Steady-state analysis of complex adaptive IIR notch filter and its application to QPSK communication systems

We present a method to analyze the steady-state performance of complex coefficient IIR adaptive notch filter which is useful for the rejection of narrow-band interference from broad-band signals in QPSK spread-spectrum communication systems. The first-order adaptive notch filter based on the simplified gradient algorithm is considered. Analytical expressions have been developed for the conditional mean and variance of the notch filter output. The signal-to-noise ratio improvement factor is also obtained from which the validity of the use of the notch filter can be concluded. Furthermore, by using the results of a first-order filter, the analysis for the cascade structure has been presented. Finally, the results of computer simulations are shown which confirm the theoretical predictions.