Hybrid MMSE Precoding for Millimeter Wave MU-MISO via Trace Maximization

In an attempt to alleviate the cost and power consumption in millimeter wave (mmWave) multiple input multiple output (MIMO) systems, hybrid precoding has been put forth as a possible solution. The hybrid precoding replaces the conventional fully digital precoding with a combination of analog and digital precoding to achieve good performance using a significantly smaller number of RF chains compared to the number of antennas. In this paper, we consider a narrowband downlink multiple user multiple-input single-output (MU-MISO) system and propose a hybrid precoding method in order to minimize the mean squared error (MSE) for all users. The analog and digital precoding design subproblems are isolated from each other. Analog precoder design is cast as a trace maximization problem, and solved by an iterative procedure based on truncated singular value decomposition (SVD). The digital precoder is determined subsequently after fixing the analog precoder, using Lagrange's method. The proposed hybrid precoder produces spectral and bit error rate (BER) performances quite close to fully digital precoder, and almost the same as existing high performance hybrid precoders, albeit at a much lower complexity. The proposed precoding method is extended to operate in wideband channel, where it exhibits equally good performance with less complexity.