This paper deals with the problem of blind estimation of the carrier frequency offset of a linearly modulated noncircular transmission through an unknown frequency-selective channel. A Frequency estimator is developed based on the unique conjugate cyclic frequency of the received signal, which is equal to twice the frequency offset. Consistency and asymptotic normality of the frequency estimator together with a closed-form expression for its asymptotic variance are also established. The closed-form expression of the asymptotic variance enables analysis of the performance of the proposed frequency offset estimator as a function of the number of estimated cyclic correlation coefficients used. It is shown that optimum is obtained if the number of correlation coefficients taken into account coincides with the degree of the channel. Numerical simulations are provided and confirm the conclusion of the theoretical asymptotic analysis.
Bibliographical noteFunding Information:
Manuscript received December 7, 2000; revised September 20, 2001. This work was supported by a DGA/CNRS fellowship. The associate editor coordinating the review of this paper and approving it for publication was Dr. Inbar Fijalkow.
- Asymptotic analysis
- Cyclic frequency
- Harmonic retrieval
- Multiplicative noise