  A multiple-antenna amplify-and-forward two-hop interference network with
multiple links and multiple relays is considered. We optimize transmit
precoders, receive decoders and relay AF matrices to maximize the achievable
sum rate. Under per user and total relay sum power constraints, we propose an
efficient algorithm to maximize the total signal to total interference plus
noise ratio (TSTINR). Computational complexity analysis shows that our proposed
algorithm for TSTINR has lower complexity than the existing weighted minimum
mean square error (WMMSE) algorithm. We analyze and confirm by simulations that
the TSTINR, WMMSE and the total leakage interference plus noise (TLIN)
minimization models with per user and total relay sum power constraints can
only transmit a single data stream for each user. Thus we propose a novel
multiple stream TSTINR model with requirement of orthogonal columns for
precoders, in order to support multiple data streams and thus utilize higher
Degrees of Freedom. Multiple data streams and larger multiplexing gains are
guaranteed. Simulation results show that for single stream models, our TSTINR
algorithm outperforms the TLIN algorithm generally and outperforms WMMSE in
medium to high Signal-to-Noise-Ratio scenarios; the system sum rate
significantly benefits from multiple data streams in medium to high SNR
scenarios.
