Optimal stochastic signaling for power-constrained binary communications systems

Cataloged from PDF version of article.Optimal stochastic signaling is studied under second and fourth moment constraints for the detection of scalar-valued binary signals in additive noise channels. Sufficient conditions are obtained to specify when the use of stochastic signals instead of deterministic ones can or cannot improve the error performance of a given binary communications system. Also, statistical characterization of optimal signals is presented, and it is shown that an optimal stochastic signal can be represented by a randomization of at most three different signal levels. In addition, the power constraints achieved by optimal stochastic signals are specified under various conditions. Furthermore, two approaches for solving the optimal stochastic signaling problem are proposed; one based on particle swarm optimization (PSO) and the other based on convex relaxation of the original optimization problem. Finally, simulations are performed to investigate the theoretical results, and extensions of the results to -ary communications systems and to other criteria than the average probability of error are discussed

Optimal channel switching for average capacity maximization

Optimal channel switching is proposed for average capacity maximization in the presence of average and peak power constraints. A necessary and sufficient condition is derived in order to determine when the proposed optimal channel switching approach can or cannot outperform the optimal single channel approach, which performs no channel switching. Also, it is stated that the optimal channel switching solution can be realized by channel switching between at most two different channels. In addition, a low-complexity optimization problem is derived in order to obtain the optimal channel switching solution. Numerical examples are provided to exemplify the derived theoretical results. © 2014 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

Optimal Randomization of Signal Constellations on Downlink of a Multiuser DS-CDMA System

Cataloged from PDF version of article.In this study, the jointly optimal power control with signal constellation randomization is proposed for the downlink of a multiuser communications system. Unlike a conventional system in which a fixed signal constellation is employed for all the bits of a user (for given channel conditions and noise power), power control with signal constellation randomization involves randomization/time- sharing among different signal constellations for each user. A formulation is obtained for the problem of optimal power control with signal constellation randomization, and it is shown that the optimal solution can be represented by a randomization among (K+1) or fewer distinct signal constellations for each user, where K denotes the number of users. In addition to the original nonconvex formulation, an approximate solution based on convex relaxation is derived. Then, detailed performance analysis is presented when the receivers employ symmetric signaling and sign detectors. Specifically, the maximum asymptotical improvement ratio is shown to be equal to the number of users, and the conditions under which the maximum and minimum asymptotical improvement ratios are achieved are derived. Numerical examples are presented to investigate the theoretical results, and to illustrate performance improvements achieved via the proposed approach. © 2002-2012 IEEE

Optimal channel switching in multiuser systems under average capacity constraints

In this paper, the optimal channel switching problem is studied for average capacity maximization in the presence of multiple receivers in the communication system. First, the optimal channel switching problem is proposed for average capacity maximization of the communication between the transmitter and the secondary receiver while fulfilling the minimum average capacity requirement of the primary receiver and considering the average and peak power constraints. Then, an alternative equivalent optimization problem is provided and it is shown that the solution of this optimization problem satisfies the constraints with equality. Based on the alternative optimization problem, it is obtained that the optimal channel switching strategy employs at most three communication links in the presence of multiple available channels in the system. In addition, the optimal strategies are specified in terms of the number of channels employed by the transmitter to communicate with the primary and secondary receivers. Finally, numerical examples are provided in order to verify the theoretical investigations. © 2017 Elsevier Inc

Optimal detector randomization in cognitive radio receivers in the presence of imperfect sensing decisions

Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent Univ., 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 36-39.In cognitive radio systems, spectrum sensing is one of the crucial tasks to be performed by secondary users in order to limit the interference to primary users. Therefore various spectrum sensing methods have been proposed in the literature. Once secondary users make a sensing decision, they adapt their communication parameters accordingly, which means that they perform communications when the channel is sensed as idle whereas they either do not transmit at all or transmit at a reduced power when the channel is sensed as busy. However, in practical systems, sensing decisions of secondary users are never perfect; hence, there can be cases in which the sensing decision is idle (busy) but primary user activity actually exists (does not exist). Therefore, the optimal design of secondary systems requires the consideration of imperfect sensing decisions. In this thesis, optimal detector randomization is developed for secondary users in a cognitive radio system in the presence of imperfect spectrum sensing decisions. Also, suboptimal detector randomization is proposed under the assumption of perfect sensing decisions. It is shown that the minimum average probability of error can be achieved by employing no more than four maximum a-posteriori probability (MAP) detectors at the secondary receiver. Optimal and suboptimal MAP detectors and generic expressions for their average probability of error are derived in the presence of possible sensing errors. Numerical results are presented and the importance of taking possible sensing errors into account is illustrated in terms of average probability of error optimization.Sezer, Ahmet DündarM.S

Optimal signaling and detector design for M-ary communication systems in the presence of multiple additive noise channels

An M-ary communication system is considered in which the transmitter and the receiver are connected via multiple additive (possibly non-Gaussian) noise channels, any one of which can be utilized for the transmission of a given symbol. Contrary to deterministic signaling (i.e., employing a fixed constellation), a stochastic signaling approach is adopted by treating the signal values transmitted for each information symbol over each channel as random variables. In particular, the joint optimization of the channel switching (i.e., time sharing among different channels) strategy, stochastic signals, and decision rules at the receiver is performed in order to minimize the average probability of error under an average transmit power constraint. It is proved that the solution to this problem involves either one of the following: (i) deterministic signaling over a single channel, (ii) randomizing (time sharing) between two different signal constellations over a single channel, or (iii) switching (time sharing) between two channels with deterministic signaling over each channel. For all cases, the optimal strategies are shown to employ corresponding maximum a posteriori probability (MAP) decision rules at the receiver. In addition, sufficient conditions are derived in order to specify whether the proposed strategy can or cannot improve the error performance over the conventional approach, in which a single channel is employed with deterministic signaling at the average power limit. Finally, numerical examples are presented to illustrate the theoretical results. © 2013 Elsevier Inc

Maximization of average number of correctly received symbols over multiple channels in the presence of idle periods

In this study, optimal channel switching (time sharing) strategies are investigated under average power and cost constraints for maximizing the average number of correctly received symbols between a transmitter and a receiver that are connected via multiple flat-fading channels with additive Gaussian noise. The optimal strategy is shown to correspond to channel switching either among at most three different channels with full channel utilization (i.e., no idle periods), or between at most two different channels with partial channel utilization. Also, it is stated that the optimal solution must operate at the maximum average power and the maximum average cost, which facilitates low-complexity approaches for obtaining the optimal strategy. For two-channel strategies, an upper bound is derived, in terms of the parameters of the employed channels, on the ratio between the optimal power levels. In addition, theoretical results are derived for characterizing the optimal solution for channel switching between two channels, and for comparing performance of single channel strategies. Sufficient conditions that depend solely on the systems parameters are obtained for specifying when partial channel utilization cannot be optimal. Furthermore, the proposed optimal channel switching problem is investigated for logarithmic cost functions, and various theoretical results are obtained related to the optimal strategy. Numerical examples are presented to illustrate the validity of the theoretical results. © 2016 Elsevier Inc. All rights reserved

Stochastic signaling for power constrained communication systems

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 93-97.In this thesis, optimal stochastic signaling problem is studied for power constrained communications systems. In the first part, optimal stochastic signaling problem is investigated for binary communications systems under second and fourth moment constraints for any given detector structure and noise probability distribution. It is shown that an optimal signal can be represented by randomization among at most three signal levels for each symbol. Next, stochastic signaling problem is studied in the presence of an average power constraint instead of second and fourth moment constraints. It is shown that an optimal signal can be represented by randomization between at most two signal levels for each symbol in this case. For both scenarios, sufficient conditions are obtained to determine the improvability and nonimprovability of conventional deterministic signaling via stochastic signaling. In the second part of the thesis, the joint design of optimal signals and optimal detector is studied for binary communications systems under average power constraints in the presence of additive non-Gaussian noise. It is shown that the optimal solution involves randomization between at most two signal levels and the use of the corresponding maximum a posteriori probability (MAP) detector. In the last part of the thesis, stochastic signaling is investigated for power-constrained scalar valued binary communications systems in the presence of uncertainties in channel state information (CSI). First, stochastic signaling is performed based on the available imperfect channel coef- ficient at the transmitter to examine the effects of imperfect CSI. The sufficient conditions are derived for improvability and nonimprovability of deterministic signaling via stochastic signaling in the presence of CSI uncertainty. Then, two different stochastic signaling strategies, namely, robust stochastic signaling and stochastic signaling with averaging, are proposed for designing stochastic signals under CSI uncertainty. For the robust stochastic signaling problem, sufficient conditions are derived to obtain an equivalent form which is simpler to solve. In addition, it is shown that optimal signals for each symbol can be written as randomization between at most two signal levels for stochastic signaling using imperfect channel coefficient and stochastic signaling with averaging as well as for robust stochastic signaling under certain conditions. The solutions of the optimal stochastic signaling problems are obtained by using global optimization techniques, specifically, Particle Swarm Optimization (PSO), and by employing convex relaxation approaches. Numerical examples are presented to illustrate the theoretical results at the end of each part.Göken, ÇağrıM.S