In various wireless applications, a receiver picks up data packets from multiple users where the packets share a common preamble, but otherwise carry different payloads, are not in temporal sync and are frequency shifted due to Doppler effect and oscillator imperfections. We pose the problem of identifying the number of interfering packets and extracting the payloads as one of finding a sparse representation in a redundant dictionary. However, because of large size of the dictionary due to unknown packet payloads, direct application of conventional recovery methods does not lead to computationally tractable estimation schemes. To overcome this issue, we propose Orthogonal Matching Pursuit with Approximate Atoms (OMP-AA) algorithm aimed to facilitate identification of packet collisions and payload extraction. The simulation study shows that the proposed method performs well compared to an oracle estimator which has perfect knowledge of the packet parameters.