Orthogonal Wavelet Transform Blind Equalization Algorithm Based On The Chaos Theory

The severe inter-symbol interference (ISI) is generally consist in the underwater acoustic communication system, it is caused by multi-path fading and channel distortion, it will not only cause the unreliability of data on the underwater, but also greatly reduces the transmission rate. If you can avoid to use the sending training sequence while track the channel, it can overcome these shortcomings, and the blind equalization techniques is arised at the historic moment. It used the statistical properties of the received signal when balanced the channel, it can reduce or even eliminate the ISI, and the utilization rate of the bandwidth can be improved, so in the current underwater acoustic communication system, the blind equalization has become frontier research subject, it has important research meaning and practical value. The orthogonal wavelet transform used its time-frequency localization characteristics to process the input signal of equalizer, and normalized the energy of the signal, it can effectively reduce the correlation between signal and noise.MMA algorithm divided the outputs of equalizer into the real part and imaginary part, selected their respective modulus in the in-phase direction and orthogonal direction, it is applicable to balance the non-constant modulus signals. Chaos is a kind of wide spread phenomenon exist in nonlinear system, the behavior is complex and approximate random, and it is able to traverse all the state not repeatedly according to its own "law" in a certain range. Use these characteristics of chaos, people put forward some chaos optimization algorithm, the ergodicity of chaos can be used to avoid the search processing lost in local minimum point. In this paper, chaos algorithm is used for processing the weight vector of the orthogonal wavelet transform blind equalization algorithm, the global search features of the chaos algorithm can obtain the right vector of the optimal solution in the shortest possible time. In order to restrain the ISI in the underwater acoustic communication, in this paper the research status and application field of chaos theory are summarized, take CMA and MMA as the main research object, several intelligent optimization algorithms is joined mainly used to initialize the weight vector of equalizer. In this study, it's mainly proceed the theoretical research and simulation experiments to the effective combination of the chaos theory and wavelet blind equalization algorithm, the main work content have the following respects:1. Analyzing orthognal wavelet transform blind equalization algorithm based on the chaotic communication systemsIntroducing chaos theory to blind equalization algorithm, combined with the orthogonal wavelet transform and the chaotic communication theory, an orthognal wavelet transform blind equalization algorithm based on the chaotic communication systems (CS-WT-CMA) is proposed. Due to the properties of ergodicity, randomicity, correlation, and ultra-wideband power spectrum of chaos, the chaotic modulation system is used to produce broadband chaotic signal as the carrier signals and spread spectrum of the transmit signals. Accordingly, it reduces the autocorrelation of the input signals of the channel, the ISI and the multi-path fading. Meanwhile, the proposed algorithm used the de-correlation ability of wavelet transform to accelerate the convergence rate. The efficiency of the algorithm was proved by computer simulations. Theory and the practical simulation results proved the superiority of the algorithm in the denoising and convergence rate.2. Analyzing orthogonal wavelet transform weighted multi-modulus blind equalization algorithm based on the chaos optimization algorithmIn order overcome the slow convergence rate and large state error of the MMA,an orthogonal wavelet transform weighted multi-modulus blind equalization algorithm based on the chaos optimization algorithm (CO-WT-MMA) was proposed. Based on the MMA, the proposed algorithm improved the convergence rate by using the orthogonal wavelet transform to normalizing the transmission signal (WT-MMA), meanwhile, using the ergodicity of chaotic to disturb the initial weights, in the search process make use of the time-varying parameter to reduce disturbance amplitude gradually, thus the weight vector can converge to the global optimal solution. Through the chaos optimization algorithm to find the global optimal solution of equalizer weight vectors, and take the vectors as the initialization vectors of orthogonal wavelet transform weighted multi-modulus blind equalization algorithm. The simulation results prove that a powerful the efficiency of the algorithm has been achieved. It not only has the better convergence rate, but also gets the smaller mean square error.3. Analyzing orthogonal wavelet transform based sign decision dual-mode fixed-weight multi-modulus blind equalization algorithmIn order to overcome the small error but slow convergence rate of the multi-modulus algorithm, based on the feature of high-order QAM signals with different modulus, introduced the orthogonal wavelet transform, combined with the Fixed-Weighted MMA (FW-MMA) and the Sign Decision Dual-Mode MMA (WT-SDDMMA), a Orthogonal Wavelet Transform based Sign Decision Dual-Mode Fixed-Weight Multi-Modulus blind equalization Algorithm (WT-FW-SDDMA) was proposed. The proposed algorithm used the FW-MMA as the first mode whereas it employed the WT-FW-SDDMA as the second mode, and the two modes alternated automatically through the sign decision. The simulation shows that the convergence rate and mean square error of the algorithm have been effectively improved, and it has very good anti-interference performance.4. Analyzing orthogonal wavelet transform weighted multi-modulus blind equalization algorithm based on the chaos particle swarm optimization algorithmMMA had slow convergence rate and large state error, the original Particle Swarm Optimization (PSO) was easy to get into the local convergence. In order to overcome of the shortcomings, an orthogonal wavelet transform weighted multi-modulus blind equalization algorithm based on the chaos particle swarm optimization algorithm (CPSO-WT-MMA) was proposed. Based on the MMA, the proposed algorithm improved the convergence rate by using the orthogonal wavelet transform to normalizing the transmission signal (WT-MMA). Meanwhile, using the ergodicity of chaotic to start the tiny disturbance of particles, in the search process, the PSO with "premature phenomenon" can be avoided to trap into local optimum by use of the chaos disturbance, thus the weight vector can converge to the global optimal solution. The simulation shows that the convergence rate and mean square error of the algorithm have been effectively improved, and it has very good anti-interference performance. 5. Analyzing orthogonal wavelet transform weighted multi-modulus blind equalization algorithm based on the immune chaos optimization algorithmCombined the local searching ability of chaotic optimization(CO) and the global searching ability of immune algorithm(IA), an orthogonal wavelet transform weighted multi-modulus blind equalization algorithm based on the immune chaos optimization algorithm(ICO-WT-MMA) was proposed. Based on the MMA, the proposed algorithm improved the convergence rate by using the orthogonal wavelet transform to normalizing the transmission signal (WT-MMA). The immune algorithm regards the weight vector of the blind equalizer as the antibodies and optimizes it, then using the ergodicity of chaotic to disturb the initial weights, in the search process make use of the time-varying parameter to reduce disturbance amplitude gradually, thus the weight vector can converge to the global optimal solution. The simulation shows that it can effectively improve the property of conventional algorithms.