Downlink Channel Covariance Matrix Estimation via Representation Learning with Graph Regularization

TL;DR

This paper introduces a novel representation learning algorithm with graph regularization for estimating downlink channel covariance matrices in FDD massive MIMO systems, emphasizing the importance of Lipschitz regularity for high accuracy.

Contribution

It presents a theoretical analysis of nonlinear embedding errors and proposes a new algorithm using Gaussian RBF kernels that outperforms benchmarks in CCM estimation.

Findings

The algorithm achieves lower estimation errors than benchmark methods.

Lipschitz regularity of the mapping function is crucial for performance.

Theoretical analysis guides the design of the learning algorithm.

Abstract

In this paper, we propose an algorithm for downlink (DL) channel covariance matrix (CCM) estimation for frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) communication systems with base station (BS) possessing a uniform linear array (ULA) antenna structure. We consider a setting where the UL CCM is mapped to DL CCM by a mapping function. We first present a theoretical error analysis of learning a nonlinear embedding by constructing a mapping function, which points to the importance of the Lipschitz regularity of the mapping function for achieving high estimation performance. Then, based on the theoretical ground, we propose a representation learning algorithm as a solution for the estimation problem, where Gaussian RBF kernel interpolators are chosen to map UL CCMs to their DL counterparts. The proposed algorithm is based on the optimization of an objective function that fits a regression model between the DL CCM and UL CCM samples in the training dataset and preserves the local geometric structure of the data in the UL CCM space, while explicitly regulating the Lipschitz continuity of the mapping function in light of our theoretical findings. The proposed algorithm surpasses benchmark methods in terms of three error metrics as shown by simulations.