Technique that succeed in the next-generation wireless communication is known as Orthogonal frequency division multiplexing is a. Channel assessment is one of the key challenges in OFDM, since high-resolution channel estimation can significantly advance the equalization at the receiver and accordingly enhance the communication performances. However, its iterative intervention cancellation algorithm will experience performance loss especially under severely fading channels with long delay and has complexity supporting high-order modulations like 256 QAM, which may not accommodate the promising ultra-high meaning television service. To resolve this difficulty, a channel estimation method for OFDM in the structure of compressive sensing is planned in our work. Firstly, by exploiting the signal structure of recently proposed TDM-OFDM scheme, the auxiliary channel information is obtained. Secondly, we propose the auxiliary information based subspace pursuit (SP) algorithm to utilize a very small amount of frequency domain pilots embedded in the OFDM block for the precise channel assessment. Moreover, the obtain auxiliary channel information is adopted to reduce the complexity of the traditional SP algorithm. Simulation results demonstrate a significant reduction of the number of pilots comparative to least-squares channel assessment and supporting high-order modulations like 256 QAM