Abstract:
We consider the optimal allocation of resources—power and bandwidth—between training and data transmissions for single-user time-selective Rayleigh flat-fading channels under the cutoff rate criterion. The transmitter exploits statistical channel state information (CSI) in the form of the channel Doppler spectrum to embed pilot symbols into the transmission stream. At the receiver, instantaneous, though imperfect, CSI is acquired through minimum mean-square estimation of the channel based on some set of pilot observations. We compute the ergodic cutoff rate for this scenario. Assuming estimator-based interleaving and -PSK inputs, we study two special cases in-depth. First, we derive the optimal resource allocation for the Gauss-Markov correlation model. Next, we validate and refine these insights by studying resource allocation for the Jakes model.

Abstract:
A distributed and cooperative link-scheduling (DCLS) algorithm is introduced for large-scale multihop wireless networks. With this algorithm, each and every active link in the network cooperatively calibrates its environment and converges to a desired link schedule for data transmissions within a time frame of multiple slots. This schedule is such that the entire network is partitioned into a set of interleaved subnetworks, where each subnetwork consists of concurrent cochannel links that are properly separated from each other. The desired spacing in each subnetwork can be controlled by a tuning parameter and the number of time slots specified for each frame. Following the DCLS algorithm, a distributed and cooperative power control (DCPC) algorithm can be applied to each subnetwork to ensure a desired data rate for each link with minimum network transmission power. As shown consistently by simulations, the DCLS algorithm along with a DCPC algorithm yields significant power savings. The power savings also imply an increased feasible region of averaged link data rates for the entire network.

Abstract:
A distributed and cooperative link-scheduling (DCLS) algorithm is introduced for large-scale multihop wireless networks. With this algorithm, each and every active link in the network cooperatively calibrates its environment and converges to a desired link schedule for data transmissions within a time frame of multiple slots. This schedule is such that the entire network is partitioned into a set of interleaved subnetworks, where each subnetwork consists of concurrent cochannel links that are properly separated from each other. The desired spacing in each subnetwork can be controlled by a tuning parameter and the number of time slots specified for each frame. Following the DCLS algorithm, a distributed and cooperative power control (DCPC) algorithm can be applied to each subnetwork to ensure a desired data rate for each link with minimum network transmission power. As shown consistently by simulations, the DCLS algorithm along with a DCPC algorithm yields significant power savings. The power savings also imply an increased feasible region of averaged link data rates for the entire network.

Abstract:
A new blind channel estimation technique is proposed for space-time coded wideband CDMA systems using aperiodic and possibly multirate spreading codes. Using a decorrelating front end, the received signal is projected onto a subspace from which channel parameters can be estimated up to a rotational ambiguity. Exploiting the subspace structure of the WCDMA signaling and the orthogonality of the unitary space-time codes, the proposed algorithm provides a blind channel estimate via least squares. A new identifiability condition is established under the assumption that the system is not heavily loaded. The mean square error of the estimated channel is compared with the Cramér-Rao bound, and the bit error rate (BER) performance of the proposed algorithm is compared with that of differential schemes.

Abstract:
A new blind channel estimation technique is proposed for space-time coded wideband CDMA systems using aperiodic and possibly multirate spreading codes. Using a decorrelating front end, the received signal is projected onto a subspace from which channel parameters can be estimated up to a rotational ambiguity. Exploiting the subspace structure of the WCDMA signaling and the orthogonality of the unitary space-time codes, the proposed algorithm provides a blind channel estimate via least squares. A new identifiability condition is established under the assumption that the system is not heavily loaded. The mean square error of the estimated channel is compared with the Cramér-Rao bound, and the bit error rate (BER) performance of the proposed algorithm is compared with that of differential schemes.

Abstract:
The problem of hypothesis testing against independence for a Gauss-Markov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, an expression for the log-likelihood ratio of detection is derived. Assuming random placement of nodes over a large region according to the Poisson or uniform distribution and nearest-neighbor dependency graph, the error exponent of the Neyman-Pearson detector is derived using large-deviations theory. The error exponent is expressed as a dependency-graph functional and the limit is evaluated through a special law of large numbers for stabilizing graph functionals. The exponent is analyzed for different values of the variance ratio and correlation. It is found that a more correlated GMRF has a higher exponent at low values of the variance ratio whereas the situation is reversed at high values of the variance ratio.

Abstract:
We consider power control in cognitive radio networks where secondary users identify and exploit instantaneous and local spectrum opportunities without causing unacceptable interference to primary users. We qualitatively characterize the impact of the transmission power of secondary users on the occurrence of spectrum opportunities and the reliability of opportunity detection. Based on a Poisson model of the primary network, we quantify these impacts by showing that (i) the probability of spectrum opportunity decreases exponentially with respect to the transmission power of secondary users, where the exponential decay constant is given by the traffic load of primary users; (ii) reliable opportunity detection is achieved in the two extreme regimes in terms of the ratio between the transmission power of secondary users and that of primary users. Such analytical characterizations allow us to study power control for optimal transport throughput under constraints on the interference to primary users. Furthermore, we reveal the difference between detecting primary signals and detecting spectrum opportunities, and demonstrate the complex relationship between physical layer spectrum sensing and MAC layer throughput. The dependency of this PHY-MAC interaction on the application type and the use of handshake signaling such as RTS/CTS is illustrated.

Abstract:
We address the design of opportunistic spectrum access (OSA) strategies that allow secondary users to independently search for and exploit instantaneous spectrum availability. Integrated in the joint design are three basic components: a spectrum sensor that identifies spectrum opportunities, a sensing strategy that determines which channels in the spectrum to sense, and an access strategy that decides whether to access based on imperfect sensing outcomes. We formulate the joint PHY-MAC design of OSA as a constrained partially observable Markov decision process (POMDP). Constrained POMDPs generally require randomized policies to achieve optimality, which are often intractable. By exploiting the rich structure of the underlying problem, we establish a separation principle for the joint design of OSA. This separation principle reveals the optimality of myopic policies for the design of the spectrum sensor and the access strategy, leading to closed-form optimal solutions. Furthermore, decoupling the design of the sensing strategy from that of the spectrum sensor and the access strategy, the separation principle reduces the constrained POMDP to an unconstrained one, which admits deterministic optimal policies. Numerical examples are provided to study the design tradeoffs, the interaction between the spectrum sensor and the sensing and access strategies, and the robustness of the ensuing design to model mismatch.

Abstract:
We formulate and study the thinnest path problem in wireless ad hoc networks. The objective is to find a path from a source to its destination that results in the minimum number of nodes overhearing the message by a judicious choice of relaying nodes and their corresponding transmission power. We adopt a directed hypergraph model of the problem and establish the NP-completeness of the problem in 2-D networks. We then develop two polynomial-time approximation algorithms that offer $\sqrt{\frac{n}{2}}$ and $\frac{n}{2\sqrt{n-1}}$ approximation ratios for general directed hypergraphs (which can model non-isomorphic signal propagation in space) and constant approximation ratios for ring hypergraphs (which result from isomorphic signal propagation). We also consider the thinnest path problem in 1-D networks and 1-D networks embedded in 2-D field of eavesdroppers with arbitrary unknown locations (the so-called 1.5-D networks). We propose a linear-complexity algorithm based on nested backward induction that obtains the optimal solution to both 1-D and 1.5-D networks. This algorithm does not require the knowledge of eavesdropper locations and achieves the best performance offered by any algorithm that assumes complete location information of the eavesdroppers.

Abstract:
The problem of anomaly localization in a resource-constrained cyber system is considered. Each anomalous component of the system incurs a cost per unit time until its anomaly is identified and fixed. Different anomalous components may incur different costs depending on their criticality to the system. Due to resource constraints, only one component can be probed at each given time. The observations from a probed component are realizations drawn from two different distributions depending on whether the component is normal or anomalous. The objective is a probing strategy that minimizes the total expected cost, incurred by all the components during the detection process, under reliability constraints. We consider both independent and exclusive models. In the former, each component can be abnormal with a certain probability independent of other components. In the latter, one and only one component is abnormal. We develop optimal simple index policies under both models. The proposed index policies apply to a more general case where a subset (more than one) of the components can be probed simultaneously and have strong performance as demonstrated by simulation examples. The problem under study also finds applications in spectrum scanning in cognitive radio networks and event detection in sensor networks.