Multi-objective approach in GNSS code discriminator design

In spread spectrum ranging system receivers such as the Global Navigation Satellite System (GNSS) receivers, a discriminator is used in the code tracking loop to provide an error signal for the tracking of incoming signals. Typically, the discriminator manipulates several correlator outputs to form the correction signal. A multi-objective approach is adopted here to design the coefficients associated with a multi-correlator-based discriminator to lead to a better performance tradeoff in large tracking range, acceptable multipath-induced bias, high sensitivity, free of ambiguity, and small variance. It is shown that the multiple-objective problem can be tackled via a quadratic/linear programming method, rendering the optimal coefficient vector for the implementation of the discriminator. In addition, as the discriminator design is often subject to conflicting requirements, it is shown that the proposed design approach is capable of establishing bounds on achievable performance. Examples with respect to BPSK (binary phase-shift keying) NRZ (nonreturn-to-zero), and BOC (binary-offset carrier) signals are given to illustrate the design approach.