On Capacity Scaling of Multi-Antenna Multi-Hop Networks: The Significance of the Relaying Strategy in the "Long Network Limit"
Consider wireless transmission from transmit antennas to an -antenna receive terminal over a random and static frequency-flat channel. Assume that each transmit antenna transmits with power, where corresponds to the sum-transmit power. If the channel coefficients between all pairs of transmit and receive antennas are identically and independently distributed (i.i.d.) random variables with zero mean and nonzero variance, (sum-)capacity scales linearly in almost surely, irrespective of whether transmit antennas can cooperate or not. More precisely, the capacity of an n x n point-to-point multiple-input multiple-output channel with white transmit covariance matrix, coincides with the sum-capacity of an uplink channel with single-antenna transmit terminals and an -antenna receive terminal.