Interference alignment with per-antenna power constraints

Interference alignment is a technique for designing transmit precoders that is known to achieve the maximum multiplexing gain in the interference channel. Prior work on interference alignment has assumed sum-power constraints in designing the transmit precoders. In practice, however, each transmit antenna has its own power amplifier which constrains the power radiated from each antenna. This paper proposes and analyzes two algorithms for performing interference alignment with per-antenna equality and inequality power constraints. It is proven that incorporating inequality constraints can be done arbitrarily and does not affect the feasibility of interference alignment. Further, we show that incorporating equality constraints is more difficult and requires more antennas for interference alignment to be feasible, especially in the case of single-stream systems. It is shown through analysis and numerical sum-rate calculations that per-antenna inequality constraints result in a systematic power loss versus the cases of per-antenna equality constraints or no constraints at all.