Closed form expression

We introduce a novel wireless device-to-device (D2D) collaboration architecture that exploits distributed storage of popular content to enable frequency reuse. We identify a funda-mental conflict between collaboration distance and interference and show how to optimize the transmission power to maximize frequency reuse. Our analysis depends on the user content request statistics which are modeled by a Zipf distribution. Our main result is a closed form expression of the optimal collaboration distance as a function of the content reuse dis-tribution parameters. We show that if the Zipf exponent of the content reuse distribution is greater than 1, it is possible to have a number of D2D interference-free collaboration pairs that scales linearly in the number of nodes. If the Zipf exponent is smaller than 1, we identify the best possible scaling in the number of D2D collaborating links. Surprisingly, a very simple distributed caching policy achieves the optimal scaling behavior and there...

Performance of cooperative relaying employing infrastructure based fixed relays having multiple antennas has been investigated. Here, both relay and destination perform maximal ratio combining combining of the signals. Closed form expressions for outage probability and bit error rate have been derived for Nakagami-m fading channels, with integer values of m. The effect of fading correlation among relay antennas and relay

The performance of digital communication systems over generalized-K (KG) fading channels is analyzed and evaluated. Novel closed form expressions for the SNR statistics, the average Shannon's channel capacity and the bit error rate (BER) are derived. These expressions are used to study important performance criteria such as the outage performance, the average capacity and the BER for a great variety of modulation formats in KG fading channels. The proposed mathematical analysis is accompanied with various performance evaluation results, which demonstrate the usefulness of the proposed approach.

This paper investigates the problem of the mechanical behavior of an interfacially cracked layered beam with possible bending-extension coupling (BEC) and residual hygrothermal stresses (RHTS), as well as shear deformations and crack-root rotations. The paper presents a mechanical model of a beam that results by assembling two sublaminates by a semi-rigid interface. The beam is clamped at its one end and interfacially cracked and generally loaded at the other. First, the mathematical problem is formulated and analytically solved in terms of the internal forces, strains, displacements, and interfacial stresses. Novel closed-form expressions are derived regarding these quantities and thoroughly reported in tables. The proposed expressions stand out for their generality; they apply to beams with arbitrary layers of random thicknesses and materials and consider general loading, BEC, and RHTS. Next, we highlight some specific cases by appropriately reducing the general expressions. As an example, we investigate the mechanical responses of composite laminates with possible BEC and RHTS using the double cantilever beam configuration. Lastly, the paper discusses new ways to deepen our knowledge of additional aspects of the fracture response of interfacially cracked beams with BEC and RHTS.

Abstract-A closed-form expression is derived for the effective aggregate throughout delivered to a population of users in a forward link 1xEV-DV cellular system. The throughput is expressed interms of two main classes. The first class consists of parameters that are associated with ...

We analyze the fundamental limits of secret-key agreement over MIMO quasi-static fading channels. In the low-power and high-power regimes, we establish closed-form expressions for secret-key capacity. In the low-power regime, we show that the optimal signaling strategy is independent of the eavesdropper's fading realization. The low-power secret-key capacity is achieved by transmitting along the direction corresponding to the maximal eigenvalue of the legitimate channel. By combining this signaling strategy with reconciliation and privacy amplification, one obtains a semi-blind key-distillation strategy in which the knowledge of the eavesdropper's fading is required for privacy amplification alone.

In this paper, the performances analysis of cooperative-diversity networks using adaptive decode-and-forward (DF) relaying over independent non-identical flat Nakagami-m fading channels is investigated. We derive closed-form expressions for the error probability, outage probability and average channel capacity, and analyze their dependence on the channel parameters. In adaptive DF relaying, among M relays that can participate, only C relays (C les M), with good channels to the source, decode and forward (retransmit) the ...

Composite multipath/shadowing fading environments are frequently encountered in different realistic scenarios. These channels are generally modeled as a mixture of Nakagami- m multipath fading and log-normal shadowing. The resulting composite probability density function (pdf) is unfortunately not in closed-form, thereby making the performance evaluation of communication links in these channels cumbersome. In this paper, we propose to model composite channels by the very general G-distribution. This pdf arises when the log-normal shadowing is substituted by the Inverse-Gaussian one. This substitution will prove to be very accurate for several shadowing conditions. In this paper we conduct an exhaustive performance evaluation of communication systems operating in these channels. Our study starts by deriving a closed-form expression for the outage probability. Then, we derive the moment generating function of the G-distribution, hence facilitating the calculation of average bit error probabilities. We also derive closed-form expressions for the channel capacity for three adaptive transmission techniques, namely, (i) optimal rate adaptation with constant power, (ii) optimal power and rate adaptation, and (iii) channel inversion with fixed rate. The different expressions that will be provided are of great importance in assessing the performance of communication systems in composite channels.

A maximum likelihood (ML) estimator for the parameters of Gaussian versions of the fractionally differenced white noise process is developed. A closed-form expression for the likelihood equation is given, and Cramer-Rao bounds are computed for finite size sample data sets. It is shown how the theory can be extended to the case where the fractionally differenced white noise process is