Partial Interference Alignment for $K$-User MIMO Interference Channels

In this paper, we consider a Partial Interference Alignment and Interference Detection (PIAID) design for
$K$
-user quasi-static MIMO interference channels with discrete constellation inputs. Each transmitter has
$M$
antennas and transmits
$L$
independent data streams to the desired receiver with
$N$
receive antennas. We focus on the case where not all
$K-1$
interfering transmitters can be aligned at every receiver. As a result, there will be residual interference at each receiver that cannot be aligned. Each receiver detects and cancels the residual interference based on the constellation map. However, there is a window of unfavorable interference profile at the receiver for Interference Detection (ID). In this paper, we propose a low complexity Partial Interference Alignment scheme in which we dynamically select the user set for IA so as to create a favorable interference profile for ID at each receiver. We first derive the average symbol error rate (SER) by taking into account of the non-Guassian residual interference due to discrete constellation. Using graph theory, we then devise a low complexity user set selection algorithm for the PIAID scheme, which minimizes the asymptotically tight bound for the average end-to-end SER performance. Moreover, we substantially simplify interference detection at the receiver using Semi-Definite Relaxation (SDR) techniques. It is shown that the SER performance of the proposed PIAID scheme has significant gain compared with various conventional baseline solutions.