Novel signals for optimized timing synchronization in direct‐sequence spread‐spectrum communication systems

The paper presents design techniques for novel signaling waveforms to optimize timing synchronization in direct‐sequence spread‐spectrum communication systems. Both coarse code timing acquisition and fine delay‐locked loop tracking systems are considered, and their performance metrics are analyzed in terms of initial acquisition detection probability and residual tracking jitter, showing a strong dependency on signal waveform spectral characteristics. Bit error performance under imperfect synchronization is also assessed. A design methodology is formulated with a low complexity parametric optimization approach based on prolate spheroidal waveform expansions for the generation of signals that minimize the probability of acquisition miss and tracking error jitter subject to additional constraints on signal energy and phase transitions. Novel optimized waveforms are synthesized with different levels of effective root mean square bandwidth occupancy and compared with conventional pulses to illustrate their advantages. Performance trade‐offs are demonstrated between the acquisition and tracking systems, whereby signals with low effective bandwidth are found to have better acquisition capability at the expense of poorer tracking jitter, while the converse holds for signals with higher effective bandwidth. It is found that an effective root mean square bandwidth occupancy in the range of 40% to 50% of the chip rate can achieve a good compromise between the requirements of the 2 code timing synchronization phases. Numerical results are presented to quantify the relative merits of representative waveforms with respect to the different performance measures in terms of acquisition capability, tracking jitter, and bit error probability.