Design of signals with favorable correlation properties

In a wide range of communication environments, the optimum (matched filter) signal detector is a correlation signal detector. This motivates the search for sets of communication signals which are maximally distinguishable with respect to correlation. The rows of an n×n Hadamard matrix provide n mutually uncorrelated binary signals. For n>2, Hadamard matrices exist only if n is a multiple of 4, and it is conjectured that they exist for all such n. From Hadamard matrices, it is possible to construct not only orthogonal signal sets, but also simplex codes and bi-orthogonal codes. Applications to radar and sonar signals are discussed