A closed-form solution for the distribution of the sum of Nakagami-m random phase vectors

The distribution of the modulus of the sum of random phase vectors, is of great practical importance in several applications which deal with sums of sinusoidal signals (wireless multipath transmissions, radars, optical communications, etc). In this letter, simple closed-form expressions are presented for the probability density function (PDF), the cumulative distribution function (CDF), the moment generating function (MGF) and the moments of the envelope distribution of the sum of L non-identical random Nakagami-m phase vectors with integer fading parameters. Moreover, the average over this distribution of the Gaussian Q-function and of the squared Q-function, are also presented in closed-form     

Equal gain combining over Nakagami-n (rice) and Nakagami-q (Hoyt) generalized fading channels

Motivated by the importance of Nakagami-n (Rice) and Nakagami-q (Hoyt) statistical models to describe channel fading in land, mobile, terrestrial, and satellite telecommunications, we present an alternative moments-based approach to the performance analysis of equal-gain combining (EGC) receivers over independent, not necessarily identically distributed Rice- and Hoyt-fading channels. Exact closed-form expressions for the moments of the signal-to-noise ratio (SNR) at the output of the combiner are derived and significant performance criteria such as, the average output SNR, the amount of fading and the spectral efficiency at the low power regime, are studied. Moreover, using Pade rational approximation to the moment-generating function of the output SNR, the average symbol error probability and the outage probability are evaluated. We also study the suitability of modeling a Hoyt-fading environment by a properly chosen Nakagami-m model, as far as the error performance of the EGC is concerned.     

Distributed Transmit Antenna Selection (DTAS) Under Performance or Energy Consumption Constraints

Motivated by the transmit antenna selection (TAS) concept, used in Multiple-Input-Multiple-Output systems, we argue for distributed transmit antenna selection (DTAS), which corresponds to a method of selecting a subset of available relays in cooperative diversity systems. Assuming amplify and forward relays, the proposed selection method represents a low-complexity tool for determining the optimum relaying set. Two optimization problems are studied: the error probability minimization subject to total energy consumption constraints, and the dual one, the total energy consumption minimization under error performance constraints. Numerical examples verify the advantage of the proposed method in adapting the number of relaying terminals to the desired performance-consumption tradeoff.     

Closed-form error analysis of the non-identical Nakagami-m relay fading channel

We present closed-form expressions for the average bit error probability (ABEP) of BPSK, QPSK and M-QAM of an amplify-and-forward average power scaling dual-hop relay transmission, over non-identical Nakagami-m fading channels, with integer values of m. Additionally, we evaluate in closed-form the ABEP under sufficiently large signal-to-noise ratio for the source-relay link, valid for arbitrary rn. Numerical and simulation results show the validity of the proposed mathematical analysis and point out the effect of the two hops unbalanced fading conditions on the error performance.     

Investigation of isolated thunderstorms lightning activity over eastern Mediterranean using Meteosat rapid scan infrared imagery

An analysis of selected spatiotemporal characteristics of isolated thunderstorms in relation to cloud-to-ground (CG) lightning over part of the eastern Mediterranean is performed. The purpose of the study is twofold: to better understand and improve the basic knowledge of the physical mechanisms of the phenomenon and to offer new means of nowcasting the lightning activity in such thunderstorms. Meteosat Second Generation (MSG) Rapid Scan Service (RSS) infrared imagery which offers the option of tracking the examined storms with a time frequency of 5 minutes is one of the two utilized datasets, the other being ZEUS very low frequency (VLF) lightning detection system’s CG discharge data. It was shown that a cloud top temperature of about ?20°C is required for the onset of lightning activity. A rapid drop of the cloud-top temperature of about 11°C in 5 minutes on average is observed a few minutes before or during lightning initiation. The maximization of the activity is usually quite close to the overall minimum cloud-top temperature of the cell. A temperature increase of 3.5°C from this overall minimum can mark the end of the activity, which is also associated to the time evolution of the cell’s horizontal extent. In fact, after the cell’s horizontal area stops to increase and/or starts to gradually diminish, CG lightning activity is expected to stop.     

A Novel Instrument for the Measurement of the Thermal Conductivity of Molten Metals. Part II: Measurements

New measurements of the thermal conductivity of molten mercury, gallium, tin, and indium are reported up to 750 K. The measurements are performed in a novel transient hot-wire instrument described elsewhere. The present experimental technique overcomes problems of convection, and it is shown that it operates in an absolute way in accord with a theoretical model. The uncertainty of the thermal conductivity results is estimated to be ± 2%, which is superior to that achieved in most earlier work. The low uncertainty of the present experimental results has allowed us to test the only significant theory for the thermal conductivity of molten metals, which relates this property to the electrical conductivity. The pattern of results among the four metals indicates that further theoretical developments would be warranted.     

Performance bounds of multihop wireless communications with blind relays over generalized fading channels

In this letter, efficient performance bounds for multihop wireless communications systems with non-regenerative blind relays over non-identical Nakagami-n (Rice), Nakagami-m and Nakagami-q (Hoyt) generalized fading channels, are presented. More specifically, the end-to-end signal-to-noise ratio (SNR) is formulated and upper bounded by using the well-known inequality between harmonic and geometric mean of positive random variables. This bound is used to study important system's performance metrics: i) the moments of the end-to-end SNR which are obtained in closed-forms, and ii) the outage probability and the average error probability for coherent and non-coherent modulations, which are accurately approximated using the moments-based approach. Furthermore, new analytical formulae are derived for the gain of previously proposed semi-blind relays in generalized fading environments. These kind of relays are used in numerical examples and computer simulations to verify the accuracy and to show the tightness of the proposed bounds.     

Closed-form statistics for the sum of squared Nakagami-m variates and its applications

We present closed-form expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the sum of non-identical squared Nakagami-m random variables (RVs) with integer-order fading parameters. As it is shown, they can be written as a weighted sum of Erlang PDFs and CDFs, respectively, while the analysis includes both independent and correlated sums of RVs. The proposed formulation significantly improves previously published results, which are either in the form of infinite sums or higher order derivatives of the fading parameter m. The obtained formulas can be applied to the performance analysis of diversity combining receivers operating over Nakagami-m fading channels.     

Semi-blind amplify-and-forward with partial relay selection

The performance of the dual-hop semi-blind amplify-and-forward relay channel, where the intermediate relay node is selected depending on the instantaneous and partial channel knowledge, is investigated. Using closed-form expressions for the cumulative distribution function of the end-to-end signal-to-noise ratio (SNR), outage probability, SNR moments and average bit error rate are derived.     

A closed-form upper-bound for the distribution of the weighted sum of Rayleigh variates

The problem of finding the distribution of the sum of more than two Rayleigh fading envelopes has never been solved in terms of tabulated functions. In this letter, we present a closed-form union upper-bound for the cumulative distribution function of the weighted sum of N independent Rayleigh fading envelopes. Computer simulation results verify the tightness of the proposed bound for several values of N. The proposed bound can be efficiently applied in various wireless applications, such as satellite communications, equal-gain receivers, and radars.