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We develop approximations for the symbol error rate in a wireless code-division multiple-access channel. We assume that each user employs spectrally efficient M-ary quadrature amplitude modulation and undergoes independent Rayleigh fading. We study the performance of linear minimum mean-squared error receivers in situations where: i) the channels of all users are known perfectly; ii) the receiver knows only the average powers of the interferers but the channel of the user of interest is still assumed to be perfectly known; iii) the channels of the interferers are unknown and there is an error in the channel estimation of the user of interest. In the last of these cases, the symbol error rate is a function of the variance of the channel estimation error. We also determine an expression for this error variance when the channel estimate is obtained from optimal linear smoothing of a sequence of pilot symbols. Recent results on the performance of linear receivers in large systems with random spreading play an important role in our developments.