Turbo Bayesian Compressed Sensing

Compressed sensing (CS) theory specifies a new signal acquisition approach, potentially allowing the acquisition of signals at a much lower data rate than the Nyquist sampling rate. In CS, the signal is not directly acquired but reconstructed from a few measurements. One of the key problems in CS is how to recover the original signal from measurements in the presence of noise. This dissertation addresses signal reconstruction problems in CS. First, a feedback structure and signal recovery algorithm, orthogonal pruning pursuit (OPP), is proposed to exploit the prior knowledge to reconstruct the signal in the noise-free situation. To handle the noise, a noise-aware signal reconstruction algorithm based on Bayesian Compressed Sensing (BCS) is developed. Moreover, a novel Turbo Bayesian Compressed Sensing (TBCS) algorithm is developed for joint signal reconstruction by exploiting both spatial and temporal redundancy. Then, the TBCS algorithm is applied to a UWB positioning system for achieving mm-accuracy with low sampling rate ADCs. Finally, hardware implementation of BCS signal reconstruction on FPGAs and GPUs is investigated. Implementation on GPUs and FPGAs of parallel Cholesky decomposition, which is a key component of BCS, is explored. Simulation results on software and hardware have demonstrated that OPP and TBCS outperform previous approaches, with UWB positioning accuracy improved by 12.8x. The accelerated computation helps enable real-time application of this work

Parameter estimation and channel reconstruction based on compressive sensing for ultra-wideband MB-OFDM systems

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Decentralized Turbo Bayesian ompressed Sensing with application to UWB Systems

In many situations, there exist plenty of spatial and temporal redundancies in original signals. Based on this observation, a novel Turbo Bayesian Compressed Sensing (TBCS) algorithm is proposed to provide an efficient approach to transfer and incorporate this redundant information for joint sparse signal reconstruction. As a case study, the TBCS algorithm is applied in Ultra-Wideband (UWB) systems. A space-time TBCS structure is developed for exploiting and incorporating the spatial and temporal a priori information for space-time signal reconstruction. Simulation results demonstrate that the proposed TBCS algorithm achieves much better performance with only a few measurements in the presence of noise, compared with the traditional Bayesian Compressed Sensing (BCS) and multitask BCS algorithms

Compressive sampling based differential detection for UWB impulse radio signals

Noncoherent detectors significantly contribute to the practical realization of the ultra-wideband (UWB) impulse-radio (IR) concept, in that they allow avoiding channel estimation and provide highly efficient reception capabilities. Complexity can be reduced even further by resorting to an all-digital implementation, but Nyquist-rate sampling of the received signal is still required. The current paper addresses this issue by proposing a novel differential detection (DD) scheme, which exploits the compressive sampling (CS) framework to reduce the sampling rate much below the Nyquist-rate. The optimization problem is formulated to jointly recover the sparse received signal as well as the differentially encoded data symbols, and is compared with both the separate approach and the scheme using the compressed received signal directly, i.e., without reconstruction. Finally, a maximum a posteriori based detector using the compressed symbols is developed for a Laplacian distributed channel, as a reference to compare the performance of the proposed approaches. Simulation results show that the proposed joint CS-based DD brings the considerable advantage of reducing the sampling rate without degrading the performance, compared with the optimal MAP detector

Collaborative Spectrum Sensing from Sparse Observations in Cognitive Radio Networks

Spectrum sensing, which aims at detecting spectrum holes, is the precondition for the implementation of cognitive radio (CR). Collaborative spectrum sensing among the cognitive radio nodes is expected to improve the ability of checking complete spectrum usage. Due to hardware limitations, each cognitive radio node can only sense a relatively narrow band of radio spectrum. Consequently, the available channel sensing information is far from being sufficient for precisely recognizing the wide range of unoccupied channels. Aiming at breaking this bottleneck, we propose to apply matrix completion and joint sparsity recovery to reduce sensing and transmitting requirements and improve sensing results. Specifically, equipped with a frequency selective filter, each cognitive radio node senses linear combinations of multiple channel information and reports them to the fusion center, where occupied channels are then decoded from the reports by using novel matrix completion and joint sparsity recovery algorithms. As a result, the number of reports sent from the CRs to the fusion center is significantly reduced. We propose two decoding approaches, one based on matrix completion and the other based on joint sparsity recovery, both of which allow exact recovery from incomplete reports. The numerical results validate the effectiveness and robustness of our approaches. In particular, in small-scale networks, the matrix completion approach achieves exact channel detection with a number of samples no more than 50% of the number of channels in the network, while joint sparsity recovery achieves similar performance in large-scale networks.Comment: 12 pages, 11 figure