Reference signals based on permutation polynomials for tensor completion of MIMO OFDM channel

The key trends of modern MIMO OFDM systems is the increase in the number of antennas, the number of subcarriers and the signal bandwidth. This results in substantial channel estimation overhead increase. Two research directions emerge to solve this problem. The first direction proposes placing pilots pseudorandomly to favor compressed sensing algorithms, while the second direction focuses on tensor processing. Existing rules for pseudorandom patterns lack compact description and typically require either additionally calculations in real time or a lot of memory to store the results. At the same time, popular tensor algorithms combine channel sensing and channel tensor recovery into one problem. This typically requires special frame structure and excessive number of symbols. We propose a new compact description of the pseudorandom pilot patterns based on permutation polynomials and prove that they are close to optimal. In addition, we divide channel tensor elements estimation and partially measured tensor completion into separate tasks. Using example of image tensors completion algorithm, we show that in context of MIMO OFDM tensors smoothing operation becomes closely related to physical parameters of the channel. Finally, we demonstrate that the proposed one-dimensional permutations can also be used to define a multidimensional sampling pattern that yields the same completion accuracy as random pattern. Compared with classical channel estimation, the proposed methods overcome the limitations of Nyquist-Kotelnikov sampling theorem and increase the spectral efficiency of the system by 47%. The proposed methods can be further used to apply general tensor completion theory to MIMO OFDM channel estimation.