New sampling and detection approaches for compressed sensing and their application to ultra wideband communications

Compressed sensing (CS) provides an efficient way to acquire and reconstruct sparse signals from a limited number of linear projection measurements leading to sub-Nyquist sampling rates. The advantages of compressed sensing include simpler hardware design, faster acquisition time, and less power consumption. In this thesis, several important applications of compressed sensing are addressed and better performance than that of existing solutions is obtained by exploiting the theory of compressed sensing.;Firstly, we focus on designing efficient sampling methods for image acquisition based on CS. A key to the success of CS is the design of the measurement ensemble. A novel variable density sampling strategy is designed, where the a priori information of the statistical distributions that natural images exhibit in the wavelet domain is exploited. The proposed variable density sampling has the following advantages: (1) the generation of the measurement ensemble is computationally efficient and requires less memory; (2) the necessary number of measurements for image reconstruction is reduced; (3) the proposed sampling method can be applied to several transform domains and leads to simple implementations. The application of our proposed method to magnetic resonance imaging (MRI) is also provided in this thesis.;Secondly, we address the detection of sparse signals within the CS domain. A new family of detectors called subspace compressive detectors are developed for the detection of sparse signals based on the theory of compressed sensing. The proposed detectors reduce the number of measurements needed for a given detection performance by exploiting the fact that the sparse signal resides in a low dimension subspace. By designing random projection operators tailored to the subspace where the signal-of-interest lies, the signal energy can be captured more efficiently leading to better detection performance. The information of the signal subspace can be learned from compressive measurements of training signals and the detectors are adaptive to the signal structure. Within the compressed sensing framework, it is shown that very limited random measurements of training signals can suffice to provide valuable information of the signal subspace for detection purposes. The performance of the proposed subspace compressive detectors is analyzed and implementation issues including the waveform quantization are discussed. Subspace compressive detection under narrowband interference is also considered in this thesis.;In the last part of this dissertation, the theory of compressed sensing is exploited in the design of a new type of suboptimal impulse ultra-wideband (I-UWB) receivers where only sub-Nyquist sampling of the received UWB signal is required. However, the proposed I-UWB receivers have simple hardware implementations and, at the same time, shares the flexibility in data processing with full-resolution digital receivers based on Nqyuist sampling. An improved symbol detection method is proposed for I-UWB communications by exploiting the sparsity of the received UWB signals, where the sparsity is mainly due to the multipath diversity introduced by I-UWB channels. A compressive pilot assisted time-hopping spread-spectrum signaling is introduced and performance analysis of the proposed receivers is provided. Compared with other suboptimal I-UWB receivers, satisfactory detection performance is achieved with simple hardware implementation.