FIR Filter Design Based On Convex Optimization Theory And Its Application In LAS-CDMA System

Over the last two decades, there have been significant advances in the research of conic optimization and interior point methods. Powerful optimization models, efficient algorithms and software tool have been produced. Recently, these advances have begun to impact various applied science and engineering fields. In the past thirty years, the work-horse algorithms in the field of digital signal processing and communication have been the gradient descent algorithm and the least square algorithm. While these algorithms have served their purpose well, they suffer from slow convergence and sensitivity to the algorithm initialization and step size selection, especially when applied to ill-conditioned or nonconvex problem formulations. One powerful way to avoid these problems is to derive an exact convex reformulation or a convex relaxation of the original nonconvex formulation. Once a convex reformulation or relaxation is obtained, we can be guaranteed of finding the globally optimal design efficiently without the usual headaches of step size selection, algorithm initialization and local minima.Through constructing spreading codes with zero correlation windows, LAS-CDMA technology gets over the drawback of traditional CDMA technology. Compared with traditional CDMA system, LAS-CDMA system has a bigger system capacity with a simpler engineering implementation.In this paper, we reformulate the problem of designing a FIR filter with spectrum mask constraints to a conic optimization problem, through using the autocorrelation of the filter's coefficients as optimization variables. Also, through expanding positive real lemma, we reformulate the infinite form of the spectrum mask constraints to a finite form. Finally, we adopt the interior point methods to solve the reformulated conic...