In this paper, we present a method to analyze the steady-state performance of a complex coefficient adaptive IIR notch filter which is useful for the rejection of multiple narrow-band interferences from broad-band signals in quadrature phase shift keying (QPSK) spread-spectrum communication systems. The adaptive notch filter based on the simplified gradient algorithm is considered. Analytical expressions have been developed for the conditional mean and variance of 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. Finally, the results of computer simulations are shown which confirm the theoretical predictions.

In this paper we propose a new lattice based second-order adaptive infinite impulse response (IIR) notch filter that uses a simplified adaptation algorithm. Steady-state analysis of the proposed structure is then studied based on the mean-squared error analysis of the steady-state variable coefficient fluctuations. The analysis is used to derive simple analytical expressions for steady-state variable coefficient variance and an upper bound for the step size adaptation constant. The results are shown to be useful in designing an FSK demodulator using the proposed structure. Computer simulation results are shown to confirm derived analytical expressions.

In this paper, a new structure which is useful for the detection of multiple sinusoids is presented. The proposed structure is based on the direct form second-order IIR notch filter using simplified adaptive algorithm. It has been shown that the convergence characteristics of the proposed structure are much improved compared with the previously proposed structure. A cascaded adaptive notch filter using the proposed second-order section is also shown. It takes multiple sinusoids corrupted by white Gaussian noise and produces the individual sinusoids at each of the outputs. The results of computer simulation are shown which confirm the theoretical prediction.

Adaptive optimization of the notch bandwidth of a lattice-based adaptive infinite impulse response (IIR) notch filter is presented in this paper. The filter is used to improve the performance of a direct sequence spread spectrum (DSSS) binary phase shift keying (BPSK) communication system by suppressing a narrow-band interference at the receiver. A least mean square (LMS) algorithm used to adapt the notch bandwidth coefficient to its optimum value which corresponds to the maximum signal to noise ratio (SNR) improvement factor is derived. Bit error rate (BER) improvement gained by the DSSS communication system using the filter with the optimized notch bandwidth is also shown. Computer simulation results are compared with those obtained analytically to demonstrate the validity of theoretical predictions for various received signal parameters.

In this paper, methods to analyze the convergence and steady-state characteristics of an adaptive notch filter with two input structure are proposed. The adaptive detection of a sinusoid with additive Gaussian noises has been investigated. Expressions for the necessary iteration of convergence are derived. An analysis of steady-state coefficient error has been also obtained. The analysis of this paper clarifies the effects of colored Gaussian noise and the noise correlation between primary input and reference input. Finally, the results of computer simulations are shown which confirm the theoretical predictions.

This paper analyzes frequency tracking characteristics of a complex-coefficient adaptive infinite impulse response (IIR) notch filter with a simplified gradient-based algorithm. The input signal to the complex notch filter is a complex linear chirp embedded in a complex zero-mean white Gaussian noise. The analysis starts with derivation of a first-order real-coefficient difference equation with respect to steady-state instantaneous frequency tracking error. Closed-form expression for frequency tracking mean square error (MSE) is then derived from the difference equation. Lastly, closed-form expressions for optimum notch bandwidth coefficient and step size constant that minimize the frequency tracking MSE are derived. Computer simulations are presented to validate the analysis.

In this paper, analysis of average bit error ratio (BER) performance of a quadriphase shift keying (QPSK) direct-sequence code-division multiple-access (DS-CDMA) system with narrow-band interference (NBI) suppression complex adaptive infinite-impulse response (IIR) notch filter is presented. QPSK DS-CDMA signal is transmitted over a Rayleigh frequency-nonselective fading channel and the NBI has a randomly-varying frequency. A closed-form expression that relates BER with complex coefficient IIR notch filter parameters, received signal-to-noise ratio (SNR), number of DS-CDMA active users and processing gain is derived. The derivation is based on the Standard Gaussian Approximation (SGA) method. Accuracy of the BER expression is confirmed by computer simulation results.

Improvement of direct sequence spread spectrum (DSSS) communication systems' performance using a lattice based adaptive infinite impulse response (IIR) notch filter with a simplified adaptation algorithm is presented. The improvement is shown to be achieved by rejection of a narrowband interference in a received DSSS binary phase shift keying (BPSK) signal. Sources of noise generated by an adaptive IIR notch filter are also studied. Apart from noise associated with input additive white gaussian noise, noise attributed to leakage sinusoids due to fluctuation of steady-state variable coefficient is also analysed. Using statistical properties of notch filter and pseudonoise (PN) correlator outputs, improvement of the performance of a DSSS system gained by the use of interference rejection filter is shown. Computer simulation results are used to confirm analytically derived expressions.

In this letter we present steady-state analyses of a gradient algorithm (GA) for second-order adaptive infinite impulse response (IIR) notch filters. A method for deriving more accurate estimation mean square error (MSE) expressions than the recently proposed method is presented. The method is based on the estimation error power spectral density (PSD). Moreover, an expression for the estimation bias for the adaptive IIR notch filter with constrained poles and zeros is shown to be obtained from the estimation MSE expression. Simulations are presented to confirm the validity of the analyses.

In this letter, a new structure of adaptive IIR notch filter is presented. The structure is based on direct form realization and uses the similar adaptation algorithm given in Ref. (4). A quantitative analysis for convergence properties is developed. It is shown that the proposed structure shows superior performance comparing with previously proposed designs. The results of computer simulations are presented to substantiate the analysis.

This paper investigates an adaptive notch digital filter that employs normal state-space realization of a single-frequency second-order IIR notch digital filter. An adaptive algorithm is developed to minimize the mean-squared output error of the filter iteratively. This algorithm is based on a simplified form of the gradient-decent method. Stability and frequency estimation bias are analyzed for the adaptive iterative algorithm. Finally, a numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive notch digital filter and the frequency-estimation bias analyzed for the adaptive iterative algorithm.

In this letter, a method to analyze the steady-state characteristics of multirale IIR adaptive notch filter is proposed. A closed-form expression for the steady-state mean square error of variable coefficient has been obtained. The results of computer simulation are shown which confirm the theoretical prediction.

This paper deals with a state-space approach for adaptive second-order IIR notch digital filters with constrained poles and zeros. A simplified iterative algorithm is derived from the gradient-descent method to minimize the mean-squared output of an adaptive notch digital filter. Then, stability and parameter-estimation bias are analyzed for the simplified iterative algorithm. A numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive state-space notch digital filter and parameter-estimation bias analysis.