A Nonlinear Approach to Interference Alignment
  Cadambe and Jafar (CJ) alignment strategy for the K-user scalar frequency-selective fading Gaussian channel, with encoding over blocks of 2n+1 random channel coefficients (subcarriers) is considered. The linear zero-forcing (LZF) strategy is compared with a novel approach based on lattice alignment and lattice decoding (LD). Despite both LZF and LD achieve the same degrees of freedom, it is shown that LD can achieve very significant improvements in terms of error rates at practical SNRs with respect to the conventional LZF proposed in the literature. We also show that these gains are realized provided that channel gains are controlled to be near constant, for example, by means of power control and opportunistic carrier and user selection strategies. In presence of relatively-small variations in the normalized channel coefficient amplitudes, CJ alignment strategy yields very disappointing results at finite SNRs, and the gain of LD over ZLF significantly reduces. In light of these results, the practical applicability of CJ alignment scheme remains questionable, in particular for Rayleigh fading channels, where channel inversion power control yields to unbounded average transmit power. 
Peyman Razaghi and Giuseppe Caire
cs.IT math.IT