A New Rank-two Semidefinite Programming Relaxation Method for the Design of FIR Filters with Discrete Coefficients

摘要

Based on the binary quadratic programming model of the design of FIR digital filters with discrete coefficients, a new rank-two semidefinite programming relaxation method is presented. The proposed method restricts the matrix variable in the semidefinite programming relaxation to be rank-two, and yields a nonlinear programming with quadratic objective function and simple quadratic constraints. A feasible direction method is used to solve the nonlinear programming. Then, the randomized method is used for the rank-two solution, and a suboptimal solution is obtained for the FIR filters design problem. Comparing with the semidefinite programming method, simulations demonstrate that the new rank-two semidefinite programming relaxation method often yields the similar BER performances for the FIR filter design problem, but the average CPU time of this method is significantly reduced.