scholarly journals An Integral Representation of the Logarithmic Function with Applications in Information Theory

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 51 ◽  
Author(s):  
Neri Merhav ◽  
Igal Sason
Keyword(s):  
Integral Representation ◽  
Random Variable ◽  
Ergodic Capacity ◽  
Logarithmic Function ◽  
Positive Random Variable ◽  
Random Parameters ◽  
Information Theoretic ◽  
Input Multiple Output ◽  
Single Input ◽  
Lossless Data Compression

We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily computable exact formulas for quantities that involve expectations and higher moments of the logarithm of a positive random variable (or the logarithm of a sum of i.i.d. positive random variables). The integral representation of the logarithm is proved useful in a variety of information-theoretic applications, including universal lossless data compression, entropy and differential entropy evaluations, and the calculation of the ergodic capacity of the single-input, multiple-output (SIMO) Gaussian channel with random parameters (known to both transmitter and receiver). This integral representation and its variants are anticipated to serve as a useful tool in additional applications, as a rigorous alternative to the popular (but non-rigorous) replica method (at least in some situations).

Secure Communications over Wireless Networks

2012 ◽  
pp. 10-37
Author(s):  
Md. Zahurul Islam Sarkar
Keyword(s):  
Fading Channels ◽  
Open Loop ◽  
Main Channel ◽  
Secrecy Capacity ◽  
Transmission Scheme ◽  
Information Theoretic ◽  
Information Theoretic Security ◽  
Input Multiple Output ◽  
Single Input ◽  
Analytical Expressions

Nakagami-m fading channel is chosen to analyze the secrecy capacity for fading channels since the Nakagami-m distribution can model fading conditions, which are more or less severe than that of Rayleigh and has the advantage of including Rayleigh as a special case. At first, secrecy capacity is defined in case of full channel state information (CSI) at the transmitter, where transmitter has access to both the main channel and eavesdropper channel gains. Secondly, secrecy capacity is defined with only main channel CSI at the transmitter. Then, optimal power allocation at the transmitter that achieves the secrecy capacity is derived for both the cases. Moreover, secrecy capacity is defined under open-loop transmission scheme, and the exact closed form analytical expression for the lower bound of ergodic secrecy capacity is derived for Nakagami-m fading single-input multiple-output (SIMO) channel. In addition, secrecy capacity is defined for the AWGN channel in order to realize the information-theoretic security of wireless channels with no fading. Finally, analytical expressions for the probability of non-zero secrecy capacity and secure outage probability are derived in order to investigate the secure outage performance of fading channels.

scholarly journals Some Useful Integral Representations for Information-Theoretic Analyses

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 707 ◽  
Author(s):  
Neri Merhav ◽  
Igal Sason
Keyword(s):  
Integral Representation ◽  
Random Variables ◽  
Direct Calculation ◽  
Random Variable ◽  
Two Dimensions ◽  
Integral Representations ◽  
Independent Random Variables ◽  
Nonnegative Random Variable ◽  
Information Theoretic ◽  
The Moment

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.

scholarly journals On the Performance of Cognitive Underlay SIMO Networks over Equally Correlated Rayleigh Fading Channels

2016 ◽  
Vol 5 (1-2) ◽  
Author(s):  
Tu Lam Thanh ◽  
Vo Nguyen Quoc Bao ◽  
Pham Thi Dan Ngoc ◽  
Tran Trung Duy
Keyword(s):  
Fading Channels ◽  
Spectrum Sharing ◽  
Rayleigh Fading ◽  
Ergodic Capacity ◽  
Cumulative Distribution ◽  
Rayleigh Fading Channels ◽  
Input Multiple Output ◽  
Single Input ◽  
Close Form ◽  
Probability Density Function Pdf

The performance of single-input multiple-output (SIMO) cognitive spectrum sharing networks with the presence of equally correlated Rayleigh fading channels is investigated. In particular, based on the truncated infinitive series of cumulative distribution function (CDF) and probability density function (PDF) of the end-to-end signal-to-noise ratios (SNRs), close-form expressions are provided for the system outage performance, bit error rate and ergodic capacity. It is shown that the system performance merely depends on the correlation coefficient between antennas. Monte-Carlo simulations are also contributed to confirm the accuracy of our analysis.

scholarly journals Compensated Single Input Multiple Output Flyback Converter

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3009
Author(s):  
Mohammad Tahan ◽  
David O. Bamgboje ◽  
Tingshu Hu
Keyword(s):  
Transient Response ◽  
Current Mode ◽  
Voltage Regulation ◽  
Buck Converter ◽  
Output Channel ◽  
Flyback Converter ◽  
Input Multiple Output ◽  
Voltage Deviation ◽  
Single Input ◽  
The Cross

A new single-input multiple-output (SIMO) converter is proposed in this work by incorporating flyback and buck converters in a master–slave configuration. The objective of this work is to address the cross regulation problem, achieve tight voltage regulation, improve the circuit form factor and attain a fast transient response for a SIMO flyback converter. The flyback converter maintains the output channels within 10% of their rated voltages and the SIMO buck converter is placed in series with the flyback converter such that it compensates for the output voltage deviation. Moreover, a time multiplexing switching scheme decouples output channel to eliminate the cross-regulation problem and remove the need for an additional winding transformer per each output channel. A type II compensator with a peak current mode controller was designed to achieve faster transient response which is critical for the proposed configuration. A thorough steady-state analysis was carried out on a triple output channel topology to obtain the design criteria and component values. MATLAB/Simscape modelling and simulation was used to validate the effectiveness of the proposed converter with the result yielding satisfactory transience even with load disturbance. Additionally, the result of the proposed converter is compared with previously published works.

On the Study of Cognitive Bidirectional Relaying with Asymmetric Traffic Demands

Frequenz ◽  
2015 ◽  
Vol 69 (5-6) ◽  
Author(s):  
Xiaodong Ji
Keyword(s):  
Ergodic Capacity ◽  
Base Station ◽  
Transmission Protocol ◽  
Splitting Algorithm ◽  
Performance Simulation ◽  
Information Theoretic ◽  
Primary Users ◽  
Operating Region ◽  
Bidirectional Relaying ◽  
Outage Probabilities

AbstractIn this paper, we consider a cognitive radio network scenario, where two primary users want to exchange information with each other and meanwhile, one secondary node wishes to send messages to a cognitive base station. To meet the target quality of service (QoS) of the primary users and raise the communication opportunity of the secondary nodes, a cognitive bidirectional relaying (BDR) scheme is examined. First, system outage probabilities of conventional direct transmission and BDR schemes are presented. Next, a new system parameter called operating region is defined and calculated, which indicates in which position a secondary node can be a cognitive relay to assist the primary users. Then, a cognitive BDR scheme is proposed, giving a transmission protocol along with a time-slot splitting algorithm between the primary and secondary transmissions. Information-theoretic metric of ergodic capacity is studied for the cognitive BDR scheme to evaluate its performance. Simulation results show that with the proposed scheme, the target QoS of the primary users can be guaranteed, while increasing the communication opportunity for the secondary nodes.

Robot Assisted Modal Analysis on a Stationary Bladed Wheel

2014 ◽  
Author(s):  
L. Bertini ◽  
B. Monelli ◽  
P. Neri ◽  
C. Santus ◽  
A. Guglielmo
Keyword(s):  
Three Dimensional ◽  
Laser Doppler Vibrometer ◽  
Testing Time ◽  
Real Representation ◽  
The Real ◽  
Complex Formulation ◽  
Frequency Matching ◽  
Input Multiple Output ◽  
Multiple Measurements ◽  
Single Input

This paper shows an automated procedure to experimentally find the eigenmodes of a bladed wheel with highly three-dimensional geometry. The stationary wheel is supported in free-free conditions, neglecting stress-stiffening effects. The single input / multiple output approach was followed. The vibration speed was measured by means of a laser-Doppler vibrometer, and an anthropomorphic robot was used for accurate orientation and positioning of the measuring laser beam, allowing multiple measurements during a limited testing time. The vibration at corresponding points on each blade was measured and the data elaborated in order to find the initial (lower frequency) modes. These modal shapes were then compared to finite element simulations and accurate frequency matching and exact number of nodal diameters obtained. Being the modes cyclically harmonic, the complex formulation could be attractive, being not affected by the angular phase of the mode representation. Nevertheless, stationary modes were experimentally detected, rather than rotating, and then the real representation was necessary. The discrete Fourier transform of the blade displacements easily allowed to find both the angular phase and the correct number of nodal diameters. Successful MAC experimental to analytical comparison was finally obtained with the real representation after introducing the proper angular phase for each mode.

The Ship Track Keeping With Roll Reduction Using a Multiple-States PD Controller on the Rudder Operation

2008 ◽  
Vol 45 (01) ◽  
pp. 21-27
Author(s):  
Ming-Chung Fang ◽  
Jhih-Hong Luo
Keyword(s):  
Numerical Model ◽  
Line Of Sight ◽  
Pd Controller ◽  
Input Multiple Output ◽  
Maneuvering In Waves ◽  
Single Input ◽  
Reduction Function ◽  
Simulation Results ◽  
Guidance Technique ◽  
Present Simulation

The paper presents a nonlinear hydrodynamic numerical model with multiple-states proportional-derivative (PD) controllers for simulating the ship's tracking in random sea. By way of the rudder operation, the track-keeping ability of the PD controller on the ship is examined using the line-of-sight (LOS) guidance technique. Furthermore, the roll-reduction function using the rudder control is also included in the PD controller. From the present simulation results, the single-input multiple-output (SIMO) heading/roll PD controller including LOS technique developed here indeed works, either for the roll reduction or for track keeping while the ship is maneuvering in waves.

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