Analysis of DFT-based frequency excision algorithms for direct-sequence spread-spectrum communications

The capacity of direct-sequence spread-spectrum modulation to reject narrow-band interference can be significantly improved by eliminating narrow-band energy at the receiver in a process called frequency excision. This paper considers several algorithms that operate on the real-time discrete Fourier transform (DFT) of the received signal to perform frequency excision. The case in which only the signal and additive white Gaussian noise (AWGN) are present at the receiver is considered as a means of comparing the relative performance of different algorithms that operate without knowledge of the power spectral density of the interference. An approach for analysis, using the postcorrelation signal-to-noise ratio (SNR) as the figure of merit, is presented that is valid for a broad class of spreading modulations. First, the algorithm that sets a fixed fraction of the frequency domain record to zero is examined using rank-order statistics as an analytical tool. This result is then generalized to confirm previous estimates of SNR degradation for the algorithm that sets all values that exceed a threshold to zero. These results are again generalized to apply to the algorithm that sets a fixed fraction of the band to a fixed amplitude while retaining phase information in an algorithm called fraction clip. The relative performances of several clip algorithm options are derived as special cases. Finally, a performance measure of the algorithms in the presence of multiple narrow-band interference is provided and illustrated with an example.