Precoding Design for Limited-Feedback MIMO Systems via Character-Polynomial Codes

Abstract

This paper presents a precoding codebook design for limited-feedback multiple-input multiple-output (MIMO) systems under the equal-gain transmission (EGT) constraint. In particular, we demonstrate that character--polynomial (CP) codes provide a structured solution that achieves constant-envelope transmission, low storage complexity, and Grassmannian packing without dependence on array geometry or channel statistics. In contrast to geometry-dependent discrete Fourier transform (DFT) codebooks used in current 5G systems and unstructured Grassmannian codebooks with high storage complexity, CP codebooks combine practical implementation advantages with near-optimal packing performance. For multiple-input single-output (MISO) systems, we derive an upper bound on the mean squared quantization error and show that the distortion relative to the EGT baseline vanishes asymptotically as the number of transmit antennas increases and the code rate approaches one. For MIMO systems with two receive antennas, we develop an iterative method to establish the EGT baseline. Simulation results under Rayleigh, correlated, and clustered delay line (CDL) channel models show that CP codebooks approach the EGT baseline across all channel conditions while outperforming phase shift keying (PSK) and 5G DFT codebooks in several operating regimes, and, in the Rayleigh fading case, incur negligible packing loss relative to numerically optimized Grassmannian codebooks obtained via the alternating projection (AP) method.

Extended version of a paper presented at IEEE ICC 2025. Submitted to IEEE Transactions on Communications, July 2026