Link-adaptation (LA) is one of the most important aspects of wireless communications where the modulation and coding scheme (MCS) used by the transmitter is adapted to the channel conditions in order to meet a certain target error-rate. In a single-user SISO (SU-SISO) system with out-of-cell interference, LA is performed by computing the post-equalization signal-to-interference-noise ratio (SINR) at the receiver. The same technique can be employed in multi-user MIMO (MU-MIMO) receivers that use linear detectors. Another important use of post-equalization SINR is for physical layer (PHY) abstraction, where several PHY blocks like the channel encoder, the detector, and the channel decoder are replaced by an abstraction model in order to speed up system-level simulations. However, for MU-MIMO systems with non-linear receivers, there is no known equivalent of post-equalization SINR which makes both LA and PHY abstraction extremely challenging. This important issue is addressed in this two-part paper. In this part, a metric called the bit-metric decoding rate (BMDR) of a detector, which is the proposed equivalent of post-equalization SINR, is presented. Since BMDR does not have a closed form expression that would enable its instantaneous calculation, a machine-learning approach to predict it is presented along with extensive simulation results.