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# Compressive sensing based positioning algorithms to locate transmitting nodes in wireless networks

thesis

posted on 2022-03-28, 23:40 authored by Audri BiswasOver the decades, the Wireless Cellular Network (WCN) and Wireless Local Area Network (WLAN) have transformed into a gigantic eco-system feeding billions of portable devices with an astronomical amount of the digital data. With modernization and miniaturization of computer electronics, this amount of data is set to hit a record high in the next few years. Unfortunately, current infrastructures of WCN and WLAN are struggling to cope with the global demand due to severe scarcity of spectral resources and outdated infrastructure. This lead to extensive research on the upcoming Fifth Generation (5G) wireless network technology. The 5G technology aims to increase the data rate by two orders of magnitude compared to the predecessor technology 4G. The technologies listed to be the key enablers for 5G include, spatial multiplexing, device-to-device communication, beam-forming and cognitive radio networks (self-conﬁguration networks). In this regard, geo-location information of the wireless devices is crucial in bounding the large-scale interference between the devices to a level producing acceptable performance degradation. Moreover, accurate positioning information plays a critical role in determining exclusion zones for wireless devices in networks, and this enables maximal spectrum reuse and spectrum eﬃciency.The thesis introduces several novel algorithms. Algorithms are introduced which accurately determine the Direction Of Arrival (DOA) of the signal at a receiver. Using these techniques at two or more receiving locations, the position of the radio transmitter may be determined with great accuracy using triangulation. In addition, the thesis proposes an algorithm to determine the position of a transmitting source using the Received Signal Strength (RSS) at several locations. The new DOA and RSS based positioning algorithms are based upon the framework of compressive sensing (CS),which is an emerging signal processing technique that oﬀers superior recovery of a signal using limited observations, especially when the signal is sparse in some given bases. For CS implementation of the DOA estimation, the problem is initially modeled with the assumption that actual DOA is one of a quantized set of angles. With this assumption, a dictionary matrix may be constructed which can be used in the CS algorithm to ﬁnd an estimated DOA which is an element of the set of quantized positions. In practical situations, the actual DOA is not always equal to an element of the quantized set of grid points, and this implies that the estimated DOA will have some quantization error. Since the number of antenna elements is typically much smaller than the number of quantization points, the matrix formulation of the solution of the vector indicating the DOA represent an under-determined set of equations. Compressive sensing is used to determine the sparsest solution to the matrix equation.A fundamentally new iterative algorithm to estimate the DOA of an incoming signal in a wireless network is introduced in the thesis. This algorithm, which utilizes compressive sensing as a foundation, eliminates the error induced due to discrete grid quantization. This enables the estimation error performance of the algorithm to achieve the theoretical Cramer Rao Lower Bound (CRLB) using just two iterations. The algorithm requires extremely low computational complexity for implementation and is general in nature. The proposed algorithm is demonstrated by applying it to two antenna array geometries, the Uniform Circular Array (UCA) and Uniform Linear Array (ULA). For both the UCA and the ULA, the CRLB performance is achieved by the new algorithm. The relative performances of the UCA and ULA were compared.The thesis also considers a novel multiresolution DOA estimation algorithm based on CS that illustrates superior performance compared to the traditional techniques.The multiresolution approach is also shown to be eﬀective in reducing the computational complexity of the estimation process.A novel RSS based localization algorithm is presented that oﬀers improvement in the structure of the dictionary matrix by selectively eliminating observations from closely placed sensors. Similar observations lead to ill-conditioned dictionary matrices and as a result, degrades the performance of CS processing. The study illustrates that diﬀerent random distributions of sensors have unique eﬀects on the structure of the measurement matrices. An in-depth analysis on the impact of diﬀerent parameters on the structure of the dictionary matrix is presented. The analysis suggests that careful manipulation of antenna array geometry parameters can signiﬁcantly enhance the structure of the dictionary matrix and therefore improve the estimation accuracy of the algorithm. In summary, the thesis investigates localization techniques based on compressive sensing processing. Several new, high-performance algorithms were described and their performances and computational complexities were analyzed. The thesis establishes a connection between the mathematical properties of the dictionary matrix and the performance of the new localization techniques. Within classes of antenna array geometries, the dictionary matrix properties are used as an enabler for the selection of antenna elements spacings that provided optimized DOA estimation performance.