Finite-Bit CSI Compression Under Feedback Constraints: Exact PCA Error Decomposition and Robust Dimension–Bit Allocation for MISO-OFDM

Finite-bit channel-state-information (CSI) feedback couples the number of retained coefficients with their encoding precision. This study combines representation-specific payload accounting, an exact orthogonal principal component analysis (PCA) error identity, and bounds on beamforming alignment and rate loss in a controlled single-user multiple-input single-output orthogonal frequency-division multiplexing system. Exact enumeration compares uniform and multi-length PCA, finite-bit singular value decomposition (SVD), direct quantization, three dense autoencoders and a CsiNet-style convolutional reference. The primary evaluation comprises 7150 run records across five scenarios, with inference based on five independent test datasets and neural training seeds averaged within each dataset. On nominal Test-A, the 256-bit multi-length PCA design attains −20.411 dB physical normalized mean square error and 7.272 bit/s/Hz, versus −14.729 dB and 7.239 bit/s/Hz for uncompressed estimated CSI. This comparison includes estimation-noise suppression by projection; the multi-length design also changes coefficient clipping ranges. The empirical minimax selection first switches to rank-2 6-bit SVD at 1164 bits. These results concern the evaluated candidates and ideal representation payloads, not universal optimality or deployment-ready feedback costs.