Recently, complex orthogonal variable spreading factor (OVSF) codes based on polyphase orthogonal codes have been proposed to support multi-user/multi-rate data transmission services in synchronous direct-sequence code-division multiple access (DS-CDMA) systems. This study investigates the low signal-envelope fluctuation property of the complex OVSF codes in terms of transmission signal trajectories. In addition, a new method is proposed to suppress the envelope fluctuation more strongly at the expense of reducing the number of spreading sequences of the codes.

The direct sequence code division multiple access (DS-CDMA) technique is widely used in various communication systems. When adopting orthogonal variable spreading factor (OVSF) codes, DS-CDMA is particularly suitable for supporting multi-user/multi-rate data transmission services. A useful property of OVSF codes is that no two code sequences assigned to different users will ever interfere with each other, even if their spreading factors are different. Conventional OVSF codes are constructed based on binary orthogonal codes, called Walsh codes, and OVSF code sequences are binary sequences. In this paper, we propose new OVSF codes that are constructed based on polyphase orthogonal codes and consist of complex sequences in which each symbol is represented as a complex number. Construction of the proposed codes is based on a tree structure that is similar to conventional OVSF codes. Since the proposed codes are generalized versions of conventional OVSF codes, any conventional OVSF code can be presented as a special case of the proposed codes. Herein, we show the method used to construct the proposed OVSF codes, after which the orthogonality of the codes, including conventional OVSF codes, is investigated. Among the advantages of our proposed OVSF codes is that the spreading factor can be designed more flexibly in each layer than is possible with conventional OVSF codes. Furthermore, combination of the proposed code and a non-binary phase modulation is well suited to DS-CDMA systems where the level fluctuation of signal envelope is required to be suppressed.