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在解码转发方式下，传统差分网络编码的中继检测复杂度高、编码环节繁杂。基于此，本文提出了复数域符号相乘的差分网络编码，并构建了中继检测方法一和中继检测方法二，能显著降低中继的检测和编解码复杂度。同时，为了获取高阶分集增益，将提出的编码方法拓展到多中继协作方式，得到了随机差分空时网络编码，其可获得的协作分集增益阶为可正确解码的中继数。理论和仿真性能均验证了提出的复数域符号相乘的差分网络编码方法在单中继和多中继协作方式下的有效性。
In the decoding and forwarding mode, the traditional differential network coding relay detection complexity is high, the coding part is complicated. Based on this, this paper proposes differential network coding of symbol multiplication in complex domain, and constructs a relay detection method and a relay detection method, which can significantly reduce the complexity of relay detection and coding and decoding. At the same time, in order to obtain high-order diversity gain, the proposed coding method is extended to multi-relay cooperation mode, and the random difference space-time network coding is obtained. The available cooperative diversity gain order is the number of relays that can be correctly decoded. Both theoretical and simulation performance verify the effectiveness of the proposed differential network coding method for multiplication of complex numbers in single relay and multi-relay cooperative modes.