Sufficient Conditions for Unique Optimizer of Two-Dimensional Atomic Norm Minimization Under Multiple Frequencies

TL;DR

This paper introduces a multi-frequency atomic norm minimization approach for 2D angle estimation in massive MIMO systems, addressing beam squint effects and ensuring unique solutions.

Contribution

It develops a multi-frequency ANM model for 2D angle estimation, proves semi-definite program equivalence, and provides certification conditions for unique optimality.

Findings

Proposed a multi-frequency ANM model for 2D angle estimation.

Established semi-definite program formulation for efficient computation.

Derived conditions guaranteeing a unique optimal solution.

Abstract

Atomic norm minimization (ANM) has been extensively applied for gridless angle estimation. However, with the increase of the number of antennas and the communication frequencies in massive MIMO systems, the accompanying beam squint effect significantly degrades angle estimation accuracy. Existing solutions either address this issue only in the one-dimensional (1D) SIMO case, or decouple the two-dimensional (2D) angle estimation into two separate 1D problems, which fails to achieve the optimal solution. In this paper, we employ the multi-frequency model to characterize the beam squint effect in MIMO channels and propose a multi-frequency version of the ANM objective for corresponding 2D angle estimation. To efficiently retrieve the angle parameters, we prove the existence of the equivalent semi-definite program formulation of the ANM objective and develop an algorithm based on the alternating direction method of multipliers for its solutions. Moreover, we derive the certification conditions of this objective to guarantee the existence of a unique optimal solution.