A study of complementary phase code pairs in frame synchronization

Frame synchronization (sync) acquisition techniques have been developed in the past for both PCM telemetry and TDMA satellite communication systems and are well documented in the literature. These techniques utilize special frame sync codewords which possess autocorrelation sequences having minimum correlation values for all relative shifts other than zero. Extensive studies have yielded expressions which can be used to select codewords which give an optimum value of false detection probability. Inherent in these expressions is the use of a serial correlation operation in which received TV-tuples are compared with an TV-bit frame sync codeword. This research considers the use of complementary phase codes, which consist of two or more codeword sequences whose combined autocorrelation sequences exactly cancel for all relative shifts other than zero. In existing frame sync systems where codewords are transmitted as QPSK sequences, the complementary phase code property can be utilized; however, measurement of the performance of these codes has received little attention in the literature. In this study, expressions were derived which provide a measure for the performance of complementary phase codes for both PCM telemetry and TDMA satellite applications. An extensive computer search was also conducted to obtain optimum codewords which minimize the probability of false detection, and a detailed study was performed to quantify the difference between the use of complementary phase codes and optimum codewords. In addition, a computer simulation of frame sync acquisition was developed for this research, and the mathematical analysis developed for this research was verified through simulation. The false detection probability of complementary codes was shown to be suboptimum for most conditions of interest. However, it was shown that one particular complementary phase code pair was very near optimal performance and would be a possible candidate in a TDMA application. Furthermore, the simple hardware required to both encode and decode complementary code pairs provides strong motivation for their use.