By sampling zero crossings at the Nyquist rate (i.e., the predetection bandwidth) the phase of a narrow-band signal may be extracted directly with respect to an arbitrary, stable reference. Analysis, simulation, and experimental results are presented validating this all-digital technique for acquisition and coherent tracking of a Doppler-shifted carrier at a low carrier/noise ratio and a large percentage bandwidth. The key advantage of this scheme for microcomputer-based implementation is that phase comparison is accomplished by arithmetic subtraction, without the coordinaterotation transformation which is necessary for conventionalI,Qsampling. Also, the phase-sampling process is independent of the phase error, which exists only as a numerical representation in the digital tracking algorithm. The technique is applicable to Costas suppressed-carrier tracking and to BPSK bit synchronization and demodulation, by programming the appropriate digital algorithms.

Casting phase tracking into a binary decoding problem, as in a previous paper, a sequential decoding algorithm is applied to a third-order system. The goal is to reduce the "tracking threshold" below that of a phase-locked loop. Simulation results are obtained by microprogramming the algorithm for a HP-2100A minicomputer.

If a Costas loop is forced to have a relatively wide bandwidth, for example, to track phase variation due to platform motion, binary phase-shift keying (BPSK) demodulator performance is significantly degraded. However, if the data bits were known, the Costas loop would become equivalent to a phase-locked loop, which has approximately a 6-dB lower tracking threshold for the same loop bandwidth. A delayed-bit estimation algorithm with a recursive structure similar to the Viterbi algorithm is described. The memory in the tracking loop is exploited to correct preliminary bit decisions, as a means of realizing most of this theoretical threshold reduction. Experimental results for a practical digital implementation of the new algorithm for a 50-bit/s data rate and a 20-Hz loop noise bandwidth show a 4-dB improvement in demodulator threshold.