Quadratic Multi-Dimensional Signaling Games and Affine Equilibria

This paper studies the decentralized quadratic cheap talk and signaling game problems when an encoder and a decoder, viewed as two decision makers, have misaligned objective functions. The main contributions of this study are the extension of Crawford and Sobel's cheap talk formulation to multi-dimensional sources and to noisy channel setups. We consider both (simultaneous) Nash equilibria and (sequential) Stackelberg equilibria. We show that for arbitrary scalar sources, in the presence of misalignment, the quantized nature of all equilibrium policies holds for Nash equilibria in the sense that all Nash equilibria are equivalent to those achieved by quantized encoder policies. On the other hand, all Stackelberg equilibria policies are fully informative. For multi-dimensional setups, unlike the scalar case, Nash equilibrium policies may be of non-quantized nature, and even linear. In the noisy setup, a Gaussian source is to be transmitted over an additive Gaussian channel. The goals of the encoder and the decoder are misaligned by a bias term and encoder's cost also includes a penalty term on signal power. Conditions for the existence of affine Nash equilibria as well as general informative equilibria are presented. For the noisy setup, the only Stackelberg equilibrium is the linear equilibrium when the variables are scalar. Our findings provide further conditions on when affine policies may be optimal in decentralized multi-criteria control problems and lead to conditions for the presence of active information transmission in strategic environments.Comment: 15 pages, 4 figure

Error Rate Analysis of Cognitive Radio Transmissions with Imperfect Channel Sensing

This paper studies the symbol error rate performance of cognitive radio transmissions in the presence of imperfect sensing decisions. Two different transmission schemes, namely sensing-based spectrum sharing (SSS) and opportunistic spectrum access (OSA), are considered. In both schemes, secondary users first perform channel sensing, albeit with possible errors. In SSS, depending on the sensing decisions, they adapt the transmission power level and coexist with primary users in the channel. On the other hand, in OSA, secondary users are allowed to transmit only when the primary user activity is not detected. Initially, for both transmission schemes, general formulations for the optimal decision rule and error probabilities are provided for arbitrary modulation schemes under the assumptions that the receiver is equipped with the sensing decision and perfect knowledge of the channel fading, and the primary user's received faded signals at the secondary receiver has a Gaussian mixture distribution. Subsequently, the general approach is specialized to rectangular quadrature amplitude modulation (QAM). More specifically, optimal decision rule is characterized for rectangular QAM, and closed-form expressions for the average symbol error probability attained with the optimal detector are derived under both transmit power and interference constraints. The effects of imperfect channel sensing decisions, interference from the primary user and its Gaussian mixture model, and the transmit power and interference constraints on the error rate performance of cognitive transmissions are analyzed

Statistics of the MLE and Approximate Upper and Lower Bounds - Part 2: Threshold Computation and Optimal Signal Design

Threshold and ambiguity phenomena are studied in Part 1 of this work where approximations for the mean-squared-error (MSE) of the maximum likelihood estimator are proposed using the method of interval estimation (MIE), and where approximate upper and lower bounds are derived. In this part we consider time-of-arrival estimation and we employ the MIE to derive closed-form expressions of the begin-ambiguity, end-ambiguity and asymptotic signal-to-noise ratio (SNR) thresholds with respect to some features of the transmitted signal. Both baseband and passband pulses are considered. We prove that the begin-ambiguity threshold depends only on the shape of the envelope of the ACR, whereas the end-ambiguity and asymptotic thresholds only on the shape of the ACR. We exploit the results on the begin-ambiguity and asymptotic thresholds to optimize, with respect to the available SNR, the pulse that achieves the minimum attainable MSE. The results of this paper are valid for various estimation problems