Tree-Structured Random Vector Quantization for Limited-Feedback Wireless Channels

TL;DR

This paper introduces a tree-structured approach to random vector quantization in wireless channels, significantly reducing search complexity while maintaining performance, and provides performance approximations for large systems.

Contribution

It proposes a tree-structured RVQ method that reduces search complexity in quantizing beamforming vectors and signature vectors, with performance predictions for large systems.

Findings

Tree-structured RVQ reduces search complexity by orders of magnitude.

Performance of TS-RVQ closely matches unstructured RVQ in large systems.

Theoretical performance approximation accurately predicts moderate-size system performance.

Abstract

We consider the quantization of a transmit beamforming vector in multiantenna channels and of a signature vector in code division multiple access (CDMA) systems. Assuming perfect channel knowledge, the receiver selects for a transmitter the vector that maximizes the performance from a random vector quantization (RVQ) codebook, which consists of independent isotropically distributed unit-norm vectors. The quantized vector is then relayed to the transmitter via a rate-limited feedback channel. The RVQ codebook requires an exhaustive search to locate the selected entry. To reduce the search complexity, we apply generalized Lloyd or $k$-dimensional (kd)-tree algorithms to organize RVQ entries into a tree. In examples shown, the search complexity of tree-structured (TS) RVQ can be a few orders of magnitude less than that of the unstructured RVQ for the same performance. We also derive the performance approximation for TS-RVQ in a large system limit, which predicts the performance of a moderate-size system very well.