Optimal resource allocation for pilot symbol aided multiuser receivers in Rayleigh faded CDMA channels

We consider a synchronous code-division multiple-access system where each user undergoes independent frequency-flat Rayleigh fading, and where pilot symbols are periodically inserted into the data stream of each user in order to assist in the coherent demodulation of the data symbols. The motivating question for this work is: for any given set of system parameters, how often should we insert pilot symbols? Along the way to answering this question, we: (1) derive and analyze the performance of the linear minimum mean-squared-error channel estimator and (2) study the performance of a linear minimum mean-squared-error data estimator which is coupled to the channel estimator. We are able to obtain a very compact expression for the average signal-to-interference ratio in terms of the key system parameters: pilot insertion period, channel fading rate, signal-to-noise ratio, and the ratio of the number of users to the spreading gain. The average signal-to-interference ratio is numerically optimized and results are presented to illustrate the optimal rate of inserting pilot symbols for a range of system parameters.