Three-dimensional orthogonal complete complementary codes

In this paper construction of a new family of Three-dimensional Orthogonal Complete Complementary Codes (3D-OCCC) is presented. The construction is based on the original ID-OCCC. The new 3D-OCCC retain all of the properties of the ID-OCCC and 2D-OCCC, such as zero crosscorrelation values of any two different pairs of signatures for every 3D shift and zero autocorrelation values of each signature for every 3D shift except the zero shift in every direction. Signature size (element count) and element´s size are both directly dependent on the maximum user count. For a given number of users, processing gain of 3D-OCCC remains the same as of 2D-OCCC or ID-OCCC, but they can be generated by much shorter ID-OCCC, what has a positive influence on modulation scheme requirements under certain circumstances. One of the challenges is the creation of a useable 3D channel, in which 3D spreading could be applied. The introduction of a third dimension increases the number of various transmission strategies, for example the possibilities of positioning the elements in a channel.