Estimating multiple frequency-hopping signal parameters via sparse linear regression

Daniele Angelosante, Georgios B Giannakis, Nikolaos Sidiropoulos

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


Frequency hopping (FH) signals have well-documented merits for commercial and military applications due to their near-far resistance and robustness to jamming. Estimating FH signal parameters (e.g., hopping instants, carriers, and amplitudes) is an important and challenging task, but optimum estimation incurs an unrealistic computational burden. The spectrogram has long been the starting non-parametric estimator in this context, followed by line spectra refinements. The problem is that hop timing estimates derived from the spectrogram are coarse and unreliable, thus severely limiting performance. A novel approach is developed in this paper, based on sparse linear regression (SLR). Using a dense frequency grid, the problem is formulated as one of under-determined linear regression with a dual sparsity penalty, and its exact solution is obtained using the alternating direction method of multipliers (ADMoM). The SLR-based approach is further broadened to encompass polynomial-phase hopping (PPH) signals, encountered in chirp spread spectrum modulation. Simulations demonstrate that the developed estimator outperforms spectrogram-based alternatives, especially with regard to hop timing estimation, which is the crux of the problem.

Original languageEnglish (US)
Article number5483106
Pages (from-to)5044-5056
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number10
StatePublished - Oct 2010

Bibliographical note

Funding Information:
Manuscript received October 26, 2009; accepted June 01, 2010. Date of publication June 10, 2010; date of current version September 15, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Sofia C. Olhede. The work in this paper was supported by NSF Grants CCF 0830480 and CON 0824007, and also through collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. Part of the results in this paper was presented at the International Conference on Acoustics, Speech and Signal Processing, Dallas, TX, April 2010.


  • Compressive sampling
  • frequency hopping signals
  • sparse linear regression
  • spectrogram
  • spread spectrum signals


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