Browsing by Subject "Semidefinite programs"
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Item Open Access ADMM based mainlobe power constrained phase-only sidelobe supression(IEEE, 2014) Alp, Yaşar Kemal; Arıkan, OrhanA novel sidelobe suppression technique is proposed for phased arrays, where only the phases of the array elements are adjusted to suppress the gain in the direction of interest while keeping the mainlobe power at a certain level. Mainlobe power constrained sidelobe suppression is formulated as a convex RSDP (Relaxed Semidefinite Program). Solution to resultant RSDP is obtained by ADMM (Alternating Direction Method of Multipliers) technique, which can handle designs for arrays with number of elements is significantly larger than that can be handled by other convex solvers such as CVX. In addition, although the available convex solvers can not provide a rank-1 solution matrix, a rank-1 solution matrix is obtained by modifying the ADMM iterations. In the conducted experiments, it is observed that proposed ADMM based method can achieve more than 10dB improvement in sidelobe levels compared to alternative techniques.Item Open Access FIR filter design by iterative convex relaxations with rank refinement(IEEE, 2014) Dedeoğlu, Mehmet; Alp, Yaşar Kemal; Arıkan, OrhanFinite impulse response (FIR) filters have been a primary topic of digital signal processing since their inception. Although FIR filter design is an old problem, with the developments of fast convex solvers, convex modelling approach for FIR filter design has become an active research topic. In this work, we propose a new method based on convex programming for designing FIR filters with the desired frequency characteristics. FIR filter design problem, which is modelled as a non-convex quadratically constrained quadratic program (QCQP), is transformed to a semidefinite program (SDP). By relaxing the constraints, a convex programming problem, which we call RSDP(Relaxed Semidefinite Program), is obtained. Due to the relaxation, solution to the RSDPs fails to be rank-1. Typically used rank-1 approximations to the obtained RSDP solution does not satisfy the constraints. To overcome this issue, an iterative algorithm is proposed, which provides a sequence of solutions that converge to a rank-1 matrix. Conducted experiments and comparisons demonstrate that proposed method successfully designs FIR filters with highly flexible frequency characteristics.