In this study joint estimation of the symbol timing offset (STO), and channel impulse response (CIR) of each active user under the presence of the carrier frequency offset (CFO) is considered for the uplink of an orthogonal frequency-division multiple access (OFDMA) system. A new method based on the compressed sensing (CS) framework using pilot symbols is proposed for the joint estimation of the STO and the CIR of each active user. Sparsity is achieved through incorporating the STO, the cyclic prefix (CP) samples, and the CIR coefficients into a new signal model. The proposed method does not require CIR coefficients to be sparse. Numerical results of the performance of the proposed method using the orthogonal matching pursuit (OMP) algorithm is presented. The presence of CTO is also considered as a perturbation to the CS dictionary of pilot symbols.