An Adaptive Approach in Channel Quantization for Small Cells Based on Per-Receiver Antenna Quantization

The widespread deployment of small cells (SCs) plays a crucial role in enhancing system capacity, coverage, and quality of service (QoS) for smart applications. However, due to the dynamic nature of user demands and the limited resources available, SCs cannot support large quantization codebooks, which are typically more suitable for macro cells (MCs) in finite rate feedback (FRF)-based multiple input single output (MISO) systems. In this paper, we propose an adaptive quantization approach for SCs that adjusts the codebook size based on the number of receiver antennas. Additionally, we address the issue of code quantization error (CQE), which arises when two distinct channels are quantized using the same code, as well as the average system error (AvgSysErr), which can increase due to elevated CQE. Our analysis shows that for SCs to achieve convergence of AvgSysErr with FRF-based MISO systems, the probability of non-unique codes in the quantization codebook must be less than 1/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i>, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of antennas at the transmitter. Similarly, the lower bound for the non-unique code probability must be less than or equal to ε, where ε represents the difference between the non-unique code probabilities of 1/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and 1/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>, given 1/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> > 1/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> denote the number of antennas at the transmitter).