  This paper investigates the linear precoder design for $K$-user interference
channels of multiple-input multiple-output (MIMO) transceivers under finite
alphabet inputs. We first obtain general explicit expressions of the achievable
rate for users in the MIMO interference channel systems. We study optimal
transmission strategies in both low and high signal-to-noise ratio (SNR)
regions. Given finite alphabet inputs, we show that a simple power allocation
design achieves optimal performance at high SNR whereas the well-known
interference alignment technique for Gaussian inputs only utilizes a partial
interference-free signal space for transmission and leads to a constant rate
loss when applied naively to finite-alphabet inputs. Moreover, we establish
necessary conditions for the linear precoder design to achieve weighted
sum-rate maximization. We also present an efficient iterative algorithm for
determining precoding matrices of all the users. Our numerical results
demonstrate that the proposed iterative algorithm achieves considerably higher
sum-rate under practical QAM inputs than other known methods.
