Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding

In this paper, we consider the problem of signal recovery from 1-bit noisy measurements. We present an efficient method to obtain an estimation of the signal of interest when the measurements are corrupted by white or colored noise. To the best of our knowledge, the proposed framework is the pioneer effort in the area of 1-bit sampling and signal recovery in providing a unified framework to deal with the presence of noise with an arbitrary covariance matrix including that of the colored noise. The proposed method is based on a constrained quadratic program (CQP) formulation utilizing an adaptive quantization thresholding approach, that further enables us to accurately recover the signal of interest from its 1-bit noisy measurements. In addition, due to the adaptive nature of the proposed method, it can recover both fixed and time-varying parameters from their quantized 1-bit samples.Comment: This is a pre-print version of the original conference paper that has been accepted at the 2018 IEEE Asilomar Conference on Signals, Systems, and Computer

Distributed Two-Step Quantized Fusion Rules via Consensus Algorithm for Distributed Detection in Wireless Sensor Networks

We consider the problem of distributed soft decision fusion in a bandwidth-constrained spatially uncorrelated wireless sensor network (WSN). The WSN is tasked with the detection of an intruder transmitting an unknown signal over a fading channel. Existing distributed consensus-based fusion rules algorithms only ensure equal combining of local data and in the case of bandwidth-constrained WSNs, we show that their performance is poor and does not converge across the sensor nodes (SNs). Motivated by this fact, we propose a two-step distributed quantized fusion rule algorithm where in the first step the SNs collaborate with their neighbors through error-free, orthogonal channels (the SNs exchange quantized information matched to the channel capacity of each link). In the second step, local 1-bit decisions generated in the first step are shared among neighbors to yield a consensus. A binary hypothesis testing is performed at any arbitrary SN to optimally declare the global decision. Simulations show that our proposed quantized two-step distributed detection algorithm approaches the performance of the unquantized centralized (with a fusion center) detector and its power consumption is shown to be 50% less than the existing (unquantized) conventional algorithm

Distributed detection and estimation in wireless sensor networks: resource allocation, fusion rules, and network security

This thesis addresses the problem of detection of an unknown binary event. In particular, we consider centralized detection, distributed detection, and network security in wireless sensor networks (WSNs). The communication links among SNs are subject to limited SN transmit power, limited bandwidth (BW), and are modeled as orthogonal channels with path loss, flat fading and additive white Gaussian noise (AWGN). We propose algorithms for resource allocations, fusion rules, and network security. In the first part of this thesis, we consider the centralized detection and calculate the optimal transmit power allocation and the optimal number of quantization bits for each SN. The resource allocation is performed at the fusion center (FC) and it is referred as a centralized approach. We also propose a novel fully $distributed$ algorithm to address this resource allocation problem. What makes this scheme attractive is that the SNs share with their neighbors just their individual transmit power at the current states. Finally, the optimal soft fusion rule at the FC is derived. But as this rule requires a-priori knowledge that is difficult to attain in practice, suboptimal fusion rules are proposed that are realizable in practice. The second part considers a fully distributed detection framework and we propose a two-step distributed quantized fusion rule algorithm where in the first step the SNs collaborate with their neighbors through error-free, orthogonal channels. In the second step, local 1-bit decisions generated in the first step are shared among neighbors to yield a consensus. A binary hypothesis testing is performed at any arbitrary SN to optimally declare the global decision. Simulations show that our proposed quantized two-step distributed detection algorithm approaches the performance of the unquantized centralized (with a FC) detector and its power consumption is shown to be 50% less than the existing (unquantized) conventional algorithm. Finally, we analyze the detection performance of under-attack WSNs and derive attacking and defense strategies from both the Attacker and the FC perspective. We re-cast the problem as a minimax game between the FC and Attacker and show that the Nash Equilibrium (NE) exists. We also propose a new non-complex and efficient reputation-based scheme to identify these compromised SNs. Based on this reputation metric, we propose a novel FC weight computation strategy ensuring that the weights for the identified compromised SNs are likely to be decreased. In this way, the FC decides how much a SN should contribute to its final decision. We show that this strategy outperforms the existing schemes

Channel Estimation Error, Oscillator Stability And Wireless Power Transfer In Wireless Communication With Distributed Reception Networks

This dissertation considers three related problems in distributed transmission and reception networks. Generally speaking, these types of networks have a transmit cluster with one or more transmit nodes and a receive cluster with one or more receive nodes. Nodes within a given cluster can communicate with each other using a wired or wireless local area network (LAN/WLAN). The overarching goal in this setting is typically to increase the efficiency of communication between the transmit and receive clusters through techniques such as distributed transmit beamforming, distributed reception, or other distributed versions of multi-input multi-output (MIMO) communication. More recently, the problem of wireless power transfer has also been considered in this setting. The first problem considered by this dissertation relates to distributed reception in a setting with a single transmit node and multiple receive nodes. Since exchanging lightly quantized versions of in-phase and quadrature samples results in high throughput requirements on the receive LAN/WLAN, previous work has considered an approach where nodes exchange hard decisions, along with channel magnitudes, to facilitate combining similar to an ideal receive beamformer. It has been shown that this approach leads to a small loss in SNR performance, with large reductions in required LAN/WLAN throughput. A shortcoming of this work, however, is that all of the prior work has assumed that each receive node has a perfect estimation of its channel to the transmitter. To address this shortcoming, the first part of this dissertation investigates the effect of channel estimation error on the SNR performance of distributed reception. Analytical expressions for these effects are obtained for two different modulation schemes, M-PSK and M2-QAM. The analysis shows the somewhat surprising result that channel estimation error causes the same amount of performance degradation in ideal beamforming and pseudo-beamforming systems despite the fact that the channel estimation errors manifests themselves quite differently in both systems. The second problem considered in this dissertation is related to oscillator stability and phase noise modeling. In distributed transmission systems with multiple transmitters in the transmit cluster, synchronization requirements are typically very strict, e.g., on the order of one picosecond, to maintain radio frequency phase alignment across transmitters. Therefore, being able to accurately model the behavior of the oscillators and their phase noise responses is of high importance. Previous approaches have typically relied on a two-state model, but this model is often not sufficiently rich to model low-cost oscillators. This dissertation develops a new three-state oscillator model and a method for estimating the parameters of this model from experimental data. Experimental results show that the proposed model provides up to 3 dB improvement in mean squared error (MSE) performance with respect to a two-state model. The last part of this work is dedicated to the problem of wireless power transfer in a setting with multiple nodes in the transmit cluster and multiple nodes in the receive cluster. The problem is to align the phases of the transmitters to achieve a certain power distribution across the nodes in the receive cluster. To find optimum transmit phases, we consider a iterative approach, similar to the prior work on one-bit feedback for distributed beamforming, in which each receive node sends a one-bit feedback to the transmit cluster indicating if the received power in that time slot for that node is increased. The transmitters then update their phases based on the feedback. What makes this problem particularly interesting is that, unlike the prior work on one-bit feedback for distributed beamforming, this is a multi-objective optimization problem where not every receive node can receive maximum power from the transmit array. Three different phase update decision rules, each based on the one-bit feedback signals, are analyzed. The effect of array sparsity is also investigated in this setting

Convergence Rate Analysis of Distributed Gossip (Linear Parameter) Estimation: Fundamental Limits and Tradeoffs

The paper considers gossip distributed estimation of a (static) distributed random field (a.k.a., large scale unknown parameter vector) observed by sparsely interconnected sensors, each of which only observes a small fraction of the field. We consider linear distributed estimators whose structure combines the information \emph{flow} among sensors (the \emph{consensus} term resulting from the local gossiping exchange among sensors when they are able to communicate) and the information \emph{gathering} measured by the sensors (the \emph{sensing} or \emph{innovations} term.) This leads to mixed time scale algorithms--one time scale associated with the consensus and the other with the innovations. The paper establishes a distributed observability condition (global observability plus mean connectedness) under which the distributed estimates are consistent and asymptotically normal. We introduce the distributed notion equivalent to the (centralized) Fisher information rate, which is a bound on the mean square error reduction rate of any distributed estimator; we show that under the appropriate modeling and structural network communication conditions (gossip protocol) the distributed gossip estimator attains this distributed Fisher information rate, asymptotically achieving the performance of the optimal centralized estimator. Finally, we study the behavior of the distributed gossip estimator when the measurements fade (noise variance grows) with time; in particular, we consider the maximum rate at which the noise variance can grow and still the distributed estimator being consistent, by showing that, as long as the centralized estimator is consistent, the distributed estimator remains consistent.Comment: Submitted for publication, 30 page