Capacity study of distributed beamforming in relation to constrained backbone communication

We investigate the capacity of a downlink channel, where all adjacent base stations are connected via capacity-constrained backbone links to transmit a message to one receiver. For the additive Gaussian case, such a virtual multiple-in single-out channel realizes the distributed transmit beamforming. Based on the model of the multiple-access channel (MAC) with partially cooperating encoders, the capacity results are first derived for the two-encoder and three-encoder settings and then extended to arbitrary N-encoder settings. By focusing on Gaussian MACs, a concept of working mode is developed to demonstrate the optimal cooperation between encoders when the total transmit power and total backbone capacity are limited at same time. By studying a massive beamforming where numerous encoders are engaged, our study reveals that a linear growth of beamforming capacity requires an exponential growth in total backbone capacity.