<p>This Master thesis deals with wave propagation and starts with wave propagation basics. It briefly presents the theory for the diffraction over terrain obstacles and describes two different path loss models, the Hata model and a FFT-based model. The significance of this paper is that it gives the simulation results for the models mentioned above and presents a comparison between the results obtained from an empirical formula and the FFT-model. The comparison shows that the approach based on Fast Fourier Transform is good enough for prediction of the path loss and that it is a time efficient method.</p>

In this paper, the precorrected-FFT method is used to solve the electromagnetic scattering from two-dimensional cavities of arbitrary shape. The integral equation is discretized by the method of moments and the resultant matrix equation is solved iteratively by the generalized conjugate residual method. Instead of directly computing the matrix-vector multiplication, which requires N² operations, this approach reduces the computation complexity to O(N log N) as well as avoids the storage of large matrices. At the same time, a technique known as the complexifying k is applied to accelerate the convergence of the iterative method in solving this resonance problem. Some examples are considered and excellent agreements of radar cross sections between these computed using the present method and those from the direct solution are observed, demonstrating the feasibility and efficiency of the present method. / Singapore-MIT Alliance (SMA)

This paper presents an accurate and efficient method-of-moments solution of the electrical-field integral equation (EFIE) for large, three-dimensional, arbitrarily shaped objects. In this method, the generalized conjugate residual method (GCR) is used to solve the matrix equation iteratively and the precorrected-FFT technique is then employed to accelerate the matrix-vector multiplication in iterations. The precorrected-FFT method eliminates the need to generate and store the usual square impedance matrix, thus leading to a great reduction in memory requirement and execution time. It is at best an O(N log N) algorithm and can be modified to fit a wide variety of systems with different Green’s functions without excessive effort. Numerical results are presented to demonstrate the accuracy and computational efficiency of the technique. / Singapore-MIT Alliance (SMA)

On présente ici un ensemble de méthodes numériques performantes pour lasimulation micromagnétique 3D reposant sur l'équation de Landau-Lifchitz-Gilbert, constituantun code nommé feeLLGood. On a choisi l'approche éléments finis pour sa flexibilitégéométrique. La formulation adoptée respecte la contrainte d'orthogonalité entre l'aimantationet sa dérivée temporelle, contrairement à la formulation classique sur-dissipative.On met au point un schéma de point milieu pour l'équation Landau-Lifchitz-Gilbert quiest stable et d'ordre deux en temps. Cela permet de prendre, à précision égale, des pas detemps beaucoup plus grands (typiquement un ordre de grandeur) que les schémas classiques.Un véritable enjeu numérique est le calcul du champ démagnétisant, non local. Oncompare plusieurs techniques de calcul rapide pour retenir celles, inédites dans le domaine,des multipôles rapides (FMM) et des transformées de Fourier hors-réseau (NFFT). Aprèsavoir validé le code sur des cas-tests et établi son efficacité, on présente les applications àla simulation des nanostructures : sélection de chiralité et résonance ferromagnétique d'unplot monovortex de cobalt, hystérésis des chapeaux de Néel dans un plot allongé de fer.Enfin, l'étude d'un oscillateur spintronique prouve l'évolutivité du code.

In a typical orthogonal frequency division multiplexing (OFDM) broadband wireless communication system, a guard interval using cyclic prefix is inserted to avoid the inter-symbol interference and the inter-carrier interference. This guard interval is required to be at least equal to, or longer than the maximum channel delay spread. This method is very simple, but it reduces the transmission efficiency. This efficiency is very low in the communication systems, which inhibit a long channel delay spread with a small number of sub-carriers such as the IEEE 802.11a wireless LAN (WLAN). To increase the transmission efficiency, it is usual that a time domain equalizer (TEQ) is included in an OFDM system to shorten the effective channel impulse response within the guard interval. There are many TEQ algorithms developed for the low rate OFDM applications such as asymmetrical digital subscriber line (ADSL). The drawback of these algorithms is a high computational load. Most of the popular TEQ algorithms are not suitable for the IEEE 802.11a system, a high data rate wireless LAN based on the OFDM technique. In this thesis, a TEQ algorithm based on the minimum mean square error criterion is investigated for the high rate IEEE 802.11a system. This algorithm has a comparatively reduced computational complexity for practical use in the high data rate OFDM systems. In forming the model to design the TEQ, a reduced convolution matrix is exploited to lower the computational complexity. Mathematical analysis and simulation results are provided to show the validity and the advantages of the algorithm. In particular, it is shown that a high performance gain at a data rate of 54Mbps can be obtained with a moderate order of TEQ finite impulse response (FIR) filter. The algorithm is implemented in a field programmable gate array (FPGA). The characteristics and regularities between the elements in matrices are further exploited to reduce the hardware complexity in the matrix multiplication implementation. The optimum TEQ coefficients can be found in less than 4µs for the 7th order of the TEQ FIR filter. This time is the interval of an OFDM symbol in the IEEE 802.11a system. To compensate for the effective channel impulse response, a function block of 64-point radix-4 pipeline fast Fourier transform is implemented in FPGA to perform zero forcing equalization in frequency domain. The offsets between the hardware implementations and the mathematical calculations are provided and analyzed. The system performance loss introduced by the hardware implementation is also tested. Hardware implementation output and simulation results verify that the chips function properly and satisfy the requirements of the system running at a data rate of 54 Mbps.

A fixed terrestrial wireless system such as the Microwave Multi-channel Distribution Service (MMDS) can be used as the ``last mile' to provide a high speed Internet connection from a base station to a home in a rural or suburban residential area. Such a broadband wireless system works very well under line-of-sight transmission. It works quite well even if the line-of-sight is obstructed with a large number of trees. However, when trees obstruct the line-of-sight, under conditions of wind, the user may experience loss of the RF signal from time to time. This is especially true under gusty conditions. As part of this research a high precision DSP-based measuring system is devised to accurately measure and characterize the distortions caused by tree foliage on the RF line-of-sight signal. The approach is to digitally generate a signal composed of several tones, up-convert the signal to 2.5 GHz and send it through tree foliage to a receiver where the signal is down-converted and sampled for a duration of five seconds. The samples collected are processed using Matlab to compute the temporal amplitude and phase variations of the tones. The measurement system provides estimates of the amplitude and phase of the receive tones with a time resolution of 3.2 ms. The standard deviation of the amplitude estimates is 0.3\% of the actual amplitude of the tones and the standard deviation of the phase estimates is 0.23 degree. This accuracy is obtained when the signal-to-noise ratio of the receive signal is greater than 20 dB. Measurement in the field with tree foliage in the line-of-sight shows that the swaying of the branches in the wind can cause rapid signal fading. This research determines the type of fade, the depth and duration of the fade, as well as the fading rate.

In a typical orthogonal frequency division multiplexing (OFDM) broadband wireless communication system, a guard interval using cyclic prefix is inserted to avoid the inter-symbol interference and the inter-carrier interference. This guard interval is required to be at least equal to, or longer than the maximum channel delay spread. This method is very simple, but it reduces the transmission efficiency. This efficiency is very low in the communication systems, which inhibit a long channel delay spread with a small number of sub-carriers such as the IEEE 802.11a wireless LAN (WLAN). To increase the transmission efficiency, it is usual that a time domain equalizer (TEQ) is included in an OFDM system to shorten the effective channel impulse response within the guard interval. There are many TEQ algorithms developed for the low rate OFDM applications such as asymmetrical digital subscriber line (ADSL). The drawback of these algorithms is a high computational load. Most of the popular TEQ algorithms are not suitable for the IEEE 802.11a system, a high data rate wireless LAN based on the OFDM technique. In this thesis, a TEQ algorithm based on the minimum mean square error criterion is investigated for the high rate IEEE 802.11a system. This algorithm has a comparatively reduced computational complexity for practical use in the high data rate OFDM systems. In forming the model to design the TEQ, a reduced convolution matrix is exploited to lower the computational complexity. Mathematical analysis and simulation results are provided to show the validity and the advantages of the algorithm. In particular, it is shown that a high performance gain at a data rate of 54Mbps can be obtained with a moderate order of TEQ finite impulse response (FIR) filter. The algorithm is implemented in a field programmable gate array (FPGA). The characteristics and regularities between the elements in matrices are further exploited to reduce the hardware complexity in the matrix multiplication implementation. The optimum TEQ coefficients can be found in less than 4µs for the 7th order of the TEQ FIR filter. This time is the interval of an OFDM symbol in the IEEE 802.11a system. To compensate for the effective channel impulse response, a function block of 64-point radix-4 pipeline fast Fourier transform is implemented in FPGA to perform zero forcing equalization in frequency domain. The offsets between the hardware implementations and the mathematical calculations are provided and analyzed. The system performance loss introduced by the hardware implementation is also tested. Hardware implementation output and simulation results verify that the chips function properly and satisfy the requirements of the system running at a data rate of 54 Mbps.

A fixed terrestrial wireless system such as the Microwave Multi-channel Distribution Service (MMDS) can be used as the ``last mile' to provide a high speed Internet connection from a base station to a home in a rural or suburban residential area. Such a broadband wireless system works very well under line-of-sight transmission. It works quite well even if the line-of-sight is obstructed with a large number of trees. However, when trees obstruct the line-of-sight, under conditions of wind, the user may experience loss of the RF signal from time to time. This is especially true under gusty conditions. As part of this research a high precision DSP-based measuring system is devised to accurately measure and characterize the distortions caused by tree foliage on the RF line-of-sight signal. The approach is to digitally generate a signal composed of several tones, up-convert the signal to 2.5 GHz and send it through tree foliage to a receiver where the signal is down-converted and sampled for a duration of five seconds. The samples collected are processed using Matlab to compute the temporal amplitude and phase variations of the tones. The measurement system provides estimates of the amplitude and phase of the receive tones with a time resolution of 3.2 ms. The standard deviation of the amplitude estimates is 0.3\% of the actual amplitude of the tones and the standard deviation of the phase estimates is 0.23 degree. This accuracy is obtained when the signal-to-noise ratio of the receive signal is greater than 20 dB. Measurement in the field with tree foliage in the line-of-sight shows that the swaying of the branches in the wind can cause rapid signal fading. This research determines the type of fade, the depth and duration of the fade, as well as the fading rate.

Denna rapport omfattar ett arbete kring att förbättra signalbehandling och målföljning av en förbränningsfrekvens i en androidapplikation för effektberäkning hos accelererande fordon. Den ursprungliga applikationen är utvecklad på i3tex AB och det var även där som arbetet utfördes. Effektberäkningen görs genom att först spela in ljudet i kupén under ett accelerationsförlopp, där inspelningen signalbehandlas och förbränningsfrekvensen målföljs, sedan sker transformering från frekvensdomänen till hastighetsdomänen, varpå effekten beräknas via multiplikation av fordonets vikt, hastighet och acceleration. Problemet med den ursprungliga implementationen av målföljningen var att algoritmen inte var tillräckligt robust mot lågt signal/brus-förhållande (snr). För att göra systemet mer robust utvecklades flermålsföljning med Kalmanfilter, där ett poängsystem bestämmer vilken av målföljarna som mest troligt har följt förbränningsfrekvensen. Den nya algoritmen presterar betydligt bättre än den ursprungliga i avseende på rmse, men är betydligt mer resurskrävande. Genom optimering av hur signalbehandlingen görs, såsom längd och typ av fönsterfunktioner och andra parametrar för korttidsfouriertransformen (stft), är exekveringstiden för hela analysen marginellt snabbare och betydligt snabbare på en androidenhet med respektive utan stöd för hårdvaruaccelererade flyttalsoperationer. Det visade sig även att, trots att inte hårdvaruspecifikationerna för Android, cdd, specificerar inspelningar av frekvenser under 100 Hz är det möjligt på alla testade androidtelefoner och med tillräckligt gott resultat för att genomföra frekvensföljning enligt ovan.

In the current study, the four most common Particle Image Velocimetry (PIV) cross-correlation algorithms were evaluated by measuring the displacement of particles in computer generated images. The synthetic images were employed to compare the methods since the particle diameter, density, and intensity could be controlled, removing some of the uncertainty found in images collected during experiments, e. g. parallax, 3-D motion, etc. The most important parameter that was controlled in the synthetic images was the particle motion. Six different displacement functions were applied to move the particles between images: uniform translation, step, sawtooth, sinusoid, line source and line vortex. The four algorithms, which all use the fast Fourier transform (FFT) to perform the cross-correlation, were evaluated with four criteria; (1) spatial resolution, (2) dynamic range, (3) accuracy and (4) robustness. The uniform translation images determined the least error possible with each method, of which the deformed FFT proved to be the most accurate. The super resolution FFT and deformed FFT methods could not properly measure the infinite displacement gradient in the step images due to the interpolation of the displacement vector field used by each method around the step. However, the predictor corrector FFT scheme, which does not require interpolation when determining the interrogation area offset, successfully measured the infinite displacement gradient in the step images. The smaller interrogation areas used by the super resolution FFT scheme proved to be the best method to capture the high frequency finite displacement gradients in the sawtooth and sinusoid images. Also shown in the sawtooth and sinusoid images is the positional bias error introduced by assuming the measured particle displacement occurs at the centre of the interrogation area. The deformed FFT method produced the most accurate results for the source and vortex images, which both contained displacement gradients in multiple directions. Experimentally obtained images were also evaluated to verify the results derived using the synthetic images. The flow in a multiple grooved channel, using both water and air as the fluid medium in separate experiments, was measured and compared to DNS simulations reported by Yang. The mean velocity, average vorticity and turbulent fluctuations determined from both experiments using the deformed FFT method compared very well to the DNS calculations.