Large system analysis of pilot symbol aided channel estimation 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 detection of the data symbols. In this paper, we derive, and analyze the performance of, the linear minimum mean-squared-error channel estimator based on the entire sequence of pilot symbols. Employing classical linear filtering theory and previous results for large systems, we are able to obtain a compact expression for the minimum mean-squared-error 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.