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Compressed Training Adaptive MIMO equalization

This article proposes an adaptive equalization framework for flat fading multi-input multi-output(MIMO) systems, where the main goal is to significantly reduce the number of training symbols. The proposed approach exploits the special boundedness property of digital communication signals along with training symbols to adapt receiver equalizer filter. The corresponding framework is built upon some convex settings where the infinity norm is used to utilize the special constellation structure for the efficient adaptation process. As a fundamental result, through the duality between ℓ∞ and ℓ1 norms, the proposed approach establishes an interesting link between adaptive equalization problem and compressed sensing problems. Using this link, the aim of the proposed optimization settings can be viewed as achieving the desired sparseness of the perfect equalization channel with compressed amount of training symbols. Based on this connection, we can prescribe that the training size is on the order of logarithm of the number of sources without any prior sparsity assumption on the wireless channel model. This promises a significant reduction in training symbols especially for the base stations employing very large number of antennas such as Massive MIMO applications. The numerical examples verify the analytical results and demonstrate the practical benefits of the proposed approach.