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Noise variance is an important parameter for single-carrier ultra- wideband systems with frequency domain equalisation. The conventional method cannot obtain the noise variance in the case of using the estimated channel coefficients by least square (LS) criteria, whereas the LS channel estimator is a promising candidate owing to its easy implementation. To overcome this contradiction, proposed is a novel noise variance estimator using the LS channel coefficient estimates with the aid of a complex pilot sequence. Also derived is the Cramer-Rao bound on the proposed estimator. In addition, Chu's sequence is chosen as the optimal pilot sequence of LS channel estimation without increase of peak-to-average power ratio and with easy realisation. Simulations demonstrate the performance of the proposed schemes.