  This paper investigates the performance of improper Gaussian signaling (IGS)
for the $K$-user multiple-input, multiple-output (MIMO) interference channel
(IC) with hardware impairments (HWI). HWI may arise due to imperfections in the
devices like I/Q imbalance, phase noise, etc. With I/Q imbalance, the received
signal is a widely linear transformation of the transmitted signal and noise.
Thus, the effective noise at the receivers becomes improper, which means that
its real and imaginary parts are correlated and/or have unequal powers.
  IGS can improve system performance with improper noise and/or improper
interference. In this paper, we study the benefits of IGS for this scenario in
terms of two performance metrics: achievable rate and energy efficiency (EE).
We consider the rate region, the sum-rate, the EE region and the global EE
optimization problems to fully evaluate the IGS performance. To solve these
non-convex problems, we employ an optimization framework based on
majorization-minimization algorithms, which allow us to obtain a stationary
point of any optimization problem in which either the objective function and/or
constraints are linear functions of rates. Our numerical results show that IGS
can significantly improve the performance of the $K$-user MIMO IC with HWI and
I/Q imbalance, where its benefits increase with the number of users, $K$, and
the imbalance level, and decrease with the number of antennas.
