Diversity with practical channel estimation

In this paper, we present a framework for evaluating the bit error probability of N_d-branch diversity combining in the presence of non-ideal channel estimates. The estimator structure presented is based on the maximum-likelihood (ML) estimate and arises naturally as the sample mean of N_p pilot symbols. The framework presented requires only the evaluation of a single integral involving the moment generating function of the norm square of the channel-gain vector, and is applicable to channels with arbitrary distribution, including correlated fading. Our analytical results show that the practical ML channel estimator preserves the diversity order of an N_d-branch diversity system, contrary to conclusions in the literature based upon a model that assumes a fixed correlation between the channel and its estimate. Finally, we investigate the asymptotic signal-to-noise ratio penalty due to estimation error and reveal a surprising lack of dependence on the number of diversity branches.