Optimum Power Randomization for the Minimization of Outage Probability

Abstract

Abstract-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.

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

“…where λ i is the channel switching factor for channel i and P c,i is the average probability of correct decision over channel i for a power level of P i , which can be calculated as P c,i = 1 − g i (P i ) (9) with g i (P i ) denoting the average probability of symbol error as computed in (4)-(6) for different types of modulations and cases. The expression in (8) corresponds to the average number of symbols that are correctly received during the communication interval of length λ i T .…”

“…Time sharing (randomization) has attracted a significant deal of interest in the literature due to its capability to provide performance improvements for communication systems [1][2][3][4][5][6][7][8][9][10][11]. In [2], it is demonstrated that the average probability of error over additive noise channels with arbitrary noise probability density functions (PDFs) can be reduced via optimal stochastic signaling, which performs time sharing among at most three different signal levels for each information symbol.…”

Average Capacity Maximization via Channel Switching in the Presence of Additive White Gaussian Noise Channels and Switching Delays

“…The proposed algorithm leads to a near-optimal capacity that is achieved without antenna selection. In addition to the capacity, other metrics such as probability of error, probability of detection, and outage probability are considered in various resource allocation problems; e.g., [7]- [15]. For example, in the detector randomization problem, the aim is to minimize the average probability of error of a communication system by optimizing time sharing factors and transmit power (signal) levels corresponding to different detectors at the receiver [7]- [9].…”

Optimal channel switching for average capacity maximization

“…Recently, benefits of randomization (or, time-sharing) have been studied for various detection and estimation problems in the literature [1]- [13]. For instance, in the context of noise enhanced detection and estimation, an additive "noise" component that is realized by a randomization among a certain number of signal levels can be injected into the input of a suboptimal detector or estimator for performance enhancement [1]- [5].…”