Browsing by Subject "Optimal signals"
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Item Open Access On the optimality of stochastic signaling under an average power constraint(IEEE, 2010-09-10) Göken, Çağrı; Gezici, Sinan; Arıkan, OrhanIn this paper, stochastic signaling is studied for scalar valued binary communications systems over additive noise channels in the presence of an average power constraint. For a given decision rule at the receiver, the effects of using stochastic signals for each symbol instead of conventional deterministic signals are investigated. First, sufficient conditions are derived to determine the cases in which stochastic signaling can or cannot outperform the conventional signaling. Then, statistical characterization of the optimal signals is provided and it is obtained that an optimal stochastic signal can be represented by a randomization of at most two different signal levels for each symbol. In addition, via global optimization techniques, the solution of the generic optimal stochastic signaling problem is obtained, and theoretical results are investigated via numerical examples. ©2010 IEEE.Item Open Access Statistics of the MLE and approximate upper and lower bounds-part II: Threshold computation and optimal pulse design for TOA estimation(Institute of Electrical and Electronics Engineers Inc., 2014) Mallat, A.; Gezici, Sinan; Dardari, D.; Vandendorpe, L.Threshold and ambiguity phenomena are studied in Part I of this paper 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.Item Open Access Stochastic signaling in the presence of channel state information uncertainty(Elsevier, 2013) Goken, C.; Gezici, Sinan; Arıkan, OrhanIn this paper, stochastic signaling is studied for power-constrained scalar valued binary communications systems in the presence of uncertainties in channel state information (CSI). First, stochastic signaling based on the available imperfect channel coefficient at the transmitter is analyzed, and it is shown that optimal signals can be represented by a randomization between at most two distinct signal levels for each symbol. Then, performance of stochastic signaling and conventional deterministic signaling is compared for this scenario, and sufficient conditions are derived for improvability and nonimprovability of deterministic signaling via stochastic signaling in the presence of CSI uncertainty. Furthermore, under CSI uncertainty, two different stochastic signaling strategies, namely, robust stochastic signaling and stochastic signaling with averaging, are proposed. For the robust stochastic signaling problem, sufficient conditions are derived for reducing the problem to a simpler form. It is shown that the optimal signal for each symbol can be expressed as a randomization between at most two distinct signal values for stochastic signaling with averaging, as well as for robust stochastic signaling under certain conditions. Finally, two numerical examples are presented to explore the theoretical results.