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High Frequency (HF) radio waves propagating in the ionospheric random inhomogeneous media exhibit a spatial nonlinearity wavefront which may limit the performance of conventional high-resolution methods for HF sky wave radar systems. In this paper, the spatial correlation function of wavefront is theoretically derived on condition that the radio waves propagate through the ionospheric structure containing irregularities. With this function, the influence of wavefront distortions on the array covariance matrix can be quantitatively described with the spatial coherence matrix, which is characterized with the coherence loss parameter. Therefore, the problem of wavefront correction is recast as the determination of coherence loss parameter and this is solved by the covariance matching (CM) technique. The effectiveness of the proposed method is evaluated both by the simulated and real radar data. It is shown numerically that an improved direction of arrival (DOA) estimation performance can be achieved with the corrected array covariance matrix.