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Low-complexity real-time signal processing for wireless communications

Many signal processing algorithms in modern wireless communication systems come with a very high computational complexity. Moreover, these algorithms must be implemented in real time. Since the computational performance of digital signal processors is limited, these two requirements—dealing with arithmetic complexity and real-time constraints—are often mutually exclusive. This thesis tries to solve this problem by trading the complexity of signal processing algorithms for accuracy. This approach is feasible if the accuracy of the underlying hardware or the accuracy requirements of the algorithm’s result is limited. The first part of this thesis deals with the real-time simulation of geometry-based channel models. Geometry-based channel models implicitly model the spatial structure of the channel and are thus ideally suited for simulating MIMO (multiple-input multiple-output) systems. However, such models are computationally expensive, since for every propagation path, every time instance, and every delay or frequency bin, a complex exponential has to be evaluated. On a real-time hardware channel simulator the number of paths P that can be simulated is thus limited by the available processing power. Time-variant, frequency-selective MIMO channels can be described as fourdimensional sequences, where the dimensions represent time, frequency, space at the receiver, and space at the transmitter. In wireless communication systems, such sequences are bandlimited by the maximum Doppler frequency in time, by the maximum delay of the channel in frequency, by the angle of arrival spread in the space at the receiver, and by the angle of departure spread at the space at the transmitter. For block based channel simulation, index-limited parts of these four-dimensional sequences need to be evaluated. It can be shown, that such index-limited parts span a low-dimensional subspace. The same subspace is spanned by the multidimensional discrete prolate spheroidal (DPS) sequences. An important contribution of this thesis is a new algorithm that allows to compute the projection of a geometry-based channel model onto the DPS subspace in O(1) arithmetic operations. By adjusting the dimension of the subspace it is possible to trade complexity for accuracy. On a 16 bit fixed-point arithmetic processor, the computational complexity can be reduced by more than one order of magnitude compared to conventional sum-of-sinusoids implementations. The second part of this thesis addresses the development and simulation of receiver