Beamforming is a spatial filtering technique using a sensor array to enhance the signal of interest (SOI) and suppress interferences and noise. It is widely used in radar, sonar, wireless communications, Global Positioning System (GPS) navigation, microphone array speech processing and many other areas. Most existing beamforming approaches are based on the minimum variance (MV) criterion. The MV approach is statistically optimal only when the desired signal, interferences and the noise are Gaussian-distributed. However, many real-world signals are non-Gaussian. For non-Gaussian signals, the higher-order statistics or fractional lower-order statistics contain useful information and can be utilized to improve the beamformer performance. In this thesis, a family of the minimum dispersion (MD) criterion-based robust beamforming algorithms, which minimize the Lp-norm (p>=1) of the array output subject to linear or nonlinear constraints, are proposed for non-Gaussian signals. The dispersion, which is a generalization of variance, implicitly exploits the higher-order statistics for p>2 or fractional lower-order statistics for p<2. We utilize the MD criterion with a single linear constraint and multiple linear constraints, which gives us the minimum dispersion distortionless response (MDDR) beamformer and linearly constrained minimum dispersion (LCMD) beamformer, respectively. The MDDR and LCMD beamformers can be tailored to Gaussian, sub-Gaussian or super-Gaussian signals and noise by adjusting the value of p. Three efficient iterative algorithms, namely, the iteratively reweighted MVDR (IR-MVDR), complex-valued full Newton’s and partial Newton’s methods, are devised to solve the resulting convex optimization problems. We extend the LCMD beamformer to the quadratically constrained minimum dispersion (QCMD) beamformer. The robustness against model uncertainty of the QCMD beamformer is significantly enhanced compared with the LCMD beamformer. A gradient projection algorithmic framework is developed to efficiently solve the resulting convex optimization problem. Furthermore, we derive a closed-form expression of the projection onto the constraint set. Note that sub-Gaussian signals that are frequently encountered in practical applications. Therefore, a minimum infinity norm criterion is then adopted by the robust linear programming beamformer (RLPB). In this way, the sub-Gaussianity of the signals can be fully exploited. We model the uncertainty region as a rhombus in which the L1-norm of the steering vector error is bounded. As a result, the proposed RLPB beamformer can be obtained by solving a linear programming (LP) problem. We also present the theoretical explanation to the reason why the RLPB can implicitly exploit the high-order statistics from the statistical perspective. / Dissertation / Doctor of Philosophy (PhD)

Com o desenvolvimento dos motores turbofan, a contribuição das estruturas hipersustentadoras no ruído total gerado pelas aeronaves tem se tornado mais considerável. Sendo que as estruturas do flape tornaram-se uma das principais fontes de ruído. Dispositivos para redução do nível sonoro nessas regiões são investigados em uma asa MD 30P30N, ensaiada em um túnel de vento adaptado para medições aeroacústicas. A localização das fontes de ruído foi obtida através de uma antena de Beamforming (técnica de identificação de fontes acústicas) com 109 microfones, dos quais 60 deles são de alta freqüência (até 40 kHz). As características aerodinâmicas foram avaliadas através de medidas de pressão na superfície do modelo, e com o mapeamento de vórtice em ponta de flape. Dentre os dispositivos avaliados para redução de ruído, foram testadas chapas porosas de diversos tamanhos. Os sinais dos microfones foram processados com o algoritmo DAMAS2 para obtenção dos espectros do Beamforming em uma região de interesse definida. As configurações com porosidade têm nível de ruído equivalente para freqüências até 2000 Hz. A partir daí, há uma redução de até 6 dB em 3200 Hz em relação ao baseline (tipo de teste aplicado à asa). Os resultados de Beamforming para duas configurações diferentes, baseline e chapa porosa foram apresentados usando uma faixa dinâmica de 12 dB, com pico de 58 dB. Observa-se que houve redução dos níveis de ruído na região selecionada. A perda de pressão total na ponta do flape mostrou que há uma aparente correlação entre o gradiente da pressão total e o nível de ruído. Estudos adicionais são necessários para entender os mecanismos de redução de ruído e assim otimizar a geometria das chapas porosas. No entanto, os resultados apresentados indicam que esses dispositivos são candidatos para aplicação em aeronaves. / With the development of high-bypass turbofan engines, the airframe contribution to the total aircraft noise has become considerable. One of the largest sources of airframe noise is the flap side-edge, which is investigated experimentally in a MD 30P30N wing. Several devices are also tested to reduce the side-edge noise, especially porous plates. Wind tunnel testing is carried out and the position of noise sources and their levels is obtained with a beamforming antenna. It has 112 microphones, in which 60 of them are suitable for acoustic measurements of up to 40 kHz. The aerodynamic characteristics are evaluated with pressure measurements on the model surface, as well as with vortex mapping on the flap side-edge. To evaluate the noise levels, microphone signals were processed with the DAMAS2 algorithm. Beamforming spectra were then obtained considering only the side-edge region. The baseline configuration and those with porous plates were tested and equivalent noise levels were obtained up to 2000 Hz. For higher frequencies, the model with porous plates has a lower noise level, reaching a difference of 6 dB in 3200 Hz, compared to the baseline configuration. Vortex mapping was carried out with a seven hole Pitot probe developed at the University for the measurement of flows with high angularity. The results for the baseline configuration allows to correlate aerodynamic and aeroacoustic data. This helps to design the side-edge region with a low noise level. Additional studies are necessary to understand the mechanisms of noise reduction and to optimize the geometry of the porous plate. However, the presented results indicate that this device is a candidate for application in aircraft, in special by its superior durability compared to the foam generally used for noise attenuation.

When antennas are placed closely spaced together, the mutual coupling and spatial correlation effects undermine the advantages provided by multiple input and multiple output (MIMO) antennas. In this thesis, we compare and analyze the performance of digital beamforming, fixed radio frequency (RF) beamforming and element based patterning with closely spaced antenna systems. In the case where only one RF-chain is available, we have demonstrated performance improvements using RF beamforming-based MIMO processing instead of element-based MIMO processing with closely spaced metamaterial antennas. The result indicates that even without mutual coupling, antenna based MIMO processing is greatly impacted when moving from rich to correlated scattering environments. In the second half of the thesis, we investigate the switch and examine receiver combining (SEC) technique. We derive the switching rate of SEC and show that even though it has the same outage probability as traditional selection combining, it has a significantly lower switching rate.

When antennas are placed closely spaced together, the mutual coupling and spatial correlation effects undermine the advantages provided by multiple input and multiple output (MIMO) antennas. In this thesis, we compare and analyze the performance of digital beamforming, fixed radio frequency (RF) beamforming and element based patterning with closely spaced antenna systems. In the case where only one RF-chain is available, we have demonstrated performance improvements using RF beamforming-based MIMO processing instead of element-based MIMO processing with closely spaced metamaterial antennas. The result indicates that even without mutual coupling, antenna based MIMO processing is greatly impacted when moving from rich to correlated scattering environments. In the second half of the thesis, we investigate the switch and examine receiver combining (SEC) technique. We derive the switching rate of SEC and show that even though it has the same outage probability as traditional selection combining, it has a significantly lower switching rate.

Com o desenvolvimento dos motores turbofan, a contribuição das estruturas hipersustentadoras no ruído total gerado pelas aeronaves tem se tornado mais considerável. Sendo que as estruturas do flape tornaram-se uma das principais fontes de ruído. Dispositivos para redução do nível sonoro nessas regiões são investigados em uma asa MD 30P30N, ensaiada em um túnel de vento adaptado para medições aeroacústicas. A localização das fontes de ruído foi obtida através de uma antena de Beamforming (técnica de identificação de fontes acústicas) com 109 microfones, dos quais 60 deles são de alta freqüência (até 40 kHz). As características aerodinâmicas foram avaliadas através de medidas de pressão na superfície do modelo, e com o mapeamento de vórtice em ponta de flape. Dentre os dispositivos avaliados para redução de ruído, foram testadas chapas porosas de diversos tamanhos. Os sinais dos microfones foram processados com o algoritmo DAMAS2 para obtenção dos espectros do Beamforming em uma região de interesse definida. As configurações com porosidade têm nível de ruído equivalente para freqüências até 2000 Hz. A partir daí, há uma redução de até 6 dB em 3200 Hz em relação ao baseline (tipo de teste aplicado à asa). Os resultados de Beamforming para duas configurações diferentes, baseline e chapa porosa foram apresentados usando uma faixa dinâmica de 12 dB, com pico de 58 dB. Observa-se que houve redução dos níveis de ruído na região selecionada. A perda de pressão total na ponta do flape mostrou que há uma aparente correlação entre o gradiente da pressão total e o nível de ruído. Estudos adicionais são necessários para entender os mecanismos de redução de ruído e assim otimizar a geometria das chapas porosas. No entanto, os resultados apresentados indicam que esses dispositivos são candidatos para aplicação em aeronaves. / With the development of high-bypass turbofan engines, the airframe contribution to the total aircraft noise has become considerable. One of the largest sources of airframe noise is the flap side-edge, which is investigated experimentally in a MD 30P30N wing. Several devices are also tested to reduce the side-edge noise, especially porous plates. Wind tunnel testing is carried out and the position of noise sources and their levels is obtained with a beamforming antenna. It has 112 microphones, in which 60 of them are suitable for acoustic measurements of up to 40 kHz. The aerodynamic characteristics are evaluated with pressure measurements on the model surface, as well as with vortex mapping on the flap side-edge. To evaluate the noise levels, microphone signals were processed with the DAMAS2 algorithm. Beamforming spectra were then obtained considering only the side-edge region. The baseline configuration and those with porous plates were tested and equivalent noise levels were obtained up to 2000 Hz. For higher frequencies, the model with porous plates has a lower noise level, reaching a difference of 6 dB in 3200 Hz, compared to the baseline configuration. Vortex mapping was carried out with a seven hole Pitot probe developed at the University for the measurement of flows with high angularity. The results for the baseline configuration allows to correlate aerodynamic and aeroacoustic data. This helps to design the side-edge region with a low noise level. Additional studies are necessary to understand the mechanisms of noise reduction and to optimize the geometry of the porous plate. However, the presented results indicate that this device is a candidate for application in aircraft, in special by its superior durability compared to the foam generally used for noise attenuation.

Transmit beamforming (precoding) is a powerful technique for enhancing the channel capacity and reliability of multiple-input and multiple-output (MIMO) wireless systems. The optimum exploitation of the benefits provided by MIMO systems can be achieved when a perfect channel state information at transmitter (CSIT) is available. In practices, however, the channel knowledge is generally imperfect at transmitter because of the inevitable errors induced by finite feedback channel capacity, quantization and other physical constraints. Such errors degrade the system performance severely. Hence, robustness has become a crucial issue. Current robust designs address the channel imperfections with the worst-case and stochastic approaches. In worst-case analysis, the channel uncertainties are considered as deterministic and norm-bounded, and the resulting design is a conservative optimization that guarantees a certain quality of service (QoS) for every allowable perturbation. The latter approach focuses on the average performance under the assumption of channel statistics, such as mean and covariance. The system performance could break down when persistent extreme errors occur. Thus, an outage probability-based approach is developed by keeping a low probability that channel condition falls below an acceptable level. Compared to the aforementioned methods, this approach can optimize the average performance as well as consider the extreme scenarios proportionally. This thesis implements the outage-probability specification into transmit beamforming design for three scenarios: the single-user MIMO system and the corresponding adaptive modulation scheme as well as the multi-user MIMO system. In a single-user MIMO system, the transmit beamformer provides the maximum average received SNR and ensures the robustness to the CSIT errors by introducing probabilistic constraint on the instantaneous SNR. Beside the robustness against channel imperfections, the outage probability-based approach also provides a tight BER bound for adaptive modulation scheme, so that the maximum transmission rate can be achieved by taking advantage of transmit beamforming. Moreover, in multi-user MIMO (MU-MIMO) systems, the leakage power is accounted by probability measurement. The resulting transmit beamformer is designed based on signal-to-leakage-plus-noise ratio (SLNR) criteria, which maximizes the average received SNR and guarantees the least leakage energy from the desired user. In such a setting, an outstanding BER performance can be achieved as well as high reliability of signal-to-interference-plus-noise ratio (SINR). Given the superior overall performances and significantly improved robustness, the probabilistic approach provides an attractive alternative to existing robust techniques under imperfect channel information at transmitter.

Medical ultrasound imaging is widely used to diagnose cardiacdiseases. The recent availability of real time 3D ultrasound posesseveral interesting challenges and opportunities, and the work of thisthesis is devoted to both challenges and opportunities. One of the key benefits of ultrasound imaging is that its images arereal time. This has been challenged with the recent introduction of 3Dimages, where the number of ultrasound beams is squared compared totraditional 2D images. One common way to alleviate this is byreceiving several closely spaced ultrasound beams from each pulsetransmission, which increases acquisition speed but affects the imagequality. Specifically, B-mode images are irregularly sampled and losespatial shift invariance while a bias in the Doppler velocityestimates causes a discontinuity in the velocity estimates in colorflow images. We have found that these artifacts can be reducedsignificantly by interpolation of the beamformed data from overlappingbeams, with the limitation of requiring at least twice the number ofbeamformers. We have also found that valvular regurgitation is one of thecardiac diseases that can benefit greatly from quantification ofseverity using 3D ultrasound. We have devised a modality that useshigh pulse repetition frequency 3D Doppler to isolate thebackscattered signal power from the vena contracta of a regurgitantjet. This measure is calibrated with a narrow reference beam insidethe jet to estimate the cross-sectional area of the vena contracta. Wehave validated this method with computer simulations, with an in vitrostudy and finally in vivo with 27 patients who had mitralregurgitation. We found that the cross-sectional area and regurgitantvolume of the vena contracta could be quantified without bias as long as the orifice was sufficiently large for a calibration beam tofit inside it. The severity of smaller regurgitations will beoverestimated, but this does not pose a clinical problem, as thesepatients can easily be identified by standard 2D Doppler examination and donot typically need further quantification. Finally, we have developed a new, fast 3D ultrasound simulation methodthat can incorporate anisotropic scattering from cardiac muscle cells. This approach is three orders of magnitudefaster than the most commonly used simulation methods, making it wellsuited for the simulation of dynamic 3D images for development and testingof quantitative diagnostic methods such as 3D speckle tracking andvolumetric measurements.

Opportunistic Beamforming is a promising scheme with potential usage in a variety of applications ranging from cellular audio/video communications to wireless mesh-networks. However, some aspects in this scheme are open to further improvements, such as effective quality of service (QoS) provisioning, and efficient handling of sparse/realistic networks. We focus on the downlink channel of a multi-rate time-division multiplexing MISO (multiple input single output) point-to-multi-point wireless communication system, and design a cross-layer scheme. We employ a two-stage opportunistic scheduler. The scheduler receives channel state information in the form of SNR (signal to noise ratio) measurements from each terminal, and schedules one terminal in each time-slot. At the first stage in a time-slot a terminal is chosen, and our gradient descent channel estimator finds an estimation of its channel vector. Then the beamformer produces a beamforming vector in an adjacent pilot channel, or in the first part of the time-slot in the data channel. Our beamforming is based on the estimation of the channel, as opposed to the random beamformer used in the opportunistic beamforming. Each terminal measures its perceived SNR even when the channel is assigned to another terminal, and sends this information back to the basestation subject to a feedback-reduction policy. The scheduler uses the new channel state information for its second stage and assigns a terminal for the succeeding time-slot. The channel estimation procedure uses the reported SNRs for each terminal, which is a significantly lower feedback rate than the amount required for coherent beamforming. Our approach efficiently handles sparse/realistic networks, and also provides a better QoS than the opportunistic beamforming scheme. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2007-06-30 07:00:20.468

Thesis (M.S. in Electrical Engineering)--Vanderbilt University, May 2008. / Title from title screen. Includes bibliographical references.

In the past few years, a possible new population of sources emitting fast and bright transient radio bursts have been discovered. To explore this new transient phase space, the next generation of radio telescopes, typically interferometers, provide wide observing bandwidths in order to achieve high sensitivity for the detection of weak sources and multi-beaming capabilities to increase the field of view. In comparison to a traditional single beam radio dish, these telescopes collect vast volumes of data and still rely on the traditional observing techniques. Localising transient events during their discovery is essential as these events might not be repeatable by nature. I describe the development and construction of a prototype phased array, the Manchester University Student Telescope (MUST), capable of multi-beam operation. I present results of the Yagi antenna beam measurements and the optimum antenna separations; the investigation of the radio frequency interference spectrum around the preferred observing band and setting the subsequent bandpass filter specifications; simulations of the optimum configurations of the MUST tiles; and finally I describe implementation of the digital back-end. For the joint task of discovery and simultaneous localisation, the advantages of single dishes and interferometers are combined in a beam forming approach. I present an investigation into the wide-bandwidth time-domain signal processing techniques for time-domain beamforming that can be used in transient and pulsar observations. I discuss the efficient polyphase decomposition for interpolation digital filters and multiplication-free fractional delay filters that can be used to reduce the complexity of the beamformer implementation and avoid high sampling rates. This reduced complexity allows more simultaneous beams to be formed using time-domain techniques. This analysis was performed for the MUST array, but is applicable to a wide range of interferometers. I have developed and analysed a new proof-of-concept non-imaging method to localise transient sources observed with interferometers or phased array feeds. It utilises the additional spectral and comparative spatial information obtained from multiple overlapping tied array beams. This allows us to estimatea transient source location with up to arc second accuracy in almost real time and allows the required high time resolution to be preserved. We demonstrate that this method can work for a variety of interferometric configurations, including for LOFAR and MeerKAT, and that the estimated angular position may be sufficient to identify a host galaxy, or other related object, without reference to other simultaneous or follow-up observations.