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

We consider a fading AWGN 2-user 2-hop network in which the channel coefficients are independently 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 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 $K$ pairs, and interference is neutralized separately by each pair of relays. For $K=1$, we previously proved a gap of $4$ bits/sec/Hz for i.i.d. uniform phase fading and approximately $4.7$ bits/sec/Hz for i.i.d. Rayleigh fading. In this paper, we give a result for general $K$. In the limit of large $K$, we characterize the ergodic sum capacity within $4((\log \pi)-1)\simeq 2.6$ bits/sec/Hz for i.i.d. uniform phase fading and $4(4-\log 3\pi)\simeq 3.1$ bits/sec/Hz for i.i.d. Rayleigh fading.