In an OFDM system, the multipath channel introduces time varying and frequency selective properties in the OFDM symbols, causing Inter-Carrier Interference (ICI) and frequency and phase offset. Thus, channel estimation is imperative for OFDM systems. In most present work, the channel estimation is implemented with merely the traditional pilot- based method. However, this paper has made a comparison under Rayleigh multipath channel between the traditional pilot-based methods including Least Square (LS) and Minimum Mean Square Error (MMSE). We also compare the emerging Machine Learning (ML)-based method and traditional method in the similar multi-path channels. Further impacts of the number of Layers for the deep neural network (DNN) as well as the number of pilots are studied in ML-based channel estimation. The effects of different mapping schemes are also studied within the traditional LS and MMSE method. Besides, a joint frequency offset estimation is provided, regarding the impacts of Cyclic prefix (CP) length and SNR on the Mean Square Error (MSE) of frequency offset estimation. Results have shown that the ML-based method can achieve a relatively good result comparing with traditional method in the similar channels. However, the ML based method has shown a much greater computational complexity than the traditional method, and as the SNR rises, the ML based method tends to have a worse performance than the MMSE method.