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.

翻译：尽管正交多码信号及其衍生形式——单纯形信号——在不同通信系统中广为人知且广泛应用，但某些应用场景可能选择采用非正交信号，以利用此类信号方法所能提供的其他优势。受一类多载波扩频系统的启发，本文对广泛的多码信号方法类别进行了详尽的符号错误率分析，重点考察其使用不一定正交的码字时的性能。我们的分析还扩展到码集包含每个码向量负值的情况，即对双正交信号的推广。此外，本文证明，当多码为正交或满足单纯形多码的相关特性时，推导出的符号错误率结果将简化为文献中已有的结论。