Signal Processing on Special Manifolds with Applications to Wireless Communication

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The demand for wireless communication is only growing, as wireless becomes the dominant means of Internet access. To meet this demand, wireless systems may employ new concepts such as multiple antennas, multiple user processing, transmitter coordination, and interference alignment to improve system capacity. Unfortunately, implementing these communication techniques requires substantial feedback from the receiver to the transmitter and more complex signal processing to reap the promised capacity gains. Fortunately, there is special manifold structure in these signal processing problems that is not yet exploited. Manifolds are generalizations of surfaces to higher dimensions and can be used to capture structure in signals. Special manifolds like the Stiefel and Grassmann manifolds are of particular interest in wireless communication systems that use multiple antennas. This research involves developing a suite of signal processing techniques for analyzing, filtering, predicting, and optimizing signals with curved manifold structure.This project applies new manifold signal processing tools to three emerging problems in wireless communication: multiple user multiple antenna communication, interference aligned transmission, and coordinated base station transmission. Each problem requires progressively more sophisticated manifold signal processing techniques to enable their eventual application in commercial and military wireless communication systems. The most immediate impact of this research will be to improve the quality and capacity of wireless communication links thus impacting their design, implementation and deployment. The long range impact will be tools and analytical techniques that influence other disciplines including control theory, optimization, image and video processing, data mining and manifold learning. Broader impacts of this research program will occur in education through the training of undergraduate and graduate students and in industry through rapid dissemination of research results through electronic preprints.