Precoding Design for Limited-Feedback MIMO Systems via Character-Polynomial Codes

TL;DR

This paper introduces a novel precoding design using character-polynomial codes for limited-feedback MIMO systems, enabling a flexible trade-off between feedback bits and beamforming gain, with theoretical and simulation validation.

Contribution

It proposes a new CP codebook-based precoding method for limited-feedback MIMO, providing theoretical bounds and demonstrating asymptotic vanishing distortion.

Findings

Distortion vanishes asymptotically with increasing feedback

CP code gain approaches EGT baseline gain in MIMO systems

Simulation results confirm effectiveness across various fading models

Abstract

We consider the problem of Multiple-Input Multiple-Output (MIMO) communication with limited feedback, where the transmitter relies on a limited number of bits associated with the channel state information (CSI), available at the receiver (CSIR) but not at the transmitter (no CSIT), sent via the feedback link. We demonstrate how character-polynomial (CP) codes, a class of analog subspace codes (also, referred to as Grassmann codes) can be used for the corresponding quantization problem in the Grassmann space. The proposed CP codebook-based precoding design allows for a smooth trade-off between the number of feedback bits and the beamforming gain, by simply adjusting the rate of the underlying CP code. We present a theoretical upper bound on the \textit{mean squared quantization error} of the CP codebook for Multiple-Input Single-Output (MISO) communication system and utilize it to upper bound the resulting \textit{distortion} with perfect CSIT. We show that the distortion vanishes asymptotically. We compute the EGT baseline gain for MIMO systems with two receive antennas and observe that the CP gain approaches the EGT gain for MIMO system. The results are also confirmed via simulations for different types of fading models for both uncorrelated and correlated channels in the MISO and MIMO systems.