Large Deviations Performance of Consensus+Innovations Distributed Detection with Non-Gaussian Observations

We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs with the decision variables of their neighbors (consensus) and 2) assimilate their new observations (innovations). This paper shows for general non-Gaussian distributions that consensus+innovations distributed detection exhibits a phase transition behavior with respect to the network degree of connectivity. Above a threshold, distributed is as good as centralized, with the same optimal asymptotic detection performance, but, below the threshold, distributed detection is suboptimal with respect to centralized detection. We determine this threshold and quantify the performance loss below threshold. Finally, we show the dependence of the threshold and performance on the distribution of the observations: distributed detectors over the same random network, but with different observations' distributions, for example, Gaussian, Laplace, or quantized, may have different asymptotic performance, even when the corresponding centralized detectors have the same asymptotic performance.Comment: 30 pages, journal, submitted Nov 17, 2011; revised Apr 3, 201

Diffusion-Based Adaptive Distributed Detection: Steady-State Performance in the Slow Adaptation Regime

This work examines the close interplay between cooperation and adaptation for distributed detection schemes over fully decentralized networks. The combined attributes of cooperation and adaptation are necessary to enable networks of detectors to continually learn from streaming data and to continually track drifts in the state of nature when deciding in favor of one hypothesis or another. The results in the paper establish a fundamental scaling law for the steady-state probabilities of miss-detection and false-alarm in the slow adaptation regime, when the agents interact with each other according to distributed strategies that employ small constant step-sizes. The latter are critical to enable continuous adaptation and learning. The work establishes three key results. First, it is shown that the output of the collaborative process at each agent has a steady-state distribution. Second, it is shown that this distribution is asymptotically Gaussian in the slow adaptation regime of small step-sizes. And third, by carrying out a detailed large deviations analysis, closed-form expressions are derived for the decaying rates of the false-alarm and miss-detection probabilities. Interesting insights are gained. In particular, it is verified that as the step-size $\mu$ decreases, the error probabilities are driven to zero exponentially fast as functions of $1/\mu$, and that the error exponents increase linearly in the number of agents. It is also verified that the scaling laws governing errors of detection and errors of estimation over networks behave very differently, with the former having an exponential decay proportional to $1/\mu$, while the latter scales linearly with decay proportional to $\mu$. It is shown that the cooperative strategy allows each agent to reach the same detection performance, in terms of detection error exponents, of a centralized stochastic-gradient solution.Comment: The paper will appear in IEEE Trans. Inf. Theor

Blind user detection in doubly-dispersive DS/CDMA channels

In this work, we consider the problem of detecting the presence of a new user in a direct-sequence/code-division-multiple-access (DS/CDMA) system with a doubly-dispersive fading channel, and we propose a novel blind detection strategy which only requires knowledge of the spreading code of the user to be detected, but no prior information as to the time-varying channel impulse response and the structure of the multiaccess interference. The proposed detector has a bounded constant false alarm rate (CFAR) under the design assumptions, while providing satisfactory detection performance even in the presence of strong cochannel interference and high user mobility.Comment: Accepted for publication on IEEE Transactions on Signal Processin