  In TDD reciprocity-based massive MIMO it is essential to be able to compute the downlink precoding matrix over all OFDM resource blocks within a small fraction of the uplink-downlink slot duration. Early implementation of massive MIMO are limited to the simple Conjugate Beamforming (ConjBF) precoding method, because of such computation latency limitation. However, it has been widely demonstrated by theoretical analysis and system simulation that Regularized Zero-Forcing (RZF) precoding is generally much more effective than ConjBF for a large but practical number of transmit antennas. In order to recover a significant fraction of the gap between ConjBF and RZF and yet meeting the very strict computation latency constraints, truncated polynomial expansion (TPE) methods have been proposed. In this paper we present a novel TPE method that outperforms all previously proposed methods in the general non-symmetric case of users with arbitrary antenna correlation. In addition, the proposed method is significantly simpler and more flexible than previously proposed methods based on deterministic equivalents and free probability in large random matrix theory. We consider power allocation with our TPE approach, and show that classical system optimization problems such as min-sum power and max-min rate can be easily solved. Furthermore, we provide a detailed computation latency analysis specifically targeted to a highly parallel FPGA hardware architecture. 
Truncated Polynomial Expansion Downlink Precoders and Uplink Detectors   for Massive MIMO