Noise reduction for digital communications – A modified Costas loop

An efficient way of noise reduction has been presented: A modified Costas loop called as Masterpiece. The basic version of the Costas loop has been developed for SSB SC demodulation, but the same circuit can be applied for QAM demodulation as well. Noise sensitivity of the basic version has been decreased. One trick is the transformation of the real channel input into complex signal, the other one is the application of our folding algorithm. The result is that the Masterpiece provides a 4QAM symbol error rate (SER) of 6*10-4 for input signal to noise ratio (SNR) of -1 dB. In this paper, an improved version of the original Masterpiece is introduced. The complex channel input signal is normalized, and rotational average is applied. The 4QAM result is SER of 3*10-4 for SNR of -1 dB. At SNR of 0 dB, the improved version produces 100 times better SER than that the original Costas loop does

Constructive Estimates of the Pull-In Range for Synchronization Circuit Described by Integro-Differential Equations

The pull-in range, known also as the acquisition or capture range, is an important characteristics of synchronization circuits such as e.g. phase-, frequency- and delay-locked loops (PLL/FLL/DLL). For PLLs, the pull-in range characterizes the maximal frequency detuning under which the system provides phase locking (mathematically, every solution of the system converges to one of the equilibria). The presence of periodic nonlinearities (characteristics of phase detectors) and infinite sequences of equilibria makes rigorous analysis of PLLs very difficult in spite of their seeming simplicity. The models of PLLs can be featured by multi-stability, hidden attractors and even chaotic trajectories. For this reason, the pull-in range is typically estimated numerically by e.g. using harmonic balance or Galerkin approximations. Analytic results presented in the literature are not numerous and primarily deal with ordinary differential equations. In this paper, we propose an analytic method for pull-in range estimation, applicable to synchronization systems with infinite-dimensional linear part, in particular, for PLLs with delays. The results are illustrated by analysis of a PLL described by second-order delay equations