Linear minimum variance filters applied to carrier tracking

A new approach is taken to the problem of tracking a fixed amplitude signal with a Brownian motion phase process. Classically, a first-order phase-lock loop (PLL) is used; here, the problem is treated via estimation of the quadrature signal components. In this space, the state dynamics are linear with white multiplicative noise. Therefore, linear, minimum-variance filters, which have a particularly simple mechanization, are suggested. The resulting error dynamics are linear at any signal/noise ( ) ratio unlike the classical PLL. During synchronization, and above threshold, this filter with constant gains degrades by 3 percent in output rms phase error with respect to the classical loop. However, up to 80 percent of the maximum possible noise improvement is obtained below threshold where the classical loop is nonoptimum, as demonstrated by a Monte Carlo analysis. Filter mechanizations are presented for beth carrier and baseband operation. An interesting bandpass filter interpretation is given.