Jean-Francois Chamberland

Decentralized detection in sensor networks

In this paper, we investigate a binary decentralized detection problem in which a network of wireless sensors provides relevant information about the state of nature to a fusion center. Each sensor transmits its data over a multiple access channel. Upon reception of the information, the fusion center attempts to accurately reconstruct the state of nature. We consider the scenario where the sensor network is constrained by the capacity of the wireless channel over which the sensors are transmitting, and we study the structure of an optimal sensor configuration. For the problem of detecting deterministic signals in additive Gaussian noise, we show that having a set of identical binary sensors is asymptotically optimal, as the number of observations per sensor goes to infinity. Thus, the gain offered by having more sensors exceeds the benefits of getting detailed information from each sensor. A thorough analysis of the Gaussian case is presented along with some extensions to other observation distributions.

Asymptotic results for decentralized detection in power constrained wireless sensor networks

In this paper, we study a binary decentralized detection problem in which a set of sensor nodes provides partial information about the state of nature to a fusion center. Sensor nodes have access to conditionally independent and identically distributed observations, given the state of nature, and transmit their data over a wireless channel. Upon reception of the information, the fusion center attempts to accurately reconstruct the state of nature. Specifically, we extend existing asymptotic results about large sensor networks to the case where the network is subject to a joint power constraint, and where the communication channel from each sensor node to the fusion center is corrupted by additive noise. Large deviation theory is used to show that having identical sensor nodes, i.e., each node using the same transmission scheme, is asymptotically optimal. Furthermore, a performance metric by which sensor node candidates can be compared is established. We supplement the theory with examples to illustrate how the results derived in this paper apply to the design of practical sensing systems.

Wireless Sensors in Distributed Detection Applications

Detection problems provide a productive starting point for the study of more general statistical inference problems in sensor networks. In this article, the classical framework for decentralized detection is reviewed and argued that, while this framework provides a useful basis for developing a theory for detection in sensor networks, it has serious limitations. The classical framework does not adequately take into account important features of sensor technology and of the communication link between the sensors and the fusion center. An alternative framework for detection in sensor networks that has emerged over the last few years is discussed. Several design and optimization strategies may be gleaned from this new framework

How Dense Should a Sensor Network Be for Detection With Correlated Observations

A detection problem in sensor networks is considered, where the sensor nodes are placed on a line and receive partial information about their environment. The nodes transmit a summary of their observations over a noisy communication channel to a fusion center for the purpose of detection. The observations at the sensors are samples of a spatial stochastic process, which is one of two possible signals corrupted by Gaussian noise. Two cases are considered: one where the signal is deterministic under each hypothesis, and the other where the signal is a correlated Gaussian process under each hypothesis. The nodes are assumed to be subject to a power density constraint, i.e., the power per unit distance is fixed, so that the power per node decreases linearly with the node density. Under these constraints, the central question that is addressed is: how dense should the sensor array be, i.e., is it better to use a few high-cost, high-power nodes or to have many low-cost, low-power nodes? An answer to this question is obtained by resorting to an asymptotic analysis where the number of nodes is large. In this asymptotic regime, the Gaumlrtner-Ellis theorem and similar large-deviation theory results are used to study the impact of node density on system performance. For the deterministic signal case, it is shown that performance improves monotonically with sensor density. For the stochastic signal case, a finite sensor density is shown to be optimal

Resource Allocation and Quality of Service Evaluation for Wireless Communication Systems Using Fluid Models

Wireless systems offer a unique mixture of connectivity, flexibility, and freedom. It is therefore not surprising that wireless technology is being embraced with increasing vigor. For real-time applications, user satisfaction is closely linked to quantities such as queue length, packet loss probability, and delay. System performance is therefore related to, not only Shannon capacity, but also quality of service (QoS) requirements. This work studies the problem of resource allocation in the context of stringent QoS constraints. The joint impact of spectral bandwidth, power, and code rate is considered. Analytical expressions for the probability of buffer overflow, its associated exponential decay rate, and the effective capacity are obtained. Fundamental performance limits for Markov wireless channel models are identified. It is found that, even with an unlimited power and spectral bandwidth budget, only a finite arrival rate can be supported for a QoS constraint defined in terms of exponential decay rate

On the effective capacities of multiple-antenna Gaussian channels

The concept of effective capacity offers a novel methodology to investigate the impact that design decisions at the physical layer may have on system performance at the link layer. Assuming a constant flow of incoming data, the effective capacity characterizes the maximum arrival rate that a wireless system can support as a function of its service requirements. Service requirements in this framework are defined in terms of the asymptotic decay-rate of buffer occupancy. This article studies the effective capacity of a class of multiple-antenna wireless systems subject to Rayleigh flat fading. The effective capacity of the multi-antenna Gaussian channel is characterized, and system performance is evaluated in the low signal-to-noise ratio regime. Additional to the power gain of the multiple receive antenna system, we show that there is a statistical gain associated with a multiple transmit antenna system. When the number of transmit and/or receive antennas becomes large, the effective capacity of the system is bounded away from zero, even under very stringent service constraints. This phenomena, which results from channel-hardening, suggests that a multiple-antenna configuration is especially beneficial to delay-sensitive traffic.

Quality of Service Analysis for Wireless User-Cooperation Networks

A wireless communication system in which multiple users cooperate to transmit information to a common destination is considered. The traffic generated by the users is subject to a stringent quality of service requirement, which is defined in terms of the asymptotic decay-rate of buffer occupancy. The performance of this communication system is analyzed, and the corresponding achievable rate-region for the two-user scenario is identified. A simple user-cooperation scheme that improves performance is proposed. This cooperative scheme is shown to significantly enlarge the achievable rate-region of the service constrained communication system, provided that the quality of the wireless link between cooperating users is better than the individual connections from the users to the intended destination. Numerical results further indicate that the gains of cooperative strategies can be substantial. This suggests that cooperation allows for a fair distribution of the wireless resources among active users.

The impact of fading on decentralized detection in power constrained wireless sensor networks

We study a binary decentralized detection problem in which a set of sensor nodes provides partial information about the state of nature to a fusion center. Sensor nodes have access to conditionally independent observations, given the state of nature, and they transmit their data over separate wireless channels. The communication link between each node and the fusion center is subject to fading, with certain nodes possibly having much better connections than others. Upon reception of the information, the fusion center attempts to accurately reconstruct the state of nature. Large deviation theory is employed to obtain design guidelines for wireless sensor networks with a large number of nodes. The normalized Chernoff information is shown to be an appropriate performance metric to compare prospective sensor nodes. For the specific example of binary sensor nodes sending data over Rayleigh fading channels, the performance loss due to fading is found to be small.

Decentralized dynamic power control for cellular CDMA systems

The control of transmit power has been recognized as an essential requirement in the design of cellular code-division multiple-access (CDMA) systems. Indeed, power control allows for mobile users to share radio resources equitably and efficiently in a multicell environment. Much of the work on power control for CDMA systems found in the literature assumes a quasi-static channel model, i.e., the channel gains of the users are assumed to be constant over a sufficiently long period of time for the control algorithm to converge. In this paper, the design of dynamic power control algorithms for CDMA systems is considered without the quasi-static channel restriction. The design problem is posed as a tradeoff between the desire for users to maximize their individual quality of service and the need to minimize interference to other users. The dynamic nature of the wireless channel for mobile users is incorporated in the problem definition. Based on a cost minimization framework, an optimal multiuser solution is derived. The multiuser solution is shown to decouple, and effectively converge, to a single-user solution in the large system asymptote, where the number of users and the spreading factor both go to infinity with their ratio kept constant. In a numerical study, the performance of a simple threshold policy is shown to be near that of the optimal single-user policy. This offers support to the threshold decision rules that are employed in current cellular CDMA systems.

Intervention in context-sensitive probabilistic Boolean networks revisited

An approximate representation for the state space of a context-sensitive probabilistic Boolean network has previously been proposed and utilized to devise therapeutic intervention strategies. Whereas the full state of a context-sensitive probabilistic Boolean network is specified by an ordered pair composed of a network context and a gene-activity profile, this approximate representation collapses the state space onto the gene-activity profiles alone. This reduction yields an approximate transition probability matrix, absent of context, for the Markov chain associated with the context-sensitive probabilistic Boolean network. As with many approximation methods, a price must be paid for using a reduced model representation, namely, some loss of optimality relative to using the full state space. This paper examines the effects on intervention performance caused by the reduction with respect to various values of the model parameters. This task is performed using a new derivation for the transition probability matrix of the context-sensitive probabilistic Boolean network. This expression of transition probability distributions is in concert with the original definition of context-sensitive probabilistic Boolean network. The performance of optimal and approximate therapeutic strategies is compared for both synthetic networks and a real case study. It is observed that the approximate representation describes the dynamics of the context-sensitive probabilistic Boolean network through the instantaneously random probabilistic Boolean network with similar parameters.