Costas arrays are permutation matrices that meet the additional Costas condition. The Costas condition requires that when a Costas array defines the frequencies in a frequency jump burst and a signal is processed with a matched filter, then for any time or Doppler offset other than both zero, only one pulse will be at peak response at a time. Specific formulations of the Costas conditions provide a vector-matrix arithmetic representation where the matrix has eigenvalues that are square roots of integers and eigenvectors that can be scaled to have elements that are all integers. Polynomials are given for squared eigenvalues and for elements of scaled right eigenvector elements. A database of these singular value decompositions is provided on IEEE DataPort for orders from 3 to 1030, with left eigenvectors to order 100. We include proofs of validity and configuration. The right eigenvectors and the eigenvalues map a Costas array vector into its eigenspace. Functions of these vectors can be associated with system performance metrics so that these mapped vectors may be used to select and rank Costas arrays and is suitable for real-time system implementation.
Singular Value Decomposition of a Matrix Representation of the Costas Condition for Costas Array Selection
IEEE Transactions on Aerospace and Electronic Systems ; 57 , 2 ; 1139-1161
2021-04-01
2508761 byte
Article (Journal)
Electronic Resource
English
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