Novel DOA Estimation Technique

• Novel DOA estimation techniques combine advanced algorithms like weighted low-rank matrix completion, gridless nonconvex ANM, and learning-based models to reliably estimate signal directions under sensor and noise constraints.
• These methods leverage continuous parameter models and supervised learning to achieve super-resolution recovery, robust noise handling, and cost-effective hardware design.
• Recent approaches demonstrate significant gains (e.g., 5–10 dB NMSE improvement and near-CRLB accuracy) in applications spanning radar, sonar, wireless communications, and integrated sensing systems.

Direction-of-Arrival (DOA) estimation is a foundational task in array signal processing, crucial for applications ranging from radar and sonar to wireless communications, acoustics, and autonomous systems. Novel DOA estimation techniques are continually developed to address array geometry constraints, hardware cost, algorithmic complexity, environmental impairments, and advanced signal models such as massive MIMO, intelligent reflecting surfaces (IRS), and integrated sensing–communication systems. Recent progress is marked by algorithms leveraging matrix completion, gridless and nonconvex sparsity, learning-driven estimation, IRS-optimized architectures, and robust large-scale MIMO formulations.

1. Matrix Completion and Weighted Low-Rank Reconstruction

A substantial advance in DOA estimation for sparse linear arrays (SLAs) is the adoption of weighted low-rank matrix completion. The method introduced in "DOA Estimation via Optimal Weighted Low-Rank Matrix Completion" (Razavikia et al., 26 Jul 2025) addresses the scenario wherein only $M$ out of $N$ ULA positions are equipped with sensors. The observation vector is first Hankel-lifted, exploiting the property that snapshots from $K$ far-field sources produce a rank-$K$ Hankel matrix. Instead of unweighted completion, optimal left and right weighting matrices $W_L, W_R$ are designed to flatten leverage-score profiles, minimizing the maximum possible uninformative sample influence. The resulting optimization

$\min_{g\in\mathbb{C}^N} \|W_L\,\mathscr{H}(g)\,W_R^H\|_* \quad \text{s.t.}\quad \|\mathcal{P}_\Omega(g) - y_\Omega\|_2\leq \sqrt{M}\,\eta\$

is solved efficiently via ADMM, where the nuclear norm encourages low rank, and the weights reduce required sample complexity to nearly the information-theoretic minimum $\mathcal{O}(K\log^4N)$. Once a full ULA snapshot is interpolated, gridless super-resolution recovery is performed by total variation norm minimization on the restored vector. Empirical results show a 5–10 dB normalized mean squared error (NMSE) gain over unweighted approaches and atomic norm minimization (ANM), especially at high SNR or low sensor budgets. This methodology is robust, off-grid (continuous angle), and requires no prior knowledge of $K$ (Razavikia et al., 26 Jul 2025).

2. Gridless and Nonconvex Atomic Norm Minimization (ANM)

Grid-based sparse recovery methods suffer from basis mismatch and resolution limits; consequently, ANM and its nonconvex variants have become essential for super-resolution DOA estimation. In "NoncovANM: Gridless DOA Estimation for LPDF System" (Zhao et al., 2023), a low-cost passive direction finding architecture exploits an IRS and a single-channel receiver. Multiple virtual array responses are acquired by sequentially configuring binary phase patterns on IRS elements, creating a measurement matrix $B$. The observed data matrix $Y$ is fit to a continuous-parameter atomic model

$$\min_Z \frac{1}{2}\|Y-B^T Z\|_F^2 + \tau\|Z\|_\mathcal{A}$$

where $\mathcal{A}$ is the set of continuous steering vectors. To bypass computationally heavy SDPs, a gradient-thresholded nonconvex algorithm (NC-ANM) is proposed, operating directly on the $\ell_{A,0}$ pseudo-norm. Saddles are escaped via random perturbations; sparsity is enforced by hard thresholding, and convergence to stationary points is guaranteed under mild smoothness. This approach outperforms classical (convex ANM, OMP, MUSIC) and grid-based methods in accuracy (RMSE $\approx$ 0.19°, nearly 2x improvement over convex ANM), achieving near-CRLB performance for moderate SNR, and is computationally competitive (Zhao et al., 2023).

3. Learning-Based Extrapolation and IRS-Aided Neural Architectures

Supervised learning offers new routes to scalable, computationally efficient DOA estimation. For MIMO radar, "Supervised Learning Based Super-Resolution DoA Estimation Utilizing Antenna Array Extrapolation" (Thanthrige et al., 2019) learns coupled dictionaries for small and large (virtual) arrays. The reduced measurements are extrapolated to full-array data, which is then processed by conventional MUSIC, yielding super-resolved DOA capability with far fewer physical antennas—matching large array performance at a fraction of hardware cost (RMSE: 0.6° vs. 0.5° full array, four targets, SNR = –10 dB).

In IRS-assisted regimes, deep end-to-end neural architectures directly optimize IRS phase profiles and subsequent DOA regressors. A key development is the embedding of a differentiable, unit-modulus-constrained "IRS layer" within a neural network (Azhdari et al., 26 Jun 2024). The entire system, including the IRS configuration, is trained via back-propagation to minimize RMSE of estimated angles. Benchmarks demonstrate up to an order-of-magnitude accuracy gain and a $10^5$-fold reduction in computational cost per prediction compared to grid-search ML approaches. The system is robust to NLoS, coherent multipath, and is state-of-the-art in high-density inference (Azhdari et al., 26 Jun 2024).

4. Robust DOA Estimation in Challenging Environments

Traditional subspace methods (e.g., MUSIC) degrade under partially correlated, colored, or non-uniform noise. Modern formulations exploit matrix decompositions and robust regularization:

• "DOA Estimation in Partially Correlated Noise Using Low-Rank/Sparse Matrix Decomposition" (Malek-Mohammadi et al., 2014) models the observed covariance as a sum of a low-rank signal term and a sparse noise component, with convex or SOCP programs efficiently separating and recovering the DOA spectrum. This approach excels when noise coupling structure is known or can be sparsified.
• Robust M-estimators combined with complex Lasso (M-Lasso) handle heavy-tailed or contaminated noise, iteratively optimizing both scale and sparse angle coefficients via zero-subgradient conditions and coordinate descent. The result is improved outlier rejection and resilience to misspecified noise models, with competitive computational complexity (Ollila, 2016).
• For massive receive MIMO, quantization-aware estimators are essential: hybrid analog–digital architectures with low-resolution ADCs degrade gracefully as ADC resolution decreases. Required bit depth to maintain within 1.76 dB of the CRLB is typically 3–4 at 10 dB SNR (Wang et al., 2021).

5. Novel Front-Ends and Algorithmic Paradigms

Innovative receiver architectures and processing frameworks further enhance DOA estimation resilience and capability:

• Sub-Nyquist sampling receivers with time–space union models (multi-coset) provide nearly uncorrelated union steering vectors. As per "Joint DOA and Frequency Estimation with Sub-Nyquist Sampling" (Liu et al., 2016), tensor- and subspace-based algorithms achieve CRLB-limited accuracy at fractional (20%) of the Nyquist sampling rate, regardless of number of sources.
• Multi-source DOA estimation via modal coherence learning in the spherical harmonic domain (using CNNs trained on single-source data) enables simultaneous 3D localization in highly reverberant, multi-source soundfields, outperforming combinatorially intensive baselines (Fahim et al., 2020).
• In integrated sensing and communication (ISAC) systems with RIS, atomic norm denoising and Hankel-based MUSIC steps afford interference suppression and super-resolution, achieving sub-degree RMSE and approaching CRLB, even with a single RF channel receiver (Chen et al., 2022).

6. Hybridization, Broadband, and Environmental Robustness

Recent work targets the joint estimation of DOA and noise covariance, enabling robust beamforming in reverberant and multi-interference settings. In (Curtarelli, 13 Nov 2025), a quasi-linear approach jointly fits all model parameters (DOA, per-bin source/interference/noise variances), operating on all frequency bins to globalize the cost function and circumvent exhaustive searches. The resulting angular errors are below 2° median, substantially improving over per-bin or MUSIC-based schemes in complex acoustic environments, and directly augmenting advanced beamforming pipelines.

Advanced MIMO-OFDM radar scenarios are addressed by decomposing high-dimensional delay–Doppler–angle spaces, reducing effective angular source density via spectral filtering before applying super-resolution (e.g., MUSIC) and ambiguity-resolving fusion, thus breaking the conventional limit of one resolvable target per antenna (Salman et al., 16 Jun 2025).

7. Future Directions and Practical Considerations

Hybrid analog–digital arrays, IRS/LPDF architectures, and nonconvex or learned inference models open further research questions regarding:

• Real-time scaling to massive arrays and high target densities.
• End-to-end joint estimation of angle, frequency, polarization, and range.
• Gridless methodologies handling arbitrary array geometries and mutual coupling.
• Resilience to synchronization, phase/gain calibration, and arbitrary noise models.
• Model-order selection and deep adaptation to environment statistics.

Substantial progress is reflected in robust super-resolution capability, physically aware neural system design, and approaches attaining (or closely approaching) the information-theoretic CRLB under practical constraints. The ongoing fusion of physics-driven modeling, optimization, and machine learning continues to define the leading edge of DOA estimation methods for next-generation sensing platforms.