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Maximum-ratio combining (MRC) is a simple and effective combining scheme for adaptive antenna arrays to combat noise, fading, and to a certain degree, cochannel interference. However, it requires estimation of the spatial signature (i.e., the channel gain and phase at each antenna element) of the desired signal across the array. Assuming that this estimate is obtained by correlation using a known training sequence of K symbols embedded in the useful signal, we proceed to develop a fully analytical assessment of the impact of estimation error on the output signal-to-noise ratio (SNR) of the array. The originality of the approach revolves around the derivation of the distribution of the normalized SNR, that is the real SNR normalized to the ideal (i.e., perfect estimation) SNR. The end result is a set of distributions which can potentially reduce or in certain cases eliminate the need for simulation to determine certain design parameters such as array size, training sequence length, etc. These are then applied to find closed-form expressions for the outage probability and the error probability in differential phase-shift keying and quarternary phase-shift keying after training in uncorrelated Rayleigh fading.
Roy et al. (Thu,) studied this question.