In this letter, a new semi-blind approach incorporating the bounded nature of communication sources with the distance between the equalizer outputs and the training sequence is proposed. By utilizing the sparsity property of l1-norm cost function, the proposed algorithm can outperform the semi-blind method based on higher-order statistics (HOS) criterion especially for transmitting sources with non-constant modulus. Experimental results demonstrate that the proposed method shows superior performance over the HOS based semi-blind method and the classical training-based method for QPSK and 16QAM sources equalization. While for 64QAM signal inputs, the proposed algorithm exhibits its superiority in low signal-to-noise-ratio (SNR) conditions compared with the training-based method.

A class of multimodulus algorithms (MMA(p)) optimized by an optimal step-size (OS) for blind equalization are firstly investigated in this letter. The multimodulus (MM) criterion is essentially a split cost function that separately implements the real and imaginary part of the signal, hence the phase can be recovered jointly with equalization. More importantly, the step-size leading to the minimum of the MM criterion along the search direction can be obtained algebraically among the roots of a higher-order polynomial at each iteration, thus a robust optimal step-size multimodulus algorithm (OS-MMA(p)) is developed. Experimental results demonstrate improved performance of the proposed algorithm in mitigating the inter-symbol interference (ISI) compared with the OS constant modulus algorithm (OS-CMA). Besides, the computational complexity can be reduced by the proposed OS-MMA(2) algorithm.