Feedback rate versus capacity loss in limited feedback MIMO systems

In this paper, a multiple-input multiple-output (MIMO) communication system employing a quantized feedback channel is considered. Because of their capacity gain benefits, MIMO communication systems are expected to be a core technology of next generation wireless systems. We study the capacity loss of such systems when the transmitted signal covariance matrix is designed using a low rate feedback channel. For the MIMO channel, we find a universal bound on the instantaneous capacity loss, and we derive a bound on the average capacity loss in the particular case when random codebooks, generated from the uniform distribution on the complex unit sphere, are used to design the transmitted signal covariance matrix. In this case, we find a closed-form expression for the capacity loss as a function of the number of feedback bits used at each channel realization, and it is that the capacity loss decreases exponentially as a function of the number of feedback bits