Capacity scaling of (long) non-regenerative MIMO multi-hop channels

We consider coherent wireless MIMO multi-hop communication where n_S non-cooperating source antennas communicate to n_D fully cooperating destination antennas via L clusters of n_R non-cooperating relay antennas each. Assuming i.i.d. zero-mean (slow) fading coefficients of finite variance, the sum-capacity of this channel is proven to scale linearly in min{n_S, n_D} in the limit Lrarrinfin, when the receive SNR is kept constant and n_RisinOmega(min{n_S, n_D}). This capacity scaling is achieved by a quantization based forwarding strategy. Moreover, we show that Slepian & Wolf compression allows to reduce the growth rate of the transmit power per cluster that is necessary to sustain a constant receive SNR at the destination antennas from exponential to linear in L.