In the present time bandwidth efficiency is one of the most important parameter to measure different modulation scheme in digital communication. Due to the separation of waveforms of all the existing modulation schemes in time domain it becomes difficult to improve their bandwidth efficiency. Hence it was become very important for researchers to proposed such a scheme that able to improves the bandwidth efficiency of our existing modulation schemes to make them more reliable as per their increasing demands. Latest study in the same field results a new scheme named as Compressive Modulation (CM) which combines Compressive Sensing (CS) with traditional BPSK pattern that leads to highly improved bandwidth efficiency of traditional BPSK. In the current work we are going to use the CS theory with traditional OFDM to make it more bandwidth efficient than traditional one.