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We investigate the design of three low-complexity joint estimation algorithms (LJEAs) for frequency offset and carrier phase. The principles of the proposed LJEAs are based on the linear interpolation of correlation values in the main-lobe of the frequency and phase spectra of the received signal. With these algorithms, the estimation ranges, Δfd×Ts, are less than 1/2Ns and 1/Ns which are comparable to conventional algorithms (fd is the frequency offset, Ts is the symbol period, Ns is the burst length). The proposed LJEAs require only 2Ns or 4Ns complex multiplications which are very simple compared with conventional algorithms. Nevertheless the estimation accuracies of the LJEAs are as good as those of the conventional algorithms.