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This paper presents a new theoretical framework for designing the minimum mean squared error (MMSE) matching network for a low noise amplifier (LNA). The MMSE matching network is determined by reformulating the matching problem as a continuous-time estimation problem and solving for the Wiener-Hopf equation. Since the MMSE matching network is in general difficult to implement, a constrained MMSE matching network is also presented. The resulting noise factor of the LNA is computed and compared against different matching strategies.