Analysis of differential non coherent detection scheme for CDMA pseudo random (PN) code acquisition

Recently, a modified non-coherent detection scheme for pseudo random (PN) code acquisition of direct sequence spread spectrum signals was introduced. The proposed scheme, known as differential non coherent (DNC) detector, promises 2 dB performance improvement over the classical non coherent detection scheme under AWGN channels. The scheme, as a method of post detection integration, has also been studied as an effective method of post detection integration when a frequency offset is present. We analyze the performance of the DNC detector under the Rayleigh fading case. The false alarm probability and detection probability are derived under a Rayleigh fading signal in AWGN. The DNC scheme enjoys a 2 dB performance improvement over the conventional non coherent detector even under the Rayleigh fading case. Also, the detector performance is analyzed when various uncertainties, like frequency offset or timing offset, are present. The performance degradation due to these uncertainties is derived. It is found that the performance degradation due to carrier frequency error is the same for DNC and NC, due to which the DNC offers SNR improvement over NC.