Generalized and average likelihood ratio testing for post detection integration

In the context of spread spectrum communications, this paper investigates the use of likelihood ratio testing techniques for the design of post detection integration (PDI) methods for code acquisition in the presence of phase and frequency uncertainty. The proposed methods are derived as theoretical and pragmatic alternatives to the conventional approach based on noncoherent integration, which would be optimal in the absence of frequency uncertainty. Two competing alternatives are introduced to handle the unknown frequency error, respectively based on the generalized and average likelihood ratio tests, and identified as generalized PDI (GPDI) and average PDI (APDI). The GPDI versus APDI tradeoff is far from trivial and leads to numerous interesting insights, particularly with respect to the impact on performance of the frequency offset entity. Performance is also contrasted to that of conventional PDI techniques, i.e., noncoherent and differential PDI, to reveal significant gains in favor of the proposed methods.