Asymptotic Performance of Box-RLS Decoders under Imperfect CSI with Optimized Resource Allocation

Abstract
This paper considers the problem of symbol detection in massive multiple-input multiple-output (MIMO) wireless communication systems. We consider hard-thresholding preceded by two variants of the regularized least squares (RLS) decoder; namely the unconstrained RLS and the RLS with a box constraint, which is called Box-RLS. For all schemes, we focus on the evaluation of the mean squared error (MSE) and the symbol error probability (SEP) for M-ary pulse amplitude modulation (M-PAM) symbols transmitted over a massive MIMO system when the channel is estimated using linear minimum mean squared error (LMMSE) estimator. Under such circumstances, the channel estimation error is Gaussian which allows for the use of the convex Gaussian min-max theorem (CGMT) to derive asymptotic approximations for the MSE and SEP when the system dimensions and the coherence duration grow large with the same pace. The obtained expressions are then leveraged to derive the optimal power distribution between pilot and data under a total transmit energy constraint. In addition, we derive an asymptotic approximation of the goodput for all schemes which is then used to jointly optimize the number of training symbols and their associated power. Numerical results are presented to support the accuracy of the theoretical results.

Citation
Alrashdi, A. M., Kammoun, A., Muqaibel, A. H., & Al-Naffouri, T. Y. (2022). Asymptotic Performance of Box-RLS Decoders under Imperfect CSI with Optimized Resource Allocation. IEEE Open Journal of the Communications Society, 1–1. https://doi.org/10.1109/ojcoms.2022.3206894

Acknowledgements
This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research under Award OSR-CRG2019-4041.

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
IEEE Open Journal of the Communications Society

DOI
10.1109/ojcoms.2022.3206894

Additional Links
https://ieeexplore.ieee.org/document/9893195/

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