A complex Lyapunov theory-based adaptive algorithm for complex signal processing

This paper presents a complex-valued version of the Lyapunov adaptive filtering algorithm. The resulting algorithm simultaneously updates the real and imaginary parts of the complex coefficients so that the complex error can converge to zero asymptotically. The proposed scheme can be applied to random and deterministic processes because only the desired signal and input signal are required. The design is independent of the stochastic properties of signals and the stability is guaranteed by the Lyapunov Stability Theory (LST). This scheme possesses distinct advantages of stability, speed of convergence, computational complexity and. robustness to additive noise or disturbance over some complex adaptive algorithms. Simulation examples are included to demonstrate the performance of the new complex adaptive algorithm.