Alle-Jan van der Veen

MULTICHANNEL INTERFERENCE MITIGATION TECHNIQUES IN RADIO ASTRONOMY

Radio-astronomical observations are increasingly corrupted by radio frequency interference, and on-line detection and filtering algorithms are becoming essential. To facilitate the introduction of such techniques into radio astronomy, we formulate the astronomical problem in an array signal processing language and give an introduction to some elementary algorithms from that field. We consider two topics in detail: interference detection by rank estimation of short-term covariance matrices and spatial filtering by subspace estimation and projection. We discuss experimental data collected at the Westerbork Synthesis Radio Telescope and illustrate the effectiveness of the spacetime detection and blanking process on the recovery of a 3C 48 absorption line in the presence of GSM mobile telephony interference.

Signal Processing Tools for Radio Astronomy

Radio astronomy is known for its very large telescope dishes, but is currently making a transition towards the use of large numbers of small elements. For example, the Low Frequency Array, commissioned in 2010, uses about 50 stations, each consisting of at least 96 low band antennas and 768 high band antennas. For the Square Kilometre Array, planned for 2024, the numbers will be even larger. These instruments pose interesting array signal processing challenges. To present some aspects, we start by describing how the measured correlation data is traditionally converted into an image, and translate this into an array signal processing framework. This paves the way for a number of alternative image reconstruction techniques, such as a Weighted Least Squares approach. Self-calibration of the instrument is required to handle instrumental effects such as the unknown, possibly direction dependent, response of the receiving elements, as well a unknown propagation conditions through the Earth’s troposphere and ionosphere. Array signal processing techniques seem well suited to handle these challenges. The fact that the noise power at each antenna element may be different motivates the use of Factor Analysis, as a more appropriate alternative to the eigenvalue decomposition that is commonly used in array processing. Factor Analysis also proves to be very useful for interference mitigation. Interestingly, image reconstruction, calibration and interference mitigation are often intertwined in radio astronomy, turning this into an area with very challenging signal processing problems.

A Low Complexity Blind Estimator of Narrowband Polynomial Phase Signals

Consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array. In practice, it is difficult to maintain a precisely calibrated array. The array manifold is then assumed to be unknown, and the estimation is referred to as blind estimation. To date, only an approximated maximum likelihood estimator (AMLE) was suggested for blindly estimating the polynomial coefficients of each signal. However, this estimator requires a multidimensional search over the entire coefficient space. Instead, we propose an estimation approach which is based on two steps. First, the signals are separated using a blind source separation technique, which exploits the constant modulus property of the signals. Then, the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal. This estimator does not involve any search in the coefficient spaces. The computational complexity of the proposed estimator increases linearly with respect to the polynomial order, whereas that of the AMLE increases exponentially. Simulation results show that the proposed estimator achieves the Cramér-Rao lower bound at moderate or high signal to noise ratio.

Joint Clock Synchronization and Ranging: Asymmetrical Time-Stamping and Passive Listening

A fully asynchronous network with one sensor and M anchors (nodes with known locations) is considered in this letter. We propose a novel asymmetrical time-stamping and passive listening (ATPL) protocol for joint clock synchronization and ranging. The ATPL protocol exploits broadcast to not only reduce the number of active transmissions between the nodes, but also to obtain more information. This is used in a simple estimator based on least-squares (LS) to jointly estimate all the unknown clock-skews, clock-offsets, and pairwise distances of the sensor to each anchor. The Cramér-Rao lower bound (CRLB) is derived for the considered problem. The proposed estimator is shown to be asymptotically efficient, meets the CRLB, and also performs better than the available clock synchronization algorithms.

Joint ranging and clock synchronization for a wireless network

Synchronization and localization are two key aspects for the coherent functioning of a wireless network. Recently, various estimators have been proposed for pairwise synchronization between two nodes based on time stamp exchanges via two way communication. In this paper, we propose a closed form centralized Global Least Squares (GLS) estimator, which exploits the two way communication information between all the nodes in a wireless network. The fusion center based GLS uses a single clock reference and estimates all the unknown clock offsets, skews and pairwise distances in the network. The GLS estimate for clock offsets and skews is shown to outperform prevalent estimators. Furthermore, a new Cramer Rao Lower Bound (CRLB) is derived for the entire network and the proposed GLS solution is shown to approach the theoretical limits.

Joint Ranging and Synchronization for an Anchorless Network of Mobile Nodes

Synchronization and localization are critical challenges for the coherent functioning of a wireless network, which are conventionally solved independently. Recently, various estimators have been proposed for pairwise synchronization between immobile nodes, based on time stamp exchanges via two-way communication. In this paper, we consider a network of mobile nodes for which a novel joint time-range model is presented, treating both unsynchronized clocks and the pairwise distances as a polynomial functions of true time. For a pair of nodes, a least squares solution is proposed for estimating the pairwise range parameters between the nodes, in addition to estimating the clock offsets and clock skews. Extending these pairwise solutions to network-wide ranging and clock synchronization, we present a central data fusion based global least squares algorithm. A unique solution is nonexistent without a constraint on the cost function e.g., a clock reference node. Ergo, a constrained framework is proposed and a new Constrained Cramér-Rao Bound (CCRB) is derived for the joint time-range model. In addition, to alleviate the need for a single clock reference, various clock constraints are presented and their benefits are investigated using the proposed solutions. Simulations are conducted and the algorithms are shown to approach the theoretical limits.

Array signal processing for radio astronomy

Radio astronomy forms an interesting application area for array signal processing techniques. Current synthesis imaging telescopes consist of a small number of identical dishes, which track a fixed patch in the sky and produce estimates of the time-varying spatial covariance matrix. The observations sometimes are distorted by interference, e.g., from radio, TV, radar or satellite transmissions. We describe some of the tools that array signal processing offers to filter out the interference, based on eigenvalue decompositions and factor analysis, which is a more general technique applicable to partially calibrated arrays. We consider detection of interference, spatial filtering techniques using projections, and discuss how a reference antenna pointed at the interferer can improve the performance. We also consider image formation and its relation to beamforming.

Joint localization and clock synchronization for wireless sensor networks

A fully-asynchronous network with one target sensor and a few anchors (nodes with known locations) is considered. Localization and synchronization are traditionally treated as two separate problems. In this paper, localization and synchronization is studied under a unified framework. We present a new model in which time-stamps obtained either via two-way communication between the nodes or with a broadcast based protocol can be used in a simple estimator based on least-squares (LS) to jointly estimate the position of the target node as well as all the unknown clock-skews and clock-offsets. The Cramér-Rao lower bound (CRLB) is derived for the considered problem and is used as a benchmark to analyze the performance of the proposed estimator.

Robust localization in sensor networkswith iterative majorization techniques

Self localization in sensor networks with measurements that include outliers is an important problem. E.g., distance measurements based on non-line-of-sight observations can be quite wrong. If not handled properly, such outliers can greatly influence the positioning accuracy. To achieve robustness we consider positioning with Huber estimators. The Huber cost function interpolates between the ℓ1 and the ℓ2 norms. The minimization of the Huber cost function can be efficiently obtained via iterative majorization techniques, with the advantageous property of guaranteed convergence to a local minimum.

A Parallel VLSI Direction Finding Algorithm

In this paper, we present a parallel VLSI architecture that is matched to a class of direction (frequency, pole) finding algorithms of type ESPRIT. The problem is modeled in such a way that it allows an easy to partition full parallel VLSI implementation, using unitary transformations only. The hard problem, the generalized Schur decomposition of a matrix pencil, is tackled using a modified Stewart Jacobi approach that improves convergence and simplifies parameter computations. The proposed architecture is a fixed size, 2-layer Jacobi iteration array that is matched to all sub-problems of the main problem: 2 QR-factorizations, 2 SVDs and a single GSD-problem. The arithmetic used is (pipelined) Cordic.