**Semi-blind joint symbols and multipath parameters estimation of MIMO systems using KRST/MKRSM coding**

*Digital Signal Processing*( IF 2.871 )

**Pub Date : 2020-11-20**

*, DOI:*

*10.1016/j.dsp.2020.102908*

S.V.N. Randriambelonoro; G. Favier; R. Boyer

In this paper, we propose a new MIMO communication system in a time-varying multipath environment, using a Khatri-Rao space-time (KRST) coding combined with a multiple Khatri-Rao product of symbol matrices (MKRSM). It is shown the signals received at the receiver form a tensor which satisfies a $(M+2)$-order nested PARAFAC model, where $(M-1)$ denotes the number of symbol matrices considered for MKRSM coding. Such a generalization of the nested PARAFAC model to $(M+N)$-order tensors is first studied from a general point of view, with the discussion of some parameter estimation methods depending on the a priori knowledge on the model. Then, a semi-blind receiver composed of three stages, is developed for jointly estimating the transmitted symbols and the multipath parameters.

In the first stage, the transmitted symbols and a matrix unfolding of the effective channel including the fading coefficients and the steering matrices, are estimated using closed-form algorithms based on Khatri-Rao factorizations. In the second one, the channel estimation is refined by means of a simplified least-squares algorithm which takes the column orthonormality assumption on the coding matrix into account. In the third one, an alternating least-squares algorithm, combined with a rectification for the Vandermonde factors containing the spatial steering vectors at the transmitter and receiver sides, is applied to estimate the multipath parameters from the estimated channel. A complexity analysis is made for the receivers, and an expected Cramer-Rao bound related to channel estimation is established. Extensive Monte Carlo simulation results show that the semi-blind receiver which combines the channel estimation refinement with the rectification technique exhibit very interesting performance.