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The paper deals with carrier recovery based on pilot symbols in single-carrier systems. The system model considered in the paper includes the channel additive white noise and the phase noise that affects the local oscillators used for up/down-conversion. Wiener's method is used to determine the optimal filter in estimation of phase noise assuming that a sequence of equally spaced pilot symbols is available. Our analysis allows to capture the cyclostationary performance of the estimate, a phenomenon that is not considered in the previous literature. In the paper, closed-form formulas for the transfer function of the optimal filter and for the mean-square phase error are derived for the case where the phase noise is modelled as random phase walk. For this case, a suboptimal filter is proposed. Numerical results are presented to substantiate the analysis.