Journal of Radio Electronics. eISSN 1684-1719. 2025. №8

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DOI: https://doi.org/10.30898/1684-1719.2025.8.3

Sub-nyquist tensor completion

for massive mimo Channel estimation:
PART 1

S.V. Dorokhin, D.V. Shuvalov, V.A. Lyashev

Moscow Institute of Physics and Technology,

9 Institutskiy per., Dolgoprudniy, Moscow Region, 141700, Russia

The paper was received May 2, 2025.

Abstract. Current trend of Massive MIMO development is the increase in size of antenna arrays, bandwidth and number of subcarriers. If conventional channel estimation methods are used, channel estimation overhead scales as well. At the same time the Nyquist limit makes overhead reduction impossible for classical methods. To overcome this limitation, we propose a new channel estimation approach. The proposed method consists of measuring the channel tensor elements in crossing slabs and further completing the measured tensor. Extending a known Canonical Polyadic Decomposition Slab Sampled Completion algorithm to Tucker and Tensor Train models, we reduce the normalized mean error from 0.22 to below 0.1. To further increase the accuracy, we propose the interleave the positions of slabs using permutation polynomial. Simulation results based on 3GPP 38.901 channel model demonstrate that the interleaving can reduce the Tucker completion NME up to 10 times. At the same time, replacing Tucker model by Tensor Train allows to greatly reduce the impact of slabs positions. For TT-based completion the difference between completion NME for regular (periodic) slabs and interleaved slabs is below 20 %. The proposed algorithms break the Nyquist limit and have good chances to provide significant overhead reduction. Next part of our work will be focused on the implementation issues and the provided overhead reduction.

Key words: MIMO, OFDM, channel estimation, tensor completion, cross-tensor approximation.

Corresponding author: Dorokhin Semyon Vladimirovich, dorohin.sv@phystech.edu

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For citation:

Dorokhin S.V., Shuvalov D.V., Lyashev V.A. Sub-Nyquist tensor completion for massive MIMO channel estimation: Part 1 // Journal of Radio Electronics. – 2025. – №. 8. https://doi.org/10.30898/1684-1719.2025.8.3 (In Russian)