Sensor Array Processing

Sensor array processing and Direction-of-Arrival (DoA) estimation, has the goal of estimating the directions of a superposition of multiple waves impinging on an array of sensors. It a fundamental and traditional research area that recently receives new momentum: Applications in automotive, radar, drone localization, parametric channel estimation in Massive MIMO systems and many more require precise sensor array processing in real-time. This development is further inspired by the emergence of new powerful and affordable multiantenna hardware platforms.

Today, we are looking back at a history of more than four decades of super resolution DoA estimation techniques. Yet, driven by newly emerging applications and advances in convex optimization techniques the research field is remarkably dynamic in its evolution. Research in this area is driven by the applications and the requirement to find new algorithms with improved trade-offs between computational complexity, estimation performance and robustness to various types of mismatch in the sensor measurements.

Mathematical Models as a Foundation for Efficient Hardware Implementations

The so-called subspace methods are computationally efficient and make use of the underlying geometric properties of the measurement tensor, i.e., the low-rank properties of the array covariance matrix. These methods achieve super-resolution performance. Unlike classical Fourier methods their resolution is not limited by the aperture size but only by the number of snapshots. In today's applications the data dimensions are constantly increasing. Signal processing algorithm are required that make efficient use of modern parallel hardware architectures such as multi-core digital signal processors (DSPs), field programmable gate arrays (FPGAs), and graphical processing units (GPUs).

Recently, convex optimization techniques emerged that exploit the sparsity of the underlying signal model and enable accurate DoA estimation from single snapshots. The sparsity in the model assumption stems from the observation that in practical applications with point sources, the directions of the impinging waves are discrete and the number of source signals is generally much smaller than the number of available measurements.

Establishing Novel Standards in DoA-Estimation at TU Darmstadt

A current trend in sensor array and multichannel signal processing is to design optimization-based

techniques that exploit the underlying structure of the signal model to enhance the quality of the

estimation. Depending on the considered DoA estimation approach it turns out that it is often convenient to deliberately ignore a specific part of the structure to achieve significant gains in the algorithms’ computational complexity. In this context, the Partial Relaxation approach has been developed at the communication systems group of TU Darmstadt as a competitive framework work for reduced complexity DoA estimation with excellent performance in the low signal-to-noise-ratio (SNR) region.


DFG Project “The partial relaxation method in direction-of-arrival estimation: Design and Analysis”PRIDE

Further Reading

Pesavento, Marius; Trinh-Hoang, Minh; Viberg, Mats: Three More Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective. 2022, arXiv, doi:10.48550/arXiv.2210.15012, Official URL, [Preprint]

Trinh-Hoang, Minh; Viberg, Mats; Pesavento, Marius: Cramér-Rao Bound for DOA Estimators Under the Partial Relaxation Framework: Derivation and Comparison. In: IEEE Transactions on Signal Processing 2020, 68, ISSN: 1941-0476, doi:10.1109/TSP.2020.2992855, [Article]

Trinh-Hoang, Minh; Viberg, Mats; Pesavento, Marius: Partial Relaxation Approach: An Eigenvalue-based DOA Estimator Framework. In: IEEE Transactions on Signal Processing 2018, 66, ISSN: 1941-0476, doi:10.1109/TSP.2018.2875853, [Article]

Steffens, Christian; Pesavento, Marius; Pfetsch, Marc E.: A Compact Formulation for the $\ell_{2,1}$ Mixed-norm Minimization Problem. In: IEEE Transactions on Signal Processing 2018, 66, [Article]

Steffens, Christian; Pesavento, Marius: Block- and Rank-Sparse Recovery for Direction Finding in Partly Calibrated Arrays. In: IEEE Transactions on Signal Processing 2018, 66, ISSN: 1941-0476, doi:10.1109/TSP.2017.2770104, [Article