Simplified Information Geometry Approach for Massive MIMO-OFDM Channel Estimation -- Part II: Convergence Analysis

TL;DR

This paper proves the convergence of a simplified information geometry method for massive MIMO-OFDM channel estimation, providing theoretical conditions and simulation validation for the iterative algorithm's stability.

Contribution

It offers a rigorous convergence analysis of the SIGA method, including conditions on initialization and damping factors specific to massive MIMO-OFDM systems.

Findings

Convergence of the common SONP is independent of damping factor with proper initialization.

A sufficient condition for the convergence of the common FONP is established.

Simulation results confirm the theoretical convergence conditions.

Abstract

In Part II of this two-part paper, we prove the convergence of the simplified information geometry approach (SIGA) proposed in Part I. For a general Bayesian inference problem, we first show that the iteration of the common second-order natural parameter (SONP) is separated from that of the common first-order natural parameter (FONP). Hence, the convergence of the common SONP can be checked independently. We show that with the initialization satisfying a specific but large range, the common SONP is convergent regardless of the value of the damping factor. For the common FONP, we establish a sufficient condition of its convergence and prove that the convergence of the common FONP relies on the spectral radius of a particular matrix related to the damping factor. We give the range of the damping factor that guarantees the convergence in the worst case. Further, we determine the range of the damping factor for massive MIMO-OFDM channel estimation by using the specific properties of the measurement matrices. Simulation results are provided to confirm the theoretical results.