Multi-stream sum-rate-maximizing interference alignment under sparsity constraints

We study the problem of per-stream joint maximum sum-rate (MSR) precoder and minimum mean-squared error (MMSE) equalizer design for interference alignment in the multi-input multi-output interference channel. We consider the general case of more than three users with more than one stream per user. We propose a new generalized iterative algorithm which directly maximizes the average overall sum-rate without assuming the signal-to-noise ratio to be infinite. The receivers' implementation complexity increases proportional to the square of the number of equalizer taps which becomes prohibitive as the network size increases. To address this issue, we examine the performance-complexity tradeoffs involved in a sparse equalizer design. Our numerical results demonstrate that, for the full-complexity MMSE equalizer design, our proposed algorithm achieves higher overall sum-rate compared to previously proposed interference alignment algorithms. In addition, we reduce the MMSE linear equalizer complexity by 30% while limiting the sum-rate loss to about 10%, at most, compared to the full-complexity design.