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Minimum selection generalized selection combining (MS-GSC) scheme has been proposed as a generalized power-saving variant of the conventional generalized selection combining (GSC) scheme. Previous analysis of the performance of MS-GSC has focused on interference-free environments. This paper aims to investigate the performance of adaptive signal-to-noise ratio (SNR)-based MS-GSC in the presence of co-channel interference over multipath fading channels. The adaptation thresholds are selected to enhance either the spectral efficiency or power efficiency of discrete-time rectangular signaling system. New closed-form expressions for the statistics of combined signal-to-interference-plus-noise ratio (SINR) are presented, which are then used to obtain analytical formulations for various performance measures. Numerical and simulation comparisons for the performance of the adaptation scheme are provided.