000198914 001__ 198914 000198914 005__ 20181203023509.0 000198914 0247_ $$2doi$$a10.1109/Tcomm.2014.012414.130439 000198914 022__ $$a0090-6778 000198914 02470 $$2ISI$$a000334112900018 000198914 037__ $$aARTICLE 000198914 245__ $$aFixed-Rank Rayleigh Quotient Maximization by an MPSK Sequence 000198914 260__ $$bInstitute of Electrical and Electronics Engineers$$c2014$$aPiscataway 000198914 269__ $$a2014 000198914 300__ $$a15 000198914 336__ $$aJournal Articles 000198914 520__ $$aCertain optimization problems in communication systems, such as limited-feedback constant-envelope beamforming or noncoherent M-ary phase-shift keying (MPSK) sequence detection, result in the maximization of a fixed-rank positive semidefinite quadratic form over the MPSK alphabet. This form is a special case of the Rayleigh quotient of a matrix and, in general, its maximization by an MPSK sequence is NP-hard. However, if the rank of the matrix is not a function of its size, then the optimal solution can be computed with polynomial complexity in the matrix size. In this work, we develop a new technique to efficiently solve this problem by utilizing auxiliary continuous-valued angles and partitioning the resulting continuous space of solutions into a polynomial-size set of regions, each of which corresponds to a distinct MPSK sequence. The sequence that maximizes the Rayleigh quotient is shown to belong to this polynomial-size set of sequences, thus efficiently reducing the size of the feasible set from exponential to polynomial. Based on this analysis, we also develop an algorithm that constructs this set in polynomial time and show that it is fully parallelizable, memory efficient, and rank scalable. The proposed algorithm compares favorably with other solvers for this problem that have appeared recently in the literature. 000198914 6531_ $$aAlgorithms 000198914 6531_ $$amaximum likelihood detection 000198914 6531_ $$aMIMO systems 000198914 6531_ $$anoncoherent communication 000198914 6531_ $$aoptimization methods 000198914 6531_ $$aphase shift keying 000198914 6531_ $$aRayleigh quotient 000198914 6531_ $$asequences 000198914 700__ $$0245321$$g199236$$uEcole Polytech Fed Lausanne, Sch Comp & Commun Sci, CH-1015 Lausanne, Switzerland$$aKyrillidis, Anastasios 000198914 700__ $$aKarystinos, George N. 000198914 773__ $$j62$$tIEEE Transactions on Communications$$k3$$q961-975 000198914 909C0 $$xU12179$$0252306$$pLIONS 000198914 909CO $$pSTI$$particle$$ooai:infoscience.tind.io:198914 000198914 917Z8 $$x199128 000198914 917Z8 $$x231598 000198914 937__ $$aEPFL-ARTICLE-198914 000198914 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL 000198914 980__ $$aARTICLE