­related with each other, and that the pilot symbols are uncorrelated with the signals transmitted by the other users in the network, both (4) and (5) are capable of eliminating the interference from the other users' signals and estimating the channel parameters with­out bias. However, the estimates may not be sufficiently accu­rate when the delayed versions of CI have significant correlations among them. We now propose a modification to the above approach that will eliminate the need to preserve zero correlation among all delayed versions of the spreading sequence. In our approach we simply replace elm) in (4) by a correlation vector Vm that satisfies the constraints (6) and V;';C\I) = 0, (7) for 1, m = 0,1,· .. , L - 1 and m =f. 1. The correlation vector Vm can be calculated using an appropriate Gram-Schmidt orthogonal­ization procedure: Remove any component of elm) that can be estimated using { e\l); I =f. m}, and then normalize the residual vector such that (6) is satisfied. For instance, if the channel length were three, the first correla­tion vector Vo can be found by first evaluating tIo, the component of e\2) that is uncorrelated with cP) as then evaluating t20, the component of e\O) that is uncorrelated with tIo and C;I) as «C;O)T c\I)C;I) /«cP)T c\1l) « c\o» T tID )tIo/ « tI o) T tI o), (9) and finally normalizing t20 with e\O)t20 as Vo = t2o/(e;O)t2o). (10) The procedure for finding VI and V2 is similar. This procedure can be easily extended to the cases where the number of coefficients in the channel model is different from three. U sing the set of correlation vectors V m, a new channel estima­tion method may be derived as hl,i(m) = P ~ 1 L rT[k]dI[k]vm . (11) k=i-P A recursive estimate of the channel parameters may also be devel­oped as hl,i(m) = oohl,i-I(m) + (1- a) (rT[i]dI[i]vm ). (12) To see why such a scheme would work, let us assume for the time being that the channel parameters are time-invariant. Therefore, h . [i] is a constant vector. Taking the statistical expectation of the p:oduct of the correlation filter output v;;;r[i] and the pilot symbol dl [i], E {v;';r[i]dl [i]} v;';e;m)hl,i(m) hl,;(m). (13) The above derivation made use of the signal model for r[i] and the fact that the data sequences generated by various users are un­correlated with each other. Since the procedures in (11) and (12) compute the averages effectively over a short number of recent samples, they are able to track slowly varying (slow relative to the window size) changes in the channel characteristics. 4. A SIMULATION EXAMPLE In this section, we present an example that compares the abilities of the channel estimation methods described in (5) and (12). We con­sider the forward link of a CDMA channel in which eight signals were transmitted with equal power. One of the signals was the pi­lot signal. All the signals were transmitted via the same multipath fading channel. The finite impulse response (FIR) of the muitipath fading channel used the statistical discrete-time model in [5]. We assumed that the CDMA chip rate was 1.23 MHz, and the carrier frequency was 900 MHz. We set the length of the FIR filter to be 3, i.e., the channel vector was hI[i] = [hl,i(O) hl,i(l) hl,i(2)]T. The maximum Doppler frequency was set to be 100 Hz, which cor­responded to a relative speed of 120 km per hour between the base and mobile stations. A set of 15-bit Gold codes were used as the spreading codes for the eight signals. All the systems used a for­ward error control code defined by a four-state convolutional code with generator matrix g = [i ~ i] [7]. The correlation values between the delayed versions of CI were (C;O))T e;l) = 0.533, (C;O))T e;2) = 0.067, and (C;I))T e;2) = 0.467, respec­tively. The forgetting factor a was chosen to be 0.95. The signal­to- noise ratio was set to be 10 dBI. The channel estimator started the estimation with the initialized vector hI [i] = [1 0 Or. 2207 I In practice, the noise level may remain unchanged for a period of time, but the received signal power will vary along with the changes of channel attenuation. Therefore, we calculated the average signal-to-noise ratios (SNRs) over the duration of the experiment in the simulation. 3 3 {·.cal 2 c~'", 2 [1 c '" 1 500 1000 1500 0 2000 0 500 1000 1500 2000 3 3 N {l2 N2 ·.ca C'", [1 c \ '" 1 500 1500 2000 500 1000 1500 2000 1.5 M "'"0 .~ c [0.5 0 0 500 1000 1500 2000 500 1000 1500 2000 Number of Iterations Number of Iterations Fig. 1. Evolution of the channel parameters with K = 8 users and /dmax = 100 Hz. Dash line: actual parameters. Solid line: estimated parameters. The channel estimation method was described in (5). [:b~ I tI0\jPV o 500 1000 1500 2000 0 500 1000 1500 2000 "W; N -'g" 1 \ !o:~ I i~~!1 o 500 1000 1500 2000 0 500 1000 1500 2000 "I ." , , . lo:~v~ I t:~1 o 500 1000 1500 2000 0 500 1000 1500 2000 Number of Iterations Number of Iterations Fig. 2. Evolution of the channel parameters with K = 8 users and fdmax = 100 Hz. Dash line: actual parameters. Solid line: estimated parameters. The channel estimation method was described in (12). 2208 Figure I displays the evolution of the three estimated channel parameters (solid line) using the RAKE receiver-type estimation method described in (5). Also displayed is the evolution of the three actual channel parameters (dash line). The left column of the figure shows the evolution of the amplitude, and the right column of the figure shows the evolution of the absolute value of phas~. The results in the figure show that the estimated channel param­eters do not follow the actual channel parameters in many cases. The reason, as explained earlier, is that the correlations among the delayed versions of C1 were quite large. The same CDMA system and the same channel were used for evaluating our method described in (12). Figure 2 displays the evo­lution of the three estimated channel parameters (solid line) along with the evolution of the three actual channel parameters (dash line), both in amplitude and absolute value of phase. The results in this figure show that the estimated channel parameters follow the actual channel parameters quite well. Such an observation was expected since in our newly proposed method the correlation fil­ter v m had been selected so as to cancel the interference from the other delayed versions of C1 . 5. CONCLUDING REMARKS This paper presented a simple but effective adaptive channel esti­mation scheme for CDMA systems. Our new method eliminates the interference among the replica signals of the user of interest while estimating each channel parameters independently. Conse­quently, our method provides better channel estimation than the current approach used in IS-95 systems [I]. Compared with the subspace based approaches [2][3], our channel estimation is also better because it does not exhibit any phase ambiguity and am­plitude ambiguity. Experimental performance evaluation of our method and comparison of the method with an existing scheme showed that our method is capable of tracking the channel parame­ters well in environments in which the relative motion between the mobile and the base station is fast and also the number of users in the network is reasonably high compared with the spreading gain. These results make us believe that our approach is a viable and better alternative to competing approaches to channel estimation available in the literature. Our channel estimation method can be easily incorporated into most multiuser receivers for CDMA systems. It can also be easily extended to the situation when there is no pilot signal available through a decision feedback mechanism. For example, the FEC decoder decision d1 [i - D] can be used in place of d1 [i]. Thus, a recursive estimate of the channel parameters is given by hl,i(m) = ahl,i-I (m)+(l-a) (v~r[i - DJ) dJ[i-DJ, (14) where we assume that the estimation delay D is much smaller that the rate at which the channel characteristics are changing. How­ever, a decision feedback algorithm would only work assuming the decisions that are made by the receiver are correct most of time, and is thus most useful when the signal-to-noise ratio in the 2Showing the absolute value of phase instead of the original value avoids the confusion caused by periodicity of phase. For example, the actual value of phase at one time could be 'If, but the estimated value could be -'If. Even though these two values are equivalent in phase, they would look quite different in a figure that shows the whole range of phase from -'If to 'If. This ambiguity could also have been avoided by unwrapping the phase, which might result in a larger dynamic range for the phase values than shown in the figure communication channel is relatively high. Performance evaluation of incorporating our channel estimation method into a blind and adaptive projection receiver is given in [8]. 2206 6. REFERENCES [I] TIA IS-95A, "Mobile station-base station compatibility stan­dard for dual-mode wideband spread spectrum cellular sys­tem." [2] M. Torlak and G. Xu, "Blind multiuser channel estimation in asynchronous CDMA systems," IEEE Trans. on Communi­cations, Vol. 45, No.1, pp. 137-147, January 1997. [3] X. Wang and H. V. Poor, "Blind equalization and multiuser detection in dispersive CDMA channels," IEEE Trans. on In­formation Theory, Vol. 46, No.1, pp. 91-103, January 1998. [4] G. D. Forney, "Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interfer­ence," IEEE Trans. on Information Theory, Vol. 18, pp. 363- 378, May 1972. [5] P. Hoeher, "A Statistical Discrete-Time Model for the WS­SUS Multipath Channel," IEEE Trans. Veh. Technol., Vol. VT-4I, No.4, pp. 461-468, Nov. 1992. [6] H. Schulze, "Stochastic models and digital simulation ofmo­bile channels," 1988 URSIIITG Conference, Kleinheubach, Germany, 1988. [7] 1. G. Proakis, Digital Communications, Third Edition, Mc­Graw Hill, New York, 1995. (8] S. Mo, Blind Adaptive Interference Cancellation for CDMA Systems, Ph.D. Dissertation, Dept. of Electrical Engineering, University of Utah, Salt Lake City, December 2000.