Compressive Sensing for Speech Signals in Mobile Systems

Compressive sensing is an emerging and revolutionary technology that strongly relies on the sparsity of the signal. In compressive sensing the signal is sparsely compressively sampled by taking a small number of random projections of the signal, which contain most of the salient information. Compressive sensing has been previously applied in areas like: image processing, radar systems and sonar systems. This research work will discuss the potential implementation of compressive sensing in mobile communication systems and how it will influence their data rates. In a typical mobile communication system, the signal of interest is sampled at least at the Nyquist rate. The Nyquist sampling theorem states that the frequency used to sample a signal should be at least twice the maximum frequency contained within the signal. However, this is not the most efficient way to compress the signal, as it places a lot of burden in sampling the entire signal while only a small percentage of the transform coefficients are needed to represent it. The recent results in compressive sampling (also known as compressive sensing) provide a new way to reconstruct the original signal with a minimal number of observations. In compressive sensing the significant information about the signal/image is directly acquired, rather than acquiring the significant information that will be eventually thrown away. The goal of this research is to propose a new mobile communication system which employs compressive sampling to compress the speech signal at the transmitter and decompress it at the receiver. The expected results from the proposed system will be an increment in the data rates of these systems. In order to simulate how compressive sensing could be applied, a small speech signal was recorded in MATLAB. The signal at the transmitter is then multiplied by the measurement matrix which in this case is composed of randomly generated numbers. The measurement matrix is chosen in such a way that the sparse signal can be exactly recovered at the receiver using one of the different optimization techniques available. Once the signal has gone through the process of compressive sampling, it is ready to be transmitted through the mobile system. The transmitted signal is then reconstructed by the receiver from a significantly small number of samples by using any of the multiple optimization techniques available. The algorithm is simulated in MATLAB. The results show that if a threshold window is applied to the transmitted speech signal and the length of the signal is kept constant, the compression rate of the speech signal is increased