• Energy Research

In this paper, we analyze and optimize the energy efficiency of downlink cellular networks. With the aid of tools from stochastic geometry, we introduce a new closed-form analytical expression of the potential spectral efficiency (bit/sec/m$^2$). In the interference-limited regime for data transmission, unlike currently available mathematical frameworks, the proposed analytical formulation depends on the transmit power and deployment density of the base stations. This is obtained by generalizing the definition of coverage probability and by accounting for the sensitivity of the receiver not only during the decoding of information data, but during the cell association phase as well. Based on the new formulation of the potential spectral efficiency, the energy efficiency (bit/Joule) is given in a tractable closed-form formula. An optimization problem is formulated and is comprehensively studied. It is mathematically proved, in particular, that the energy efficiency is a unimodal and strictly pseudo-concave function in the transmit power, given the density of the base stations, and in the density of the base stations, given the transmit power. Under these assumptions, therefore, a unique transmit power and density of the base stations exist, which maximize the energy efficiency. Numerical results are illustrated in order to confirm the obtained findings and to prove the usefulness of the proposed framework for optimizing the network planning and deployment of cellular networks from the energy efficiency standpoint. To appear in IEEE Transactions on Wireless Communications

In this paper, we introduce an analytical approach for modeling and analyzing the performance of multi-tier cellular networks that are powered by the power grid and by renewable energy sources. The proposed approach relies on modeling the locations of the base stations, either powered by the power grid or by renewable energy sources, by using Poisson point processes. The availability of renewable energy is modeled by using a Poisson point process in the time domain. In addition, the temporal dynamics of the batteries of the base stations powered by renewable energy sources are modeled by using a discrete Markov chain with a number of states that is equal to the finite storage capacity of the batteries. In particular, the coverage probability, the spectral efficiency, and the energy efficiency of the considered network model are formulated in an analytical, closed-form, expression, which depends on the probability that the typical base station is available, i.e., it has sufficient power to serve at least one mobile terminal in its cell. This latter probability is shown to be the solution of the steady state equation of the Markov chain that models the temporal dynamics of the batteries of the base stations. Under the assumption that the batteries of the base stations can be either empty or fully charged, we formulate an optimization problem in order to maximize the energy efficiency as a function of the transmit power and the deployment density of the base stations, and identify sufficient conditions for which the problem admits a unique solution. The accuracy of the proposed approach and the performance trends inferred from it are substantiated with the aid of extensive Monte Carlo simulations.

ABSTRACTThe average transmit power and coverage probability (Pcov) of uplink energy harvesting-enabled long-range networks are investigated in the present paper. Particularly, we model the end-device (EDs) according to the homogeneous Poisson point process while the power beacon is randomly distributed on the circle in the middle of the network. All EDs rely on the harvested energy to perform their operations and transmissions. Under this context, the upper bound of the average transmit power of an end-device is derived in the closed-form expression. The signal-to-noise-ratio condition of the coverage probability is given in the closed-form expression as well. Simulation results are provided to corroborate the accuracy of the derived mathematical framework as well as to feature the impact of some key parameters on the considered metrics. Our findings unveil that increasing either the number of power beacons or their transmit power will monotonically ameliorate the Pcov. Nevertheless, rising the average number of EDs will significantly decline the Pcov's performance.

ABSTRACTThe secrecy performance of wireless networks powered up by a dedicated power beacon (PB) is addressed in this work. Particularly, the closed-form expression of the secrecy outage probability (SOP) under the presence of multiple eavesdroppers is given. The considered networks are asymmetric since there are multiple eavesdroppers but only a single legitimate receiver. As a consequence, two wiretap schemes are employed, namely, non-colluding and colluding schemes, to take advantage of multiple eavesdroppers. To draw insights from the derived framework, the asymptotic framework of the SOP under the high transmit power regime is also provided. Next, Monte Carlo simulations are provided to validate the theoretical foundations of the proposed approach. Our findings show that by increasing the transmit power from −10 dB to 30 dB, the SOP ameliorates almost a thousand times. Additionally, the SOP is a monotonic decreasing function with a time-switching ratio. We also make comparisons with work in the literature in which the full-duplex relay is employed to help the legitimate link. Numerical results illustrate that the proposed network outperforms those described in the literature. Particularly, through reliance on the setup, the SOP under the proposed system is better than those of the literature by about twofold.

In the present letter, a closed-form framework is derived for the system-level modelling, analysis and optimization of the energy efficiency (EE) in LoRa networks. The proposed framework is derived by exploiting stochastic geometry tools and associates the Long Range (LoRa) EE with the density of end-devices (EDs) and the ED transmit power. The analysis reveals the trends of the EE curve with respect to each of the two parameters while revealing the existence of an optimal transmit power that maximizes the EE. Thus, the proposed framework arises as a valuable tool, of significant practical value, for the optimization of the receiver/transmitter design, and of the network deployment in LoRa networks. The robustness of the framework is verified even at the asymptotic cases of fully-loaded or sparsely-loaded LoRa networks.