Efficient computation of the binary vector that maximizes a rank-deficient quadratic formEfficient computation of the binary vector that maximizes a rank-deficient quadratic form Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-232010enThe maximization of a full-rank quadratic form over the binary alphabet can be performed through exponential-complexity exhaustive search. However, if the rank of the form is not a function of the problem size, then it can be maximized in polynomial time. By introducing auxiliary spherical coordinates, we show that the rank-deficient quadratic-form maximization problem is converted into a double maximization of a linear form over a multidimensional continuous set, the multidimensional set is partitioned into a polynomial-size set of regions which are associated with distinct candidate binary vectors, and the optimal binary vector belongs to the polynomial-size set of candidate vectors. Thus, the size of the candidate set is reduced from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size candidate set in polynomial time and show that it is fully parallelizable and rank-scalable. Finally, we demonstrate the efficiency of the proposed algorithm in the context of adaptive spreading code design.Δημοσίευση σε επιστημονικό περιοδικό http://creativecommons.org/licenses/by/4.0/IEEE Transactions on Information Theory7563581 - 3593 Karystinos Georgios Καρυστινος Γεωργιος Liavas Athanasios Λιαβας Αθανασιος Institute of Electrical and Electronics Engineers Binary sequences code-division multiple-access (CDMA) code-division multiplexing maximization of quadratic forms optimization signal waveform design