Construction of Complementary Code Matrices for Waveform Design

Abstract

A set of unimodular code vectors is complementary if the sum, over all code vectors, of the aperiodic autocorrelation sidelobes is zero. Complementary code sets are constructed using a matrix formulation in which code vectors form the columns of a matrix, called a complementary code matrix (CCM). Known construction methods for Hadamard matrices are examined and found to apply to the larger class of CCMs, in some cases with the addition or strengthening of conditions. These constructions include the Sylvester, Williamson, and Kronecker product constructions. Additional approaches for creating new CCMs from available CCMs are introduced and discussed. A future paper will focus on existence results for binary CCMs and on parametric families of unimodular CCMs. Special cases of CCMs are binary CCMs and Hadamard matrices.