Deterministic Spreading Sequences for the Reverse Link of DS-CDMA With Noncoherent $M$-ary Orthogonal Modulation: Impact and Optimization

M-ary orthogonal modulation with noncoherent detection is an attractive scheme for the reverse link of direct-sequence code-division multiple access (DS-CDMA). The performance analysis of such DS-CDMA systems with random spreading sequences has been thoroughly studied. However, little satisfactory work has been done for systems with deterministic spreading sequences, regardless of their importance from the viewpoint of multiple-access interference reduction. To fill this void, we consider deterministic spreading sequences in this paper. We first present a detailed error performance analysis for the reverse link of DS-CDMA with -ary orthogonal modulation on both additive white Gaussian noise (AWGN) and multipath Rayleigh-fading channels. Then, we formulate the design of spreading sequences for the DS-CDMA system as a nonlinear discrete optimization problem. Two steps are taken to complete the task of sequence optimization: (1) A large code space is generated by permutating a single binary code matrix and imposing a Kronecker product structure on candidate code matrices, and (2) an evolutionary algorithm is applied to efficiently perform optimization. Numerical examples show that the optimized sequences considerably improve the system performance, especially when the number of users is relatively small or an AWGN channel is considered. In addition, our proposed approach can make a good tradeoff between code performance and search complexity.