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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 π) - 1) ≃ 2.6 bits/sec/Hz for i.i.d. uniform phase fading and 4(4 - log3π) ≃ 3.1 bits/sec/Hz for i.i.d. Rayleigh fading.