Spectrum Coordination in Energy Efficient Cognitive Radio Networks

Device coordination in open spectrum systems is a challenging problem, particularly since users experience varying spectrum availability over time and location. In this paper, we propose a game theoretical approach that allows cognitive radio pairs, namely the primary user (PU) and the secondary user (SU), to update their transmission powers and frequencies simultaneously. Specifically, we address a Stackelberg game model in which individual users attempt to hierarchically access to the wireless spectrum while maximizing their energy efficiency. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium is conducted. In particular, we show that a spectrum coordination naturally occurs when both actors in the system decide sequentially about their powers and their transmitting carriers. As a result, spectrum sensing in such a situation turns out to be a simple detection of the presence/absence of a transmission on each sub-band. We also show that when users experience very different channel gains on their two carriers, they may choose to transmit on the same carrier at the Stackelberg equilibrium as this contributes enough energy efficiency to outweigh the interference degradation caused by the mutual transmission. Then, we provide an algorithmic analysis on how the PU and the SU can reach such a spectrum coordination using an appropriate learning process. We validate our results through extensive simulations and compare the proposed algorithm to some typical scenarios including the non-cooperative case and the throughput-based-utility systems. Typically, it is shown that the proposed Stackelberg decision approach optimizes the energy efficiency while still maximizing the throughput at the equilibrium.Comment: 12 pages, 10 figures, to appear in IEEE Transactions on Vehicular Technolog

On the Two-user Multi-carrier Joint Channel Selection and Power Control Game

In this paper, we propose a hierarchical game approach to model the energy efficiency maximization problem where transmitters individually choose their channel assignment and power control. We conduct a thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium. Interestingly, we formally show that a spectrum orthogonalization naturally occurs when users decide sequentially about their transmitting carriers and powers, delivering a binary channel assignment. Both analytical and simulation results are provided for assessing and improving the performances in terms of energy efficiency and spectrum utilization between the simultaneous-move game (with synchronous decision makers), the social welfare (in a centralized manner) and the proposed Stackelberg (hierarchical) game. For the first time, we provide tight closed-form bounds on the spectral efficiency of such a model, including correlation across carriers and users. We show that the spectrum orthogonalization capability induced by the proposed hierarchical game model enables the wireless network to achieve the spectral efficiency improvement while still enjoying a high energy efficiency.Comment: 31 pages, 13 figures, accepted in IEEE Transactions on Communication

A Game Theoretic Analysis for Energy Efficient Heterogeneous Networks

Smooth and green future extension/scalability (e.g., from sparse to dense, from small-area dense to large-area dense, or from normal-dense to super-dense) is an important issue in heterogeneous networks. In this paper, we study energy efficiency of heterogeneous networks for both sparse and dense two-tier small cell deployments. We formulate the problem as a hierarchical (Stackelberg) game in which the macro cell is the leader whereas the small cell is the follower. Both players want to strategically decide on their power allocation policies in order to maximize the energy efficiency of their registered users. A backward induction method has been used to obtain a closed-form expression of the Stackelberg equilibrium. It is shown that the energy efficiency is maximized when only one sub-band is exploited for the players of the game depending on their fading channel gains. Simulation results are presented to show the effectiveness of the proposed scheme.Comment: 7 pages, 3 figures, in Wiopt 201

Microhollow Cathode Discharge Excimer Lamps

Microhollow cathode discharges are non-thermal discharges of such small sizes that thermalization of the electrons is prevented. By reducing the diameter of the cathode opening in these discharge geometries to values on the order of 100 $\mu$m we were able to operate discharges in argon and xenon in a direct current mode up to atmospheric pressure. The large concentration of high electrons, in combination with high pressures favors three body processes such as excimer formation. This was confirmed by experiments in xenon and argon where emission of excimer radiation at 172 nm and 130 nm, respectively, was observed when the pressure was increased beyond 50 Torr. The intensity of excimer radiation in xenon excimer emitters was found to have a maximum at 400 Torr. At this pressure, the VUV radiant flux of a single discharge operating at currents greater than 2 mA and a forward voltage of 220 V reaches values between 6% and 9% of the input electrical power. These are values, which are comparable to those achieved in barrier discharge excimer lamps. Results of a simple rate equation model indicate that even higher efficiencies (40%) might be achievable. The VUV intensity scales linearly with discharge current, which makes analog control of the excimer emission with semiconductor devices possible. The possibility to form arrays of these discharges will allow the generation of dc-flat panel excimer lamps with radiant emittances exceeding 60 W/cm2. Applications for such lamps are lighting, flat panel displays, optical surface processing, pollution control and many others

An agate bowl from Egypt

7 pages ; illustrations"Amongst the treasures which have come down to us from the ancient Mediterranean world are vessels carved from semiprecious stones. 1 Agate, onyx and sardonyx, all subvarieties of chalcedony, seem to have been the stones most commonly used for this purpose, and of these agate was perhaps the most usual. Perfume bottles, aryballoi, cups and bowls of various shapes were carved out of these hard, colorful materials. Such chalcedony vessels continued to be valued in the medieval and Renaissance periods, when they were often mounted in gold and silver, set with precious stones. One example, a perfect illustration of the esteem in which these ancient vases were held, is Abbot Suger's chalice now in the National Gallery, Washington.4 So popular were these vases that relatively few have survived in their original, unadorned state. One which is so preserved is an agate bowl in the Museum of Art and Archaeology of the University of Missouri. ... The Missouri bowl 5 is simple in shape. Its base is very slightly convex, making it stand unevenly; its sides flare outward to an incurved rim, the upper edge of which is flat. The surface of the vase is highly polished. In contrast to the simplicity of the shape, the colors of the agate are rich and varied. They range from milky-white to various shades of brown-reddish-brown through honey-colored to dark brown. The milky-white striations form irregular patterns or swirl around the vase, with small honey-colored patches interspersed on the dark brown background. Around the rim runs a continuous uneven hand of pale brown. The whole vase is highly translucent; with the light shining through in differing degrees of intensity and its brilliant polished surface, the general effect is one of great subtlety and beauty."--Pages 28-29

Generation of Intense Excimer Radiation From High-Pressure Hollow Cathode Discharges

By reducing the diameter of the cathode opening in a hollow cathode discharge geometry to values on the order of 100 μm, we were able to operate these discharges in noble gases in a direct current mode up to atmospheric pressure. High-pressure discharges in xenon were found to be strong sources of excimer radiation. Highest intensities at a wavelength of 172 nm were obtained at a pressure of 400 Torr. At this pressure, the vacuum ultraviolet (VUV) radiant power of a single discharge operating at a forward voltage of 220 V and currents exceeding 2 mA reaches values between 6% and 9% of the input electrical power. The possibility to form arrays of these discharges allows the generation of flat panel VUV lamps with radiant emittances exceeding 50 W/cm2

Emission of Excimer Radiation From Direct Current, High-Pressure Hollow Cathode Discharge

A novel, nonequilibrium, high-pressure, direct current discharge, the microhollow cathode discharge, has been found to be an intense source of xenon and argon excimer radiation peaking at wavelengths of 170 and 130 nm, respectively. In argon discharges with a 100 μm diam hollow cathode, the intensity of the excimer radiation increased by a factor of 5 over the pressure range from 100 to 800 mbar. In xenon discharges, the intensity at 170 nm increased by two orders of magnitude when the pressure was raised from 250 mbar to 1 bar. Sustaining voltages were 200 V for argon and 400 V for xenon discharges, at current levels on the order of mA. The resistive current–voltage characteristics of the microdischarges indicate the possibility to form arrays for direct current, flat panel excimer lamps