Series Expansions and Approximations of the Nakagami-m Sum Probability Density Function

The numerical evaluation of the pdf of a sum of Nakagami-m random variables is considered in this letter. Different methods are proposed to obtain this approximation: i) a power series expansion based on elementary properties of unilateral convolution of power signals; ii) a Laplace approximation stemming from Laplace's method for asymptotic integral approximations; and iii) a Gaussian series expansion capturing the deviation of the wanted pdf from the Gaussian with the same mean and variance. Numerical results are included for validation and comparison with the literature and a critical assessment of the different methods is provided

Information Rate Optimization for the Non-Regenerative Linear MIMO Relay Channel with a Direct Link and Variable Duty Cycle

We consider the optimization of a two-hop linear relay channel based on an amplify-and-forward Multiple-Input Multiple-Output (MIMO) relay. The relay is assumed to derive the output signal by applying a Relay Transform Matrix (RTM) applied to the input signal. Assuming perfect channel state information about the channel at the relay and iid transmitted symbols, the RTM is optimized according to two different criteria: i) MIMO information rate; ii) information rate based on Orthogonal Space–Time Block Codes. The two assumptions have been addressed in part in the literature. The optimization problem is reduced to a manageable convex form, whose KKT equations are explicitly solved. Then, a parametric solution is given, which yields the power constraint and the information rate achieved with uncorrelated transmitted symbols as functions of a positive indeterminate. The solution for a given average power constraint at the relay is amenable to a water-filling-like algorithm, and extends earlier literature results addressing the case without the direct link. The duty cycle of the two-hop relaying process is also addressed in the general form of the achievable rate. Simulation results are reported, which are relevant to a Rayleigh fading MIMO relay channel and the role of the direct link SNR is precisely assessed. Duty cycle optimization is also considered by a numerical example

Information Rate Optimization for Joint Relay and Link in Non-Regenerative MIMO Channels∗

The optimization of the Relay Transform Matrix (RTM) in a two-hop relay network with an average relay power constraint and perfect channel state information at the relay is addressed in this paper. The study considers the most general case in terms of number of transmit and receive antennas at the source, relay, and destination, with arbitrary correlation of the received noise at all terminals. The optimization problem is reduced to a manageable convex form, which is solved by linear algebra transformation and the KKT equations. A parametric solution is given, which yields the power constraint and the capacity achieved with uncorrelated transmitted data. The solution is shown to be amenable to a water-filling-like algorithmic implementation, which extends earlier literature results addressing the case without the direct link. Simulation results are reported concerning a Rayleigh relay network where, in particular, the role of the direct link SNR is precisely assessed

A Simple Method to Calculate Random-Coding Union Bounds for Ultra-Reliable Low-Latency Communications

Ultra-Reliable Low-Latency Communications are based on very short codes whose performances cannot be evaluated correctly by using the Shannon capacity formula holding for asymptotically large code lengths. The use of Random-Coding Union Bounds (RCUB's) has been suggested in the literature as an alternative for this application. Unfortunately, their calculation is difficult and the Gaussian approximation may lead to erroneous results. The saddlepoint approximation has been proposed as an alternative to overcome the limitations of the Gaussian approximation. Though this technique is valid in many cases, situations exist where the exact calculation provides different results. A simple numerical technique is proposed in this letter to calculate numerically the exact value of the RCUB. Its accuracy is compared to that of the Gaussian and saddlepoint approximations in some cases of interest

Outage Information Rate of Spatially Correlated Multi-Cluster Scattering MIMO Channels

A one-sided spatially-correlated multi-cluster scattering Rayleigh MIMO channel is considered in this work and its outage probability is derived in an analytic form based on Meijer function determinants. First, the spatially-uncorrelated case is addressed and the Moment Generating Function (MGF) of the information rate is expressed in an analytic closed-form. The MGF is then used to obtain the outage probability. A few special cases are addressed to provide a confirmation of the analytic results. Next, the MGF in the one-sided spatially correlated case is derived with the constraint of distinct positive spatial correlation eigenvalues. Numerical results are included to provide confirming evidence of the analytic results. These results are then used to assess the outage probability degradation due to spatial correlation in a selected exampl

The sunspot cycle recorded in the thermoluminescence profile of the GT89/3 Ionian sea core

We measured the thermoluminescence (TL) depth profile of the GT89O3 shallow-water Ionian sea core. This profile has been transformed into a time series using the accurate sedimentation rate previously determined by radiometric and tephroanalysis methods. The TL measurements were performed in samples of equal thickness of 2 mm, corresponding to a time interval of 3.096 y. The TL time series spans A1800 y. The DFT power spectral densities in the decadal periodicity range of this TL series show significant periodicities at 10.7, 11.3 and 12 y closely similar to the periodicities present in the sunspot number series. These results confirm that the TL signal in recent sea sediments faithfully records the solar variability, as we previously proposed

The global and persistent millennial-scale variability in the thermoluminescence profiles of shallow and deep Mediterranean sea cores

In this paper we present the thermoluminescence (TL) profile in the last 7500 y, measured in the upper part of the deep Tyrrhenian sea core CT85-5. This core was dated with tephroanalysis and radiocarbon techniques: a constant sedimentation rate (10 cm/ky) was found up to 200 cm. The sampling interval adopted for obtaining the TL profile is 2.5 mm, corresponding to 25 y. Using different spectral-analysis methods, we show the presence of a millennial-scale variability, corresponding to an average period of about 1315 y. This oscillation has been noted also in other climatic indices measured in North Atlantic sea sediment cores and in the Greenland GISP2 ice core. This result indicates that this millennial oscillation is the expression of climate changes of worldwide extent. We show that this millennial periodicity persisted during the last deglaciation. The transition to Holocene was determined in our core by the oxygen isotope ratio d 18O measured in Globigerina bulloides. The fact that the observed TL changes do not have a local character is also suggested by the excellent agreement between this deep sea TL profile of the uppermost part of the core and the TL profile measured in the shallow Ionian sea GT89-3 core over the last 2500 y, with a time resolution of 3.096 y

22 year cycle in the planktonic 18 of a shallow-water Ionian sea core

The d18 O profile of Globigerinoides ruber was measured in the GT90/3 Ionian sea core between 1205 and 1898 AD. The high temporal resolution of 3.87 y allowed us to determine the presence in the time series of an 11 y component with an amplitude of 0.07‰, at significance level of 99% (by Monte Carlo singular spectrum analysis, MC-SSA). Here we focus attention on the 22 y periodicity in the time series and we show that SSA principal components (PCs) 15 and 16 carry this oscillation, in phase with the Hale solar cycle, obtained by inverting the odd cycles of the sunspot number series. This result shows that the even and odd Schwabe cycles do not have the same influence on this climatic record

Temperature and precipitation in Northeast China during the last 150 years: relationship to large-scale climatic variability

The analysis of two historical time series of temperature and precipitation in Northeast China, spanning, respectively, 1870–2004 and 1841–2004, performed by continuous wavelet transform and other classical and advanced spectral methods, is presented here. Both variables show a particular trend and oscillations of about 85, 60, 35 and 20 years that are highly significant, with a phase opposition at the centennial scale and at the 20-year scale. The analysis of the four temperature series relative to single seasons shows that the 20-year cycle is typical of the summer monsoon season, while the 35-year cycle is most evident in winter. The cycles of ~ 60 years and longer are present in all seasons. The centennial variation of temperature and precipitation describes well the 1970–1980 transition between a period of relatively strong East Asian Summer Monsoon (EASM), corresponding to high precipitation and relatively cool temperatures in Northeast China, and a conditions of weak EASM (low precipitation and warm temperatures). The connection of the detected local variations with large-scale climatic variability is deduced from the comparison with different climatic records (Northern Hemisphere temperature, Pacific Decadal Oscillation and Atlantic Multidecadal Oscillation indexes)

Cosmogenic isotopes and geomagnetic signals in a Mediterranean sea sediment at 35000 y BP

In this paper we present the results on the relative changes of the geomagnetic field intensity measured in the Tyrrhenian sea core CT85-5 between 23 and 51 ky BP in order to investigate the origin of the enhancement of the cosmogenic isotope 10Be concentration, recently reported in the same core at 35 ky BP