Blind estimation of unknown channel parameters and data symbol detection represent major open problems in non-cooperative communication systems such as automatic modulation classification (AMC). This thesis focuses on estimating the symbol rate and detecting the data symbols. A blind oversampling-based signal detector under the circumstance of unknown symbol period is proposed. The thesis consists of two parts: a symbol rate estimator and a symbol detector. First, the symbol rate is estimated using the EM algorithm. In the EM algorithm, it is difficult to obtain the closed form of the log-likelihood function and the density function. Therefore, both functions are approximated by using the Particle Filter (PF) technique. In addition, the symbol rate estimator based on cyclic correlation is proposed as an initialization estimator since the EM algorithm requires initial estimates. To take advantage of the cyclostationary property of the received signal, there is a requirement that the sampling period should be at least four times less than the symbol period on the receiver side. Second, the blind data symbol detector based on the PF algorithm is designed. Since the signal is oversampled at the receiver side, a delayed multi-sampling PF detector is proposed to manage inter-symbol interference, which is caused by over- sampling, and to improve the demodulation performance of the data symbols. In the PF algorithm, the hybrid importance function is used to generate both data samples and channel model coe±cients, and the Mixture Kalman Filter (MKF) algorithm is used to marginalize out the fading channel coe±cients. At the end, two resampling schemes are adopted.

For ultra-wideband (UWB) communications, acquisition is challenging. The reason is from the ultra short pulse shape and ultra dense multipath interference. Ultra short pulse indicates the acquisition region is very narrow. Sampling is another challenge for UWB design due to the need for ultra high speed analog-to digital converter.<p>A sub-optimum and under-sampling scheme using pilot codes as transmitted reference is proposed here for acquisition. The sampling rate for the receiver is at the symbol rate. A new architecture, the reference aided matched filter is studied in this project. The reference aided matched filter method avoids using complex rake receiver to estimate channel parameters and high sampling rate for interpolation. A limited number of matched filters are used as a filter bank to search for the strongest path. Timing offset for acquisition is then estimated and passed to an advanced verification algorithm. For optimum performance of acquisition, the adaptive post detection integration is proposed to solve the problem from dense inter-symbol interference during the acquisition. A low-complex early-late gate tracking loop is one element of the adaptive post detection integration. This tracking scheme assists in improving acquisition accuracy. The proposed scheme is evaluated using Matlab Simulink simulations in term of mean acquisition time, system performance and false alarm. Simulation results show proposed algorithm is very effective in ultra dense multipath channels. This research proves reference aided acquisition with tracking loop is promising in UWB application.

For ultra-wideband (UWB) communications, acquisition is challenging. The reason is from the ultra short pulse shape and ultra dense multipath interference. Ultra short pulse indicates the acquisition region is very narrow. Sampling is another challenge for UWB design due to the need for ultra high speed analog-to digital converter.<p>A sub-optimum and under-sampling scheme using pilot codes as transmitted reference is proposed here for acquisition. The sampling rate for the receiver is at the symbol rate. A new architecture, the reference aided matched filter is studied in this project. The reference aided matched filter method avoids using complex rake receiver to estimate channel parameters and high sampling rate for interpolation. A limited number of matched filters are used as a filter bank to search for the strongest path. Timing offset for acquisition is then estimated and passed to an advanced verification algorithm. For optimum performance of acquisition, the adaptive post detection integration is proposed to solve the problem from dense inter-symbol interference during the acquisition. A low-complex early-late gate tracking loop is one element of the adaptive post detection integration. This tracking scheme assists in improving acquisition accuracy. The proposed scheme is evaluated using Matlab Simulink simulations in term of mean acquisition time, system performance and false alarm. Simulation results show proposed algorithm is very effective in ultra dense multipath channels. This research proves reference aided acquisition with tracking loop is promising in UWB application.

We propose to develop new non-data aided (NDA) digital feedforward symbol timing estimators for linear and nonlinear modulations, with a view to reducing the sampling rate of the estimators. The proposed estimators rely on the fact that sufficient statistics exist for a signal sampled at the Nyquist rate. We propose an ad hoc extension to the timing estimator based on the log nonlinearity which performs better than existing estimators at this rate when the operating signal-to-noise ratio (SNR) and the excess bandwidth are low. We propose another alternative estimator for operating at the Nyquist rate that has reduced self-noise at high SNR for large rolloff factors. This can be viewed as an extension of the timing estimator based on the square law nonlinearity. For continuous phase modulations (CPM), we propose two novel estimators that can operate at the symbol rate for MSK type signals. Among the class of NDA feedforward timing estimators we are not aware of any other estimator that can function at symbol rate for this type of signals. We also propose several new estimators for the MSK modulation scheme which operate with reduced sampling rate and are robust to carrier frequency offset and phase offset.

This thesis proposes a blind receiver for the Nyquist pulse shaped quadratureamplitude modulation (QAM) signals. The focus is on single carrier signals. The blind receiver includes the estimation of the symbol rate, the roll-off factor of the filter, the optimal sample phase, the frequency offset, the phase offset and as well as the correction of frequency and phase offsets. The blind receiver is proposed for the cognitive radio applications. Cognitive radios are intelligent devices which can adapt themselves according to its user and its environment, i.e. they are aware of the user and the environment. Another importance of cognitive radios is they can detect the incoming signal and demodulate it and also respond to the transmitting node with the same parameters. In order to demodulate the signal and to respond the transmitter node, there are some parameters which are needed to be known. The estimation starts with the bandwidth and carrier frequency, continued by the estimation of the symbol rate, which is a crucial factor. After the estimation and restrictions of these parameters, the roll-off factor of the filter is estimated for match filtering to remove the inter symbol interference (ISI) effect. Then the optimal sample phase is detected and the signal is downsampled. The following procedures include the modulation identification and estimation and correction of both frequency and phase offsets. The estimation algorithms performance is compared to the performances of the other algorithms available in the literature. These simulation results are presented and discussed in this thesis.

In this thesis work, automatic recognition algorithms for digital modulated signals are surveyed. Feature extraction and classification algorithm stages are the main parts of a modulation recognition system. Performance of the modulation recognition system mainly depends on the prior knowledge of some of the signal parameters, selection of the key features and classification algorithm selection. Unfortunately, most of the features require some of the signal parameters such as carrier frequency, pulse shape, time of arrival, initial phase, symbol rate, signal to noise ratio, to be known or to be extracted. Thus, in this thesis, features which do not require prior knowledge of the signal parameters, such as the number of the peaks in the envelope histogram and the locations of these peaks, the number of peaks in the frequency histogram, higher order moments of the signal are considered. Particularly, symbol rate and signal to noise ratio estimation methods are surveyed. A method based on the cyclostationarity analysis is used for symbol rate estimation and a method based on the eigenvector decomposition is used for the estimation of signal to noise ratio. Also, estimated signal to noise ratio is used to improve the performance of the classification algorithm. Two methods are proposed for modulation recognition: 1) Decision tree based method 2) Bayesian based classification method A method to estimate the symbol rate and carrier frequency offset of minimum-shift keying (MSK) signal is also investigated.

Quadrature modulator (demodulator) is used in transmitting (receiving) part of many devices. Unwanted imbalance can influence amplitude, phase or DC offset of modulator (demodulator). Correction of imbalance was a main subject of thesis. Simulations of these methods were created in MATLAB and results were compared. Basics of methods were implement on programmable logic field by program Xilinx ISE. Development kit V2MB1000 with analogue board Memec P160 was chosen for this purpose. In the last part were compare simulation results with practical measurement.

<p dir="ltr">This work will introduce a channel conceptualization and possible coding scheme for Graph-and-Symbol (GS) Communication. While Claude Shannon’s mathematical model for communication employed graphs to describe relationships and confusability among traditional time-sequenced signals, little work as been done to describe non-linear communication <i>with</i> graphs where we transmit and receive physical structures of information. The principal contribution of this work is to introduce a mathematical framework for communication with graphs which have symbols assigned to vertices. This looks like a molecule, and so we may think of these messages as coded forms of molecular communication.</p><p dir="ltr">At this time, many problems in this area will (and may remain) computationally intractable, but as the field of graph theory continues to develop, new tools and techniques may emerge to solve standing problems in this new subfield of communication.</p><p dir="ltr">Graphs present two difficulties: first, they contain ambiguities among their vertices and do not have an <i>a priori</i> canonical ordering, and second, the relationships among graphs lack structural regularities which we see in traditional error control coding lattices. There are no Galois fields to exploit over graph-based codes as we have with cyclic codes, for example. Furthermore, the shear number of graphs of order n grows so rapidly that it is difficult to account for the neighborhoods around codewords and effectively reduce communication errors which may occur. The more asymmetric a graph is, the more orderings on symbols it can support. However, asymmetries complicate the computation of channel transition probabilities, which are the cornerstone of all communication theory.</p><p dir="ltr">In the prologue, the reader will be introduced to a new educational tool for designing traditional binary cyclic codes.</p><p dir="ltr">1 through 10 will detail the development of Graph-and-Symbol (GS) Commu- nication to date followed by two example codes which demonstrate the power of structuring information on graphs.</p><p dir="ltr">Chapter 13 onward will review the preliminary work in another area of research, disjoint from the main body. It is included here for posterity and special interests in applying graphs to solving other problems in signal processing. It begins with an introduction of spacetime raythic graphs. We propose a new chamfering paradigm for connecting neighboring pixels which approximates solutions to the eikonal equation. We show that some raythic graphs possess structures with multiple, differing solutions to eikonal wavefront propagation which are essential to the construction of the Umbral Transform. This umbral transform emulates ray casting effects, such as shadows and diffraction within an image space, from a network-flow algorithm.</p><p dir="ltr">This work may be duplicated in whole or in part for educational purposes only. All other rights of this work are reserved by the author, Timothy Arthur Terlep Jr., of Rose-Hulman Institute of Technology, Terre Haute, IN (effective August 2024), and subject to the rules and regulations of the Graduate School of Purdue University.</p><p dir="ltr">Readers may contact the author with any comments and questions at <b>taterlep@gmail.com</b></p>