Pulse Pairs (PPs) generated by Distance Measure Equipment (DME) cause severe interference on L-band Digital Aeronautical Communication System type 1 (L-DACS1) which is based on Orthogonal Frequency Division Multiplexing (OFDM). In this paper, a novel and practical PP mitigation approach is proposed. Different from previous work, it adopts only time domain methods to mitigate interference, so it will not affect the subsequent signal processing in frequency domain. At the receiver side, the proposed approach can precisely reconstruct the deformed PPs (DPPs) which are often overlapped and have various parameters. Firstly, a filter bank and a correlation scheme are jointly used to detect non-overlapped DPPs, also a weighted average scheme is used to automatically measure the waveform of DPP. Secondly, based on the measured waveform, sparse estimation is used to estimate the precise positions of DPPs. Finally, the parameters of each DPP are estimated by a non-linear estimator. The key point of this step is, a piecewise linear model is used to approximate the non-linear carrier frequency of each DPP. Numerical simulations show that comparing with existing work, the proposed approach is more robust, closer to interference free environment and its Bit Error Rate is reduced by about 10dB.