Optimal diversity combining based on noisy channel estimation

The performances of coherent diversity receivers with noisy channel estimation are examined. Fading channel gain estimates are modeled as sums of the true fading channel gain values plus independent Gaussian distributed estimation errors. The optimal diversity receiver for coherent reception with noisy channel state information and independent and identically distributed fading channels is derived. Exact expressions for the average error probability of optimal diversity MPSK with noisy channel estimation are derived for Rayleigh and Ricean fading channels; closed-form expressions are obtained for some special cases. Some interesting observations regarding practical diversity receiver design for higher-order modulation formats are drawn.