Advances in Engineering Advances in Engineering features breaking research judged by Advances in Engineering advisory team to be of key importance in the Engineering field. Papers are selected from over 10,000 published each week from most peer reviewed journals.
Signal Processing, Volume 93, Issue 4, 2013, Pages 866–873.
Ashkan Ashrafi.
Department of Electrical and Computer Engineering, San Diego State University, 5500 Campanile Dr., San Diego, CA 92182, USA.
Abstract
In this paper, a novel method to design linear phase square-root Nyquist filters is introduced. The design procedure is posed as a quadratic programming problem with linear and quadratic constraints that can be solved using convex optimization packages. The flatness of the filter’s pass-band, i.e., the pass-band ripple energy, is formulated as a quadratic function of the impulse response of the filter. By minimizing this quadratic function through a proxy function called the pseudo-ISI, one can optimize the ISI energy of the filter while the frequency response of the filter satisfies a spectral mask. It is shown that the optimization of the pseudo-ISI results in an optimized ISI energy if the spectral mask is tight enough. The Qualcomm’s Code Division Multiple Access (CDMA) IS-95 and The European Telecommunications Standards Institute’a Universal Mobile Communications Systems (UMTS) standards are used to define the spectral masks. The designed filters show superior inter-symbol interference and stop-band energies compared to the previously proposed designs for CDMA and UMTS standards.
Additional Information:
This paper presents a technique based on the convex optimization that solves the classic problem of designing linear-phase finite impulse response (FIR) square-root Nyquist filters with optimum inter-symbol interference (ISI). This problem is non-convex in nature, which makes it impossible to find the global optimum point. A novel approximation technique is introduced in this paper that can make the problem convex; therefore, a global optimum point can be found with the readily available solvers. The presented method showed to be very effective in designing linear-phase square-root Nyquist FIR matched filters for the current wireless mobile technologies including CDMA IS-95 and UMTS. For example, using the this method, an optimum linear-phase square-root Nyquist FIR filter is designed that satisfies the UMTS standard constraints. The designed filter has an ISI that is two orders of magnitude less than that of the square-root raised-cosine filter suggested in the UMTS standard, while satisfying the same spectral constraint. The incorporation of this optimum filter in the wireless systems can significantly improve the quality of the mobile communications.
