In this paper, to further improve the filtering performance and enhance the poor tracking capability of the conventional combined step-size affine projection sign algorithm (CSS-APSA) in system identification, we propose a simplified CSS-APSA (SCSS-APSA) by applying the first-order Taylor series expansion to the sigmoidal active function (of which the independent variable is symmetric) of CSS-APSA. SCSS-APSA has lower computational complexity, and can achieve comparable, or even better filtering performance than that of CSS-APSA. In addition, we propose a modification of the sigmoidal active function. The modified sigmoidal active function is a form of scaling transformation based on the conventional one. Applying the modified function to the CSS-APSA, we can obtain the modified CSS-APSA (MCSS-APSA). Moreover, the extra parameter of MCSS-APSA provides the power to accelerate the convergence rate of CSS-APSA. Following the simplification operations of SCSS-APSA, the computational complexity of MCSS-APSA can also be reduced. Therefore, we get the simplified MCSS-APSA (SMCSS-APSA). Simulation results demonstrate that our proposed algorithms are able to achieve a faster convergence speed in system identification.

With the popularity of multi-core and many-core platform, multi-core-oriented parallel programming and optimization has become a research hotspot in computer field. However, the vast majority of programmers are still continuing the traditional serial programming habits. Meanwhile, the mainstream algorithms are still in serial. Therefore, how to parallelize the serial programs effectively and write the multi-core programs efficiently is becoming an urgent problem in the field of multi-core programming. In this paper, the optimization of the heap sort algorithm has been achieved adopting the parallel technology based on openMP. Firstly, based on the hypercube model, the heap data to be sorted are divided into n (n is the computer thread amount) blocks called sub-heap which will be sorted respectively. Thus, the scale of the problem is decomposed into 1/n, secondly, the sorted sub-heaps will be merged using merge sort algorithm, finally, the parallel optimized heap sort algorithm is compared to the traditional heap sort algorithm. When the data quantity comes up to ten million bytes, the execution efficiency of the optimized parallel heap sort algorithm of this paper is improved significantly compared with the traditional serial heap sort algorithm on the experimental computer. Furthermore, the efficiency gap between the two algorithms will be intensified prominently with the increasing data quantity.