The quality and intelligibility of speech is degraded with the presence of background noise in the speech signal, which affects the listeners ability to understand the speech clearly. Speech enhancement is the process with which the background noise can be suppressed to improve the quality and intelligibility of the speech signal. With the development of speech based human computer interfaces, the demand for speech enhancement is growing. There are many applications like hand free mobile communication, teleconferencing, automatic speech recognition, hearing aids etc where there is a requirement for speech enhancement due to the noise interruption in the speech signal. Among all the applications mentioned, hearing aids are the ones which drew attention. This motivated us to go in depth with the research on hearing aids using different speech enhancement techniques and algorithms to enhance the quality of the speech at the end user. There are many algorithms and techniques that can be used to enhance the speech signals quality and intelligibility. Several beamforming techniques using multi microphone arrays are widely used at present in the field of speech enhancement. In this thesis, Elko and Wiener beamforming algorithms with first order differential microphone arrays are being used to enhance the speech signal in an application, especially like hearing aids. The main reason for using Elko algorithm is: it tracks and attenuates the background noise or interference present in the back half plane of the microphone array. The Wiener beamformer is used as; it is a minimum mean square error beamformer which has the ability to nullify all the interference signals and sustains a high level of performance by getting signals from the desired direction. In this thesis, the assemblage of Elko and Wiener beamformers is also implemented as the Elko-Wiener Beamformer. These algorithms were implemented in a computer simulated anechoic chamber using MATLAB R2008. Recorded male and female speech signals sampled at 16 KHz were used as inputs to the system, where female speech is the target signal vocalizing from forward direction to the microphone array and male speech is the interference signal impinging from the backward direction to the microphone array. The performance metrics used to measure the quality of the speech signal are signal to-noise ratio increment (SNRI), speech and noise distortions and ITU-T recommended PESQ MOS values. The simulation results show that the Elko-Wiener Beamformer has the advantages of individual Elko and Wiener Beamformers giving 29dB SNRI. The Elko and the Wiener Beamformers has 10 dB and 17 dB SNRI respectively. Hence the Elko-Wiener joint Beamformer outperforms its individual beamformers in its class.