Frequency estimation for a mixture of sinusoids: A near-optimal sequential approach

Mamandipoor, Babak; Ramasamy, Dinesh; Madhow, Upamanyu

doi:10.1109/globalsip.2015.7418186

Cited by 9 publications

(3 citation statements)

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“…We present NOMP within an application-independent abstraction, recognizing the fundamental nature and widespread utility of the frequency estimation problem. We have reported on a version of NOMP in a recent conference paper [35] (although the algorithm in [35] omits a least squares step included here for establishing convergence rate results, but with little impact on practical performance). The present paper goes beyond [35] in providing a detailed convergence analysis, and a comprehensive comparison with the state of the art.…”

Section: B Related Workmentioning

confidence: 99%

“…We perform 300 simulation runs for each of the four scenarios characterized by ∆ω min and SNR values. The settings for different scenarios are summarized in Table I In Scenarios 1 and 2, the nominal SNR for each sinusoid is set as SNR nom = 25 dB, whereas for Scenarios 3 and 4, the SNR values are chosen uniformly from [15,35] dB, with mean equal to the nominal SNR of 25 dB. In each simulation run, the gain magnitudes are set to |g l | = σ √ SNR l , while the phases {∠g l } are chosen uniformly from [0, 2π).…”

Section: Simulation Set-upmentioning

confidence: 99%

“…In Scenarios 3 and 4, the SNRs are drawn independently and uniformly at random from the interval [15,35] dB. In order to evaluate the frequency MSE in these scenarios, we fix the SNR of one of the sinusoids in the mixture at a given value, while letting the other (K − 1) SNRs to be realized randomly.…”

Section: A Frequency Estimation Accuracy 1) Distribution Of Errormentioning

confidence: 99%

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Newtonized Orthogonal Matching Pursuit: Frequency Estimation Over the Continuum

Mamandipoor¹,

Ramasamy²,

Madhow³

2016

IEEE Trans. Signal Process.

185

132

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Abstract-We propose a fast sequential algorithm for the fundamental problem of estimating frequencies and amplitudes of a noisy mixture of sinusoids. The algorithm is a natural generalization of Orthogonal Matching Pursuit (OMP) to the continuum using Newton refinements, and hence is termed Newtonized OMP (NOMP). Each iteration consists of two phases: detection of a new sinusoid, and sequential Newton refinements of the parameters of already detected sinusoids. The refinements play a critical role in two ways: (1) sidestepping the potential basis mismatch from discretizing a continuous parameter space, (2) providing feedback for locally refining parameters estimated in previous iterations. We characterize convergence, and provide a Constant False Alarm Rate (CFAR) based termination criterion. By benchmarking against the Cramér Rao Bound, we show that NOMP achieves near-optimal performance under a variety of conditions. We compare the performance of NOMP with classical algorithms such as MUSIC and more recent Atomic norm Soft Thresholding (AST) and Lasso algorithms, both in terms of frequency estimation accuracy and run time.

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Section: B Related Workmentioning

confidence: 99%

Section: Simulation Set-upmentioning

confidence: 99%

Section: A Frequency Estimation Accuracy 1) Distribution Of Errormentioning

confidence: 99%

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