Product Quantization for Limited Feedback MISO and RIS-Aided Wireless Communication Systems

Recently, scalar quantization (SQ) and vector quantization (VQ) have been widely adopted in wireless communication systems. VQ outperforms SQ, making it an attractive choice for low-dimensional channel vectors. Despite the dominance, VQ demands a large storage capacity for codevectors and a fast-searching algorithm. Thus, VQ may not be the most desirable solution in many applications. To address these concerns, we introduce a novel product quantization (PQ) in this letter. Our PQ has applications in reconfigurable intelligent surface (RIS)-aided systems as well as multiple-input single-output antenna systems. It differs from the original PQ, designed for source coding, in three key aspects: (i) the encoded vector is complex-valued and comprises a single feature, (ii) a shared codebook is used for quantization, and (iii) the quantization of one sub-vector is influenced by other previously quantized sub-vectors. By properly adjusting the quantization parameters, the proposed PQ needs significantly less hardware and computational resources compared with VQ. Further, it outperforms SQ with a comparable hardware and computational complexity. The numerical assessments reveal the superiority of the proposed PQ.