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This paper studies receiver design in single-input multiple-output (SIMO)slow fading channels with imperfect channel state information (CSI) at thereceiver only. Using generalized mutual information (GMI) as achievable rate,we study the outage behavior when the receiver employs certain generalized formof the nearest neighbor decoding rule. Our study reveals that linearlyshrinking the linear minimum meansquared error (LMMSE) estimate of the CSIreduces the outage probability when the number of receive antennas is finite.Only in the asymptotic regime where the number of receive antennas growswithout bound, the LMMSE estimate of the CSI minimizes the outage probability.Numerical results demonstrate that the proposed linear shrinkage receiverachieves evident outage probability reduction.

Linear shrinkage receiver for slow fading channels under imperfect channel state information