We consider a two sensor distributed detection system transmitting a binary non-uniform source over a Gaussian multiple access channel (MAC). We model the network via binary sensors whose outputs are generated by binary symmetric channels of different noise levels. We prove an optimal one dimensional constellation design under individual sensor power constraints which minimizes the error probability of detecting the source. Three distinct cases arise for this optimization based on the parameters in the problem setup. In the most notable case (Case III), the optimal signaling design is to not necessarily use all of the power allocated to the more noisy sensor (with less correlation to the source). We compare the error performance of the optimal one dimensional constellation to orthogonal signaling. The results show that the optimal one dimensional constellation achieves lower error probability than using orthogonal channels.

翻译：我们考虑一个双传感器分布式检测系统，该系统通过高斯多址接入信道(Gaussian multiple access channel, MAC)传输二值非均匀信源。我们利用输出由不同噪声水平的二进制对称信道生成的二进制传感器对网络进行建模。在单个传感器功率约束下，我们证明了一种最优的一维星座设计，该设计能最小化检测信源的错误概率。根据问题设置中的参数，该优化问题出现三种不同情形。在最显著的情形（情形III）中，最优信号设计不一定需要使用分配给噪声较大（与信源相关性较小）传感器的全部功率。我们将最优一维星座的错误性能与正交信令进行了比较。结果表明，最优一维星座可实现比使用正交信道更低的错误概率。