Precoding Schemes for Millimeter Wave Massive MIMO Systems

In an effort to cut high cost and power consumption of radio frequency (RF) chains, millimeter wave (mmWave) multiple input multiple output (MIMO) deploys hybrid architecture in which precoding is implemented as a combination of digital precoding and analog precoding, accomplished by using a smaller number of RF chains and a network of phase shifters respectively. The mmWave MIMO, which usually suffers from blockages, needs to be supported by Reconfigurable Intelligent Surface (RIS) to make communication possible. Along with the hybrid precoding in mmWave MIMO, the passive precoding of Reconfigurable Intelligent Surface (RIS) is investigated in a downlink RIS-assisted mmWave MIMO. The hybrid precoding and passive precoding are challenged by the unit modulus constraints on the elements of analog precoding matrix and passive precoding vector. The coupling of analog and digital precoders further complicates the hybrid precoding.

One of the approaches taken in proposed hybrid precoding algorithms is the use of alternating optimization in which analog precoder and digital precoder are optimized alternately keeping the other fixed. Analog precoder is determined by solving a semidefinite programming problem, and from the unconstrained least squares solution during each iteration. In another approach taken in the proposed methods, the hybrid precoding is split into separate analog and digital precoding subproblems. The analog precoding subproblems are simplified using some approximations, and solved by using iterative power method and employing a truncated singular value decomposition method in two different hybrid precoding algorithms. In the prooposed codebook-based precoder, analog precoder is constructed by choosing precoding vectors from a codebook to maximize signal-to-leakage-and-noise ratio (SLNR).

The passive precoding at the RIS in a single user MIMO is designed to minimize mean square error between the transmit signal and the estimate of received signal by using an iterative algorithm that solves the joint optimization problem of precoding, passive precoding and combiner. The problem of designing energy efficient RIS is solved by maximizing energy efficiency which is a joint optimization problem involving precoder, passive precoding matrix and power allocation matrix. The proposed hybrid precoding and passive precoding algorithms deliver very good performances and prove to be computationally efficient.