Optimizing Channel Feedback Using Lloyd Algorithm-Based AoD-Adaptive Subspace Codebook for 5G FDD Massive MIMO

Abstract

Efficient Channel State Information (CSI) feedback remains a critical bottleneck for 5G Frequency Division Duplex (FDD) massive MIMO due to the lack of channel reciprocity. While existing feedback schemes exploit channel sparsity, their quantization efficiency is suboptimal. This paper introduces a novel Angle-of-Departure (AoD)-adaptive subspace codebook optimized via a Complex Spherical Lloyd (CSL) algorithm. By reformulating the codebook design as a vector quantization problem within the low-dimensional AoD subspace, our method reduces feedback overhead from $\mathcal{O}\left( {{N_t}} \right)$ to $\mathcal{O}\left( L \right)$, where L ≪ N<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</inf> is the number of dominant paths. The proposed CSL codebook converges efficiently and supports real-time implementation. Simulations under 3GPP standards show it achieves near-optimal spectral efficiency (6.3 bps/Hz) with only 6 feedback bits, a 7.3× reduction in uplink overhead and a 1.2 bps/Hz gain over 5G NR Type-II benchmarks. The solution is scalable, hardware-feasible, and robust in multi-user and wideband scenarios, offering a practical path for 5G-Advanced and 6G systems.