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A focal plane array feed of electrically small elements has been proposed as a means for achieving high sensitivity for radio astronomy applications in the presence of radio frequency interference (RFI). For a broadband system, mutual coupling effects become significant as the array element spacing becomes small relative to the electromagnetic wavelength. We present a theoretical framework for modeling the effects of mutual coupling and for determining the optimal multiport matching network between array elements and front-end transistor low-noise amplifiers for maximum signal-to-noise ratio (SNR). Numerical results are given for a model scenario including spillover and amplifier thermal noise and point signal and interference sources. A suboptimal self-impedance matching network yields performance close to that of a full network match.