Gu Yuantao

Superior step-size theorem and its application

With independence assumption, this paper proposes and proves the superior step-size theorem on least mean square (LMS) algorithm, from the view of minimizing mean squared error (MSE). Following the theorem we construct a parallel variable step-size LMS filters algorithm. The theoretical model of the proposed algorithm is analyzed in detail. Simulations show the proposed theoretical model is quite close to the optimal variable step-size LMS (OVS-LMS) model. The experimental learning curves of the proposed algorithm also show the fastest convergence and fine tracking performance. The proposed algorithm is therefore a good realization of the OVS-LMS model.

Optimal variable step-size LMS model and algorithm with independence assumption

To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.

Optimal multicast opportunistic routing based on Markov chain

Improving the network capacity is one of the most important topics in the area of wireless networks. The broadcasting and fading feature of the wireless communications has not been sufficiently exploited in traditional routings. However, in opportunistic routing, they are able to be used to provide diversity. In this paper, the multicast opportunistic routing problem is studied in a Markov chain method, and the optimal algorithm called Least ETX Multicast Opportunistic Routing (LEMOR) is designed and proved to have the least end-to-end ETX. Simulation results show that LEMOR is able to significantly improve the network throughput by exploiting both opportunistic routing and multicast compared to the algorithms using either of them.

Sparse constraint multidelay frequency adaptive filtering algorithm for echo cancellation

Sparse constraint Least Mean Square (LMS) is a recently proposed efficient adaptive algorithm for sparse system identification. However, its computational complexity is quite high especially when the filter length is long and convergence is slow for colored input signal. This paper extends the idea of sparse constraint into multidelay frequency adaptive filter (MDF) algorithm and proposes the sparse MDF algorithm for echo cancellation. The proposed algorithm perserves both the advantage of sparse LMS which has fast convergence performance for sparse system and MDF algorithm which has temporal decorrelation effect with lower implementation complexity. Two typical sparse constraints, l1-norm and an approximate l0-norm, are employed. And their performances of various aspects are simulated. Experiments show they have better performance than existing algorithms.

Exact convergence analysis of LMS algorithm for tapped-delay i.i.d. input with large step-size

The celebrated least mean square (LMS) algorithm is the widely used system identification approach which can be easily implemented. With the assumption of no dependence among the tapped-delay input vectors, the mean square analysis of LMS algorithm based on independence theory is only an approximate description of its convergence behavior, especially when updated with a large step-size. In this paper, we propose a modified mean square error (MSE) update formula that exactly describes the convergence process of LMS for tapped-delay independent identical distributed (i.i.d.) input data. The qualitative analysis is presented to reveal the significance and rationality of the proposed formula. Moreover, the simulations in various conditions validate that, even with a large step-size used, the study curves produced by the proposed formula are much more accurate in predicting the convergence behavior, compared with that based on independence assumption.