On Detection of a PN Spread-Spectrum Signal in Colored Noise

The theory of detection of signals in colored noise is applied to PN spread-spectrum, noting the fact that the detection of a PN spread-spectrum signal in colored noise is a dual problem of the detection of a signal in white noise. In particular, the unrealizable and realizable whitening filters and the adaptive noise cancelling techniques are discussed to improve the output signal-to-noise ratio (SNR) of a spread-spectrum receiver. Infinite improvement in SNR, without signal distortion, can be achieved with adaptive noise cancellers. However, if whitening filters are employed, the improvement in SNR is greater for the unrealizable Wiener filter in comparison to the realizable Wiener filter. For uniform spectral-density of the signal and a strong narrowband interference, the improvement by unrealizable Wiener filter is approximately two-times the geometric mean of the bandwidth ratio of signal and interference spectrum and the ratio of interference and signal power and the improvement by realizable Wiener filter is half that of unrealizable Wiener filter. Finally, it is shown that, for nonuniform spectral-density of a PN spread-spectrum signal, the processing gain (without using a whitening filter) is reduced approximately by a factor of 2 for a narrowband interference and is dependent on the spectral-density of the interference.