Single channel steepest descent algorithm for the correction of cycle frequency error

The beneficial characteristics of signal cyclostationarity have been widely exploited in varied domains. However, one common problem is that algorithms adopting cyclostationarity would suffer from severe performance degradation when there is an error or mismatch in the cycle frequency (CF) involved. Hence, the authors attempt to propose a single channel correction method for CF error (CFE). First, a new cyclostationary spectral feature function is introduced which reaches its maxima at CFs; second, the steepest descent algorithm is deduced for the correction of CFE, the convergence property of which is also discussed. The main contributions of the novel scheme are that first, the estimation accuracy is remarkably improved compared with most existing algorithms adopting cyclic feature functions. Second, the steepest descent scheme holds an advantage in computational complexity compared with previous works based on linear search. Moreover, the proposed algorithm is robust against the pulse shape variation and multipath fading. Simulation works are carried out, which demonstrate the performance of the algorithm under varied environment conditions, and results fit well with theoretical analysis. Comparisons with existing methods are also presented, together with examples to illustrate how the correction scheme can be applied in real systems.