Aimed at the problems that the inter symbol interference is severe and the bit error rate is high at the receiving end of slow decaying variable air multipath channels,on the basis of SC-FDE system, the sparsity of airborne multipath channels is analyzed, the airborne channel estimation model is taken as arecovery problem for sparse signals, and a PN-SAMP channel estimation algorithm is proposed based on a compressionaware framework by using PN sequences to construct a deterministic measurement matrix with SAMP as the recovery algorithm. The estimated mean square errors of compressionaware algorithms are compared to that of the traditional PN and LS algorithms, and the error performance of several estimation methods applied in SC-FDE systems is compared in conjunction with MMSE equalization. The simulation results show that the estimation errors and the bit error rates of compressionaware class algorithms are smaller and lower than that of the traditional PN and LS algorithms respectively, and the bit error rate of the compressionaware class algorithms is less than at a signaltonoise ratio of 20dB. The robust of the PN-SAMP algorithm is better than that of the OMP algorithm in the case of unknown sparsity, further meeting the estimation needs of sparse channels in the timevarying slowdecay aviation.