TY - EJOUR
DO - 10.1109/Tcomm.2014.012414.130439
AB - Certain 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.
T1 - Fixed-Rank Rayleigh Quotient Maximization by an MPSK Sequence
IS - 3
DA - 2014
AU - Kyrillidis, Anastasios
AU - Karystinos, George N.
JF - IEEE Transactions on Communications
SP - 961-975
VL - 62
EP - 961-975
PB - Institute of Electrical and Electronics Engineers
PP - Piscataway
ID - 198914
KW - Algorithms
KW - maximum likelihood detection
KW - MIMO systems
KW - noncoherent communication
KW - optimization methods
KW - phase shift keying
KW - Rayleigh quotient
KW - sequences
SN - 0090-6778
ER -