  The unsourced random access (URA) has emerged as a viable scheme for
supporting the massive machine-type communications (mMTC) in the sixth
generation (6G) wireless networks. Notably, the tensor-based URA (TURA), with
its inherent tensor structure, stands out by simultaneously enhancing
performance and reducing computational complexity for the multi-user
separation, especially in mMTC networks with a large numer of active devices.
However, current TURA scheme lacks the soft decoder, thus precluding the
incorporation of existing advanced coding techniques. In order to fully explore
the potential of the TURA, this paper investigates the Polarcoded TURA (PTURA)
scheme and develops the corresponding iterative Bayesian receiver with feedback
(IBR-FB). Specifically, in the IBR-FB, we propose the Grassmannian
modulation-aided Bayesian tensor decomposition (GM-BTD) algorithm under the
variational Bayesian learning (VBL) framework, which leverages the property of
the Grassmannian modulation to facilitate the convergence of the VBL process,
and has the ability to generate the required soft information without the
knowledge of the number of active devices. Furthermore, based on the soft
information produced by the GM-BTD, we design the soft Grassmannian demodulator
in the IBR-FB. Extensive simulation results demonstrate that the proposed PTURA
in conjunction with the IBR-FB surpasses the existing state-of-the-art
unsourced random access scheme in terms of accuracy and computational
complexity.
