We consider the problem of making a quick decision in favor of one of two possible physical models while the numerical measurements are acquired by sensing devices featuring minimal digitization complexity. Therefore, the digital data streams available for statistical processing are binary and exhibit temporal and spatial dependencies. Such a setting is of relevance when designing radio systems that have to perform time-critical monitoring tasks in noisy environments with low energy consumption. We assess the latency penalty in sequential decision-making resulting from using analog-to-binary instead of high-resolution analog-to-digital conversion at the front-ends. To handle the intractable multivariate binary data model, we first consider sequential tests for exponential family distributions. Within this generic probabilistic framework, we identify approximations for the log-likelihood ratio and the Kullback-Leibler divergence. The results allow designing sequential detectors for binary radio systems and analyzing their average run-time along classical arguments of Wald. In particular, the derived tests exploit the structure of the spatio-temporal correlation of the analog sensor signals engraved into the binary radio data stream. As an application, we consider the specification of binary sensing architectures in the context of cognitive radio and satellite-based synchronization where our results characterize the detection latency as a function of the temporal oversampling and the number of antennas. Finally, we evaluate the efficiency of the proposed algorithms and illustrate the accuracy of our analysis via Monte-Carlo simulations.
Quantized sequential decision-making has been studied predominantly for sensor networks where measurement nodes forward compressed statistics of their observations to minimize the communication overhead @cite_16 @cite_38 @cite_29 @cite_34 @cite_9 @cite_42 @cite_41 . In such a setup, it is usually assumed that the sensing nodes have access to the unquantized digital observations and compress them, for example, by quantizing the likelihood ratio. Here we discuss sequential detection when employing binary sensing front-ends. Therefore, the nodes do not have access to the high-resolution observations, and the central decision is exclusively based on hard-limited measurements. This case is less well studied, and the focus of existing works is on the design of optimal quantizers @cite_44 @cite_18 @cite_33 @cite_15 .
@cite_38 @cite_18 @cite_33 @cite_41 @cite_29 @cite_9 @cite_42 @cite_34 @cite_44 @cite_15 @cite_16
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Optimum detection schemes based on quantized data are of great interest in radar and sonar applications. The design and properties of multisensor schemes are considered here for detection of weak random signals in additive, possibly non-Gaussian, noise. Signal-to-noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent. Analytical expressions describing the best way to fuse the quantized observations for cases with any given observation sample size are provided. The best schemes for originally quantizing the observations are also studied for the case of asymptotically large observation sample sizes. These schemes are shown to minimize the mean-squared error between the best weak-signal test statistic based on unquantized observations and the best weak-signal test statistic based on quantized observations (under signal absent). Numerical results indicate it is sometimes best for each quantizer to use different size alphabets when a quantizer is located at each sensor. > We consider the problem of sequential decentralized detection, a problem that entails the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two competing hypotheses), and a set of quantization rules (the local decisions on the basis of which the global decision is made). The main result of this paper is to resolve an open problem posed by (1993) concerning whether optimal local decision functions for the Bayesian formulation of sequential decentralized detection can be found within the class of stationary rules. We provide a negative answer to this question by exploiting an asymptotic approximation to the optimal cost of stationary quantization rules, and the asymmetry of the Kullback-Leibler divergences. In addition, we show that asymptotically optimal quantizers, when restricted to the space of blockwise stationary quantizers, are likelihood-based threshold rules The quantization of the observed data for sequential signal detection is studied. The criteria used are the minimizations of the average sample number under the hypothesis, the average sample number under the alternative, and the maximum average sample number. Numerical results show that the performance is not very sensitive to different criteria. Using a sequential probability ratio test (SPRT), the performances of optimum quantizers are compared to systems with unquantized data. The asymptotic relative efficiencies of the quantizerSPRT's with respect to the SPRT for unquantized data are derived for symmetric noise densities. The relation between these asymptotic relative efficiencies and those of fixed-sample-size detectors is noted. Distributed sensor systems composed of spatially distributed micro sensor nodes have been proposed for large scale monitoring applications. In these systems, nodes aggregate their sensor data to provide real time information about the underlying state. To extend the lifetime each node of the system has to limit the complexity of the sequential fusion algorithm. In this paper we derive optimal likelihood quantization rules for maximizing sequential detection performance. The resulting sequential detection algorithm is in the form of a finite state machine ideal for implementation in low complexity low power devices. A class of decentralized sequential detection problems is investigated. Under appropriate independence assumptions, it is shown that at each time instant the optimal local strategies are given by threshold tests on the likelihood of ratios. Furthermore, local decisions depend not only on the present and past observations, but on the past local decision as well. That is, for each local processor a different threshold exists for every different sequence of past decisions. Examples, computational techniques, discussions of the difficulties at hand, and suggestions for further exploration of the problem are presented. >