Carrier phase and amplitude estimation for phase shift keying using pilots and data

Robby G. McKilliam, André Pollok, William Cowley, I. Vaughan L Clarkson, Barry G. Quinn

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    We consider least squares estimators of carrier phase and amplitude from a noisy communications signal that contains both pilot signals, known to the receiver, and data signals, unknown to the receiver. We focus on signaling constellations that have symbols evenly distributed on the complex unit circle, i.e., M-ary phase shift keying. We show, under reasonably mild conditions on the distribution of the noise, that the least squares estimator of carrier phase is strongly consistent and asymptotically normally distributed. However, the amplitude estimator is asymptotically biased and converges to a positive real number that is a function of the true carrier amplitude, the noise distribution and the size of the constellation. This appears to be the first time that the statistical properties of a non-data-aided estimator for carrier amplitude have been analyzed theoretically. The results of Monte Carlo simulations are provided and these agree with the theoretical results.

    Original languageEnglish
    Article number6843974
    Pages (from-to)3976-3989
    Number of pages14
    JournalIEEE Transactions on Signal Processing
    Issue number15
    Publication statusPublished - 1 Aug 2014


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