The Capacity Region of the MIMO Interference Channel and Its Reciprocity to Within a Constant Gap

Abstract

The capacity region of the 2-user multi-input multi-output (MIMO) Gaussian interference channel (IC) is characterized to within a constant gap that is independent of the channel matrices for the general case of the MIMO IC with an arbitrary number of antennas at each node. An achievable rate region and an outer bound to the capacity region of a class of interference channels were obtained in previous work by Telatar and Tse as unions over all possible input distributions. In contrast to that previous work on the MIMO IC, a simple and an explicit achievable coding scheme are obtained here and shown to have the constantgap-to-capacity property and in which the sub-rates of the common and private messages of each user are explicitly specified for each achievable rate pair. The constant-gap-to-capacity results are thus proved in this work by first establishing explicit upper and lower bounds to the capacity region. A reciprocity result is also proved which is that the capacity of the reciprocal MIMO IC is within a constant gap of the capacity region of the forward MIMO IC.

Capacity region of two interfering MIMO Multiple Access channels with strong interference

“…A similar set of upper bounds were proved in [19] and [17] in the context of 2-user MIMO IC, where there were 2 transmitters in the network.…”

“…In the previous section we studied the so called 2-user interference channel While there are plethora of research articles on ICs [18], [19], research efforts on the IMAC is almost non-existing. To the best of our knowledge, the only previous result on IMAC was reported in [20], where the authors consider an IMAC with single antennal (SISO) nodes and finds capacity region where the interfering nodes have mixed strong [6] and very strong [5] interference, or both the interferers have stronger than the so called strong interference.…”

Vector bin-and-cancel for MIMO distributed full-duplex

“…The point-to-point outer bounds on R dl and R ul can be easily obtained following the same argument in Lemma 1 of [22], which are given by…”

“…Using the covariance matrix, we derived in (69), and invoking Lemma 8 in [22], we can upper bound (82) as follows:…”

Superposition Signaling in Broadcast Interference Networks

“…Inspired by [7], references [16] and [17] derived the covariances of private and common Gaussian messages for H-K signalling, which achieve the capacity region of twouser multiple-input multiple-output (MIMO) GINs to within a constant gap. A similar result for the K-user cyclic GIN was obtained in [18].…”