The Technology Of Adaptive Equalization Based On Wavelet Analysis

Adaptive equalization technology is used widely to reduce the inter symbol interference in the modern communications. The signal received will usually pass the filter which is called equalizer. Its property is contrary to the channel's. We have known that different equalizers have different algorithms and the most simple one is linear equalizer (LE) based on least mean square (LMS) algorithm, which can be implemented by FIR filter. Its structure is simple and its realization is easy. Not only that, it has lower complexity of algorithm and higher stability. But it converges slowly so that it is confined to use in some extent. This paper focuses on the principle of LE and properties of linear equalization algorithm. Based on the analysis of the traditional linear equalization algorithm, the wavelet is introduced into the adaptive equalization. Adaptive linear equalization based on wavelet analysis is discussed and analyzed in detail. Based on linear equalization algorithm based on wavelet transform (WTLE), a novel algorithm is presented in this paper—a adaptive equalization algorithm with variable step size based on wavelet transform (VSWTLE), because a adaptive LMS algorithm with fixed step size can't solve the contradiction between convergence speed and steady state error. Theoretical analysis and computer simulation demonstrate that the novel algorithm has the better convergence property than the modified ones.Although classical LMS algorithm has simple complexity and is easy to be implemented, its convergence speed is very slow. In order to speedup the convergence process, one can increase the step size, but at the same time, the steady state error will be large and even the algorithm may become unstable. Fixed step size cannot result in fast convergence speed and low residual error simultaneously. In order to solve this problem, we can build a nonlinear function relationship between step size factor and the error signal, that is, we can adopt a adaptive LMS algorithm with a variable step size. At the same time, the eigenvalue spread, that is, the condition number of auto-correlation matrix of the input signal, mainly affects the convergence rate of LE algorithm. The larger the condition number is, the slower the algorithm converges. And vice versa. The method that a wavelet is introduced into the adaptive equalizer can solve this problem very well because the wavelet has the good capacity to decrease the correlation property of the input vector. The condition number of the auto-correlation matrix of the input signal of the equalizer is reduced by wavelet transform so that the convergence rate of the algorithm is faster. Now in order to improve the convergence speed and the stability of traditional LMS further, a novel algorithm based on WTLE algorithm is presented in this paper. A variable step size LMS and transform domain LMS are immerged into one, which is applied to adaptive equalization system. The excellent properties of the novel algorithm are confirmed by theoretical analysis and computational complexity is very slow. Especially, another new non-linear functional relationship between step size factor and error signal (e(n)) is adopted in this new algorithm. The functional relationship is not only simpler than Sigmoid functional relationship, but also has the property of slight change e(n) near to zero. Therefore it is superior to Sigmoid functional relationship in the process of step size change of adaptive steady state. Computer simulation results and theoretical analysis show the algorithm performance is better than that of former algorithms.Firstly, the paper discusses the application background of adaptive equalization technology and the great meaning of applying adaptive equalization technology to the communication system. Besides the merits and demerits of some adaptive equalization algorithms are analyzed and summarized, and so are the problems existed in algorithms. Meanwhile, wavelet analysis applied to adaptive equalization is also discussed. Present conditions and development...