Vector Quantization Methods for Access Point Placement in Cell-Free Massive MIMO Systems

We examine the problem of uplink cell-free access point (AP) placement in the context of optimal throughput. In this regard, we formulate two main placement problems, namely the sum rate and minimum rate maximization problems, and discuss the challenges associated with solving the underlying optimization problems with the help of some simple scenarios. As a practical solution to the AP placement problem, we suggest a vector quantization (VQ) approach. The suitability of the VQ approach to cell-free AP placement is investigated by examining three VQ-based solutions. First, the standard VQ approach, that is the Lloyd algorithm (using the squared error distortion function) is described. Second, the tree-structured VQ (TSVQ), which performs successive partitioning of the distribution space is applied. Third, a probability density function optimized VQ (PDFVQ) procedure is outlined, enabling efficient, low complexity, and scalable placement, and is aimed at a massive distributed multiple-input-multiple-output scenario. While the VQ-based solutions do not explicitly solve the cell-free AP placement problems, numerical experiments show that their sum and minimum rate performances are good enough, and offer a good starting point for gradient-based optimization methods. Among the VQ solutions, PDFVQ, with its distinct advantages, offers a good trade-off between sum and minimum rates.