Cost minimization of measurement devices under estimation accuracy constraints in the prsence of Gaussian noise

Cataloged from PDF version of article.Novel convex measurement cost minimization problems are proposed based on various estimation accuracy constraints for a linear system subject to additive Gaussian noise. Closed form solutions are obtained in the case of an invertible system matrix. In addition, the effects of system matrix uncertainty are studied both from a generic perspective and by employing a specific uncertainty model. The results are extended to the Bayesian estimation framework by treating the unknown parameters as Gaussian distributed random variables. Numerical examples are presented to discuss the theoretical results in detail. © 2012 Elsevier Inc. All rights reserved

Detector Randomization and Stochastic Signaling for Minimum Probability of Error Receivers

Cataloged from PDF version of article.Optimal receiver design is studied for a communications system in which both detector randomization and stochastic signaling can be performed. First, it is proven that stochastic signaling without detector randomization cannot achieve a smaller average probability of error than detector randomization with deterministic signaling for the same average power constraint and noise statistics. Then, it is shown that the optimal receiver design results in a randomization between at most two maximum a-posteriori probability (MAP) detectors corresponding to two deterministic signal vectors. Numerical examples are provided to explain the results

Average Fisher information maximisation in presence of cost-constrained measurements

Cataloged from PDF version of article.An optimal estimation framework is considered in the presence of cost-constrained measurements. The aim is to maximise the average Fisher information under a constraint on the total cost of measurement devices. An optimisation problem is formulated to calculate the optimal costs of measurement devices that maximise the average Fisher information for arbitrary observation and measurement statistics. In addition, a closed-form expression is obtained in the case of Gaussian observations and measurement noise. Numerical examples are presented to explain the results

Comments on 'a representation for the symbol error rate using completely monotone functions'

It was shown in the above-titled paper by Rajan and Tepedelenlioglu (see ibid., vol. 59, no. 6, p. 3922-31, June 2013) that the symbol error rate (SER) of an arbitrary multidimensional constellation subject to additive white Gaussian noise is characterized as the product of a completely monotone function with a nonnegative power of signal-to-noise ratio (SNR) under minimum distance detection. In this comment, it is proved that the probability of correct decision of an arbitrary constellation admits a similar representation as well. Based on this fact, it is shown that the stochastic ordering { G α} proposed by the authors as an extension of the existing Laplace transform order to compare the average SERs over two different fading channels actually predicts that the average SERs are equal for any constellation of dimensionality smaller than or equal to 2α. Furthermore, it is noted that there are no positive random variables X1 and X2 such that the proposed stochastic ordering is satisfied in the strict sense, i.e., X1<Gα X2, when α=N/2 for any positive integer N. Additional remarks are noted about the fading scenarios at low SNR and the generalization to additive compound Gaussian noise originally discussed in the subject paper. © 1963-2012 IEEE

Convexity Properties of Detection Probability Under Additive Gaussian Noise: Optimal Signaling and Jamming Strategies

Cataloged from PDF version of article.In this correspondence, we study the convexity properties for the problem of detecting the presence of a signal emitted from a power constrained transmitter in the presence of additive Gaussian noise under the Neyman-Pearson (NP) framework. It is proved that the detection probability corresponding to the α-level likelihood ratio test (LRT) is either strictly concave or has two inflection points such that the function is strictly concave, strictly convex, and finally strictly concave with respect to increasing values of the signal power. In addition, the analysis is extended from scalar observations to multidimensional colored Gaussian noise corrupted signals. Based on the convexity results, optimal and near-optimal time sharing strategies are proposed for average/peak power constrained transmitters and jammers. Numerical methods with global convergence are also provided to obtain the parameters for the proposed strategies. © 1991-2012 IEE

Universal bounds on the derivatives of the symbol error rate for arbitrary constellations

The symbol error rate (SER) of the minimum distance detector under additive white Gaussian noise is studied in terms of generic bounds and higher order derivatives for arbitrary constellations. A general approach is adopted so that the recent results on the convexity/concavity and complete monotonicity properties of the SER can be obtained as special cases. Novel universal bounds on the SER, which depend only on the constellation dimensionality, minimum and maximum constellation distances are obtained. It is shown that the sphere hardening argument in the channel coding theorem can be derived using the proposed bounds. Sufficient conditions based on the positive real roots (with odd multiplicity) of an explicitly-specified polynomial are presented to determine the signs of the SER derivatives of all orders in signal-to-noise ratio. Furthermore, universal bounds are given for the SER derivatives of all orders. As an example, it is shown that the proposed bounds yield a better characterization of the SER for arbitrary two-dimensional constellations over the complete monotonicity property derived recently. © 2014 IEEE

Optimal stochastic signal design and detector randomization in the neyman-pearson framework

Power constrained on-off keying communications systems are investigated in the presence of stochastic signaling and detector randomization. The joint optimal design of decision rules, stochastic signals, and detector randomization factors is performed. It is shown that the solution to the most generic optimization problem that employs both stochastic signaling and detector randomization can be obtained as the randomization among no more than three Neyman-Pearson (NP) decision rules corresponding to three deterministic signal vectors. Numerical examples are also presented. © 2012 IEEE

Optimum Power Randomization for the Minimization of Outage Probability

Cataloged from PDF version of article.The optimum power randomization problem is studied to minimize outage probability in flat block-fading Gaussian channels under an average transmit power constraint and in the presence of channel distribution information at the transmitter. When the probability density function of the channel power gain is continuously differentiable with a finite second moment, it is shown that the outage probability curve is a nonincreasing function of the normalized transmit power with at least one inflection point and the total number of inflection points is odd. Based on this result, it is proved that the optimum power transmission strategy involves randomization between at most two power levels. In the case of a single inflection point, the optimum strategy simplifies to on-off signaling for weak transmitters. Through analytical and numerical discussions, it is shown that the proposed framework can be adapted to a wide variety of scenarios including log-normal shadowing, diversity combining over Rayleigh fading channels, Nakagami-m fading, spectrum sharing, and jamming applications. We also show that power randomization does not necessarily improve the outage performance when the finite second moment assumption is violated by the power distribution of the fading. © 2013 IEEE

Optimal signaling and detector design for power constrained on-off keying systems in Neyman-Pearson framework

Optimal stochastic signaling and detector design are studied for power constrained on-off keying systems in the presence of additive multimodal channel noise under the Neyman-Pearson (NP) framework. The problem of jointly designing the signaling scheme and the decision rule is addressed in order to maximize the probability of detection without violating the constraints on the probability of false alarm and the average transmit power. Based on a theoretical analysis, it is shown that the optimal solution can be obtained by employing randomization between at most two signal values for the on-signal (symbol 1) and using the corresponding NP-type likelihood ratio test at the receiver. As a result, the optimal parameters can be computed over a significantly reduced optimization space instead of an infinite set of functions using global optimization techniques. Finally, a detection example is provided to illustrate how stochastic signaling can help improve detection performance over various optimal and sub-optimal signaling schemes. © 2011 IEEE