Efficient Architectures for the Generation and Correlation of Binary CSS Derived From Different Kernel Lengths

Abstract

Complementary Sets of Sequences (CSS) are used as basic building blocks for the development of Generalized Orthogonal (GO) sequences. In the design of practical sequences are desirable both optimal correlation properties and an efficient implementation of their corresponding correlators (i.e., with a reduced number of operations per input sample). Traditionally, the efficient algorithms for the generation/correlation of K binary CSS have been constrained to those of lengths L=K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> , where K ≥ 2 and N is a non-negative integer. This constraint implies that many binary CSS of known lengths cannot be generated and correlated efficiently, thus limiting their practical application. This paper proposes novel efficient architectures for the generation and correlation of K binary CSS of length L=(K/2)·2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> ·10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sup> ·26 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sup> with N, M and P non-negative integers. The proposal allows the efficient generation and correlation of binary CSS of many more lengths than previous efficient architectures can handle. Therefore, the use of the proposed architectures allows selecting with more flexibility the processing gain needed for each particular application.