Uncertainty-Weighted Multi-Task CNN for Joint DoA and Rain-Rate Estimation Under Rain-Induced Array Distortions

TL;DR

The paper addresses joint DoA estimation and rain-rate inference for uniform linear arrays operating under rain-induced distortions by introducing a covariance-domain model where rain affects the distortion covariance 𝑹_b(θ) via a rain-rate dependent correlation 𝛼. It proposes a CNN with a shared backbone and two task heads that treat DoA as multi-label classification over a grid 𝔾 and rain-rate as multi-class classification, trained with an uncertainty-weighted objective to automatically balance tasks. Experimental results in a two-source scenario show DoA RMSE improvements over classical estimators and rain-rate classification accuracy above 94% across several SNRs, highlighting robustness to rain distortions. The approach offers a practical pathway for robust DoA sensing in adverse weather by jointly estimating environmental rain-rate and source directions, with potential extensions to real data and continuous rain-rate regression.

Abstract

We investigate joint direction-of-arrival (DoA) and rain-rate estimation for a uniform linear array operating under rain-induced multiplicative distortions. Building on a wavefront fluctuation model whose spatial correlation is governed by the rain-rate, we derive an angle-dependent covariance formulation and use it to synthesize training data. DoA estimation is cast as a multi-label classification problem on a discretized angular grid, while rain-rate estimation is formulated as a multi-class classification task. We then propose a multi-task deep CNN with a shared feature extractor and two task-specific heads, trained using an uncertainty-weighted objective to automatically balance the two losses. Numerical results in a two-source scenario show that the proposed network achieves lower DoA RMSE than classical baselines and provides accurate rain-rate classification at moderate-to-high SNRs.

Figures (2)

• Figure 1: Proposed multi-task network for joint DoA and rain-rate estimation. The input tensor $\mathbf{X}\in\mathbb{R}^{M\times M\times 3}$ stacks the real, imaginary, and phase channels of the sample covariance matrix and is processed by a shared CNN encoder. Two task-specific heads output DoA logits $\hat{\mathbf{y}}_{\mathrm{DoA}}\in\mathbb{R}^{G}$ and rain-rate logits $\hat{\mathbf{y}}_{\mathrm{rain}}\in\mathbb{R}^{R}$, which are jointly optimized via a multi-task loss.
• Figure 2: DoA RMSE versus SNR on the test set under rain-induced array distortions. The proposed uncertainty-weighted network is compared with its fixed-weighting variants and classical baselines.