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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In passive monitoring using sensor networks, low energy supplies drastically constrain sensors in terms of calculation and communication abilities. Designing processing algorithms at the sensor level that take into account these constraints is an important problem in this context. Here we study the estimation of correlation functions between sensors using compressed acquisition and one-bit-quantization. The estimation is achieved directly using compressed samples, without considering any reconstruction of the signals. We show that if the signals of interest are far from white noise, estimation of the correlation using @math compressed samples out of @math can be more advantageous than estimation of the correlation using @math consecutive samples. The analysis consists of studying the asymptotic performance of the estimators at a fixed compression rate. We provide the analysis when the compression is realized by a random projection matrix composed of independent and identically distributed entries. The framework includes widely used random projection matrices, such as Gaussian and Bernoulli matrices, and it also includes very sparse matrices. However, it does not include subsampling without replacement, for which a separate analysis is provided. When considering one-bit-quantization as well, the theoretical analysis is not tractable. However, empirical evidence allows the conclusion that in practical situations, compressed and quantized estimators behave sufficiently correctly to be useful in, for example, time-delay estimation and model estimation. 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 Quantization of compressed sensing measurements is typically justified by the robust recovery results of Candes, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size ź is used to quantize m measurements y=źx of a k-sparse signal xźźN, where ź satisfies the restricted isometry property, then the approximate recovery x# via l1-minimization is within O(ź) of x. The simplest and commonly assumed approach is to quantize each measurement independently. In this paper, we show that if instead an rth-order ΣΔ (Sigma---Delta) quantization scheme with the same output alphabet is used to quantize y, then there is an alternative recovery method via Sobolev dual frames which guarantees a reduced approximation error that is of the order ź(k m)(rź1 2)ź for any 0<ź<1, if mźr,źk(logN)1 (1źź). The result holds with high probability on the initial draw of the measurement matrix ź from the Gaussian distribution, and uniformly for all k-sparse signals x whose magnitudes are suitably bounded away from zero on their support. This paper studies the uplink of a cloud radio access network (C-RAN) where the cell sites are connected to a cloud-computing-based central processor (CP) with noiseless backhaul links with finite capacities. We employ a simple compress-and-forward scheme in which the base stations (BSs) quantize the received signals and send the quantized signals to the CP using either distributed Wyner-Ziv coding or single-user compression. The CP first decodes the quantization codewords and then decodes the user messages as if the remote users and the cloud center form a virtual multiple-access channel (VMAC). This paper formulates the problem of optimizing the quantization noise levels for weighted sum rate maximization under a sum backhaul capacity constraint. We propose an alternating convex optimization approach to find a local optimum solution to the problem efficiently, and more importantly, to establish that setting the quantization noise levels to be proportional to the background noise levels is near optimal for sum-rate maximization when the signal-to-quantization-noise-ratio (SQNR) is high. In addition, with Wyner-Ziv coding, the approximate quantization noise level is shown to achieve the sum-capacity of the uplink C-RAN model to within a constant gap. With single-user compression, a similar constant-gap result is obtained under a diagonal dominant channel condition. These results lead to an efficient algorithm for allocating the backhaul capacities in C-RAN. The performance of the proposed scheme is evaluated for practical multicell and heterogeneous networks. It is shown that multicell processing with optimized quantization noise levels across the BSs can significantly improve the performance of wireless cellular networks.