In this paper, we developed a theoretical and experimental framework for the mapping of obstacles using WiFi, based on a small number of wireless channel samples. This is very challenging due to the numerous channel coefficients to be estimated over the time-varying channel and the channel estimation of a wireless signal transmission to be considered for compressive sampling. In a typical communication system, the signal is sampled at least twice at the highest frequency contained in the signal. However, this limits efficient ways to compress the signal, as it places a huge burden on sampling the entire signal while only a small number of the transform coefficients are needed to represent the signal. To tackle this problem, we will focused on a mathematical optimization problem for the most efficient compressed sensing method called $\ell_1$-norm, known as Basis Pursuit. Before optimizing the problem, the noise was removed from the signal, namely, multipath fading. Our experimental results show the improved performance in the number of iterations for obtaining a framework for the mapping of obstacles.