On Kaczmarz Signal Processing Technique in Massive MIMO
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To exploit the benefits of massive multiple-input multiple-output (M-MIMO) technology in scenarios where base stations need to be inexpensive, the computational complexity of classical signal processing schemes for spatial multiplexing must be reduced. This calls for suboptimal or "relaxed" schemes that perform well the required combining/precoding steps while achieve low computational complexities. Herein, modifications are proposed aiming to improve its rate of convergence with a rising performance-computational complexity trade-off solution for the M-MIMO combining/precoding problems. Such improvements are motivated by observed negative effects of pathloss and shadowing, originally presented here, over the rate of convergence granted by the KA, which consequently worsens its achievable spectral efficiency (SE). Specifically, the randomized version of KA (rKA) is used when conceiving the signal processing schemes due to its global convergence properties, where our adaptations can be seen as a fairness policy for algorithm initialization that guarantees the converge of all combining/precoding vectors, whether they be from center located users or those located at the edge of the cell. Two different rKA-based schemes are in fact discussed, of which only one is considered applicable, given the constraints placed by the underlying scenario. To ensure that the proposed method outclasses the original proposal, a mathematical characterization is presented along with numerical results that employ more realistic system and channel conditions. The simulations embrace the least-squares and minimum mean-squared error estimators of the channel responses, also taking into account uncorrelated and correlated Rayleigh fading channels. The spatial correlation of the latter is modeled using the exponential correlation model combined with large-scale fading variations over the array.
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