Upper bounds on MIMO channel capacity with channel Frobenius norm constraints

The motivation of this paper is to find the class of channels that provides the largest capacity with both the transmit power constraint and channel Frobenius norm constraints. We study both the point-to-point case and the broadcast case. For point-to-point MIMO channels, the optimal channels must have T* equal singular values, where T* is dependent on the available transmit power and the channel Frobenius norm. This result agrees with the previous work by Chiurtu et al. For multiuser broadcast channels, we obtain an upper bound on the sum capacity. We also show that the bound is asymptotically tight for high SNR when all user channels have the same Frobenius norm constraint and N_t ≥ KN_r, where N_t and N_r are the numbers of transmit and receive antennas and K is the number of users.