Rapid coarse acquisition of dsss signals using an expanding-search algorithm
John S. Seybold · Journal of International Crisis and Risk Communication Research · 1995
Direct Sequence Spread Spectrum (DSSS) communication systems rely on a code phase search to estimate sequence code phase closely enough to permit the tracking loops to acquire and track the signal. The search portion of code acquisition (to within 1/2 chip) is called coarse acquisition and is the subject of this dissertation. The size of the region to be searched (number of code phases) and the a priori probability density function of the uncertainty impact the efficacy of any particular algorithm. For a periodic code, with a relatively short period, the probability density function (pdf) is usually assumed to be uniform and the region is searched in a serial fashion using an algorithm such as the Conventional Sliding Correlator (CSC). When the sequence period is extremely long, or the sequence is aperiodic, the search region must be limited. In such cases a uniform pdf may still be assumed, or more information may be available about the actual code phase and a pdf such as a truncated Gaussian may be assumed. When the pdf is peaked, such as for the truncated Gaussian, algorithms other than the serial search or the CSC are a better choice. Such algorithms include the expanding-sweep algorithm which comprises progressively longer sweeps starting at the center of the uncertainty region until acquisition is obtained or the edge of the uncertainty region is reached and the scan is restarted. This research presents an expanding-search algorithm that is different from what has been previously published. This expanding-search algorithm consists of starting at the center of the uncertainty region and stepping out from the center such that each cell is searched only once during a complete scan. This dissertation provides a thorough characterization of the CSC when applied to a uniform pdf code-phase uncertainty. This includes simulation results and adaptation of analytic expressions from the literature. For the case of the Gaussian pdf, the expanding search is defined and thoroughly characterized. A model is developed which provides a viable implementation for this search technique. An analytic expression for the expanding search mean acquisition time is then presented for both a fixed code phase uncertainty and a random code phase uncertainty with a Gaussian pdf. This expression is validated using the results from the model and a MATLAB simulation using just the probabilities involved. The performance of the CSC and the expanding search are compared, using a uniform pdf and Gaussian pdf's truncated at $\pm1\sigma, \pm2\sigma$ and $\pm3\sigma$. These results show that the performance of the CSC is equivalent to that of the expanding search when the underlying pdf is uniform and that both algorithms are optimal in this case. It is also shown that as the pdf becomes more peaked ($\pm3\sigma$ case) the advantage of using the expanding search over the CSC becomes more pronounced. Using a maximum-likelihood criteria, regions where the expanding search is optimal are determined. These results indicate that in many cases of interest, particularly in the context of the Global Positioning System (GPS), the expanding search is the optimal search algorithm, as opposed to the expanding sweep algorithms which are more complex to implement and must be optimized for a particular signal-to-noise ratio in order to approach optimality.