Single front-end architecture with parasitic antenna element (PAE) in compact array system has been proposed for enhancing spectral efficiency and miniaturizing the receiver. Although most of studies paid attention to design optimal receiver with antenna mutual coupling on fading correlation, relatively little attention has been paid to noise. In this paper, we propose a low noise model for single front-end MIMO receiver system with PAE which includes arbitrary signal and noise coupling. The proposed model articulates physical noise sources and relates their spatial correlation with array receive antennas, parasitic element, front-end and matching circuit. A matching circuit is designed to achieve minimum noise figure. After that, the optimal PAE value is derived to maximize channel capacity. We present numerical analysis to verify the proposed system on certain conditions.