Signal group based alignment in K-user MIMO Y channel

In this paper, we consider a K-user MIMO (multiple input multiple output) Y channel consisting of K, K ≥3, users and a relay. Each user has K - 1 independent messages for all the other K-1 users. With the deployment of multiple antennas at both end users and the relay, K(K - 1) messages can be conveyed to their desired receivers within two time slots for a network operating in a half-duplex mode. A signal group based alignment scheme is proposed which divide all K(K - 1) signals into K groups when K is odd and K - 1 groups when K is even. Then the signals in each group are aligned into a smaller subspace at the relay. If each user is equipped with M antennas and the relay is equipped with N antennas, we show that in order to exchange K(K - 1) messages, the requirements on M and N are KM ≥ N +K - 1 and N ≥ (K - 1)² for even K and (K - 1)M ≥ N +1 and N ≥ K(K - 2) for odd K. In our proposed approach we significantly decrease the minimum M at the expense of higher N for a given number of users K, compared to an existing approach.