Effect of Least Square Channel Estimation Errors on Achievable Rate in MIMO Fading Channels

The achievable rate of a multiple input multiple output (MIMO) fading channel is derived in the form of generalized mutual information (GMI) when least square (LS) channel estimation is employed to gain channel state information at receivers. The derived average GMI of a channel with LS channel estimation is compared with the known average GMI (equivalently, the lower bound on the ergodic capacity) of a channel with linear minimum mean square error channel estimation. An effective approximation method is also proposed to ease the numerical calculation of the average GMI of a MIMO channel with LS channel estimation.