  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.
