Efficient FFT-based Circulant Embedding Method and Subspace Algorithms for Wideband Single-carrier Equalization

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In single-carrier transmission systems, wider bandwidth allows higher data rate by transmitting narrower pulses. For wireless applications, however, this means that the effective channel response is longer and the number of significant taps increases. This results in higher computational burden at the receiver. In this paper, we first review some well-known equalization methods and their shortcomings. Then we will propose the use of the circulant embedding method and the CG algorithm as efficient equalizers that are specifically well suited in dealing with long delay spread channels. These methods take advantage of the low computational complexity of the FFT algorithm, resulting in the same overall computational complexity of N log(N). Furthermore, when the CG algorithm is used correctly, it may perform better than the MMSE equalizer at a much lower cost
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