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High-Rate Vector Quantization for the Neyman–Pearson Detection of Correlated Processes

机译：用于相关过程的Neyman-Pearson检测的高速向量量化

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摘要

This paper investigates the effect of quantization on the performance of the Neyman–Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through an $N$-point quantizer and transmitted to a decision device which performs a binary hypothesis test. For any false alarm level, it is shown that the miss probability of the Neyman–Pearson test converges to zero exponentially as the number of samples tends to infinity, assuming that the observed process satisfies certain mixing conditions. The main contribution of this paper is to provide a compact closed-form expression of the error exponent in the high-rate regime, i.e., when the number $N$ of quantization levels tends to infinity, generalizing previous results of Gupta and Hero to the case of nonindependent observations. If $d$ represents the dimension of one sample, it is proved that the error exponent converges at rate $N^{2/d}$ to the one obtained in the absence of quantization. As an application, relevant high-rate quantization strategies which lead to a large error exponent are determined. Numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error.
机译：本文研究了量化对Neyman–Pearson检验性能的影响。假设传感单元观察到相关的平稳遍历多元过程的样本。每个样本都通过$ N $点量化器，然后传输到执行二进制假设检验的决策设备。对于任何假警报级别，都表明，假设观察到的过程满足某些混合条件，则随着样本数量趋于无穷大，Neyman–Pearson检验的漏失概率呈指数收敛至零。本文的主要贡献是提供高速率状态下误差指数的紧凑闭合形式表示，即当量化级别的数量$ N $趋于无穷大时，将古普塔和英雄的先前结果推广到非独立观察的情况。如果$ d $表示一个样本的维数，则证明误差指数以速率$ N ^ {2 / d} $收敛到没有量化的情况下获得的误差指数。作为一种应用，确定了导致大误差指数的相关高速率量化策略。数值结果表明，在检测误差方面，所提出的量化规则可以比现有的量化规则产生更好的性能。

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