We present a hardware implementation of channel estimation based on compressive sensing method. To reduce the hardware overhead, we leverage the orthogonal property of codebook to reduce computational complexity. In frequency domain stage, the inverse matrix operation of the sensing matrix is simplified to a conjugate transpose. In time domain, the sensing matrix is disassembled to lower dimension matrices. Then, based on the benefits of gOMP and Cholesky decomposition, we perform an efficient hardware implementation of this problem. Finally, the quantization error of the system is evaluated and the optimal amount of word length to achieve proper performance is determined.