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Institutional Repository [SANDBOX]
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/58DFFAC4-8C48-4E54-A0EB-5725C486F8C3 | ||
| Year | 2011 | ||
| Type of Item | Conference Full Paper | ||
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| Bibliographic Citation | A. T. Kyrillidis and G. N. Karystinos, “Rank-deficient quadratic-form maximization over M-phase alphabet: Polynomialcomplexity solvability and algorithmic developments,” in Proc. IEEE - Intern. Conf. Acoust., Speech and Signal Proc.,(ICASSP '11) pp. 3856-3859, doi: 10.1109/ICASSP.2011.5947193 https://doi.org/10.1109/ICASSP.2011.5947193 | ||
| Appears in Collections |
The maximization of a positive (semi)definite complex quadratic form over a finite alphabet is NP-hard and achieved through exhaustive search when the form has full rank. However, if the form is rank-deficient, the optimal solution can be computed with only polynomial complexity in the length N of the maximizing vector. In this work, we consider the general case of a rank-D positive (semi)definite complex quadratic form and develop a method that maximizes the form with respect to a M-phase vector with polynomial complexity. The proposed method efficiently reduces the size of the feasible set from exponential to polynomial. We also develop an algorithm that constructs the polynomial-size candidate set in polynomial time and observe that it is fully parallelizable and rank-scalable.
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