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The applicability of the second-order Newton gradient descent method for blind equalization of complex signals based on the Constant Modulus algorithm is studied. The Constant Modulus loss function is real with complex valued arguments, and, hence, non analytic. Therefore, the authors use the framework of the Wirtinger calculus to derive a useful and insightful form of the Hessian for noiseless FIR channels and re-derive the known fact that the full Hessian of the CM loss function is always singular in a simpler manner. They performed simulations on full rank channels and found that the full Newton method, based on a regularized full Hessian performs better than the pseudo-Newton method.
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