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Precoding for decentralized detection of unknown deterministic signals

机译：用于未知确定性信号的分散检测的预编码

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摘要

We consider a decentralized detection problem in which a number of sensor nodes collaborate to detect the presence of an unknown deterministic vector signal. To cope with the power/bandwidth constraints inherent in wireless sensor networks (WSNs), each sensor compresses its observations using a linear precoder. The compressed messages are transmitted to the fusion center (FC), where a global decision is made by resorting to a generalized likelihood ratio test (GLRT). The aim of the work presented here is to develop effective linear precoding strategies and study their detection error exponents under the asymptotic regime where the number of sensors tends to infinity. Two precoding strategies are introduced: a random precoding scheme which generates its precoding vectors following a Gaussian distribution, and a sign-assisted random precoding scheme which assumes the knowledge of the plus/minus signs of the signal components and designs its precoding vectors with the aid of this prior knowledge. Performance analysis shows that utilizing the sign information can radically improve the detection performance. Also, it is found that precoding-based schemes are more effective than the energy detector in detecting weak signals that are buried in noise. Specifically, the sign-assisted random precoding scheme outperforms the energy detector when the observation signal-to-noise ratio (SNR) is less than 1/(π ??? 2). Numerical results are conducted to corroborate our theoretical analysis and to illustrate the effectiveness of the proposed algorithms.
机译：我们考虑一个分散的检测问题，其中许多传感器节点协作以检测未知的确定性矢量信号的存在。为了应对无线传感器网络（WSN）固有的功率/带宽限制，每个传感器都使用线性预编码器压缩其观测值。压缩后的消息被传输到融合中心（FC），在融合中心通过采用广义似然比测试（GLRT）做出全局决策。本文提出的工作目的是开发有效的线性预编码策略，并研究在传感器数量趋于无穷大的渐近状态下其检测误差指数。引入了两种预编码策略：一种随机预编码方案，该方案根据高斯分布生成其预编码矢量；以及一种符号辅助随机预编码方案，该方案假设了解信号分量的正负号，并借助其设计预编码矢量。这些先验知识。性能分析表明，利用标志信息可以从根本上提高检测性能。而且，发现基于预编码的方案在检测掩埋在噪声中的微弱信号方面比能量检测器更有效。具体地说，当观察信噪比（SNR）小于1 /（π≤2）时，符号辅助随机预编码方案的性能优于能量检测器。进行数值结果以证实我们的理论分析并说明所提出算法的有效性。

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