Construction of Complementary Code Matrices for Waveform Design

Group symmetries of complementary code matrices

“…. There are even more that you can read about yet all the ones from Coxson and Haloupek focus, as we said, on creating a CCM from a smaller dimension CCM to decrease the search space [1]. We can also look at creating a quad-phase CCM from the ternary CCMs.…”

“…In order to correlate incoming with outgoing signals these codes should have nice sharp peak-sidelobe characteristics in terms of their auto-correlation functions. Usually in radar and communications, Barker codes and Golay pairs of codes are employed, but there is increased interest in more general codes called complementary code sets, i.e., complementary sets of codes whose composite auto-correlation function has zero sidelobe levels ( [1,4]). When expressed in matrix form, complementary code sets are referred to as complementary code matrices (CCMs).…”

Efficient exhaustive search for binary complementary code sets

“…The following theorem details these CCM-preserving operations. A proof can be found in [2], where the theorem is given in the more general context of unimodular CCMs (in which elements are restricted to the unit circle rather than the set {−1, 1}). (iv) Form QP for P any K × K permutation matrix (for a definition, see [14]).…”

“…Although binary Hadamard matrices exist only as square matrices of order 1, 2, or a multiple of 4 ( [7], [3]), a richer source are the binary complementary code matrices (CCMs) which exist in rectangular forms with fewer restrictions on their dimensions. Complementary code matrices include Hadamard matrices as a special case [2]. The added generality of the complementary code matrices comes at a slight cost -in general, only the columns of CCMs give complementary code sets.…”

“…The added generality of the complementary code matrices comes at a slight cost -in general, only the columns of CCMs give complementary code sets. Many of the Hadamard matrix constructions may be extended to general CCMs either directly or with at most modest changes in conditions that must be satisfied [2].…”