Tracking analysis of the constant modulus algorithm

• Published in: 2008 IEEE International Conference on Acoustics, Speech and Signal Processing pp. 3561 - 3564
• Main Authors: Silva, M.T.M., Nascimento, V.H.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.03.2008
• Subjects: Adaptive filters; Algorithm design and analysis; blind equalization; Blind equalizers; Constant Modulus Algorithm; energy conservation; Estimation error; Feedback; Finite impulse response filter; Performance analysis; Stability; Steady-state; Systems engineering and theory; tracking analysis
• ISBN: 9781424414833; 1424414830
• ISSN: 1520-6149
• DOI: 10.1109/ICASSP.2008.4518421

Recently, we proposed a model for the steady-state estimation error of real-valued constant-modulus-based algorithms as a function of the a priori error and of a term that measures the variability in the modulus of the transmitted signal. In this paper, we extend this model to complex-valued data and use it in conjunction with the feedback analysis method to obtain an analytical expression for the steady-state excess mean-square error (EMSE) of the Constant Modulus Algorithm (CMA). Such expression is more accurate for larger step-sizes than the previous ones in the literature, as confirmed by the good agreement between analytical and simulation results. Furthermore, from the EMSE expression, we obtain an estimate for the CMA step-size interval to ensure its convergence and stability, when it is initialized sufficiently close to the zero-forcing solution.