Research On Blind Equalization Techniques Based On Optimization Theory

In recent years, the rapid development of industrialization makes the open electromagnetic environment more complex, the inter-symbol interference which is introduced by the unideal channel is more serious in wireless communicaitons, which introduce more challenges of signal receiving and restoring, and higher requirement of the blind equalizer’s performance. Based on this, this dissertation studies the blind equalization techniques based on optimization theory and ideas to improve the performance of blind equalizer. Using modern optimization methods, such as linear programming, semi-definite programming, vector norm theory, we investigate the methods of improving blind equalizer convergence rate, design some cost functions which can better reflect the statistical characteristics of transmitted signals to reduce the steady-state error, and construct new convex cost function to guarantee the convergence of equalizer. The main work is as follows:1. A method to improve the speed of equalizer convergence is studied. We study the gradient searching method for the cost function, and present a novel steepest descent batch implementation method for multimodulus blind equalization algorithm, which does not generate intermediate receiver output in the iteration, and can avoid long delay due to the reuse of channel output data, making it well suited for parallel real-time processing. The new iterative method has faster convergence and smaller steady-state error. As long as the total processing time does not exceed the data buffer time, the new method can be realized in real-time pipelined process, making it well suited for packet transmission applications.2. Aiming at the problem that the cost functions of Bussgang algorithms are non-convex and have multi-modal distribution, they are prone to undesirable local convergence, upon which the equalizer fails to remove sufficient inter-symbol interference. This dissertation presents a new convex cost function which be solved by fast linear programming for QAM signals blind equalization. The new algorithm under constant constraint has less variables and constraint functions so that the complexity can be reduced. To overcome the potential non-uniqueness problem for some channels, a novel adaptive constraint convex cost function is proposed. The new algorithm has an improved performance after several iterations while needing less signal samples. Compared to conventional MMA algorithm, the new method uses a convex cost function, ensuring that the equalizer can converge to ideal value.3. Aiming at the problem that Bussgang algorithms don’t fully utilize the information that signals contains, resulting in high steady-state error. This dissertation designs a new cost function which can better reflect the characteristics of the signal statistical to reduce the steady-state error of the equalizer. According to the vector norm nature, and the way of converting constraint equation to unconstrained equation, a new unconstrained blind equalization criterion is proposed, Based on the convergence proof under noiseless condition, we show that a perfect equalization solution is achieved at every local optimum of the function, and the amplitude of input signal can be recovered. Batch data processing and online processing are presented to update the equalizer coefficients. Automatic gain control doesn’t need, while the steady-state error is smaller.4. Aiming at the problem that traditional blind equalization algorithms based on kurtosis maximization cannot rectify the phase offset of equalizer output, and power maximization based algorithms’performance will degrade in low SNR. In this dissertation, based on the vector norm nature and kurtosis maximization, a new criterion for QAM signal blind equalization and carrier phase recovery is proposed, which is more robust to additive Gaussian noise. Based on a formal proof, we show that a perfect equalization solution and carrier-phase recovery is obtained at every local optimum of the objective function. Batch data processing is presented to update the equalizer coefficients. Compared to traditional kurtosis maximization based algorithms, such as Donoho algorithm, CMA algorithm, SW algorithm and SFA algorithm, the new algorithm can recover the phase offset of equalizer output. The new proposed algorithm is more robust to Gaussian noise in comparison to existing methods such as QP-FSE and adaptive βMMA algorithm that maximize the equalizer output’s power.5. Aiming at the problem that the non-convex cost function of blind equalization are prone to undesirable local convergence and sensitive to initialization condition and iteration step. This dissertation utilizes the optimization theory of semi-definite programming to improve the performance of traditional blind equalization algorithm which is optimized via stochastic gradient descent method. Through amendments to MSOSA algorithm, a new blind equalization algorithm based on semi-definite programming is proposed, and be relaxed to convex programming. Compared to MSOSA algorithm realized by stochastic gradient descent method, the new algorithm need less samples, and can achieve lower steady-state error, making it well suited for applications with few amounts of data.