MIMO BC with imperfect and delayed channel state information at the transmitter and receivers

In the setting of the two-user (M, N) multiple-input multiple-output (MIMO) broadcast channel (BC), recent work by Maddah-Ali and Tse, and Vaze and Varanasi have revealed the usefulness of delayed channel state information at the transmitter (perfect delayed CSIT). Our work studies the general case of communicating with imperfect delayed CSIT, and proceeds to present novel precoding schemes and degrees-of-freedom (DoF) bounds that are often tight, and to constructively reveal that even substantially imperfect delayed-CSIT, is in fact sufficient to achieve the optimal DoF performance previously associated to perfect delayed CSIT. Going one step further, we also constructively show that, this same optimal performance can in fact be achieved in the presence of additional imperfection of the global CSIR - i.e., even with imperfect receiver estimates of the channel of the other receiver. Specifically, for feedback-quality exponent β describing the high-SNR asymptotic rate-of-decay of the mean square error of the delayed CSIT estimate, the derived DoF d(β) for a given exponent β ϵ [0,1], reveals that the optimal two-user MIMO-BC DoF region previously associated to perfect delayed CSIT, can in fact be achieved for any imperfect β ≥ N/min(M, 2N) + N. Interestingly, for all the cases studied here, the derived quality threshold β* ≡Δ arg minβ{d(β) = d'} for any given symmetric DoF d', accepts the simple form of β* = (d'-d(0))/(d(l)-d(0)), describing the fraction of the DoF gap - between the no-CSIT and the full delayed CSIT case - that is covered to reach the target d'. The potential of an up to 1/β*-fold reduction in feedback bits, can be advantageous in the presence of feedback links with limited reliability and limited capacity.