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In this paper, we investigate the design of linear precoders formultiple-input multiple-output (MIMO) multiple access channels (MAC). We assumethat statistical channel state information (CSI) is available at thetransmitters and consider the problem under the practical finite alphabet inputassumption. First, we derive an asymptotic (in the large-system limit) weightedsum rate (WSR) expression for the MIMO MAC with finite alphabet inputs andgeneral jointly-correlated fading. Subsequently, we obtain necessary conditionsfor linear precoders maximizing the asymptotic WSR and propose an iterativealgorithm for determining the precoders of all users. In the proposedalgorithm, the search space of each user for designing the precoding matricesis its own modulation set. This significantly reduces the dimension of thesearch space for finding the precoding matrices of all users compared to theconventional precoding design for the MIMO MAC with finite alphabet inputs,where the search space is the combination of the modulation sets of all users.As a result, the proposed algorithm decreases the computational complexity forMIMO MAC precoding design with finite alphabet inputs by several orders ofmagnitude. Simulation results for finite alphabet signalling indicate that theproposed iterative algorithm achieves significant performance gains overexisting precoder designs, including the precoder design based on the Gaussianinput assumption, in terms of both the sum rate and the coded bit error rate.

Linear MIMO Precoding in Jointly-Correlated Fading Multiple Access Channels with Finite Alphabet Signaling