volume | PIER Journals

Abstract

Unlike some traditional polynomial phase signal (PPS) parameter estimation methods restricted to monocomponent case, this paper focuses on the parameter estimation of multicomponent PPSs mixed in a single channel, which is more sophisticated and always involves the cross-term issue. In this investigation, based on the model of multicomponent PPSs in additional white Gaussian noise, we partition the maximum likelihood estimation into two consecutive steps. The first one involving estimation of polynomial coefficients is intensively studied using importance sampling, while the second one involving the estimation of amplitude and initial phase is trivial. Numerical experiments show satisfactory estimation performance even if the parameters are closely spaced.

1. Abatzoglou, T. J., "Fast maximum likelihood joint estimation of frequency and frequency rate," IEEE Transactions on Aerospace and Electronic Systems, Vol. 22, No. 6, 708-715, 1986.
doi:10.1109/TAES.1986.310805 Google Scholar

2. Angeby, J., "Estimating signal parameters using the nonlinear instantaneous least squares approach," IEEE Transactions on Signal Processing, Vol. 48, No. 10, 2721-2732, 2000.
doi:10.1109/78.869022 Google Scholar

3. Pham, D. S. and A. M. Zoubir, "Analysis of multicomponent poly-nomial phase signals," IEEE Transactions on Signal Processing, Vol. 55, No. 1, 56-65, 2007.
doi:10.1109/TSP.2006.882085 Google Scholar

4. Peleg, S. and B. Porat, "Estimation and classification of polynomial-phase signals," IEEE Transactions on Information Theory, Vol. 37, No. 2, 422-430, 1991.
doi:10.1109/18.75269 Google Scholar

5. Peleg, S. and B. Friedlander, "The discrete polynomial-phase transform," IEEE Transactions on Signal Processing, Vol. 43, No. 8, 1901-1914, 1995.
doi:10.1109/78.403349 Google Scholar

6. Porat, B. and B. Friedlander, "Asymptotic statistical analysis of the high-order ambiguity function for parameter estimation of polynomial-phase signals ," IEEE Transactions on Information Theory, Vol. 42, No. 3, 995-1001, 1996.
doi:10.1109/18.490563 Google Scholar

7. Peleg, S. and B. Friedlander, "Multicomponent signal analysis using the polynomial-phase transform," IEEE Transactions on Aerospace and Electronic Systems, Vol. 32, No. 1, 378-387, 1996.
doi:10.1109/7.481277 Google Scholar

8. Kay, S. and S. Saha, "Mean likelihood frequency estimation," IEEE Transactions on Signal Processing, Vol. 48, No. 7, 1937-1946, 2000.
doi:10.1109/78.847780 Google Scholar

9. Saha, S. and S. M. Kay, "Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling ," IEEE Transactions on Signal Processing, Vol. 50, No. 2, 224-230, 2002.
doi:10.1109/78.978378 Google Scholar

10. Kay, S. M., Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, 1993.

11. Pincus, M., "A closed form solution for certain programming problems," Oper. Res., 690-694, 1962. Google Scholar

12. Stoica, P. and A. Nehorai, "MUSIC, maximum likelihood, and Cramer-Rao bound," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 37, No. 5, 720-741, 1989.
doi:10.1109/29.17564 Google Scholar

13. Yau, S. F. and Y. Bresler, "A compact Cramer-Rao bound expression for parametric estimation of superimposed signals," IEEE Transactions on Signal Processing, Vol. 40, No. 5, 1226-1230, 1992.
doi:10.1109/78.134484 Google Scholar

Mr. Hao Cheng

Dr. Deguo Zeng

Dr. Jun Zhu

Dr. Bin Tang