Interference widely exists in communication systems and is often not
optimally treated at the receivers due to limited knowledge and/or
computational burden. Evolutions of receivers have been proposed to balance
complexity and spectral efficiency, for example, for 6G, while commonly used
performance metrics, such as capacity and mutual information, fail to capture
the suboptimal treatment of interference, leading to potentially inaccurate
performance evaluations. Mismatched decoding is an information-theoretic tool
for analyzing communications with suboptimal decoders. In this work, we use
mismatched decoding to analyze communications with decoders that treat
interference suboptimally, aiming at more accurate performance metrics.
Specifically, we consider a finite-alphabet input Gaussian channel under
interference, representative of modern systems, where the decoder can be
matched (optimal) or mismatched (suboptimal) to the channel. The matched
capacity is derived using Mutual Information (MI), while a lower bound on the
mismatched capacity under various decoding metrics is derived using the
Generalized Mutual Information (GMI). We show that the decoding metric in the
proposed channel model is closely related to the behavior of the demodulator in
Bit-Interleaved Coded Modulation (BICM) systems. Simulations illustrate that
GMI/MI accurately predicts the throughput performance of BICM-type systems.
Finally, we extend the channel model and the GMI to multiple antenna cases,
with an example of multi-user multiple-input-single-output (MU-MISO) precoder
optimization problem considering GMI under different decoding strategies. In
short, this work discovers new insights about the impact of interference,
proposes novel receivers, and introduces a new design and performance
evaluation framework that more accurately captures the effect of interference.