Wideband Waveform Design for Robust Target Detection

Future radar systems are expected to use waveforms of a high bandwidth, where the main advantage is an improved range resolution. In this paper, a technique to design robust wideband waveforms for a Multiple-Input-Single-Output system is developed. The context is optimal detection of a single object with partially unknown parameters. The waveforms are robust in the sense that, for a single transmission, detection capability is maintained over an interval of time-delay and time-scaling (Doppler) parameters. A solution framework is derived, approximated, and formulated as an optimization by means of basis expansion. In terms of probabilities of detection and false alarm, numerical evaluation shows the efficiency of the proposed method when compared with a Linear Frequency Modulated signal and a Gaussian pulse.Comment: This paper is submitted for peer review to IEEE letters on signal processin

Partial Relaxation Approach: An Eigenvalue-Based DOA Estimator Framework

In this paper, the partial relaxation approach is introduced and applied to DOA estimation using spectral search. Unlike existing methods like Capon or MUSIC which can be considered as single source approximations of multi-source estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the interference parameters. The conventional multidimensional optimization problem reduces, thanks to this relaxation, to a simple spectral search. Following this principle, we propose estimators based on the Deterministic Maximum Likelihood, Weighted Subspace Fitting and covariance fitting methods. To calculate the pseudo-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that the performance of the proposed estimators is superior to the conventional methods especially in the case of low Signal-to-Noise-Ratio and low number of snapshots, irrespectively of any specific structure of the sensor array while maintaining a comparable computational cost as MUSIC.Comment: This work has been submitted to IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Low PAPR waveform synthesis with application to wideband MIMO radar

This paper considers the problem of waveform synthesis given a desired power spectrum. The properties of the designed waveforms are such that the overall system performance is increased. The metric used to evaluate the optimality of the synthesized time domain signals is the peak-to-average power ratio (PAPR). We discuss how to synthesize waveforms using the technique of partial transmit sequence (PTS). The key point is that the gradient can explicitly be derived from the objective function. Furthermore, the result is extended by allowing the power spectrum to deviate from its original shape, yielding a further reduction in the PAPR. The method is applied to derived power spectra for wideband multiple-input-multiple-output (MIMO) radar. It is shown that the proposed technique can achieve optimal or near optimal performance with PAPR below 0.5 dB

On the resolution of the LASSO-based DOA estimation method

This paper investigates the consistency of the LASSO-based DOA estimation of the narrow-band signals in infinitely high SNR. Such a method provides a robust and accurate approximation of the Maximum Likelihood estimation. However, as we show, unlike the standard techniques such as subspace methods the LASSO-based estimation is generally not consistent in high SNRs. In return, considering the true DOA's, we show that the method is consistent for certain configuration of the sources. This approach leads us to relate such a conditional consistency to the resolution concept. We next give a condition to verify the consistency of a given set of directions and simplify it to a computationally fast equivalent algorithm. The results show that the resolution in infinitely high SNR case for m sensors decreases by speed 1 over m

Fast LASSO based DOA tracking

In this paper, we propose a sequential, fast DOA tracking technique using the measurements of a uniform linear sensor array in the far field of a set of narrow band sources. Our approach is based on sparse approximation technique LASSO (Least Absolute Shrincage and Selection Operator), which has recently gained considerable interest for DOA and other estimation problems. Considering the LASSO optimization as a Bayesian estimation, we first define a class of prior distributions suitable for the sparse representation of the model and discuss its relation to the priors over DOAs and waveforms. Inspired by the Kalman filtering method, we introduce a nonlinear sequential filter on this family of distributions. We derive the filter for a simple random walk motion model of the DOAs. The method consists of consecutive implementation of weighted LASSO optimizations using each new measurement and updating the LASSO weights for the next step

Maximum a Posteriori Based Regularization Parameter Selection

The l(1) norm regularized least square technique has been proposed as an efficient method to calculate sparse solutions. However, the choice of the regularization parameter is still an unsolved problem, especially when the number of nonzero elements is unknown. In this paper we first design different ML estimators by interpreting the l(1) norm regularization as a MAP estimator with a Laplacian model for data. We also utilize the MDL criterion to decide on the regularization parameter. The performance of these new methods are evaluated in the context of estimating the Directions Of Arrival (DOA) for the simulated data and compared. The simulations show that the performance of the different forms of the MAP estimator are approximately equal in the one snapshot case, where MDL may not work. But for the multiple snapshot case both methods can be used

Fast Candidate Points Selection in the LASSO Path

The LASSO sparse regression method has recently received attention in a variety of applications from image compression techniques to parameter estimation problems. This paper addresses the problem of regularization parameter selection in this method in a general case of complex-valued regressors and bases. Generally, this parameter controls the degree of sparsity or equivalently, the estimated model order. However, with the same sparsity/model order, the smallest regularization parameter is desired. We relate such points to the nonsmooth points in the path of LASSO solutions and give an analytical expression for them. Then, we introduce a numerically fast method of approximating the desired points by a recursive algorithm. The procedure decreases the necessary number of solutions of the LASSO problem dramatically, which is an important issue due to the polynomial computational cost of the convex optimization techniques. We illustrate our method in the context of DOA estimation