Differential combining for acquiring weak GPS signals

Abstract

By implementing rigorous mathematical analysis, this paper proves that differential combining (DFC) outperforms conventional non-coherent integration (NCH) in the detection of weak GPS signals. The processing loss induced by NCH can be decreased through the use of DFC by approximately 3 dB at low carrier-to-noise density ratios ( C/ N 0). This improvement can decreases the acquisition time, a substantial improvement in the context of weak GPS signals. Monte-Carlo simulation verifies the accuracy of the theoretical derivation. Statistical properties including probability of false alarm and probability of detection are essential to set a detection threshold, which identifies a decision variable level (and corresponding signal-to-noise ratio) beyond which desired performance of acquisition and tracking can be achieved. Conditional probability density functions (CPDFs) of the DFC-based decision variable are necessary to analyze detector performance in a statistical sense, but are too complicated to express in closed-form formula. This paper, based on the statistical expectation and variance of the decision variable, uses curve fitting to approximate CPDFs produced by Monte-Carlo simulation. The curve-fitting results, although not rigorously accurate, can provide a practical reference for this complicated problem. Analysis of the resultant CPDFs substantiates that, due to the lower processing loss, the DFC is superior to NCH in improving the sensitivity by 1.2–1.6 dB provided the false alarm is fixed to 0.1% and the detection threshold is set to 90%.