Approximate Ergodic Capacity of a Class of Fading 2-user 2-hop Networks

We consider a fading AWGN 2-user 2-hop network where the channel coefficients are independent and identically distributed (i.i.d.) drawn from a continuous distribution and vary over time. For a broad class of channel distributions, we characterize the ergodic sum capacity to within a constant number of bits/sec/Hz, independent of signal-to-noise ratio. The achievability follows from the analysis of an interference neutralization scheme where the relays are partitioned into $M$ pairs, and interference is neutralized separately by each pair of relays. When $M=1$, the proposed ergodic interference neutralization characterizes the ergodic sum capacity to within $4$ bits/sec/Hz for i.i.d. uniform phase fading and approximately $4.7$ bits/sec/Hz for i.i.d. Rayleigh fading. We further show that this gap can be tightened to $4\log \pi-4$ bits/sec/Hz (approximately $2.6$) for i.i.d. uniform phase fading and $4-4\log( \frac{3\pi}{8})$ bits/sec/Hz (approximately $3.1$) for i.i.d. Rayleigh fading in the limit of large $M$.