The relative transfer function generalized sidelobe canceler (RTF-GSC) is a popular method for implementing multichannel speech enhancement. However, an accurate estimation of channel transfer function ratios pose a challenge, especially in noisy environment. In this work, we demonstrate that even a very low order RTF estimate can give superior performance in terms of noise reduction without incurring excessive speech distortion. We show that noise reduction is dependent on the correlation between the input noise and the noise reference generated by the Blocking Matrix (BM), and that a low order RTF estimate preserves this correlation better than a high order one. The performance for both high order and low order RTF estimates are compared using output SNR, Noise Reduction and a perceptual measure for speech quality.