Στην παρούσα διπλωματική εργασία επιχειρείται η ανάλυση και η εκτίμηση της συχνότητας απλών ημιτονοειδών σημάτων υπό την παρουσία λευκού Γκαουσιανού θορύβου (AWGN).Η εκτίμηση παραμέτρων απλών ημιτονοειδών σημάτων υπό την παρουσία προσθετικού Γκαουσιανού θορύβου αποτελεί ένα κλασσικό πρόβλημα και σημαντικό αντικείμενο μελέτης εξαιτίας της πληθώρας των εφαρμογών που έχει στην θεωρία ελέγχου, στην επεξεργασία σημάτων, στις ψηφιακές επικοινωνίες, στην βιοϊατρική τεχνολογία κ.α.Η εκτίμηση της συχνότητας είναι συνήθως το θέμα ‘ζωτικής σημασίας’ του προβλήματος για δύο σημαντικούς λόγους. Αφ’ενός οι συχνότητες πρέπει να εκτιμηθούν διότι αποτελούν μη-γραμμικές συναρτήσεις στην ληφθείσα ακολουθία δεδομένων και αφ’ ετέρου έχοντας καθοριστεί οι συχνότητες, οι υπόλοιπες παράμετροι του σήματος όπως είναι το πλάτος και η φάση του, μπορούν να υπολογιστούν άμεσα. Αρχικά γίνεται μία σύντομη εισαγωγή στις βασικές έννοιες πάνω στις οποίες δομείται η εκτίμηση παραμέτρων ενός ημιτονοειδούς σήματος και έπειτα παρουσιάζονται μερικοί αλγόριθμοι εκτίμησης. Πιο συγκεκριμένα παρουσιάζεται η διαδικασία κατασκευής τους και αναλύονται οι επιδόσεις τους. Τέλος παραθέτουμε και προσομοιώσεις μέσω υπολογιστή για κάθε αλγόριθμο ξεχωριστά και συγκρίνουμε την επίδοση του καθενός με τους υπόλοιπους. Από την σύγκριση αυτή γίνεται εξαγωγή χρήσιμων συμπερασμάτων σχετικά με τον προσδιορισμό των παραμέτρων κάθε αλγόριθμου αλλά και με την καταλληλότητα κάθε αλγόριθμου για συγκεκριμένες συνθήκες θορύβου. / In this thesis attempts to analyze and estimate the frequency of single sinusoid signals in Additive White Gaussian Noise (AWGN). Parameter estimation of sinusoids has been a classical problem and it is still an important research topic because of its numerous applications in multiple disciplines such as control theory, signal processing, digital communications, biomedical engineering etc. Estimation of the frequencies is often the crucial step in the problem for two principally reasons. Firstly, frequencies should be estimated because they are nonlinear functions in the received data sequence and secondly, once frequencies have been determined, the remaining parameters, such as amplitude and phase, can then be computed straightforwardly. Primarily we introduce some basic concepts on parameters estimation of sinusoid signals and then several estimation algorithms. More specifically shows the fabrication process of these algorithms and analyze their performance. Finally, we quote computer simulations for each algorithm separately and compare their performance. From these comparisons we can draw conclusions on the determination of parameters for each algorithm and the appropriateness of algorithms for specific noise conditions.

A Broadcast Channel is a communication path between a single source and two or more receivers or users. The source intends to communicate independent information to the users. A particular case of interest is the Gaussian Broadcast Channel (GBC) where the noise at each user is additive white Gaussian noise (AWGN). The capacity region of GBC is well known and the input to the channel is distributed as Gaussian. The capacity region of another special case of GBC namely Fading Broadcast Channel (FBC)was given in [Li and Goldsmith, 2001]and was shown that superposition of Gaussian codes is optimal for the FBC (treated as a vector degraded Broadcast Channel). The capacity region obtained when the input to the channel is distributed uniformly over a finite alphabet(Constellation)is termed as Constellation Constrained(CC) capacity region [Biglieri 2005]. In this thesis the CC capacity region for two-user GBC and the FBC are obtained. In case of GBC the idea of superposition coding with input from finite alphabet and CC capacity was explored in [Hupert and Bossert, 2007]but with some limitations. When the participating individual signal sets are nearly equal i.e., given total average power constraint P the rate reward α (also the power sharing parameter) is approximately equal to 0.5, we show via simulation that with rotation of one of the signal sets by an appropriate angle the CC capacity region is maximally enlarged. We analytically derive the expression for optimal angle of rotation. In case of FBC a heuristic power allocation procedure called finite-constellation power allocation procedure is provided through which it is shown (via simulation)that the ergodic CC capacity region thus obtained completely subsumes the ergodic CC capacity region obtained by allocating power using the procedure given in[Li and Goldsmith, 2001].It is shown through simulations that rotating one of the signal sets by an optimal angle (obtained by trial and error method)for a given α maximally enlarges the ergodic CC capacity region when finite-constellation power allocation is used. An expression for determining the optimal angle of rotation for the given fading state, is obtained. And the effect of rotation is maximum around the region corresponding to α =0.5. For both GBC and FBC superposition coding is done at the transmitter and successive decoding is carried out at the receivers.

Image De-noising forms an integral part of image processing. It is used as a standalone algorithm for improving the quality of the image obtained through camera as well as a starting stage for image processing applications like face recognition, super resolution etc. Non Local Means (NL-Means) and Bilateral Filter are two computationally complex de-noising algorithms which could provide good de-noising results. Due to its computational complexity, the real time applications associated with these letters are limited. In this thesis, we propose the use of hardware accelerators such as GPU (Graphics Processing Units) and FPGA (Field Programmable Gate Arrays) to speed up the filter execution and efficiently implement using them. GPU based implementation of these letters is carried out using Open Computing Language (Open CL). The basic objective of this research is to perform high speed de-noising without compromising on the quality. Here we implement a basic NL-Means filter, a Fast NL-Means filter, and Bilateral filter using Gauss Polynomial decomposition on GPU. We also propose a modification to the existing NL-Means algorithm and Gauss Polynomial Bilateral filter. Instead of Gaussian Spatial Kernel used in standard algorithm, Box Spatial kernel is introduced to improve the speed of execution of the algorithm. This research work is a step forward towards making the real time implementation of these algorithms possible. It has been found from results that the NL-Means implementation on GPU using Open CL is about 25x faster than regular CPU based implementation for larger images (1024x1024). For Fast NL-Means, GPU based implementation is about 90x faster than CPU implementation. Even with the improved execution time, the embedded system application of the NL-Means is limited due to the power and thermal restrictions of the GPU device. In order to create a low power and faster implementation, we have implemented the algorithm on FPGA. FPGAs are reconfigurable devices and enable us to create a custom architecture for the parallel execution of the algorithm. It was found that the execution time for smaller images (256x256) is about 200x faster than CPU implementation and about 25x faster than GPU execution. Moreover the power requirements of the FPGA design of the algorithm (0.53W) is much less compared to CPU(30W) and GPU(200W).

Approved for public release, distribution is unlimited / Orthogonal frequency division multiplexing (OFDM) is being successfully used in numerous applications. It was chosen for IEEE 802.11a wireless local area network (WLAN) standard, and it is being considered for the fourthgeneration mobile communication systems. Along with its many attractive features, OFDM has some principal drawbacks. Sensitivity to frequency errors is the most dominant of these drawbacks. In this thesis, the frequency offset and phase noise effects on OFDM based communication systems are investigated under a variety of channel conditions covering both indoor and outdoor environments. The simulation performance results of the OFDM system for these channels are presented. / Lieutenant Junior Grade, Turkish Navy

We implement a package for the construction of a new class of Low Density Parity Check (LDPC) codes based on a new random high girth graph construction technique, and study the performance of the codes so constructed on both the Additive White Gaussian Noise (AWGN) channel as well as the Binary Erasure Channel (BEC). Our codes are “near regular”, meaning thereby that the the left degree of any node in the Tanner graph constructed varies by at most 1 from the average left degree and so also the right degree. The simulations for rate half codes indicate that the codes perform better than both the regular Progressive Edge Growth (PEG) codes which are constructed using a similar random technique, as well as the MacKay random codes. For high rates the ARG (Almost Regular high Girth) codes perform better than the PEG codes at low to medium SNR’s but the PEG codes seem to do better at high SNR’s. We have tried to track both near codewords as well as small weight codewords for these codes to examine the performance at high rates. For the binary erasure channel the performance of the ARG codes is better than that of the PEG codes. We have also proposed a modification of the sum-product decoding algorithm, where a quantity called the “node credibility” is used to appropriately process messages to check nodes. This technique substantially reduces the error rates at signal to noise ratios of 2.5dB and beyond for the codes experimented on. The average number of iterations to achieve this improved performance is practically the same as that for the traditional sum-product algorithm.

This work is focused on the subject of the interference modelling for xDSL technologies. First, the xDSL technologies are explained. Following is the presentation and description of the different kinds of the xDSL technologies. The next part deals with the basic parameters of metallic cable lines – especially the primary and secondary parameters. Nowadays wider bandwidths are used for the achievement of higher data transmission rates. During a higher frequency signal transmission a more intensive line attenuation appears. To identify the transfer characteristics of the lines while using an xDSL system, mathematic models of transmission lines are applied. That is why these mathematic models are dealt with in the next chapter. At the end of this section the mathematic models are compared using the modular and phase characteristics. The main aim of the work is to describe the different impacts which influence the efficiency of the xDSL systems. First, the causes interfering from the inside of the cable are deeply explained: Near End Crosstalk (NEXT), Far End Crosstalk (FEXT), Additive White Gaussian Noise (AWGN). Following is the explanation of the external interfering impacts: Radio Frequency Interference (RFI) and Impulse Noise. The next goal of this thesis is a design of a workstation for the tests of spectral features and the efficiency of the xDSL systems. The work also presents a designed GUI application and its description. The GUI application is an instrument for the choice or data entry of the final interference. The last chapter describes a realization of a measurement and shows the measured characteristics which were recorded on the ADSL tester and oscilloscope.

The thesis concerns the problem of interference modelling for xDSL technologies and Ethernet. The introduction describes the origin of crosstalk, that arise during the operation of the systems and the physical properties of the lines, therefore, the next section describes the properties of the primary and secondary parameters of the homogenous line and their modelling. In order to achieve higher data rates on the metallic line, systems with larger frequency spectrum are applied, resulting in a greater attenuation of the line. This issue and the characteristics determination of the transmission systems are subjects of the mathematical models, which are divided according to the modelling of primary or secondary parameters. The main goal of this work is to describe the effects which influence the performance of data transfer via xDSL and Ethernet technology focusing on internal and external disturbances acting on the cable lines. This is the crosstalk at the near and far end, adaptive white noise, radio frequency interference RFI and impulse noise. Following part of the thesis deals with the properties of xDSL technologies, specifically ADSL2+ and VDSL2 and Ethernet. Another aim is to design applications which enable to test the performance of xDSL and Ethernet transmission systems with its own award simulations interference. The conclusion describes the design and implementation of laboratory experiments for measuring of the efficiency and spectral properties of xDSL. The proposed laboratory protocols are annexed to this thesis, including the measured waveforms.