Walsh-Like Nonlinear Phase Orthogonal Codes for Direct Sequence CDMA Communications

Walsh codes are perfectly orthogonal binary (antipodal) block codes that found their use in many popular applications over several decades including synchronous multiuser communications. It is well known in the literature that they perform poorly for the case of asynchronous multiuser communications. Therefore, the near-orthogonal and nonlinear phase gold codes with better performance are the preferred user codes in asynchronous direct sequence code division multiple access (DS-CDMA) communications standards. In this paper, we relaxed linear phase requirements and new sets of Walsh-like nonlinear phase binary orthogonal user codes (transforms) are obtained for asynchronous and synchronous spread spectrum multiuser communications. It is shown that the proposed binary user code family outperforms the Walsh codes significantly and they match in performance with the popular, nearly orthogonal gold codes closely for asynchronous multiuser communications in additive white Gaussian noise (AWGN) channels. It is also shown that all of the binary code families considered in this paper performed comparable for Rayleigh flat-fading channels. We present in this paper that there are a good number of such desirable code sets available in the binary sample space with different transform sizes. These new binary sets with good performance and flexible code lengths might help us to improve the spread spectrum multiplexing capabilities of future wireline and wireless CDMA communications systems.