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The joint linear precoder and decoder minimum mean squared error (MMSE) design represents a low complexity yet powerful solution for spatial multiplexing MIMO systems. Its performance, however, critically depends on the availability of timely channel state information (CSI) at both transmitter and receiver. In practice, the latter assumption can be severely challenged, due to channel time variations that lead to outdated CSI at the transmitter. State-of-the-art designs mistakenly use the outdated CSI to design the linear precoder and rely on the receiver to reduce the induced degradation. In this paper, we propose a robust Bayesian joint linear precoder and decoder solution that takes into account the uncertainty of the true channel, given the outdated CSI at the transmitter. We finally assess the robustness of our design to channel time variations through Monte-Carlo analysis of the system's MMSE and average bit-error rate (BER) performance.