In recent years a great deal of effort has been expended to develop methods that determine the quality of speech through the use of comparative algorithms. These methods are designed to calculate an index value of quality that correlates to a mean opinion score given by human subjects in evaluation sessions. In this work PESQ (ITU-T Recommendation P.862) which is the new ITU-T benchmarking for objective measurement of speech quality. In mobile phone acoustics, the presence of noise and room reverberation play a vital role in degrading the speech signal and therefore, spectral subtraction and Elko’s beamformer has been used for noise reduction. Weighted Overlap and Add method (WOLA) filter bank is used for frequency domain analysis of the speech signal. Elko’s algorithm is used for designing a differential microphone array, implemented by connecting two omni directional elements to form back-to-back cardioid directional microphones. The output from the Elko’s beamformer is then used as an input to spectral subtraction based on minimum statistics reducing further noise and to enhance the quality of the speech signal. The performance of this system is analysed by calculating the value of PESQ as a speech quality measure. The better the value the PESQ, the better is the output speech quality. Signal to Noise Ratio (SNR) is used to measure the amount of noise in the restored speech signal. Reverberation Index is also used to measure the amount of reverberation effect present in the restored speech signal.