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The hybrid precoding problem in point-to-point millimeter wave (mmWave) multiple input multiple output (MIMO) for narrowband channel has been established as a Frobenius norm minimization problem. It is translated into trace minimization problem, and two algorithms are proposed to solve it. In the first method based on alternating minimization, we alternately determine the analog precoder and digital precoder, keeping the other constant to minimize the trace. The analog precoding subproblem with the fixed digital precoder is converted into a semi-definite programming (SDP) problem and solved by block coordinate descent (BCD) algorithm with suitable modifications. In the second method, we segregate the analog precoding and digital precoding subproblems by considering orthogonality of analog precoder. The analog precoding is further rephrased as a trace maximization problem and solved by an iterative power method by enforcing orthogonality constraint on the analog precoder. The adapted form of modified Gramm-Schmidt orthogonalization procedure is employed to impose orthogonality on the analog precoder. The proposed methods are extended for wideband channel by considering orthogonal frequency division multiplexing (OFDM). The proposed methods not only exhibit a good performance but also come with lower computational complexity when compared to existing methods with comparable performances.

Hybrid Precoding for Millimeter Wave MIMO: Trace Optimization Approach