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In this paper, a method for steady-state analysis of gradient-based algorithms for a complex coefficient adaptive infinite impulse response (IIR) notch filter is presented. Accurate expressions of estimation mean square error (MSE) for variable coefficients are derived by approximating the power spectral densities (PSD) of estimation errors. Suppression of a complex sinusoidal interference in a direct-sequence quadrature phase shift keying (DS QPSK) system using the algorithms is also presented. Computer simulations are presented to support the validity of the analysis.