Delay Optimal Event Detection on Ad Hoc Wireless Sensor Networks

We consider a small extent sensor network for event detection, in which nodes periodically take samples and then contend over a random access network to transmit their measurement packets to the fusion center. We consider two procedures at the fusion center for processing the measurements. The Bayesian setting, is assumed, that is, the fusion center has a prior distribution on the change time. In the first procedure, the decision algorithm at the fusion center is network-oblivious and makes a decision only when a complete vector of measurements taken at a sampling instant is available. In the second procedure, the decision algorithm at the fusion center is network-aware and processes measurements as they arrive, but in a time-causal order. In this case, the decision statistic depends on the network delays, whereas in the network-oblivious case, the decision statistic does not. This yields a Bayesian change-detection problem with a trade-off between the random network delay and the decision delay that is, a higher sampling rate reduces the decision delay but increases the random access delay. Under periodic sampling, in the network-oblivious case, the structure of the optimal stopping rule is the same as that without the network, and the optimal change detection delay decouples into the network delay and the optimal decision delay without the network. In the network-aware case, the optimal stopping problem is analyzed as a partially observable Markov decision process, in which the states of the queues and delays in the network need to be maintained. A sufficient decision statistic is the network state and the posterior probability of change having occurred, given the measurements received and the state of the network. The optimal regimes are studied using simulation.

Training for Antenna Selection in Time-Varying Channels: Optimal Selection, Energy Allocation, and Energy Efficiency Evaluation

Single receive antenna selection (AS) is a popular method for obtaining diversity benefits without the additional costs of multiple radio receiver chains. Since only one antenna receives at any time, the transmitter sends a pilot multiple times to enable the receiver to estimate the channel gains of its N antennas to the transmitter and select an antenna. In time-varying channels, the channel estimates of different antennas are outdated to different extents. We analyze the symbol error probability (SEP) in time-varying channels of the N-pilot and (N+1)-pilot AS training schemes. In the former, the transmitter sends one pilot for each receive antenna. In the latter, the transmitter sends one additional pilot that helps sample the channel fading process of the selected antenna twice. We present several new results about the SEP, optimal energy allocation across pilots and data, and optimal selection rule in time-varying channels for the two schemes. We show that due to the unique nature of AS, the (N+1)-pilot scheme, despite its longer training duration, is much more energy-efficient than the conventional N-pilot scheme. An extension to a practical scenario where all data symbols of a packet are received by the same antenna is also investigated.

Online client-AP association in WLANs

In many IEEE 802.11 WLAN deployments, wireless clients have a choice of access points (AP) to connect to. In current systems, clients associate with the access point with the strongest signal to noise ratio. However, such an association mechanism can lead to unequal load sharing, resulting in diminished system performance. In this paper, we first provide a numerical approach based on stochastic dynamic programming to find the optimal client-AP association algorithm for a small topology consisting of two access points. Using the value iteration algorithm, we determine the optimal association rule for the two-AP topology. Next, utilizing the insights obtained from the optimal association ride for the two-AP case, we propose a near-optimal heuristic that we call RAT. We test the efficacy of RAT by considering more realistic arrival patterns and a larger topology. Our results show that RAT performs very well in these scenarios as well. Moreover, RAT lends itself to a fairly simple implementation.

On the problem of spurious patterns in neural associative memory models

The problem of spurious patterns in neural associative memory models is discussed, Some suggestions to solve this problem from the literature are reviewed and their inadequacies are pointed out, A solution based on the notion of neural self-interaction with a suitably chosen magnitude is presented for the Hebb learning rule. For an optimal learning rule based on linear programming, asymmetric dilution of synaptic connections is presented as another solution to the problem of spurious patterns, With varying percentages of asymmetric dilution it is demonstrated numerically that this optimal learning rule leads to near total suppression of spurious patterns. For practical usage of neural associative memory networks a combination of the two solutions with the optimal learning rule is recommended to be the best proposition.

Antenna Selection in Interference-Constrained Underlay Cognitive Radios: SEP-Optimal Rule and Performance Benchmarking

In the underlay mode of cognitive radio, secondary users are allowed to transmit when the primary is transmitting, but under tight interference constraints that protect the primary. However, these constraints limit the secondary system performance. Antenna selection (AS)-based multiple antenna techniques, which exploit spatial diversity with less hardware, help improve secondary system performance. We develop a novel and optimal transmit AS rule that minimizes the symbol error probability (SEP) of an average interference-constrained multiple-input-single-output secondary system that operates in the underlay mode. We show that the optimal rule is a non-linear function of the power gain of the channel from the secondary transmit antenna to the primary receiver and from the secondary transmit antenna to the secondary receive antenna. We also propose a simpler, tractable variant of the optimal rule that performs as well as the optimal rule. We then analyze its SEP with L transmit antennas, and extensively benchmark it with several heuristic selection rules proposed in the literature. We also enhance these rules in order to provide a fair comparison, and derive new expressions for their SEPs. The results bring out new inter-relationships between the various rules, and show that the optimal rule can significantly reduce the SEP.

Robust/optimal temperature profile control using neural networks

An approximate dynamic programming (ADP) based neurocontroller is developed for a heat transfer application. Heat transfer problem for a fin in a car's electronic module is modeled as a nonlinear distributed parameter (infinite-dimensional) system by taking into account heat loss and generation due to conduction, convection and radiation. A low-order, finite-dimensional lumped parameter model for this problem is obtained by using Galerkin projection and basis functions designed through the 'Proper Orthogonal Decomposition' technique (POD) and the 'snap-shot' solutions. A suboptimal neurocontroller is obtained with a single-network-adaptive-critic (SNAC). Further contribution of this paper is to develop an online robust controller to account for unmodeled dynamics and parametric uncertainties. A weight update rule is presented that guarantees boundedness of the weights and eliminates the need for persistence of excitation (PE) condition to be satisfied. Since, the ADP and neural network based controllers are of fairly general structure, they appear to have the potential to be controller synthesis tools for nonlinear distributed parameter systems especially where it is difficult to obtain an accurate model.

Tunable Locally-Optimal Geographical Forwarding in Wireless Sensor Networks with Sleep-Wake Cycling Nodes

We consider a wireless sensor network whose main function is to detect certain infrequent alarm events, and to forward alarm packets to a base station, using geographical forwarding. The nodes know their locations, and they sleep-wake cycle, waking up periodically but not synchronously. In this situation, when a node has a packet to forward to the sink, there is a trade-off between how long this node waits for a suitable neighbor to wake up and the progress the packet makes towards the sink once it is forwarded to this neighbor. Hence, in choosing a relay node, we consider the problem of minimizing average delay subject to a constraint on the average progress. By constraint relaxation, we formulate this next hop relay selection problem as a Markov decision process (MDP). The exact optimal solution (BF (Best Forward)) can be found, but is computationally intensive. Next, we consider a mathematically simplified model for which the optimal policy (SF (Simplified Forward)) turns out to be a simple one-step-look-ahead rule. Simulations show that SF is very close in performance to BF, even for reasonably small node density. We then study the end-to-end performance of SF in comparison with two extremal policies: Max Forward (MF) and First Forward (FF), and an end-to-end delay minimising policy proposed by Kim et al. 1]. We find that, with appropriate choice of one hop average progress constraint, SF can be tuned to provide a favorable trade-off between end-to-end packet delay and the number of hops in the forwarding path.

Robust/Optimal Temperature Profile Control of a High-Speed Aerospace Vehicle Using Neural Networks

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A I-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems.

Interplay Between Optimal Selection Scheme, Selection Criterion, and Discrete Rate Adaptation in Opportunistic Wireless Systems

An opportunistic, rate-adaptive system exploits multi-user diversity by selecting the best node, which has the highest channel power gain, and adapting the data rate to selected node's channel gain. Since channel knowledge is local to a node, we propose using a distributed, low-feedback timer backoff scheme to select the best node. It uses a mapping that maps the channel gain, or, in general, a real-valued metric, to a timer value. The mapping is such that timers of nodes with higher metrics expire earlier. Our goal is to maximize the system throughput when rate adaptation is discrete, as is the case in practice. To improve throughput, we use a pragmatic selection policy, in which even a node other than the best node can be selected. We derive several novel, insightful results about the optimal mapping and develop an algorithm to compute it. These results bring out the inter-relationship between the discrete rate adaptation rule, optimal mapping, and selection policy. We also extensively benchmark the performance of the optimal mapping with several timer and opportunistic multiple access schemes considered in the literature, and demonstrate that the developed scheme is effective in many regimes of interest.

SEP-optimal antenna selection for average interference constrained underlay cognitive radios

In the underlay mode of cognitive radio, secondary users can transmit when the primary is transmitting, but under tight interference constraints, which limit the secondary system performance. Antenna selection (AS)-based multiple antenna techniques, which require less hardware and yet exploit spatial diversity, help improve the secondary system performance. In this paper, we develop the optimal transmit AS rule that minimizes the symbol error probability (SEP) of an average interference-constrained secondary system that operates in the underlay mode. We show that the optimal rule is a non-linear function of the power gains of the channels from secondary transmit antenna to primary receiver and secondary transmit antenna to secondary receive antenna. The optimal rule is different from the several ad hoc rules that have been proposed in the literature. We also propose a closed-form, tractable variant of the optimal rule and analyze its SEP. Several results are presented to compare the performance of the closed-form rule with the ad hoc rules, and interesting inter-relationships among them are brought out.

Optimal Joint Antenna Selection and Power Adaptation in Underlay Cognitive Radios

Transmit antenna selection (AS) is a popular, low hardware complexity technique that improves the performance of an underlay cognitive radio system, in which a secondary transmitter can transmit when the primary is on but under tight constraints on the interference it causes to the primary. The underlay interference constraint fundamentally changes the criterion used to select the antenna because the channel gains to the secondary and primary receivers must be both taken into account. We develop a novel and optimal joint AS and transmit power adaptation policy that minimizes a Chernoff upper bound on the symbol error probability (SEP) at the secondary receiver subject to an average transmit power constraint and an average primary interference constraint. Explicit expressions for the optimal antenna and power are provided in terms of the channel gains to the primary and secondary receivers. The SEP of the optimal policy is at least an order of magnitude lower than that achieved by several ad hoc selection rules proposed in the literature and even the optimal antenna selection rule for the case where the transmit power is either zero or a fixed value.

Low-complexity near-optimal signal detection in underdetermined large-MIMO systems

In this paper, we consider signal detection in nt × nr underdetermined MIMO (UD-MIMO) systems, where i) nt >; nr with a overload factor α = nt over nr >; 1, ii) nt symbols are transmitted per channel use through spatial multiplexing, and iii) nt, nr are large (in the range of tens). A low-complexity detection algorithm based on reactive tabu search is considered. A variable threshold based stopping criterion is proposed which offers near-optimal performance in large UD-MIMO systems at low complexities. A lower bound on the maximum likelihood (ML) bit error performance of large UD-MIMO systems is also obtained for comparison. The proposed algorithm is shown to achieve BER performance close to the ML lower bound within 0.6 dB at an uncoded BER of 10-2 in 16 × 8 V-BLAST UD-MIMO system with 4-QAM (32 bps/Hz). Similar near-ML performance results are shown for 32 × 16, 32 × 24 V-BLAST UD-MIMO with 4-QAM/16-QAM as well. A performance and complexity comparison between the proposed algorithm and the λ-generalized sphere decoder (λ-GSD) algorithm for UD-MIMO shows that the proposed algorithm achieves almost the same performance of λ-GSD but at a significantly lesser complexity.

Direct Link-Aware Optimal Relay Selection and a Low Feedback Variant for Underlay CR

Cooperative relaying combined with selection has been extensively studied in the literature to improve the performance of interference-constrained secondary users in underlay cognitive radio (CR). We present a novel symbol error probability (SEP)-optimal amplify-and-forward relay selection rule for an average interference-constrained underlay CR system. A fundamental principle, which is unique to average interference-constrained underlay CR, that the proposed rule brings out is that the choice of the optimal relay is affected not just by the source-to-relay, relay-to-destination, and relay-to-primary receiver links, which are local to the relay, but also by the direct source-to-destination (SD) link, even though it is not local to any relay. We also propose a simpler, practically amenable variant of the optimal rule called the 1-bit rule, which requires just one bit of feedback about the SD link gain to the relays, and incurs a marginal performance loss relative to the optimal rule. We analyze its SEP and develop an insightful asymptotic SEP analysis. The proposed rules markedly outperform several ad hoc SD link-unaware rules proposed in the literature. They also generalize the interference-unconstrained and SD link-unaware optimal rules considered in the literature.

Optimal barrier subdivision for Kramers' escape rate

We examine the effect of subdividing the potential barrier along the reaction coordinate on Kramers' escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate.

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.