Convergence analysis of iterative Interference Alignment algorithms

Interference Alignment (IA) is more appropriated for the high Signal-to-Noise Ratio (SNR) regime and it is considered suboptimal for low to middle SNR values, where mixed criteria algorithms that also take the direct channel into consideration are expected to be better. In this paper we investigate the performance of some of the most well known iterative algorithms for IA in the low and high SNR regimes, the Min Leakage algorithm, which is a pure IA algorithm, and the Max Signal-to-Interference-plus-Noise Ratio (SINR) and Minimum Mean-Square Error (MMSE) algorithms, which also take the direct channel into account. We illustrate that although the Max SINR and MMSE algorithms can find solutions close to IA at the high SNR regime, they are not as stable in that regime and a pure IA algorithm might perform better. To obtain good performance in both low and high SNR regimes we propose to initialize the mixed criteria algorithms with a pure IA solution, which does not degrade performance at low SNR values but increases stability and performance at the high SNR regime.