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This paper considers the problem of communication over a discrete memoryless channel (DMC) or an additive white Gaussian noise (AWGN) channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. Specifically, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a DMC whose output distribution induced by the "off" input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum amount of information that can be transmitted under this criterion scales like the square root of the blocklength. The same is true for the AWGN channel. Exact expressions for the scaling constant are also derived.Index Terms-Low probability of detection, covert communication, information-theoretic security, Fisher information.This work was presented in part at the 2015 IEEE International Symposium of Information Theory (ISIT) in Hong Kong.L. Wang is with ETIS (Equipes

The current study of the low SNR fading channels focuses on two extreme cases: the coherent case with perfect channel state information (CSI) available at the receiver, and the non-coherent case with no hope to obtain the channel information at all. Most of practical channels, with a low SNR and a slowly varying channel, lies in between these two extremes. In this paper, we use training based schemes to take the advantage of such channel coherence in the low SNR regime. We characterize how slowly the channel can change over time such that a "near coherent" performance to be achieved. We demonstrate that use training scheme in a flashy fashion can improve the performance. We also defined the notion of "operation coherence level", which is used to describe a continuum between the coherent and the non-coherent extremes.

Abstract-We study the problem of transmission-side diversity and routing in a static wireless network. It is assumed that each node in the network is equipped with a single omnidirectional antenna and that multiple nodes are allowed to coordinate their transmissions in order to obtain energy savings. We derive analytical results for achievable energy savings for both line and grid network topologies. It is shown that the energy savings of 39% and 56% are achievable in line and grid networks with a large number of nodes, respectively. We then develop a dynamic-programming-based algorithm for finding the optimal route in an arbitrary network, as well as suboptimal algorithms with polynomial complexity. We show through simulations that these algorithms can achieve average energy savings of about 50% in random networks, as compared to the noncooperative schemes.

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