ML Estimation and Detection of Multiple Frequencies Through Periodogram Estimate Refinement

This letter presents a method to detect and estimate multiple frequencies based on the maximum-likelihood principle. The method addresses the three main difficulties in this kind of computation, which are the detection of the number of frequencies, the coarse localization of the cost function's global maximum, and the iterative refinement of an initial estimate. Fundamentally, it consists of first detecting and estimating single frequencies or frequency clusters using the periodogram, and then refining this last estimate through a Newton-type method. This second step is fast because its complexity is independent of the number of samples, once a single fast Fourier transform (FFT) has been computed. These two steps are iteratively repeated until no mode frequency is above a fixed detection threshold. The main advantage of the proposed method is its low complexity, given that its computational burden is just that of a few FFTs in typical scenarios. The method is assessed in a numerical example.This work was supported by the Spanish Ministry of Economy and Competitiveness and EU FEDER under project TIN2014-55413-C2-2-P

Deterministic Algorithms for Four-Dimensional Imaging in Colocated MIMO OFDM-Based Radar Systems

In this manuscript, the problem of detecting multiple targets and jointly estimating their spatial coordinates (namely, the range, the Doppler and the direction of arrival of their electromagnetic echoes) in a colocated multiple-input multiple-output radar system employing orthogonal frequency division multiplexing is investigated. It is well known its optimal solution, namely the joint maximum likelihood estimator of an unknown number of targets, is unfeasible because of its huge computational complexity. Moreover, until now, sub-optimal solutions have not been proposed in the technical literature. In this manuscript a novel approach to the development of reduced complexity solutions is illustrated. It is based on the idea of separating angle estimation from range-Doppler estimation, and of exploiting known algorithms for solving these two sub-problems. A detailed analysis of the accuracy and complexity of various detection and estimation methods based on this approach is provided. Our numerical results evidence that one of these methods is able to approach optimal performance in the maximum likelihood sense with a limited computational effort in different scenarios

Global testing against sparse alternatives in time-frequency analysis

In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the rareness and weakness of the complex sinusoids hidden in the series. The OPHC test is shown to be asymptotically powerful in the detectable region. Numerical simulations illustrate and verify the effectiveness of the proposed test. Furthermore, the periodogram over-sampled by $O(\log N)$ is proven universally optimal in global testing for periodicities under a mild minimum separation condition.Comment: Published at http://dx.doi.org/10.1214/15-AOS1412 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Variational Bayesian Inference of Line Spectra

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a more complete Bayesian treatment by estimating the posterior probability density functions (pdfs) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional parameters. We propose an accurate representation of the pdfs of the frequencies by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does not require parameter tuning, can easily include prior knowledge about the frequencies and provides approximate posterior pdfs based on which the uncertainty in line spectral estimation can be quantified. Simulation results show that accounting for the uncertainty of frequency estimates, rather than computing just point estimates, significantly improves the performance. The performance of VALSE is superior to that of state-of-the-art methods and closely approaches the Cram\'er-Rao bound computed for the true model order.Comment: 15 pages, 8 figures, accepted for publication in IEEE Transactions on Signal Processin

Multidimensional Frequency Estimation with Applications in Automotive Radar

This thesis considers multidimensional frequency estimation with a focus on computational efficiency and high-resolution capability. A novel framework on multidimensional high-resolution frequency estimation is developed and applied to increase the range, radial velocity, and angular resolution capcability of state-of-the-art automotive radars

An Approximate Maximum Likelihood Method for the Joint Estimation of Range and Doppler of Multiple Targets in OFDM-Based Radar Systems

In this manuscript, an innovative method for the detection and the estimation of multiple targets in a radar system employing orthogonal frequency division multiplexing is illustrated. The core of this method is represented by a novel algorithm for detecting multiple superimposed two-dimensional complex tones in the presence of noise and estimating their parameters. This algorithm is based on a maximum likelihood approach and combines a single tone estimator with a serial cancellation procedure. Our numerical results lead to the conclusion that the developed method can achieve a substantially better accuracy-complexity trade-off than various related techniques in the presence of closely spaced targets