This thesis investigates the systems for hands-free mobile communication. In hands-free communication, there are various kinds of disturbances in the microphone reception due to the distance between the source and the receiver. The disturbances are mainly background noise and reverberation. To overcome these problems, this thesis uses two techniques: one is first-order adaptive differential microphone array, referred to as Elko’s beamformer and the other is spectral subtraction using a minimum statistics approach. The two techniques have different approaches in the way they process the signals. In the adaptive beamforming technique, the basic principle of noise suppression is purely based on phase information; based on the obtained phase information the beam is steered to the direction of desired signal and reducing the noise coming from other directions. Spectral subtraction, on the other hand, is a single channel speech enhancement technique typically using omnidirectional microphone, which does not use any phase information to process the signal. The spectral subtraction algorithm estimates the noise spectrum in speech pauses and subtracts it from the noisy speech spectrum to give an enhanced speech output. In this thesis, Elko’s beamformer is realized by combining two omnidirectional microphones to forms back-to-back cardioid. By using adaptive capabilities of the system, the first order microphone null is restricted to rear half plane and it can significantly improve the signal-to-noise ratio in hands-free communication. The other technique involved is spectral subtraction using a minimum statistic approach. This technique ignores the conventional way of approach, which estimates noise based on voice active detection (VAD). The minimum statistic approach is capable of dealing with non-stationary noise signals and requires low computational complexity. In this thesis the two techniques, beamforming and spectral subtraction are combined to give an even better system in terms of noise reduction. The systems individual performance and also combined performance is tested. Though the proposed algorithm shows lacking performance in the case of reverberant environment, but outperforms in case of anechoic environment with the average SNR-I of 19.5 dB and the average PESQ scores of 3.1.Thus, by taking these results into consideration, it can be concluded that the proposed method yield’s improved speech quality in an anechoic environment.