8 research outputs found
The Maximum Squared Correlation, Sum Capacity, and Total Asymptotic Efficiency of Minimum Total-Squared-Correlation Binary Signature Sets
Efficient computation of the binary vector that maximizes a rank-3 quadratic form
Μη διαθέσιμη περίληψηNot available summarizationΠαρουσιάστηκε στο: 44th Annual Allerton Conference on Communication, Control, and Computin
Efficient computation of the binary vector that maximizes a rank-deficient quadratic form
Summarization: The 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.Παρουσιάστηκε στο: IEEE International Conference on Acoustics, Speech, and Signal Processin