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Multi-input multi-output (MIMO) radio channel sounders commonly employ time-division multiplexing (TDM) techniques to switch between the elements of the transmit and receive antenna arrays. However, phase noise of the local oscillators in the transmitter and the receiver of a TDM MIMO channel sounder can significantly affect the accuracy of estimates of relevant channel parameters, such as the channel capacity and the parameters of propagation paths. In this paper we derive a new SAGE algorithm for path parameter estimation that compensates for the effect of phase noise. Monte Carlo simulations show that the new algorithm always outperforms the traditional SAGE algorithm and that it is able to practically mitigate this effect, provided the phase noise variance is below a certain threshold. The general conclusion is that the new SAGE algorithm is able to compensate for the effect of phase noise in practical channel sounding equipments, provided the used sounding sequences are sufficiently short. Further investigations are needed to quantitatively assess the relationship between the maximum duration of the used sounding sequences and the short-term statistics of phase noise for this compensation to be effective.