  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
problem 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, which enables efficient, low
complexity, and scalable placement, and is aimed at a massive distributed
multiple-input-multiple-output (MIMO) scenario. While the VQ-based solutions do
not solve the cell-free AP placement problems explicitly, 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 advantages over the other VQ methods, offers a good
trade-off between sum and minimum rates.
