Sparse Array DFT Beamformers for Wideband Sources

Sparse arrays are popular for performance optimization while keeping the hardware and computational costs down. In this paper, we consider sparse arrays design method for wideband source operating in a wideband jamming environment. Maximizing the signal-to-interference plus noise ratio (MaxSINR) is adopted as an optimization objective for wideband beamforming. Sparse array design problem is formulated in the DFT domain to process the source as parallel narrowband sources. The problem is formulated as quadratically constraint quadratic program (QCQP) alongside the weighted mixed $l_{1-\infty}$-norm squared penalization of the beamformer weight vector. The semidefinite relaxation (SDR) of QCQP promotes sparse solutions by iteratively re-weighting beamformer based on previous iteration. It is shown that the DFT approach reduces the computational cost considerably as compared to the delay line approach, while efficiently utilizing the degrees of freedom to harness the maximum output SINR offered by the given array aperture

Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch

It is well known that the performance of the minimum variance distortionless response (MVDR) beamformer is very sensitive to steering vector mismatch. Such mismatches can occur as a result of direction-of-arrival (DOA) errors, local scattering, near-far spatial signature mismatch, waveform distortion, source spreading, imperfectly calibrated arrays and distorted antenna shape. In this paper, an adaptive beamformer that is robust against the DOA mismatch is proposed. This method imposes two quadratic constraints such that the magnitude responses of two steering vectors exceed unity. Then, a diagonal loading method is used to force the magnitude responses at the arrival angles between these two steering vectors to exceed unity. Therefore, this method can always force the gains at a desired range of angles to exceed a constant level while suppressing the interferences and noise. A closed-form solution to the proposed minimization problem is introduced, and the diagonal loading factor can be computed systematically by a proposed algorithm. Numerical examples show that this method has excellent signal-to-interference-plus-noise ratio performance and a complexity comparable to the standard MVDR beamformer

Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling

Solving linear regression problems based on the total least-squares (TLS) criterion has well-documented merits in various applications, where perturbations appear both in the data vector as well as in the regression matrix. However, existing TLS approaches do not account for sparsity possibly present in the unknown vector of regression coefficients. On the other hand, sparsity is the key attribute exploited by modern compressive sampling and variable selection approaches to linear regression, which include noise in the data, but do not account for perturbations in the regression matrix. The present paper fills this gap by formulating and solving TLS optimization problems under sparsity constraints. Near-optimum and reduced-complexity suboptimum sparse (S-) TLS algorithms are developed to address the perturbed compressive sampling (and the related dictionary learning) challenge, when there is a mismatch between the true and adopted bases over which the unknown vector is sparse. The novel S-TLS schemes also allow for perturbations in the regression matrix of the least-absolute selection and shrinkage selection operator (Lasso), and endow TLS approaches with ability to cope with sparse, under-determined "errors-in-variables" models. Interesting generalizations can further exploit prior knowledge on the perturbations to obtain novel weighted and structured S-TLS solvers. Analysis and simulations demonstrate the practical impact of S-TLS in calibrating the mismatch effects of contemporary grid-based approaches to cognitive radio sensing, and robust direction-of-arrival estimation using antenna arrays.Comment: 30 pages, 10 figures, submitted to IEEE Transactions on Signal Processin

On the detection of spectral ripples from the Recombination Epoch

Photons emitted during the epochs of Hydrogen ($500 \lesssim z \lesssim 1600$) and Helium recombination ($1600 \lesssim z \lesssim 3500$ for HeII $\rightarrow$ HeI, $5000 \lesssim z \lesssim 8000$ for HeIII $\rightarrow$ HeII) are predicted to appear as broad, weak spectral distortions of the Cosmic Microwave Background. We present a feasibility study for a ground-based experimental detection of these recombination lines, which would provide an observational constraint on the thermal ionization history of the Universe, uniquely probing astrophysical cosmology beyond the last scattering surface. We find that an octave band in the 2--6 GHz window is optimal for such an experiment, both maximizing signal-to-noise ratio and including sufficient line spectral structure. At these frequencies the predicted signal appears as an additive quasi-sinusoidal component with amplitude about $8$ nK that is embedded in a sky spectrum some nine orders of magnitude brighter. We discuss an algorithm to detect these tiny spectral fluctuations in the sky spectrum by foreground modeling. We introduce a \textit{Maximally Smooth} function capable of describing the foreground spectrum and distinguishing the signal of interest. With Bayesian statistical tests and mock data we estimate that a detection of the predicted distortions is possible with 90\% confidence by observing for 255 days with an array of 128 radiometers using cryogenically cooled state-of-the-art receivers. We conclude that detection is in principle feasible in realistic observing times; we propose APSERa---Array of Precision Spectrometers for the Epoch of Recombination---a dedicated radio telescope to detect these recombination lines.Comment: 33 pages, 16 figures, submitted to ApJ, comments welcom

Time domain synthesis of pulsed arrays

Pulsed arrays are becoming popular in new ultrawideband applications to enhance the robustness of transmitted and received signals in complex environments and to identify the angle of arrival of multiple echoes. A global synthesis technique is here proposed to shape the array field in accordance to given angle-time constraints. The synthesis problem is cast as the inverse Radon transform of a desired array mask, applying the alternate projections method to include constraints over the input signals' waveform and to improve the synthesis robustness. The unknown array currents are generated as linear combinations of Hermite-Rodriguez functions in order to achieve a simple and realizable beamforming network. The effectiveness of the method is demonstrated by many examples

Understanding synthesis imaging dynamic range

We develop a general framework for quantifying the many different contributions to the noise budget of an image made with an array of dishes or aperture array stations. Each noise contribution to the visibility data is associated with a relevant correlation timescale and frequency bandwidth so that the net impact on a complete observation can be assessed. All quantities are parameterised as function of observing frequency and the visibility baseline length. We apply the resulting noise budget analysis to a wide range of existing and planned telescope systems that will operate between about 100 MHz and 5 GHz to ascertain the magnitude of the calibration challenges that they must overcome to achieve thermal noise limited performance. We conclude that calibration challenges are increased in several respects by small dimensions of the dishes or aperture array stations. It will be more challenging to achieve thermal noise limited performance using 15 m class dishes rather than the 25 m dishes of current arrays. Some of the performance risks are mitigated by the deployment of phased array feeds and more with the choice of an (alt,az,pol) mount, although a larger dish diameter offers the best prospects for risk mitigation. Many improvements to imaging performance can be anticipated at the expense of greater complexity in calibration algorithms. However, a fundamental limitation is ultimately imposed by an insufficient number of data constraints relative to calibration variables. The upcoming aperture array systems will be operating in a regime that has never previously been addressed, where a wide range of effects are expected to exceed the thermal noise by two to three orders of magnitude. Achieving routine thermal noise limited imaging performance with these systems presents an extreme challenge. The magnitude of that challenge is inversely related to the aperture array station diameter.Comment: 27 pages, 24 figures, accepted in A&A, final versio

MVDR broadband beamforming using polynomial matrix techniques

This paper presents initial progress on formulating minimum variance distortionless response (MVDR) broadband beamforming using a generalised sidelobe canceller (GSC) in the context of polynomial matrix techniques. The quiescent vector is defined as a broadband steering vector, and we propose a blocking matrix design obtained by paraunitary matrix completion. The polynomial approach decouples the spatial and temporal orders of the filters in the blocking matrix, and decouples the adaptive filter order from the construction of the blocking matrix. For off-broadside constraints the polynomial approach is simple, and more accurate and considerably less costly than a standard time domain broadband GSC