1400 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 4, JULY 2005 Symbol/Bit-Error Rate of LMMSE Receiver for M -ary QAM in Multipath Faded CDMA Channels Kegen Yu, Member, IEEE, and Ian Oppermann, Senior Member, IEEE Abstract—This letter investigates the performance analysis of a linear minimum mean square error receiver for M -ary quadratic- amplitude modulation in multipath fading channels. Both channel gain variances and instantaneous channel gains of the interferers are considered for receiver implementation. Approximate expres- sions for symbol and bit error rates are derived only when the receiver knows the channel gain variances of the interferers. In de- riving the analytical expressions, we exploit large system analysis and results in single-user multipath combining. The receiver per- formance and the accuracy of the theoretical results are examined via simulations. Index Terms—Bit-error rate, CDMA, LMMSE receiver, M -ary QAM, multipath Rayleigh fading, symbol error rate. I. I NTRODUCTION T HE linear minimum mean square error (LMMSE) re- ceiver has been widely studied for multiuser detection in code division multiple access (CDMA) systems [1]. The MMSE receiver offers a good tradeoff between performance and complexity. It is near–far resistant and can be implemented adaptively without requiring much side information. Recently, many authors have contributed to the design and analysis of the MMSE receiver and other multiuser receivers in dynamic fad- ing channels. However, most of the existing multiuser receivers deal with only binary phase-shift keying (BPSK) or quaternary phase-shift keying signals. Higher order transmission schemes are more spectrally efficient and have been considered in [2]–[4]. This letter aims to approximate the symbol error rate (SER) and bit-error rate (BER) of the LMMSE receiver for M -ary quadratic-amplitude modulation (QAM) signals in multipath fading channels. Receiver design and analysis of the signal-to- interference ratio (SIR) have been considered in [5] for BPSK signals under multipath fading using the channel gain variances of the interferers. The SER analysis of the LMMSE receiver for M -ary QAM under single-path fading has been accomplished in [4]. The main contribution of this letter lies in the SER and BER evaluation of the multiuser LMMSE receiver in multipath fading channels for M -ary QAM under two different scenarios: either the channel gain variances or the instantaneous channel gains of the interferers are available to the receiver. Performance comparisons of the two receiver implementations Manuscript received September 24, 2003; revised March 17, 2004; accepted April 30, 2004. The editor coordinating the review of this paper and approving it for publication is J. Cavers. The authors are with the Centre for Wireless Communications, University of Oulu, Oulu FIN-90014, Finland (e-mail: kegen@ee.oulu.fi; ian@ee.oulu.fi). Digital Object Identifier 10.1109/TWC.2005.850285 have been performed under different system loadings. Accurate analytical expressions for approximating the M -ary QAM SER and BER are derived for the case of the channel gain variances of the interferers available to the receiver. In particular, the approximate M -ary QAM BER expressions are novel to our knowledge. In Section II, the received signal model in CDMA multipath fading channels is given. In Section III, the LMMSE receiver is studied. In Section IV, the error probability analysis is performed. In Section V, simulation results are shown and a BER approximation for M -ary QAM in Gaussian channels is presented in the Appendix. II. SIGNAL MODEL Consider a synchronous multiuser direct sequence CDMA system. The model for the received signal for any symbol time after down conversion and chip-matched filtering is given by r = K  k=1 L k  ℓ=1 a kℓ b k s kℓ + n (1) where r is a column received signal vector of length N (the processing gain), k ∈{1, 2,...,K} indexes the multiple user, and L k denotes the number of paths of user k. Also, b k is the data symbol of user k, a kℓ is the channel coefficient for path ℓ of user k with Rayleigh-distributed amplitude and uniformly distributed phase, and s kℓ is the signature sequence for path ℓ of user k. Also, n is the noise vector. Let s k =[ s k1 s k2 ··· s kL k ] a k =[ a k1 a k2 ··· a kL k ] T . Also let S =[ s 1 s 2 ··· s K ] A = diag{a 1 , a 2 ,..., a K } b =[ b 1 b 2 ··· b K ] T . Then, (1) can be written in a compact form as r = SAb + n. (2) We further assume that: 1) the data process {b k } is a white random process with each b k chosen equally likely from an M -ary QAM alphabet with E[b k ]=0 and E[|b k | 2 ]=1; 2) the channel process {a kℓ } is a stationary complex random process with E[a kℓ ]=0; 3) the signature sequence {s kℓ } is assumed 1536-1276/$20.00 © 2005 IEEE