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arXiv 2402.04424cs.ITmath.IT
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两传感器高斯多址信道网络的最优二进制信号设计

Optimal Binary Signaling for a Two Sensor Gaussian MAC Network

Luca Sardellitti, Glen Takahara, Fady Alajaji

AI总结:

针对两传感器高斯多址信道分布式检测系统,提出最优一维星座设计,在个体功率约束下最小化检测错误概率,并证明其优于正交信号。

摘要:

我们考虑一个两传感器分布式检测系统,该系统通过高斯多址信道(MAC)传输二元非均匀信源。我们通过二进制传感器对网络进行建模,这些传感器的输出由不同噪声水平的二进制对称信道生成。我们证明了在个体传感器功率约束下的最优一维星座设计,该设计最小化检测信源的错误概率。基于问题设置中的参数,该优化出现三种不同情形。在最显著的情形(情形III)中,最优信号设计是不必使用分配给噪声较大(与信源相关性较小)的传感器的所有功率。我们将最优一维星座的误差性能与正交信号进行比较。结果表明,最优一维星座比使用正交信道实现了更低的错误概率。

英文摘要:

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.

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