Antenna arrays with discrete antenna elements have been conventionally used in multiple-input multiple-output (MIMO) communications. Improved spectral efficiency resulting from more antenna elements has motivated the idea of packing very large numbers of elements in an array, yielding continuous-like antennas. This paper conducts a performance analysis of continuous antennas, employing matched filtering. We derive a gamma approximation for the instantaneous received signalto-noise ratio (SNR) under a Rician channel with a spatiallycorrelated non-line-of-sight (NLoS) component. We also derive the mean and an upper bound for achievable rate. Numerical results demonstrate the accuracy of our approximations across a range of parameters.