Outage Capacity and Optimal Transmission for Dying Channels

In wireless networks, communication links may be subject to random fatal impacts: for example, sensor networks under sudden power losses or cognitive radio networks with unpredictable primary user spectrum occupancy. Under such circumstances, it is critical to quantify how fast and reliably the information can be collected over attacked links. For a single point-to-point channel subject to a random attack, named as a \emph{dying channel}, we model it as a block-fading (BF) channel with a finite and random delay constraint. First, we define the outage capacity as the performance measure, followed by studying the optimal coding length $K$ such that the outage probability is minimized when uniform power allocation is assumed. For a given rate target and a coding length $K$, we then minimize the outage probability over the power allocation vector \mv{P}_{K}, and show that this optimization problem can be cast into a convex optimization problem under some conditions. The optimal solutions for several special cases are discussed. Furthermore, we extend the single point-to-point dying channel result to the parallel multi-channel case where each sub-channel is a dying channel, and investigate the corresponding asymptotic behavior of the overall outage probability with two different attack models: the independent-attack case and the $m$-dependent-attack case. It can be shown that the overall outage probability diminishes to zero for both cases as the number of sub-channels increases if the \emph{rate per unit cost} is less than a certain threshold. The outage exponents are also studied to reveal how fast the outage probability improves over the number of sub-channels.Comment: 31 pages, 9 figures, submitted to IEEE Transactions on Information Theor

Estimation Diversity and Energy Efficiency in Distributed Sensing

Distributed estimation based on measurements from multiple wireless sensors is investigated. It is assumed that a group of sensors observe the same quantity in independent additive observation noises with possibly different variances. The observations are transmitted using amplify-and-forward (analog) transmissions over non-ideal fading wireless channels from the sensors to a fusion center, where they are combined to generate an estimate of the observed quantity. Assuming that the Best Linear Unbiased Estimator (BLUE) is used by the fusion center, the equal-power transmission strategy is first discussed, where the system performance is analyzed by introducing the concept of estimation outage and estimation diversity, and it is shown that there is an achievable diversity gain on the order of the number of sensors. The optimal power allocation strategies are then considered for two cases: minimum distortion under power constraints; and minimum power under distortion constraints. In the first case, it is shown that by turning off bad sensors, i.e., sensors with bad channels and bad observation quality, adaptive power gain can be achieved without sacrificing diversity gain. Here, the adaptive power gain is similar to the array gain achieved in Multiple-Input Single-Output (MISO) multi-antenna systems when channel conditions are known to the transmitter. In the second case, the sum power is minimized under zero-outage estimation distortion constraint, and some related energy efficiency issues in sensor networks are discussed.Comment: To appear at IEEE Transactions on Signal Processin

Optimal Power Allocation for Parameter Tracking in a Distributed Amplify-and-Forward Sensor Network

We consider the problem of optimal power allocation in a sensor network where the sensors observe a dynamic parameter in noise and coherently amplify and forward their observations to a fusion center (FC). The FC uses the observations in a Kalman filter to track the parameter, and we show how to find the optimal gain and phase of the sensor transmissions under both global and individual power constraints in order to minimize the mean squared error (MSE) of the parameter estimate. For the case of a global power constraint, a closed-form solution can be obtained. A numerical optimization is required for individual power constraints, but the problem can be relaxed to a semidefinite programming problem (SDP), and we show that the optimal result can be constructed from the SDP solution. We also study the dual problem of minimizing global and individual power consumption under a constraint on the MSE. As before, a closed-form solution can be found when minimizing total power, while the optimal solution is constructed from the output of an SDP when minimizing the maximum individual sensor power. For purposes of comparison, we derive an exact expression for the outage probability on the MSE for equal-power transmission, which can serve as an upper bound for the case of optimal power control. Finally, we present the results of several simulations to show that the use of optimal power control provides a significant reduction in either MSE or transmit power compared with a non-optimized approach (i.e., equal power transmission).Comment: 28 pages, 6 figures, accepted by IEEE Transactions on Signal Processing, Jan. 201

Robust Power Allocation and Outage Analysis for Secrecy in Independent Parallel Gaussian Channels

This letter studies parallel independent Gaussian channels with uncertain eavesdropper channel state information (CSI). Firstly, we evaluate the probability of zero secrecy rate in this system for (i) given instantaneous channel conditions and (ii) a Rayleigh fading scenario. Secondly, when non-zero secrecy is achievable in the low SNR regime, we aim to solve a robust power allocation problem which minimizes the outage probability at a target secrecy rate. We bound the outage probability and obtain a linear fractional program that takes into account the uncertainty in eavesdropper CSI while allocating power on the parallel channels. Problem structure is exploited to solve this optimization problem efficiently. We find the proposed scheme effective for uncertain eavesdropper CSI in comparison with conventional power allocation schemes.Comment: 4 pages, 2 figures. Author version of the paper published in IEEE Wireless Communications Letters. Published version is accessible at http://dx.doi.org/10.1109/LWC.2015.249734

Optimal Save-Then-Transmit Protocol for Energy Harvesting Wireless Transmitters

In this paper, the design of a wireless communication device relying exclusively on energy harvesting is considered. Due to the inability of rechargeable energy sources to charge and discharge at the same time, a constraint we term the energy half-duplex constraint, two rechargeable energy storage devices (ESDs) are assumed so that at any given time, there is always one ESD being recharged. The energy harvesting rate is assumed to be a random variable that is constant over the time interval of interest. A save-then-transmit (ST) protocol is introduced, in which a fraction of time {\rho} (dubbed the save-ratio) is devoted exclusively to energy harvesting, with the remaining fraction 1 - {\rho} used for data transmission. The ratio of the energy obtainable from an ESD to the energy harvested is termed the energy storage efficiency, {\eta}. We address the practical case of the secondary ESD being a battery with {\eta} < 1, and the main ESD being a super-capacitor with {\eta} = 1. The optimal save-ratio that minimizes outage probability is derived, from which some useful design guidelines are drawn. In addition, we compare the outage performance of random power supply to that of constant power supply over the Rayleigh fading channel. The diversity order with random power is shown to be the same as that of constant power, but the performance gap can be large. Furthermore, we extend the proposed ST protocol to wireless networks with multiple transmitters. It is shown that the system-level outage performance is critically dependent on the relationship between the number of transmitters and the optimal save-ratio for single-channel outage minimization. Numerical results are provided to validate our proposed study.Comment: This is the longer version of a paper to appear in IEEE Transactions on Wireless Communication

Wireless Information Transfer with Opportunistic Energy Harvesting

Energy harvesting is a promising solution to prolong the operation of energy-constrained wireless networks. In particular, scavenging energy from ambient radio signals, namely wireless energy harvesting (WEH), has recently drawn significant attention. In this paper, we consider a point-to-point wireless link over the narrowband flat-fading channel subject to time-varying co-channel interference. It is assumed that the receiver has no fixed power supplies and thus needs to replenish energy opportunistically via WEH from the unintended interference and/or the intended signal sent by the transmitter. We further assume a single-antenna receiver that can only decode information or harvest energy at any time due to the practical circuit limitation. Therefore, it is important to investigate when the receiver should switch between the two modes of information decoding (ID) and energy harvesting (EH), based on the instantaneous channel and interference condition. In this paper, we derive the optimal mode switching rule at the receiver to achieve various trade-offs between wireless information transfer and energy harvesting. Specifically, we determine the minimum transmission outage probability for delay-limited information transfer and the maximum ergodic capacity for no-delay-limited information transfer versus the maximum average energy harvested at the receiver, which are characterized by the boundary of so-called "outage-energy" region and "rate-energy" region, respectively. Moreover, for the case when the channel state information (CSI) is known at the transmitter, we investigate the joint optimization of transmit power control, information and energy transfer scheduling, and the receiver's mode switching. Our results provide useful guidelines for the efficient design of emerging wireless communication systems powered by opportunistic WEH.Comment: to appear in IEEE Transactions on Wireless Communicatio