Gaussian interference channels with multiple receive antennas: Capacity and generalized degrees of freedom

Gaussian interference channels with multiple receive antennas are studied. First we investigate the two-user Gaussian interference channel with two receive antennas, and it turns out that the angles among channel vectors play a central role in how the additional antenna helps increase the capacity. We formulate the notion of generalized degrees of freedom and show that optimal g.d.o.f. is achieved by superposition Gaussian random coding. Remarkably, the operating regime for the best linear scheme (MMSE followed by treating interference as noise) achieves optimal g.d.o.f. is enlarged when angle is large. Second, a three-to-one Gaussian interference channel in which the interfered receiver has two receive antennas is studied. Unlike the single-antenna case, the idea of interference alignment on signal scales is not directly applicable, and a natural generalization of Han-Kobayashi-type scheme with Gaussian random codes can achieve the capacity region within a number of bits, which depends only on the angle between two interfering channel vectors. We use the notion of generalized degrees of freedom to analyze the problem, and it turns out the HK-type scheme is not g.d.o.f.-optimal. We propose a new scheme, partial interference alignment, which well exploits both the receiver joint processing gain and interference alignment structural gain, and it outperforms HK-type scheme and single-antenna interference alignment scheme.