Acquisition of Multi-Band Signals via Compressed Sensing

The Compressed Sensing (CS) approach allows sampling of signals below the conventional Nyquist rate, if signals are sparse in some basis. Basically, the CS framework comprises of two stages: a sub-Nyquist sampling and a signal reconstruction. The signal reconstruction is formulated as an underdetermined inverse problem, which can be solved by a variety of methods. Therefore in CS, the lack of signal samples is compensated by a more complicated reconstruction procedure in comparison to the Nyquist rate sampling. The CS approach can improve characteristics of some acquisition instruments, for example Signal Analyzers (SA). SA is a measurement tool that can replace a spectrum and a vector analyzer. With the development of wireless communications, the demand for SA with better characteristics also increases. For example, the LTE specification uses high frequency and wide-band signals. However, the complexity and price of the analog front-end and ADCs that operate at such frequencies is high. Hence, it is beneficial to improve the SA capability by better utilizing the existing hardware, and CS may be a means for doing it. In this thesis, we focused on two CS architectures that can be used for SA applications. These architectures are Single-channel Nonuniform Sampling (SNS) and Multi-Coset Sampling (MCS). One of their advantages is a relatively simple front-end that can be implemented with minimum modification of the SA hardware. The considered aspects include the performance and the reconstruction complexity of the various reconstruction methods. As the main scenario, we assume the acquisition of multi-band frequency sparse signals corrupted with additive white Gaussian noise. This scenario reflects the tendency of the modern wireless communication specifications, like LTE, to utilize a number of narrow bands distributed over a wide bandwidth. With extensive numerical simulations, we highlight the performance of the various reconstruction methods under the different sampling conditions and provide the recommendations for the most appropriate reconstruction methods. We propose the multi-coset emulation as a means to reduce the reconstruction complexity for the SNS acquisition. Depending on the acquisition scenario, the multi-coset emulation may retain, improve or degrade the reconstruction quality. However, for all scenarios, this emulation reduces the reconstruction complexity by at least an order of magnitude.