This paper investigates the performance of direct-sequence code-division multiple-access (CDMA) communication systems in Gaussian noise channels using binary and M-ary non-coherent signaling schemes with complex signature sequences. Differential-phase-shift-keyed (DPSK) signaling with differentially coherent demodulation and frequency-shift-keyed (FSK) signaling with noncoherent demodulation are considered. Upper and lower bounds are presented for the probability of bit error (p.b.e.) of binary DPSK and binary FSK systems when the number of users is small. Simulation and Gaussian approximation are used to obtained the p.b.e. when the number of users is large. Two types of complex sequences (FZC and 4-phase sequences) and one type of binary sequences (Gold sequences) are used for evaluating numerical results. Results show that complex sequences outperform binary sequence when the number of users is small. However, as the number of users gets large, all sequences have similar performances. These suggest that complex sequences should be used when the number of users is small, but binary sequences should be used when the number of users is large, as binary sequences are easier to generate.