scholarly journals Design and Performance Analysis of Probabilistically Shaped QAM Signals for Coherent FSO Systems with Gamma-Gamma Turbulence Channels

2021 ◽  
Vol 11 (21) ◽  
pp. 9805
Author(s):  
Ruotong Tian ◽  
Zhiyong Wu ◽  
Shuang Ma ◽  
Yucong Gu ◽  
Xueliang Li
Keyword(s):  
Error Rate ◽  
Simulation Method ◽  
Mass Function ◽  
Symbol Error Rate ◽  
Coded Modulation ◽  
Modulation Scheme ◽  
Probability Mass Function ◽  
Free Space Optical ◽  
Probability Mass ◽  
And Performance

Probabilistic shaping (PS) is a promising technique to approach the Shannon limit. In this paper, we design a practical coded modulation scheme based on PS to improve the capacity of coherent free-space optical (FSO) links with quadrature amplitude modulation (QAM), where the fading channel follows the Gamma-Gamma distribution. The aim of this paper is to optimize the probability mass function (PMF) of the QAM signal points to achieve the maximum channel capacity. Due to the complexity of the objective function, the heuristic algorithm was employed to solve the optimization problem. To the best of the authors’ knowledge, the closed-form pairwise error probability (PEP) is first derived with the non-uniform signals under the turbulence channel. In addition, we measure the average symbol error rate (SER) and post-FEC bit error rate (BER) by the Monte Carlo simulation method. The numerical simulation results of both capacity and BER show that the proposed PS scheme is better than the uniform distribution. The post-FEC BER results show that the proposed PS scheme provides significant gains compared with the uniform scheme.

scholarly journals Performances of BICM-ID system using CRSC code in optical transmissions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hocine Fekih ◽  
Boubakar Seddik Bouazza ◽  
Keltoum Nouri
Keyword(s):  
Bit Error Rate ◽  
Error Rate ◽  
Iterative Decoding ◽  
Optical Transmission ◽  
Coded Modulation ◽  
Modulation Scheme ◽  
Coding Gain ◽  
Decoding Algorithms ◽  
Qam Modulation ◽  
Short Code

AbstractRecently, using iterative decoding algorithms to achieve an interesting bit error rate for spectrally efficient modulation become a necessity for optical transmission, in this paper, we propose a coded modulation scheme based on bit interleaving circular recursive systematic convolutional (CRSC) code and 16-QAM modulation. The proposal system considered as a serial concatenation of a channel encoder, a bit interleaver and M-ary modulator can be flexible easy to implement using a short code length. For a spectral efficiency $\eta =3\text{bit}/s/Hz$, the coding gain at a bit error rate of 10−6 is about 8 dB.

scholarly journals Modified Recursions for a Class of Compound Distributions

1996 ◽  
Vol 26 (2) ◽  
pp. 213-224 ◽  
Author(s):  
Karl-Heinz Waldmann
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Mass Function ◽  
Cumulative Distribution ◽  
Probability Mass Function ◽  
Initial Value ◽  
Compound Distributions ◽  
Claim Frequency ◽  
Probability Mass ◽  
Stop Loss

AbstractRecursions are derived for a class of compound distributions having a claim frequency distribution of the well known (a,b)-type. The probability mass function on which the recursions are usually based is replaced by the distribution function in order to obtain increasing iterates. A monotone transformation is suggested to avoid an underflow in the initial stages of the iteration. The faster increase of the transformed iterates is diminished by use of a scaling function. Further, an adaptive weighting depending on the initial value and the increase of the iterates is derived. It enables us to manage an arbitrary large portfolio. Some numerical results are displayed demonstrating the efficiency of the different methods. The computation of the stop-loss premiums using these methods are indicated. Finally, related iteration schemes based on the cumulative distribution function are outlined.

Quantification of Low-Cycle Fatigue Life for a Gas Turbine Compressor Vane Carrier Under Varying Operating Conditions

2020 ◽  
Author(s):  
Zixi Han ◽  
Zixian Jiang ◽  
Sophie Ehrt ◽  
Mian Li
Keyword(s):  
Low Cycle Fatigue ◽  
Computational Cost ◽  
Mass Function ◽  
Operating Conditions ◽  
Probability Mass Function ◽  
Assessment Approach ◽  
Probability Mass ◽  
Gas Turbine Compressor ◽  
Operating Cycles ◽  
Operational Data

Abstract The design of a gas turbine compressor vane carrier (CVC) should meet mechanical integrity requirements on, among others, low-cycle fatigue (LCF). The number of cycles to the LCF failure is the result of cyclic mechanical and thermal strain effects caused by operating conditions on the components. The conventional LCF assessment is usually based on the assumption on standard operating cycles — supplemented by the consideration of predefined extreme operations and safety factors to compensate a potential underestimate on the LCF damage caused by multiple reasons such as non-standard operating cycles. However, real operating cycles can vary significantly from those standard ones considered in the conventional methods. The conventional prediction of LCF life can be very different from real cases, due to the included safety margins. This work presents a probabilistic method to estimate the distributions of the LCF life under varying operating conditions using operational fleet data. Finite element analysis (FEA) results indicate that the first ramp-up loading in each cycle and the turning time before hot-restart cycles are two predominant contributors to the LCF damage. A surrogate model of LCF damage has been built with regard to these two features to reduce the computational cost of FEA. Miner’s rule is applied to calculate the accumulated LCF damage on the component and then obtain the LCF life. The proposed LCF assessment approach has two special points. First, a new data processing technique inspired by the cumulative sum (CUSUM) control chart is proposed to identify the first ramp-up period of each cycle from noised operational data. Second, the probability mass function of the LCF life for a CVC is estimated using the sequential convolution of the single-cycle damage distribution obtained from operational data. The result from the proposed method shows that the mean value of the LCF life at a critical location of the CVC is significantly larger than the calculated result from the deterministic assessment, and the LCF lives for different gas turbines of the same class are also very different. Finally, to avoid high computational cost of sequential convolution, a quick approximation approach for the probability mass function of the LCF life is given. With the capability of dealing with varying operating conditions and noises in the operational data, the enhanced LCF assessment approach proposed in this work provides a probabilistic reference both for reliability analysis in CVC design, and for predictive maintenance in after-sales service.

ON SEVERAL PROPERTIES OF A CLASS OF PREFERENTIAL ATTACHMENT TREES—PLANE-ORIENTED RECURSIVE TREES

2020 ◽  
pp. 1-19
Author(s):  
Panpan Zhang
Keyword(s):  
Continuous Time ◽  
Preferential Attachment ◽  
Mass Function ◽  
Probability Mass Function ◽  
Zagreb Index ◽  
Exact Probability ◽  
Probability Mass ◽  
Proper Scaling ◽  
Recursive Trees ◽  
Degree Variable

In this paper, several properties of a class of trees presenting preferential attachment phenomenon—plane-oriented recursive trees (PORTs) are uncovered. Specifically, we investigate the degree profile of a PORT by determining the exact probability mass function of the degree of a node with a fixed label. We compute the expectation and the variance of degree variable via a Pólya urn approach. In addition, we study a topological index, Zagreb index, of this class of trees. We calculate the exact first two moments of the Zagreb index (of PORTs) by using recurrence methods. Lastly, we determine the limiting degree distribution in PORTs that grow in continuous time, where the embedding is done in a Poissonization framework. We show that it is exponential after proper scaling.

scholarly journals A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 163 ◽  
Author(s):  
Qian Pan ◽  
Deyun Zhou ◽  
Yongchuan Tang ◽  
Xiaoyang Li ◽  
Jichuan Huang
Keyword(s):  
Evidence Theory ◽  
Mass Function ◽  
Probability Mass Function ◽  
Main Work ◽  
Basic Probability ◽  
Open Issue ◽  
Belief Entropy ◽  
Probability Mass ◽  
Hartley Entropy ◽  
Theory Framework

Dempster-Shafer evidence theory (DST) has shown its great advantages to tackle uncertainty in a wide variety of applications. However, how to quantify the information-based uncertainty of basic probability assignment (BPA) with belief entropy in DST framework is still an open issue. The main work of this study is to define a new belief entropy for measuring uncertainty of BPA. The proposed belief entropy has two components. The first component is based on the summation of the probability mass function (PMF) of single events contained in each BPA, which are obtained using plausibility transformation. The second component is the same as the weighted Hartley entropy. The two components could effectively measure the discord uncertainty and non-specificity uncertainty found in DST framework, respectively. The proposed belief entropy is proved to satisfy the majority of the desired properties for an uncertainty measure in DST framework. In addition, when BPA is probability distribution, the proposed method could degrade to Shannon entropy. The feasibility and superiority of the new belief entropy is verified according to the results of numerical experiments.

scholarly journals Accurate and Practical Energy Detection over α-μ Fading Channels

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 754 ◽  
Author(s):  
Kaitian Cao ◽  
Ping Qian ◽  
Jing An ◽  
Li Wang
Keyword(s):  
Sample Size ◽  
Fading Channels ◽  
Small Sample Size ◽  
Energy Detection ◽  
Mass Function ◽  
Detection Performance ◽  
Small Sample ◽  
Closed Form Expression ◽  
Probability Mass Function ◽  
Probability Mass

In this study, a novel and exact closed-form expression for detection probability of energy detection (ED) in terms of Meijer’s G-function over α-μ generalized fading channels was derived. It is more accurate and practical than the existing exact expressions and has wide application prospects in the performance evaluations in various areas of wireless communications, especially in the wireless sensor network (WSN) and the cognitive radio network (CRN). Furthermore, an exact and simple analytical solution for the sample size meeting the desired detection performance in terms of the probability mass function of a Poisson distribution was also solved. Simulations verified the detection performance and accuracy of our derived expressions with a small sample size compared to the existing exact expressions and approximations.

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