Analysis of the Code Phase Migration and Doppler Frequency Migration Effects in the Coherent Integration of Direct-Sequence Spread-Spectrum Signals

Coherent integration of direct-sequence spread-spectrum (DSSS) signals is a commonly used technique to improve receiver performance. However, this approach is susceptible to the code phase migration (CPM) and Doppler frequency migration (DFM) effects resulting from the relative motion between transmitter and receiver. In this paper, the CPM and DFM effects are explored and characterized. To evaluate the CPM effect, a simple analytic expression for the coherent integration results under motions of arbitrary orders is developed. In addition, the theoretically derived integration loss and time synchronization error caused by CPM are quantitatively examined. The DFM effect is evaluated under the motions of arbitrary orders by Fresnel integration and numerical fitting. The obtained closed-form expressions are verified by simulation and are shown to be useful for the performance analysis and the DSSS receiver design. The theoretical and the numerical results show that when the amount of CPM is larger than about one code chip duration, the signal-to-noise ratio gain obtained by coherent integration no longer increases because of the integration loss caused by CPM. In addition, the integration loss (in decibel units) caused by DFM is approximately inversely proportional to the square of the time-bandwidth product when the time-bandwidth product is small, and it is inversely proportional to the logarithm of the time-bandwidth product when this product is large.