# Sensor Array Signal Processing

Array signal processing considers the problem of signal processing in multi-antenna systems and is essential for many applications such as radar, sonar, radio astronomy, and seismic exploration. Traditional applications in array signal processing include beamforming and direction-of-arrival estimation. In beamforming, also referred to as spatial filtering, the goal is reconstruction of an inmpinging signal from noisy and interfered measurements. Direction-of-arrival (DOA) estimation considers the problem of estimating the angular direction of emitting source and can be considered as a special instance of parameter estimation. In the communication systems group we investigate DOA estimation methods by means of sparse signal reconstruction and decentralized approaches, as well as MIMO radar and array calibration techniques for radio interferometry.

## Sparse Signal Reconstruction

Subspace-based methods for parameter estimation such as the MUSIC algorithm have been shown to perform close to optimal in many practical situations. However, there are some specific cases in which MUSIC fails, e.g. in the case of few number of measurements. Sparse signal reconstruction (SSR) is based on a relatively new paradigm and it has been shown in literature that SSR methods operate well in these challenging scenarios such that SSR can be considered as a complement to subspace-based methods.

The subject of sparse signal reconstruction (SSR) provides a highly attractive field of research with various types applications in engineering, including direction-of-arrival estimation, spectral analysis, image processing, magnetic resonance tomography, machine learning, and many more. The underlying theory covers many aspects of signal processing, reaching from the field of parameter estimation up to the field of convex and discrete optimization. Sparse reconstruction can be performed by various techniques such as greedy algorithms, e.g., orthogonal matching pursuit, or convex optimization techniques, e.g., LASSO, where the latter category usually shows better reconstruction performance at the cost of higher computational complexity.

In the communication systems group we consider SSR for parameter estimation on the basis of convex optimization. Within the EXPRESS project we focus on parameter estimation in array processing and consider SSR by exploiting different types structure, i.e., structure in the measurement system, structure in the signal, structure in the sparsity and structure in the measurements, as illustrated in Figure 2. In the ADEL project we focus on the application of collaborative spectrum sensing in wireless communications as an enabler to licensed shared access in 5G mobile communication networks.

**Associated Researchers:**

**Projects and Colaborations:**

## Decentralized Array Signal Processing

Traditional array processing application consider a centralized signal processing approach, i.e., all measurements are collected and processed in a central fucion center. For this approach it is furthermore assumed, that the overall array response is perfectly known, i.e., a fully-calibrated array is considered.

In recent years, centralized processing has been considered to have several drawbacks, such as lack of robustness in form of an error-prone fusion center, lack of flexibility or communication overhead. Dencentralized processing approaches are considered to be a promising alternative to overcome the aforementioned drawbacks. In the context of array singal processing, a decentralized array is usually considered to be composed of multiple subarrays, where the subarray responses are perfectly known while the overall array response is unavailable, which is referred to as partly calibrated array. While there exist methods to deal with the partly-calibrated array structure, such as subspace-based ESPRIT, other challenges in the decentralized approach lie in the decentralized signal processing and the requirement of a low communication overhead. One method to address these challenges is given by the averaging consensus protocol, which admitts decentralized computation of the signal subspace.

In the communication systems group we investigate decentralized signal processing methods for parameter estimation with focus on low communication cost, robustness against array imperfections, such as, timing errors between the subarrays and unknown displacements between the arrays. Within the ADEL project we extend our results to the related field of collaborative spectrum sensing.

**Associated Researcher:**

**Projects and Colaborations:**

## MIMO Radar Under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model, which is a two-scale, complex, compound Gaussian process with random power, structured as the product of two components: a complex Gaussian process with zero mean and unknown covariance matrix (called the speckle), and the square root of a positive scalar random process (called the texture).

In the communication systems group, we focus on the target parameter estimation and performance analysis for the MIMO radar under the SIRP clutter. Our research includes the design of algorithms for the direction-of-departure (DOD)/direction of arrival (DOA) estimation of the targets, the investigation of performance tools such as the Cramer-Rao-type bounds (CRTBs) and the resolution limit (RL) in this context.

**Associated Researcher:**

**Collaboration:**

- ENS Cachan, Paris

## Array Calibration for Radio Interferometers

Astronomical instruments measure cosmic particles or electromagnetic waves impinging on the Earth. Astronomers use the data generated by these instruments to study physical phenomena outside the Earth’s atmosphere. Since the 1980s, radio telescopes are interferometers and measure the correlation of the signals received by antennas spaced at a certain distance. These telescopes use Earth rotation to obtain a sequence of correlations for varying antenna baselines, resulting in high-resolution images via synthesis mapping.

The radio astronomy community is currently commissioning a new generation of radio interferometers for low frequency observations, including the Low Frequency Array (LOFAR) in Europe. These exploit phased array technology (in opposite with classical big dishes) to form a large collecting area with 1000 to 50 000 receiving elements. The world’s largest physically connected telescopes, the SKA (Square Kilometer Array), are planned to start operation in 2024. These future radio interferometers should be one to two orders of magnitude more sensitive than any radio telescope built to date. The individual antennas in a phased array telescope have an extremely wide Field-Of-View, often the entire visible sky. This poses a number of signal processing challenges, because certain assumptions that work well for small Fields-of-View (celestial sphere approximated by a plane, homogeneous propagation conditions over the Field-of-View) are no longer valid. At low frequencies, the ionospheric disturbances are particularly problematic and the algorithms must be suitable for huge data volumes and real-time processing. The signal processing community accompanies this technological change and brings its knowledge and mathematical tools, for dealing with these challenges in calibration, imaging and interference suppression. The application at the NTS group include the calibration problem, that must solve for the unknown antenna gains and phases, as well as the unknown atmospheric and ionospheric disturbances.

**Associated Researcher:**

- Martin Brossard

**Collaboration:**

- ENS Cachan, Cachan (France)