On the Variations in Capacity of MIMO Communication Systems to Channel Perturbations

It is known that the capacity of a multi-antenna flat non-fading Gaussian channels (MIMO capacity) can be improved if the transmitter has perfect knowledge of channel. The channel information affects the input allocation and hence there is capacity degradation when the transmitter does not know the channel perfectly. In this work variation in MIMO capacity due to small perturbations that do not change the rank of the channel is studied. The need for the analysis is highlighted by the fact that at high SNR, most channel estimation algorithms give small errors. Expressions and bounds for capacity are derived using first order perturbation analysis. Further to this, the dependence of capacity on the channel parameters and total power is studied. It is shown that the upper bound on degradation in capacity for small errors varies as the square of the spectral norm of perturbation. Further the degradation has an approximate inverse square relation with total power used and channel singular values. These results are extended to a general class of communication systems and results for MIMO-OFDM systems over frequency selective channels are presented.