  We consider a dense fading multi-user network with multiple active
multi-antenna source-destination pair terminals communicating simultaneously
through a large common set of $K$ multi-antenna relay terminals in the full
spatial multiplexing mode. We use Shannon-theoretic tools to analyze the
tradeoff between energy efficiency and spectral efficiency (known as the power-
bandwidth tradeoff) in meaningful asymptotic regimes of signal-to-noise ratio
(SNR) and network size. We design linear distributed multi-antenna relay
beamforming (LDMRB) schemes that exploit the spatial signature of multi-user
interference and characterize their power-bandwidth tradeoff under a system
wide power constraint on source and relay transmissions. The impact of multiple
users, multiple relays and multiple antennas on the key performance measures of
the high and low SNR regimes is investigated in order to shed new light on the
possible reduction in power and bandwidth requirements through the usage of
such practical relay cooperation techniques. Our results indicate that
point-to-point coded multi-user networks supported by distributed relay
beamforming techniques yield enhanced energy efficiency and spectral
efficiency, and with appropriate signaling and sufficient antenna degrees of
freedom, can achieve asymptotically optimal power-bandwidth tradeoff with the
best possible (i.e., as in the cutset bound) energy scaling of $K^{-1}$ and the
best possible spectral efficiency slope at any SNR for large number of relay
terminals.
