Effective Lock Detectors Based on Costas Loop Output for SBPSK Mobile Communications

In this study, we address the problem of lock detection at the output of a Costas loop when robust modulations for bandwidth-constrained military communications are used. In this respect, we propose two novel detectors that share the important constant false alarm rate property with respect to the noise power. The first decision scheme is an improvement of the detector proposed in (Nan et al., 2021), whereas the second architecture is grounded on the likelihood ratio test where in place of the unknown parameters suitable estimates are used. Such estimates are obtained through an iterative strategy relying on the Expectation Maximization algorithm. Moreover, when possible, we provide exact statistical characterizations of the considered decision schemes (including the competitors) or, in the other case, suitable approximations that allow for a straightforward performance evaluation. The numerical examples are obtained by means of simulated data and in comparison with the most common lock detectors for this kind of communications. The numerical results highlight that the proposed detectors represent a viable means to manage real-time lock detection.