Fourier Expansion of the Riemann zeta function and applications

We study the distribution of values of the Riemann zeta function $\zeta(s)$ on vertical lines $\Re s + i \mathbb{R}$, by using the theory of Hilbert space. We show among other things, that, $\zeta(s)$ has a Fourier expansion in the half-plane $\Re s \geq 1/2$ and its Fourier coefficients are the binomial transform involving the Stieltjes constants. As an application, we show explicit computation of the Poisson integral associated with the logarithm of $\zeta(s) - s/(s-1)$. Moreover, we discuss our results with respect to the Riemann and Lindel\"{o}f hypotheses on the growth of the Fourier coefficients.Comment: 21 page

Equity-Based free channels assignment for secondary users in a cognitive radio network

The present paper addresses the equity issue among the secondary users in a cognitive radio network. After using a multi scheduler algorithm and a fairness metric namely Jain’s Equity Index; we enhance the equity between the secondary users’ transfer rates by 0.64 in average, relative to a previous work

Monopoly-Market-Based Cooperation in Cognitive Radio Networks

In a cognitive radio network (CRN), the primary users (PUs) do not operate their spectra, full time. Thus, they can sell them to the secondary users (SUs), for a second use, during the free time slots. In this article, we assume that the market is perfect, monopolized by a single PU, and all players are rational. After formulating the PU’s profit, we established a necessary and sufficient condition that guarantees the introduction of the PU into the market. In addition, the expressions of the SUs’ profits, showed us that in non-cooperative form, some ones got zero profit, even after maximizing their profits. Therefore, we have considered to study the effect of cooperation on the profits of this category of SUs. By following this step, we established a cooperation strategy, to avoid zero profits for all SUs. In order to analyze the impact of this cooperation on the PU, we have expressed the profits of the PU in the cooperative and non-cooperative forms; as result, we found that the cooperation between SUs brought better than the non-cooperative form

Decentralization of Services Through Three Tiers in Wireless Body Area Networks

The Wireless Body Area Network (WBAN) contains a set of sensors, placed in the patient’s environment, to detect the vital signs and transmit the results towards the relevant services that interact in urgent cases. The present work exposes a functional WBAN architecture formed by three layers: closest, intermediate and farthest. The closest layer senses the chemical and biological signs. If the case is normal, or it can be locally regulated, the service stops there; else the intermediate service, namely the local hospital, is consulted to make treatments. Therefore, the patient will be transported into the hospital for examinations. If this condition is established the processus stopped there, otherwise, the request of help from an outside hospital becomes necessary. This request passes through a manager that supervises a network of hospitals and looks for a free place to welcome the patient. After the localization of a hospital, its coordinates will be forwarded into the customer hospital, for transporting the patient. The simulation results show that this design increases the patient’s probability of healing and maximizes the use of the available resources, relative to the centralization of services at a single layer or at two layers

Energy efficient power control for device to device communication in 5G networks

Next generation cellular networks require high capacity, enhanced energy efficiency and guaranteed quality of service (QoS). In order to meet these targets, device-to device (D2D) communication is being considered for future 5th generation especially for certain applications that require the proximity gain, the reuse gain, and the hop gain. In this paper, we investigate energy efficient power control for the uplink of an OFDMA (orthogonal frequency-division multiple access) single-cell communication system composed of both regular cellular users and device to device (D2D) pairs. Firstly, we analyze and mathematically model the actual requirements forD2D communications and traditional cellular links in terms of minimum rate and maximum power requirement. Secondly, we use fractional programming in order to transform the original problem into an equivalent concave one and we use the non-cooperative Game theory in order to characterize the equilibrium. Then, the solution of the game is given as a water-filling power allocation. Furthermore, we implement a distributed power allocation scheme using three ways: a) Fractional programming techniques b) Closed form expression (the novelty is the use of wright omega function). c) Inverse water filling. Finally, simulations in both static and dynamic channel setting are presented to illustrate the improved performance in term of EE, SE (spectral efficiency) and time of execution of the iterative algorithm (Dinkelbach) than the closed form algorithms

Improving the selection of MPRs in OLSR protocol: a survey of methods and techniques

Multi Point Relays (MPRs) are those nodes that are calculated and determined by the Optimized Link State Routing protocol (OLSR) in order to minimize and avoid overload inside the Mobile Ad hoc Network (MANET). In this paper, we will present a synthetic study of many techniques and methods for calculating and selecting the MPR nodes using a set of criteria namely energy, mobility, bandwidth, the quality of links, etc. The result of this study shows that most techniques consider a limited number of metrics for selecting the MPR nodes and therefore they are insufficient to allow the OLSR protocol to be quite complete and efficient because several metrics can occur at the same time in the real execution environment