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.