Sparsity Enhanced Decision Feedback Equalization

For single-carrier systems with frequency domain equalization, decision feedback equalization (DFE) performs better than linear equalization and has much lower computational complexity than sequence maximum likelihood detection. The main challenge in DFE is the feedback symbol selection rule. In this paper, we give a theoretical framework for a simple, sparsity based thresholding algorithm. We feed back multiple symbols in each iteration, so the algorithm converges fast and has a low computational cost. We show how the initial solution can be obtained via convex relaxation instead of linear equalization, and illustrate the impact that the choice of the initial solution has on the bit error rate performance of our algorithm. The algorithm is applicable in several existing wireless communication systems (SC-FDMA, MC-CDMA, MIMO-OFDM). Numerical results illustrate significant performance improvement in terms of bit error rate compared to the MMSE solution

A compressed sensing approach to block-iterative equalization: connections and applications to radar imaging reconstruction

The widespread of underdetermined systems has brought forth a variety of new algorithmic solutions, which capitalize on the Compressed Sensing (CS) of sparse data. While well known greedy or iterative threshold type of CS recursions take the form of an adaptive filter followed by a proximal operator, this is no different in spirit from the role of block iterative decision-feedback equalizers (BI-DFE), where structure is roughly exploited by the signal constellation slicer. By taking advantage of the intrinsic sparsity of signal modulations in a communications scenario, the concept of interblock interference (IBI) can be approached more cunningly in light of CS concepts, whereby the optimal feedback of detected symbols is devised adaptively. The new DFE takes the form of a more efficient re-estimation scheme, proposed under recursive-least-squares based adaptations. Whenever suitable, these recursions are derived under a reduced-complexity, widely-linear formulation, which further reduces the minimum-mean-square-error (MMSE) in comparison with traditional strictly-linear approaches. Besides maximizing system throughput, the new algorithms exhibit significantly higher performance when compared to existing methods. Our reasoning will also show that a properly formulated BI-DFE turns out to be a powerful CS algorithm itself. A new algorithm, referred to as CS-Block DFE (CS-BDFE) exhibits improved convergence and detection when compared to first order methods, thus outperforming the state-of-the-art Complex Approximate Message Passing (CAMP) recursions. The merits of the new recursions are illustrated under a novel 3D MIMO Radar formulation, where the CAMP algorithm is shown to fail with respect to important performance measures.A proliferação de sistemas sub-determinados trouxe a tona uma gama de novas soluções algorítmicas, baseadas no sensoriamento compressivo (CS) de dados esparsos. As recursões do tipo greedy e de limitação iterativa para CS se apresentam comumente como um filtro adaptativo seguido de um operador proximal, não muito diferente dos equalizadores de realimentação de decisão iterativos em blocos (BI-DFE), em que um decisor explora a estrutura do sinal de constelação. A partir da esparsidade intrínseca presente na modulação de sinais no contexto de comunicações, a interferência entre blocos (IBI) pode ser abordada utilizando-se o conceito de CS, onde a realimentação ótima de símbolos detectados é realizada de forma adaptativa. O novo DFE se apresenta como um esquema mais eficiente de reestimação, baseado na atualização por mínimos quadrados recursivos (RLS). Sempre que possível estas recursões são propostas via formulação linear no sentido amplo, o que reduz ainda mais o erro médio quadrático mínimo (MMSE) em comparação com abordagens tradicionais. Além de maximizar a taxa de transferência de informação, o novo algoritmo exibe um desempenho significativamente superior quando comparado aos métodos existentes. Também mostraremos que um equalizador BI-DFE formulado adequadamente se torna um poderoso algoritmo de CS. O novo algoritmo CS-BDFE apresenta convergência e detecção aprimoradas, quando comparado a métodos de primeira ordem, superando as recursões de Passagem de Mensagem Aproximada para Complexos (CAMP). Os méritos das novas recursões são ilustrados através de um modelo tridimensional para radares MIMO recentemente proposto, onde o algoritmo CAMP falha em aspectos importantes de medidas de desempenho

Recovery of Missing Samples Using Sparse Approximation via a Convex Similarity Measure

In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of image signal. This problem is also known as inpainting in the context of image processing and for this purpose, we suggest an iterative sparse recovery algorithm based on constrained $l_1$-norm minimization with a new fidelity metric. The proposed metric called Convex SIMilarity (CSIM) index, is a simplified version of the Structural SIMilarity (SSIM) index, which is convex and error-sensitive. The optimization problem incorporating this criterion, is then solved via Alternating Direction Method of Multipliers (ADMM). Simulation results show the efficiency of the proposed method for missing sample recovery of 1D patch vectors and inpainting of 2D image signals

Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

This paper considers three problems in sparse filter design, the first involving a weighted least-squares constraint on the frequency response, the second a constraint on mean squared error in estimation, and the third a constraint on signal-to-noise ratio in detection. The three problems are unified under a single framework based on sparsity maximization under a quadratic performance constraint. Efficient and exact solutions are developed for specific cases in which the matrix in the quadratic constraint is diagonal, block-diagonal, banded, or has low condition number. For the more difficult general case, a low-complexity algorithm based on backward greedy selection is described with emphasis on its efficient implementation. Examples in wireless channel equalization and minimum-variance distortionless-response beamforming show that the backward selection algorithm yields optimally sparse designs in many instances while also highlighting the benefits of sparse design.Texas Instruments Leadership University Consortium Progra

High mobility in OFDM based wireless communication systems

Orthogonal Frequency Division Multiplexing (OFDM) has been adopted as the transmission scheme in most of the wireless systems we use on a daily basis. It brings with it several inherent advantages that make it an ideal waveform candidate in the physical layer. However, OFDM based wireless systems are severely affected in High Mobility scenarios. In this thesis, we investigate the effects of mobility on OFDM based wireless systems and develop novel techniques to estimate the channel and compensate its effects at the receiver. Compressed Sensing (CS) based channel estimation techniques like the Rake Matching Pursuit (RMP) and the Gradient Rake Matching Pursuit (GRMP) are developed to estimate the channel in a precise, robust and computationally efficient manner. In addition to this, a Cognitive Framework that can detect the mobility in the channel and configure an optimal estimation scheme is also developed and tested. The Cognitive Framework ensures a computationally optimal channel estimation scheme in all channel conditions. We also demonstrate that the proposed schemes can be adapted to other wireless standards easily. Accordingly, evaluation is done for three current broadcast, broadband and cellular standards. The results show the clear benefit of the proposed schemes in enabling high mobility in OFDM based wireless communication systems.Orthogonal Frequency Division Multiplexing (OFDM) wurde als Übertragungsschema in die meisten drahtlosen Systemen, die wir täglich verwenden, übernommen. Es bringt mehrere inhärente Vorteile mit sich, die es zu einem idealen Waveform-Kandidaten in der Bitübertragungsschicht (Physical Layer) machen. Allerdings sind OFDM-basierte drahtlose Systeme in Szenarien mit hoher Mobilität stark beeinträchtigt. In dieser Arbeit untersuchen wir die Auswirkungen der Mobilität auf OFDM-basierte drahtlose Systeme und entwickeln neuartige Techniken, um das Verhalten des Kanals abzuschätzen und seine Auswirkungen am Empfänger zu kompensieren. Auf Compressed Sensing (CS) basierende Kanalschätzverfahren wie das Rake Matching Pursuit (RMP) und das Gradient Rake Matching Pursuit (GRMP) werden entwickelt, um den Kanal präzise, robust und rechnerisch effizient abzuschätzen. Darüber hinaus wird ein Cognitive Framework entwickelt und getestet, das die Mobilität im Kanal erkennt und ein optimales Schätzungsschema konfiguriert. Das Cognitive Framework gewährleistet ein rechnerisch optimales Kanalschätzungsschema für alle möglichen Kanalbedingungen. Wir zeigen außerdem, dass die vorgeschlagenen Schemata auch leicht an andere Funkstandards angepasst werden können. Dementsprechend wird eine Evaluierung für drei aktuelle Rundfunk-, Breitband- und Mobilfunkstandards durchgeführt. Die Ergebnisse zeigen den klaren Vorteil der vorgeschlagenen Schemata bei der Ermöglichung hoher Mobilität in OFDM-basierten drahtlosen Kommunikationssystemen

Adaptive Greedy Algorithm With Application to Nonlinear Communications

Greedy algorithms form an essential tool for compressed sensing. However, their inherent batch mode discourages their use in time-varying environments due to significant complexity and storage requirements. In this paper two existing powerful greedy schemes developed in the literature are converted into an adaptive algorithm which is applied to estimation of a class of nonlinear communication systems. Performance is assessed via computer simulations on a variety of linear and nonlinear channels; all confirm significant improvements over conventional methods.Engineering and Applied Science