Low complexity precoding for large millimeter wave MIMO systems

Millimeter wave (mmWave) systems must overcome heavy signal attenuation to support high-throughput wireless communication links. The small wavelength in mmWave systems enables beamforming using large antenna arrays to combat path loss with directional transmission. Beamforming with multiple data streams, known as precoding, can be used to achieve even higher performance. Both beamforming and precoding are done at baseband in traditional microwave systems. In mmWave systems, however, the high cost of mixed-signal and radio frequency chains (RF) makes operating in the passband and analog domains attractive. This hardware limitation places additional constraints on precoder design. In this paper, we consider single user beamforming and precoding in mmWave systems with large arrays. We exploit the structure of mmWave channels to formulate the precoder design problem as a sparsity constrained least squares problem. Using the principle of basis pursuit, we develop a precoding algorithm that approximates the optimal unconstrained precoder using a low dimensional basis representation that can be efficiently implemented in RF hardware. We present numerical results on the performance of the proposed algorithm and show that it allows mmWave systems to approach waterfilling capacity.