Physically Parameterized Differentiable MUSIC for DoA Estimation with Uncalibrated Arrays

TL;DR

Problem: DoA estimation for $M$ sources with uncalibrated arrays in ISAC, modeled as $X = A_{zeta}(theta) S + N$ with $A_{zeta}(theta)$ depending on unknown gains and locations. Approach: a differentiable MUSIC (diffMUSIC) that replaces the non-differentiable argmax with a softmax-based convex combination over a grid of DoAs, enabling gradient-based learning of array parameters $zeta$. Contributions: (i) differential integration of the array model, (ii) supervised losses $L_{SL,theta}$ and $L_{SL,P}$ and unsupervised $L_{UL}$, (iii) demonstration that learned impairments compensate for location and gain errors and that diffMUSIC outperforms nominal MUSIC. Significance: provides an interpretable, parameter-efficient route to calibrate uncalibrated arrays in ISAC and sensing tasks, with potential online adaptation in low data or low-SNR regimes.

Abstract

Direction of arrival (DoA) estimation is a common sensing problem in radar, sonar, audio, and wireless communication systems. It has gained renewed importance with the advent of the integrated sensing and communication paradigm. To fully exploit the potential of such sensing systems, it is crucial to take into account potential hardware impairments that can negatively impact the obtained performance. This study introduces a joint DoA estimation and hardware impairment learning scheme following a model-based approach. Specifically, a differentiable version of the multiple signal classification (MUSIC) algorithm is derived, allowing efficient learning of the considered impairments. The proposed approach supports both supervised and unsupervised learning strategies, showcasing its practical potential. Simulation results indicate that the proposed method successfully learns significant inaccuracies in both antenna locations and complex gains. Additionally, the proposed method outperforms the classical MUSIC algorithm in the DoA estimation task.

Figures (6)

• Figure 1: System model: purple antennas are the physical antennas, black antennas represent the nominal antennas
• Figure 2: MUSIC performance under gain and location impairments: nominal, resp. physical, represents the spectrum without, resp. with, hardware impairment knowledge
• Figure 3: Learned parameters comparison for $M=5$, $30$dB SNR
• Figure 4: MUSIC spectrums with learned arrays, $M=5$, $T=100$, $10$dB SNR
• Figure 5: RMSPE evolution with sensing SNR, $T=100$