1. A method of transmitting a sparse signal in a sparse signal transmitting device, the method comprising: receiving a target signal transmitted by the sparse signal transmitting device that is based on an input signal, wherein the input signal is obtained by adding a noise signal to a measurement signal that is generated from the sparse signal transmitting device, and wherein the noise signal includes noise added in a wireless channel environment and quantization noise added in a quantization step; simultaneously sensing and compressing the target signal based on a sensing matrix consisting of a zero element and a non-zero element; transferring a compressed signal to a sparse signal recovering device through a transmit channel, wherein the sensing matrix has a number of rows less than a number of columns, wherein the sparse signal recovering device configured to receive the compressed signal, update a posterior probability using a likelihood probability, and recover the target signal by performing a maximum a posterior estimation with respect to an updated posterior probability.