Cosine function variable step-size transform domain least mean square algorithm based on matrix rotation

A novel cosine function variable step-size transform domain least mean square (LMS) algorithm based on matrix rotation (COS-ROTDCT-LMS-DFE) was put forward. Based on the discrete cosine transform domain LMS (DCT-LMS) algorithm, it was first processed by matrix rotation in an anticlockwise direction to resolve the problem of self-interference between signals, which effectively sped up the convergence of the algorithm. Subsequently, a cosine function variable step-size algorithm was developed considering that its curve was characterized by a smooth top and fast rising and falling speed so as to further improve the convergence speed of the algorithm. Subsequently, the decision feedback equalizer (DFE) was introduced into the algorithm to compensate signal distortion and noise. The convergence performance of the algorithm was simulated in typical multipath underwater acoustic channels. The simulation results showed that the convergence performance of the new algorithm was equivalent to that of recursive least squares (RLS). The convergence speed of COS-ROTDCT-LMS-DFE was even better than that of the recursive least square decision feedback equalizer (RLS-DFE) algorithm. The new algorithm performed well in terms of both convergence speed and steady-state error and could be easily implemented.