Compressive Sampling for Wireless Communications

TL;DR: This thesis proposes CS-based energy detectors for IR-UWB pulse position modulation (PPM) systems in multipath fading environments and uses the principles of generalized maximum likelihood to propose detectors which require the reconstruction of the original signal from compressed samples and detectors which skip this recon- struction step and carry out detection on the compressed samples directly, thereby further reducing the complexity.

Abstract: Wireless communications is undergoing massive development in all forms of its manifestations. In the field of short-range communications, technologies like ultra- wideband (UWB) systems are promising very high data rates, fine timing resolution and coexistence with other physical layer standards. Along with these benefits, the promise of low-cost and low-complexity devices makes UWB systems a highly sought-after option. The main reason for these benefits is the utilization of a very large bandwidth. However, these benefits come at a price, that is the high sampling rate required to receive such signals. According to the Nyquist sampling theorem, a signal can be fully determined if sampled at twice its maximum frequency. This means that the UWB signals may require a sampling rate in the order of Giga samples per second. At the receiver, the sampling is carried out by an analog-to-digital converter (ADC). The power consumption of an ADC is proportional to its sampling rate. A very high sampling rate means stressing the ADC in terms of power consumption. This can put the whole idea of low-cost and low-complexity UWB systems in jeopardy. Therefore, using subsampling methods is indispensable. In this regard, we propose the utilization of compressive sampling (CS) for UWB systems. CS promises a reasonable reconstruction performance of the complete signal from very few compressed samples, given the sparsity of the signal. In this thesis, we concentrate on impulse-radio (IR) UWB systems. IR-UWB signals are known to be sparse, meaning, a large part of the received signal has zero or insignificant components. We exploit this time-domain sparsity and reduce the sampling rate much below the Nyquist rate but still develop efficient detectors. We propose CS-based energy detectors for IR-UWB pulse position modulation (PPM) systems in multipath fading environments. We use the principles of generalized maximum likelihood to propose detectors which require the reconstruction of the original signal from compressed samples and detectors which skip this recon- struction step and carry out detection on the compressed samples directly, thereby further reducing the complexity. We provide exact theoretical expressions for the bit error probability (BEP) to assess the performance of our proposed detectors. These expressions are further verified by numerical simulations. We also propose CS-based differential detectors for IR-UWB signals. These detectors work on consecutive symbols. We develop detectors with separate recon- struction and detection stages as well as detectors that perform these steps jointly. We further present detectors which do not need reconstruction at all and can work directly on the compressed samples. However, this can put some limitations on the overall flexibility of the detector in terms of the measurement process. To assess the performance of all these detectors, we also provide maximum a posteriori (MAP) based detectors. We provide numerical simulations to display the detection results. We extend the CS-based classical differential detectors to the case of multiple symbol differential detectors. To keep the implementation complexity at its min- imum, we work only with compressed samples directly. We use the principles of the generalized likelihood ratio test (GLRT) to eliminate the limitations on such de- tectors, in terms of the measurement process. Apart from focusing on compressed detectors which contain full timing information, we also propose detectors which need such information at symbol level only. This effectively results in low-cost and low-complexity detectors. Finally, we present some work on the theoretical aspects of CS. We develop algorithms which exploit the block sparse structure of the signal. This block spar- sity is combined with varying block sizes and signal coefficients having smooth transitions. Such signals are often encountered in a wide range of engineering and biological fields.