RESEARCH OF SIGNAL DETECTION ALGORITHMS IN COGNITIVE RADIO NETWORKS

Основной темой являются некоторые из алгоритмов сканирования радиоспектра и обнаружения сигналов в системе когнитивного радио, а также само когнитивное радио. Данная тема является актуальной, так как применение широкополосных каналов является одним из вариантов организации связи, но при этом возникают некоторое трудности. Например, из-за большого числа пользователей необходимо более рационально использовать спектр радиочастот. Рассматриваются основные аспекты обнаружения сигнала в узкополосных и широкополосных диапазонах. Рассказывается о недостатках адаптивных алгоритмов обнаружения, основанных на стандартных законах распределения. Приведены примеры как параметрических, так и непараметрических алгоритмов обнаружения. Подробно описывается алгоритм, основанный на критерии Уилкоксона. При помощи критерия Неймана-Пирсона можно сравнивать обнаружители между собой. Сделаны выводы о целесообразности применения для мониторинга радиоспектра непараметрических алгоритмов обнаружения. Для случая постоянного положительного сигнала на фоне гауссовской помехи сравнение значений асимптотической относительной эффективности для критерия Уилкоксона со значением линейного обнаружителя составляет порядка 0,955. Это значение говорит о том, что оба обнаружителя практически не уступают друг другу в таких условиях The article discusses some of the algorithms for scanning the radio spectrum and detecting signals in the cognitive radio system, as well as the cognitive radio itself. This topic is relevant since the use of broadband channels is one of the options for organizing communication. Due to a large number of users, it is necessary to more rationally use the radio frequency spectrum. We considered the main aspects of the detection of the signal in narrowband and broadband bands. We described the lack of adaptive detection algorithms based on the standard distribution laws. We give examples of both parametric and non-parametric detection algorithms. We described the algorithm based on Wilcoxon's criteria in detail. Using the Neuman-Pearson's criterion, you can compare the detectors among themselves. We made conclusions about the feasibility of application for monitoring the radiospectract of non-parametric detection algorithms. For the case of a constant positive signal against the background of Gaussian interference, comparing the values of asymptotic relative efficiency for the Wilcoxon’s criterion with the value of the linear detector is about 0.955. This value suggests that both detectors are practically inferior to each other in such conditions

Cross-tissue eQTL mapping in the presence of missing data via surrogate outcome analysis

Missing data are prevalent in the Genotype-Tissue Expression (GTEx) project, where measurements from certain inaccessible tissues, such as the substantia nigra (SSN), are available at much smaller sample sizes than those from accessible tissues, such as blood. This severely limits power for identifying tissue-specific expression quantitative trait loci (eQTL). Here we propose Surrogate Phenotype Regression Analysis (Spray) for leveraging information from a correlated surrogate outcome (e.g. expression in blood) to improve inference on a partially missing target outcome (e.g. expression in SSN). Rather than regarding the surrogate outcome as a proxy for the target outcome, Spray jointly models the target and surrogate outcomes within a bivariate regression framework. Unobserved values of either outcome are regarded as missing data. We describe and implement an expectation conditional maximization algorithm for performing estimation in the presence of bilateral outcome missingness. We then demonstrate analytically, via the asymptotic relative efficiency, and empirically, through simulations and tissue-specific eQTL mapping, that in comparison with marginally modeling the target outcome, jointly modeling the target and surrogate outcomes increases estimation precision and improves power.

On Optimal and Asymptotic Properties of a Fuzzy L2 Estimator

A fuzzy least squares estimator in the multiple with fuzzy-input–fuzzy-output linear regression model is considered. The paper provides a formula for the L2 estimator of the fuzzy regression model. This paper proposes several operations for fuzzy numbers and fuzzy matrices with fuzzy components and discussed some algebraic properties that are needed to use for proving theorems. Using the proposed operations, the formula for the variance, provided and this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. The confidence regions of the coefficient parameters and the asymptotic relative efficiency (ARE) are also discussed. In addition, several examples are provided including a Monte Carlo simulation study showing the validity of the proposed theorems.

A General Class of Tests for Testing Homogeneity of Location Parameters against Umbrella Alternatives

In this paper, a general class of non-parametric tests for testing homogeneity of location parameter against umbrella alternatives is proposed. Testing for umbrella alternatives has many applications in the field of biology, medicine, botany, dose level testing, engineering, economics, psychology, zoology. As an example, the effectiveness of a drug is likely to increase with increase of dose up to a certain level and then its effect begins to decrease. The proposed test is based on linear combination of two-sample U-statistics. The null distribution of the test statistics is developed. We compare the test with some other competing tests in terms of Pitman asymptotic relative efficiency. To see execution of the test, a numerical example is provided. Simulation study is carried out to assess the power of proposed class of tests.

Robust Estimations for the Tail Index of Weibull-Type Distribution

Based on suitable left-truncated or censored data, two flexible classes of M-estimations of Weibull tail coefficient are proposed with two additional parameters bounding the impact of extreme contamination. Asymptotic normality with n -rate of convergence is obtained. Its robustness is discussed via its asymptotic relative efficiency and influence function. It is further demonstrated by a small scale of simulations and an empirical study on CRIX.

On Comparison of Local Polynomial Regression Estimators for P=0 and P=1 in a Model Based Framework

This article discusses the local polynomial regression estimator for and the local polynomial regression estimator for in a finite population. The performance criterion exploited in this study focuses on the efficiency of the finite population total estimators. Further, the discussion explores analytical comparisons between the two estimators with respect to asymptotic relative efficiency. In particular, asymptotic properties of the local polynomial regression estimator of finite population total for are derived in a model based framework. The results of the local polynomial regression estimator for are compared with those of the local polynomial regression estimator for studied by Kikechi et al (2018). Variance comparisons are made using the local polynomial regression estimator for and the local polynomial regression estimator for which indicate that the estimators are asymptotically equivalently efficient. Simulation experiments carried out show that the local polynomial regression estimator outperforms the local polynomial regression estimator in the linear, quadratic and bump populations.