Theoretical Analysis of Multi-coding with Non-orthogonal Signaling

Even though orthogonal multi-code signaling and its derivative, simplex signaling, are well known and widely used in different communication systems, certain applications may choose to adopt non-orthogonal signaling to benefit from other advantages that such signaling methods can offer. Motivated by a class of multi-carrier spread spectrum systems, this paper presents a thorough symbol error rate analysis of the broad class of multi-code signaling methods when they make use of codes which are not necessarily orthogonal. Our analysis is also extended to the case where the code set includes the negative of each code vector, i.e., an extension to biorthogonal signaling. Moreover, it is shown that the symbol error rate results derived in this paper reduce to those available in the literature when the multi-codes are orthogonal or satisfy the correlation property of simplex multi-codes.