Due to the widespread acceptance of Synthetic Aperture Radar (SAR) imagery by the scientific community in recent years, SAR system design faces ever increasing demands for wide coverage of high resolution images. This represents a challenging task, since conventional monostatic SAR system are inherently subject to a compromise between the achievable resolution and the width of the imaged swath. In this context, multi-channel SAR systems arise as a promising alternative to overcome this limitation and achieve high-resolution wide-swath (HRWS) SAR imaging. Their operation requires the acquisition of more information about the scene through multiple channels and suitable digital beamforming techniques to adequately combine the output data. The innovative Multi-Channel Reconstruction Algorithm (MCRA) was recently introduced as a suitable alternative for the processing required by multi-channel SAR systems in azimuth. This thesis performs and evaluates on a demonstration of the capabilities of this algorithm employing real SAR multi-channel data acquired by DLR's new airborne system F-SAR. The combination of up to four different channels is performed, and analyzes of the algorithm performance follow, especially with regard to ambiguity suppression. The impact of channel imbalances in the residual ambiguity levels is considered and different channel balancing methods are assessed. Following the algorithm's success in yielding high quality reconstructed images given adequately balanced channels, focus is turned to balancing alternatives, with special interest in methods applicable to aliased data. Blind equalization techniques are employed to develop a version of the reconstruction algorithm with increased robustness to channel imbalances following a certain error model. Performance assessments of the alternative strategy are performed both for controlled imbalances following the design model and real unknown imbalances found on F-SAR data.

[pt] Nesta dissertação, diversos algoritmos adaptativos para processamento de sinais com seleção de dados são desenvolvidos e estudados, com o objetivo de resolver dois problemas diferentes. O primeiro problema envolve ambientes com sistemas esparsos, onde uma função penalidade é incorporada na função de custo para aproveitar a esparsidade do modelo. Nesta perspectiva, são propostos três algoritmos com função penalidade ajustável, o primeiro baseado na função penalidade l1 é denominado SM-NLMS com atração para zero e função penalidade ajustável (ZA-SM-NLMS-ADP). O segundo algoritmo está baseado na função penalidade log-sum e o terceiro na função penalidade l0 , denominados SM-NLMS com atração ponderada para zero e função de penalidade ajustável (RZA-SM-NLMS-ADP) e SM-NLMS com atração para zero exponencial e função de penalidade ajustável (EZA-SM-NLMSADP), respectivamente. Além disso, foi desenvolvida uma análise estatística do algoritmo SM-NLMS com uma função penalidade genérica, obtendo expressões matemáticas para o erro médio quadrático em estado estacionário. O segundo problema abordado, considera algoritmos adaptativos não lineares baseados em funções de kernels. Neste contexto, são desenvolvidos dois algoritmos com seleção de dados, o algoritmo SM-NKLMS e o algoritmo SM-KAP, os quais possuem a capacidade de limitar o crescimento da estrutura criada pelas funções de kernels, tratando um dos maiores problemas que surge quando se utilizam algoritmos baseados em kernels. Os algoritmos baseados em kernels foram testados para predição de séries temporais. Também é realizada uma análise estatística do algoritmo SM-NKLMS. As simulações mostram que os algoritmos desenvolvidos superam os algoritmos lineares e não lineares convencionais tanto na velocidade de convergência quanto no erro médio quadrático atingido. / [en] In this dissertation, several data-selective adaptive signal processing algorithms are derived and investigated for solving two different problems. The first one involves scenarios handling sparse systems, where we introduce a framework in which a general penalty function is incorporated into the cost function for exploiting the sparsity of the model. Under this scope, we propose three algorithms with an adjustable penalty function, the first one based on the l1 - norm, which we term zero-attracting SM-NLMS with adjustable penalty function (ZA-SM-NLMS-ADP). The second algorithm is based on the log-sum penalty function and the third one on the l0 - norm, named reweighted ZASM- NLMS (RZA-SM-NLMS-ADP) and the exponential ZA-SM-NLMS (EZASM- NLMS-ADP), respectively. We also carry out a statistical analysis of the sparsity-aware SM-NLMS algorithms with a general penalty function, arriving at mathematical expressions for the mean-square error at steady state. The second problem addressed considers nonlinear adaptive algorithms based on kernel functions. In this context, we develop two data selective algorithms, the Set-Membership Normalized Kernel Least Mean Squares (SM-NKLMS) algorithm and the Set-Membership Kernel Affine Projection (SM-KAP) algorithm, which have the capability of naturally limiting the growing structure created by the kernels, dealing with one of the major problems presented when working with kernel algorithms. The kernel algorithms developed have been tested for a time series prediction task. A statistical analysis of the proposed SM-NKLMS algorithm is also developed. Simulation results show that the proposed algorithms, outperform standard linear and nonlinear adaptive algorithms in both convergence rate and steady state performance.