Theses supervised by Yrd. Doç. Dr. Sinan Gezici
10 theses · İhsan Doğramacı Bilkent University
Gürültü ile geliştirilmiş sezim
Performance of some suboptimal detectors can be improved by adding independent noise to their measurements. Improving the performance of a detector by adding a stochastic signal to the measurement can be considered in the framework of stochastic resonance (SR), which can be regarded as the observation of "noise benefits" related to signal transmission in nonlinear systems. Such noisebenefits can be in various forms, such as a decrease in probability of error, or an increase in probability of detection under a false-alarm rate constraint. The main focus of this thesis is to investigate noise benefits in the Bayesian, minimax and Neyman-Pearson frameworks, and characterize optimal additional noisecomponents, and quantify their effects.In the first part of the thesis, a Bayesian framework is considered, and the previous results on optimal additional noise components for simple binary hypothesis-testing problems are extended to M-ary composite hypothesis-testing problems. In addition, a practical detection problem is considered in the Bayesian framework. Namely, binary hypothesis-testing via a sign detector is studied for antipodal signals under symmetric Gaussian mixture noise, and the effects of shifting the measurements (observations) used by the sign detector are investigated. First, a sufficient condition is obtained to specify when the sign detector based on the modified measurements (called the "modified" sign detector) can have smaller probability of error than the original sign detector. Also, two sufficient conditions under which the original sign detector cannot be improved by measurement modification are derived in terms of desired signal and Gaussian mixture noise parameters. Then, for equal variances of the Gaussian components in the mixture noise, it is shown that the probability of error for the modified detector is a monotone increasing function of the variance parameter, which is not always true for the original detector. In addition, the maximum improvement, specified as the ratio between the probabilities of error for the original and the modified detectors, is specified as 2 for infinitesimally small variances of the Gaussian components in the mixture noise. Finally, numerical examples are presented to support the theoretical results, and some extensions to the case of asymmetric Gaussian mixture noise are explained.In the second part of the thesis, the effects of adding independent noise to measurements are studied for M-ary hypothesis-testing problems according to the minimax criterion. It is shown that the optimal additional noise can be represented by a randomization of at most M signal values. In addition, a convexrelaxation approach is proposed to obtain an accurate approximation to the noise probability distribution in polynomial time. Furthermore, sufficient conditions are presented to determine when additional noise can or cannot improve the performance of a given detector. Finally, a numerical example is presented.Finally, the effects of additional independent noise are investigated in the Neyman-Pearson framework, and various sufficient conditions on the improvability and the non-improvability of a suboptimal detector are derived. First, a sufficient condition under which the performance of a suboptimal detector cannot be enhanced by additional independent noise is obtained according to the Neyman-Pearson criterion. Then, sufficient conditions are obtained to specify when the detector performance can be improved. In addition to a generic condition, various explicit sufficient conditions are proposed for easy evaluation ofimprovability. Finally, a numerical example is presented and the practicality of the proposed conditions is discussed.
Darbe doppler radar sistemlerinde doppler frekansı kestirimi
Pulse Doppler radar systems are one of the most common types of radar systems, especially in military applications. These radars are mainly designed to estimate two basic parameters of the targets, range and Doppler frequency. A common procedure of estimating those parameters is matched filtering, followed by pulse Doppler processing, and finally one of the several constant false alarm rate (CFAR) algorithms. However, because of the structure of the waveform obtained after pulse Doppler processing, CFAR algorithms cannot always findthe Doppler frequency of a target accurately. In this thesis, two different algorithms, maximum selection and successive cancelation, are proposed and their performances are compared with the optimal maximum likelihood (ML) solution. These proposed algorithms both utilize the advantage of knowing the waveform structure of a point target obtained after pulse Doppler processing in the Doppler frequency domain. Maximum selection basically chooses the Doppler frequency cells with the largest amplitudes to be the ones where there is a target. On the other hand, successive cancelation is an iterative algorithm. In each iteration,it finds a target that minimizes a specific cost function, until there are no more targets. The performances of these algorithms are investigated for several different point target scenarios. Moreover, the performances of the algorithms are tested on some realistic target models. Based on all those observations, it is concluded that maximum selection is a good choice for high SNR values when a low-complexity algorithm is needed, on the other hand, successive cancelation performs almost as well as the optimal solution at all SNR values.
Bilişsel radyo sistemlerinde ve çok girişli çok çıkışlı sistemlerde zaman gecikmesi kestirimi
In this thesis, the time-delay estimation problem is studied for cognitive radio systems, multiple-input single-output (MISO) systems, and cognitive single-input multiple-output (SIMO) systems. A two-step approach is proposed for cognitive radio and cognitive SIMO systems in order to perform time-delay estimation with significantly lower computational complexity than the optimal maximum likelihood (ML) estimator. In the first step of this two-step approach, an ML estimator is used for each receiver branch in order to estimate the unknown parameters of the signal received via that branch. Then, in the second step, the estimates from the first step are combined in various ways in order to obtain the final time-delay estimate. The combining techniques that are used in the second step are called optimal combining, signal-to-noise ratio (SNR) combining, selection combining, and equal combining. It is shown that the performance of the optimal combining technique gets very close to the Cramer-Rao lower bound (CRLB) at high SNRs. These combining techniques provide various mechanisms for diversity combining for time-delay estimation and extend the concept of diversity in communications systems to the time-delay estimation problem in cognitive radio and cognitive SIMO systems. Simulation results are presented to evaluate the performance of the proposed estimators and to verify the theoretical analysis. For the solution of the time-delay estimation problem in MISO systems, ML estimation based on a genetic global optimization algorithm, namely, differential evolution (DE), is proposed. This approach is proposed in order to decrease the computational complexity of the ML estimator, which results in a complex optimization problem in general. A theoretical analysis is carried out by deriving the CRLB. Simulation studies for Rayleigh and Rician fading scenarios are performed to investigate the performance of the proposed algorithm.
Dikgen frekans bölmeli çoğullamaya dayalı akıllı radyo sistemlerinde varış zamanı kestirimi
Cognitive radio (CR) systems can efficiently utilize the radio spectrum due to their ability to sense environmental conditions and adapt their communications parameters (such as power,carrier frequency, and modulation) so as to enable dynamic reuse of the available spectrum. In this thesis, theoretical limits on time-of-arrival (TOA) estimation are derived for CRsystems in the presence of interference. Specifically, closed form expressions are obtained for Cramer-Rao bounds (CRBs) on TOA estimation in orthogonal frequency division multiplexing(OFDM) based CR systems in various scenarios. Based on the CRB expressions, an optimal power allocation strategy that provides the best possible TOA estimation accuracy is proposed. This strategy considers the constraints imposed by regulatory emission mask and the sensed interference spectrum.The maximum likelihood (ML) TOA estimator is derived for an OFDM-based signalling scheme, and its performance is investigated against the theoretical limits offered by the CRBexpressions. In addition, numerical results for the CRBs and ML TOA estimator are obtained and the effects of the optimal power allocation strategy on the accuracy of ML TOA estimator are examined in the absence / presence of interference. The use of optimal power allocation strategy insteadof the conventional power assignment scheme is demonstrated to provide significant gains in terms of the TOA estimation accuracy. Analysis of the performance sensitivity of the optimal powerallocation strategy to the uncertainty in spectrum estimation is performed, and the performance of optimal power allocation is observed to be consistently superior to that of the uniform powerallocation even for substantially high values of spectral estimation errors.
Nicemlenmiş gözlemler kullanarak gürültü ile geliştirilmiş parametre kestirimi
In this thesis, optimal additive noise is characterized for both single and multiple parameter estimation based on quantized observations. In both cases, first, optimal probability distribution of noise that should be added to observations is formulated in terms of a Cramer-Rao lower bound (CRLB) minimization problem. In the single parameter case, it is proven that optimal additive ``noise'' can be represented by a constant signal level, which means that randomization of additive signal levels (equivalently, quantization levels) are not needed for CRLB minimization. In addition, the results are extended to the cases in which there exists prior information about the unknown parameter and the aim is to minimize the Bayesian CRLB (BCRLB). Then, numerical examples are presented to explain the theoretical results. Moreover, performance obtained via optimal additive noise is compared to performance of the commonly used dither signals. Furthermore, mean-squared error (MSE) performances of maximum likelihood (ML) and maximum a-posteriori probability (MAP) estimates are investigated in the presence and absence of additive noise. In the multiple parameter case, the form of the optimal random additive noise is derived for CRLB minimization. Next, the theoretical result is supported with a numerical example, where the optimum noise is calculated by using the particle swarm optimization (PSO) algorithm. Finally, the optimal constant noise in the multiple parameter estimation problem in the presence of prior information is discussed.
Darbe-doppler radar sistemlerinde parazit yankı tespiti
Among various types of radar systems, the pulse-Doppler radar is the most widely used one, especially in military applications. Pulse Doppler radars have a primary objective to detect and estimate the range and the radial velocity of the targets. In order to have a basis for the detection, first reflected echo signals are matched filtered and then the time-alligned pulse returns are transformed to the Fourier domain to obtain the range-Doppler matrix. The resulting range-Doppler matrix is input to target detection algorithms. For this purpose, constant false alarm rate (CFAR) algorithms are run on the range-Doppler matrix. It is useful to run different CFAR algorithms inside the clutter region and outside the clutter region because the statistics are different inside and outside of the clutter. In order to achieve this discrimination, the position of the clutter has to be detected in the range-Doppler matrix. Moreover, the clutter may not always appear around zero Doppler frequency when realistic terrain models and moving platforms are considered. Two algorithms for clutter detection using range-Doppler matrix elements are investigated and their performance analysis is presented in this thesis. The first algorithm has higher error rates but lower computational complexity, whereas, the second one has lower error rates but higher computational complexity. Both algorithms detect clutter position by filtering the range-Doppler matrix elements via non-linear filters. In addition to the probabilistic error rate analysis, simulation results on some realistic cases are presented. It is concluded that the first algorithm is a good choice for low clutter-to-noise ratio values when a low-complexity algorithm is required. On the other hand, the second algorithm has better performance in all clutter-to-noise ratio values but it requires more computational power.
Güç kısıtlamalı haberleşme sistemleri için stokastik işaretleme
In this thesis, optimal stochastic signaling problem is studied for power constrained communications systems. In the first part, optimal stochastic signaling problem is investigated for binary communications systems under second and fourth moment constraints for any given detector structure and noise probability distribution. It is shown that an optimal signal can be represented by randomizationamong at most three signal levels for each symbol. Next, stochastic signaling problem is studied in the presence of an average power constraint instead of second and fourth moment constraints. It is shown that an optimal signal can be represented by randomization between at most two signal levels for each symbol in this case. For both scenarios, sufficient conditions are obtained to determine the improvability and nonimprovability of conventional deterministic signaling via stochastic signaling. In the second part of the thesis, the joint design of optimal signals and optimal detector is studied for binary communications systems under average power constraints in the presence of additive non-Gaussian noise. It is shown that the optimal solution involves randomization between at most two signal levels and the use of the corresponding maximum a posteriori probability (MAP) detector. In the last part of the thesis, stochastic signaling is investigated for power-constrained scalar valued binary communications systems in the presence of uncertainties in channel state information (CSI). First, stochastic signaling is performed based on the available imperfect channel coefficient at the transmitter to examine the effects of imperfect CSI. The sufficient conditions are derived for improvability and nonimprovability of deterministic signaling via stochastic signaling in the presence of CSI uncertainty. Then, two different stochastic signaling strategies, namely, robust stochastic signaling and stochastic signaling with averaging, are proposed for designing stochastic signals under CSI uncertainty. For the robust stochastic signaling problem, sufficient conditions are derived to obtain an equivalent form which is simpler to solve. In addition, it is shown that optimal signals for each symbol can be written as randomization between at most two signal levels for stochastic signaling using imperfect channel coefficient and stochastic signaling with averaging as well as for robust stochastic signaling under certain conditions. The solutions of the optimal stochastic signaling problems are obtained by using global optimization techniques, specifically, Particle Swarm Optimization (PSO), and by employing convex relaxation approaches. Numerical examples are presented to illustrate the theoretical results at the end of each part.
Referans kodlamalı ultra geniş bantlı bir sistemin gerçeklenmesi
Coded-reference ultra-wideband (CR UWB) systems provide orthogonalizationof the reference and data signals in the code domain to facilitate communicationswithout the need for complex channel estimation and have significantadvantages over the previous techniques in terms of performance and/or implementationcomplexity. This thesis presents a UWB testbed as a general experimentalplatform to explore pulse-based UWB communications and discussesdesign and implementation issues. A testbed is built as a flexible solution forhardware implementation of a CR UWB system.
Kısmi bilgi bulunan hipotez sınama problemlerinde alternatif yaklaşımlar ve gürültü kazanımları
Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In the first part of the dissertation, the effects of additive noise are studied according to the restricted Bayes criterion, which provides a generalization of the Bayes and minimax criteria. Based on a generic M-ary composite hypothesis-testing formulation, the optimal probability distribution of additive noise is investigated. Also, sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived. In addition, simple hypothesis-testing problems are studied in more detail, and additional improvability conditions that are specific to simple hypotheses are obtained. Furthermore, the optimal probability distribution of the additive noise is shown to include at most M mass points in a simple M-ary hypothesis-testing problem under certain conditions. Then, global optimization, analytical and convex relaxation approaches are considered to obtain the optimal noise distribution. Finally, detection examples are presented to investigate the theoretical results.In the second part of the dissertation, the effects of additive noise are studied for M-ary composite hypothesis-testing problems in the presence of partial prior information. Optimal additive noise is obtained according to two criteria, which assume a uniform distribution (Criterion 1) or the least-favorable distribution (Criterion 2) for the unknown priors. The statistical characterization of the optimal noise is obtained for each criterion. Specifically, it is shown that the optimal noise can be represented by a constant signal level or by a randomization of a finite number of signal levels according to Criterion 1 and Criterion 2, respectively. In addition, the cases of unknown parameter distributions under some composite hypotheses are considered, and upper bounds on the risks are obtained. Finally, a detection example is provided to illustrate the theoretical results.In the third part of the dissertation, the effects of additive noise are studied for binary composite hypothesis-testing problems. A Neyman-Pearson (NP) framework is considered, and the maximization of detection performance under a constraint on the maximum probability of false-alarm is studied. The detection performance is quantified in terms of the sum, the minimum and the maximum of the detection probabilities corresponding to possible parameter values under the alternative hypothesis. Sufficient conditions under which detection performance can or cannot be improved are derived for each case. Also, statistical characterization of optimal additive noise is provided, and the resulting false-alarm probabilities and bounds on detection performance are investigated. In addition, optimization theoretic approaches for obtaining the probability distribution of optimal additive noise are discussed. Finally, a detection example is presented to investigate the theoretical results.Finally, the restricted NP approach is studied for composite hypothesis testing problems in the presence of uncertainty in the prior probability distribution under the alternative hypothesis. A restricted NP decision rule aims to maximize the average detection probability under the constraints on the worst-case detection and false-alarm probabilities, and adjusts the constraint on the worst-case detection probability according to the amount of uncertainty in the prior probability distribution. Optimal decision rules according to the restricted NP criterion are investigated, and an algorithm is provided to calculate the optimal restricted NP decision rule. In addition, it is observed that the average detection probability is a strictly decreasing and concave function of the constraint on the minimum detection probability. Finally, a detection example is presented, and extensions to more generic scenarios are discussed.
Bilişsel radyo sistemlerinde kısıtlı Neyman-Pearson yaklaşımı tabanlı spektrum sezme
Over the past decade, the demand for wireless technologies has increased enormously, which leads to a perceived scarcity of the frequency spectrum. Meanwhile, static allocation of the frequency spectrum leads to under-utilization of the spectral resources. Therefore, dynamic spectrum access has become a necessity. Cognitive radio has emerged as a key technology to solve the conflicts between spectrum scarcity and spectrum under-utilization. It is an intelligent wireless communication system that is aware of its operating environment and can adjust its parameters in order to allow unlicensed (secondary) users to access and communicate over the frequency bands assigned to licensed (primary) users when they are inactive. Therefore, cognitive radio requires reliable spectrum sensing techniques in order to avoid interference to primary users. In this thesis, the spectrum sensing problem in cognitive radio is studied. Specifically, the restricted Neyman-Pearson (NP) approach, which maximizes the average detection probability under the constraints on the minimum detection and false alarm probabilities, is applied to the spectrum sensing problem in cognitive radio systems in the presence of uncertainty in the prior probability distribution of primary users? signals. First, we study this problem in the presence of Gaussian noise and assume that primary users? signals are Gaussian. Then, the problem is reconsidered for non-Gaussian noise channels. Simulation results are obtained in order to compare the performance of the restricted NP approach with the existing methods such as the generalized likelihood ratio test (GLRT) and energy detection. The restricted NP approach outperforms energy detection in all cases. It is also shown that the restricted NP approach can provide important advantages over the GLRT in terms of the worst-case detection probability, and sometimes in terms of the average detection probability depending on the situationin the presence of imperfect prior information for Gaussian mixture noise channels.