Effect of the channel estimation on the accuracy of the capacity estimation

Systems with multiple element transmitter and receiver arrays have been shown to achieve very high spectral efficiencies. The theoretically achievable Shannon capacity is a function of the channel between the transmitters and the receivers. On the simulation level, one assumes certain statistical characteristics for the channel, but on a practical level, the actual channel is measured. We show that the accuracy of the measurements affects the accuracy of the Shannon capacity estimation. We study analytically how the channel estimation error appears in the capacity formula, and we derive mathematical expressions for the first and second order approximations of the error. We present simulation results that show the effect of the system size, the measurement accuracy, the system signal-to-noise ratio and the nature of the channel itself on the accuracy of the estimation of the channel capacity