We describe a non-cooperative interference alignment (IA) technique which
allows an opportunistic multiple input multiple output (MIMO) link (secondary)
to harmlessly coexist with another MIMO link (primary) in the same frequency
band. Assuming perfect channel knowledge at the primary receiver and
transmitter, capacity is achieved by transmiting along the spatial directions
(SD) associated with the singular values of its channel matrix using a
water-filling power allocation (PA) scheme. Often, power limitations lead the
primary transmitter to leave some of its SD unused. Here, it is shown that the
opportunistic link can transmit its own data if it is possible to align the
interference produced on the primary link with such unused SDs. We provide both
a processing scheme to perform IA and a PA scheme which maximizes the
transmission rate of the opportunistic link. The asymptotes of the achievable
transmission rates of the opportunistic link are obtained in the regime of
large numbers of antennas. Using this result, it is shown that depending on the
signal-to-noise ratio and the number of transmit and receive antennas of the
primary and opportunistic links, both systems can achieve transmission rates of
the same order.Comment: Submitted to IEEE Trans. in Signal Processing. Revised on 23-11-0