Half-sine and triangular despreading chip waveforms for coherent delay-locked tracking in DS/SS systems

The performance of a coherent delay-locked tracking scheme for direct-sequence/spread-spectrum systems using half-sine or triangular chip waveforms for early and late despreading sequences is analyzed. The effect of band-limiting on the received signals is considered. Mean time to lose lock (MTLL) and root mean square (rms) tracking error of the delay-locked loop (DLL) are compared with that of a conventional DLL which uses rectangular chip despreading waveforms. Linear and nonlinear (based on the renewal process approach) analyses are employed to evaluate the performance of the DLL. Results show that the use of either the half-sine or triangular chip waveform reduces the rms tracking error and increases the MTLL considerably when the early–late spacing is approximately between 0.7–1.3 chip times. The results apply in particular to the commonly used DLL using one chip early–late spacing. Computer simulation for band-limited signals confirms the analytical results. The use of these despreading chip waveforms also reduces tracking offset in multipath environments.