Phase tracking: what do we gain from optimality? Particle filtering versus phase-locked loops

• Published in: Signal processing Vol. 83; no. 1; pp. 151 - 167
• Main Authors: Amblard, P.O., Brossier, J.M., Moisan, E.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 2003; Elsevier Science; Elsevier
• Subjects: Applied sciences; Costas loop; Decision feedback loop; Detection, estimation, filtering, equalization, prediction; Digital phase-locked loops; Engineering Sciences; Exact sciences and technology; Information, signal and communications theory; Particle filtering; Signal and communications theory; Signal and Image processing; Signal, noise; Telecommunications and information theory; Decision feedback loop; Particle filtering; Digital phase-locked loops; Costas loop; Performance evaluation; Monte Carlo method; Filtering; Optimal filter; Signal estimation; Phase locked loop; Mean square error; Phase estimation; Convergence rate; Particle filter
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/S0165-1684(02)00386-9

This paper studies the problem of tracking a Brownian phase with linear drift observed to within one digital modulation and one additive white Gaussian noise. This problem is of great importance as it models the problem of carrier synchronization in digital communications. The ultimate performances achievable for this problem are evaluated and are compared to the performances of three solutions of the problem. The optimal filter cannot be explicitly calculated and one goal of the paper is to implement it using recent sequential Monte-Carlo techniques known as particle filtering. This approach is compared to more traditional loops such as the Costas loop and the decision feedback loop. Moreover, since the phase has a linear drift, the loops considered are second-order loops. To make fair comparisons, we exploit all the known information to put the loops in their best configurations (optimal step sizes of the loops). We show that asymptotically, the loops and the particle filter are equivalent in terms of mean square error. However, using Monte-Carlo simulations we show that the particle filter outperforms the loops when considering the mean acquisition time (convergence rate), and we argue that the particle filter is also better than the loops when dealing with the important problem of mean time between cycle slips.