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.

在本文中，我们提出了一种时变多径环境中的新型MIMO通信系统，该系统使用Khatri-Rao空时（KRST）编码与符号矩阵的多个Khatri-Rao乘积（MKRSM）相结合。示出了在接收器处接收的信号形成满足以下条件的张量：$（\mathrm{中号}+2）$阶嵌套PARAFAC模型，其中 $（\mathrm{中号}-\mathrm{1个}）$表示考虑用于MKRSM编码的符号矩阵的数量。嵌套PARAFAC模型的这种推广$（\mathrm{中号}+ñ）$首先从一般的角度研究阶数张量，并根据模型的先验知识讨论一些参数估计方法。然后，开发了由三个阶段组成的半盲接收机，用于联合估计发射的符号和多径参数。

在第一阶段，使用基于Khatri-Rao分解的封闭形式算法来估计传输符号和有效信道的矩阵展开，包括衰落系数和导引矩阵。在第二种方法中，通过简化的最小二乘算法完善了信道估计，该算法考虑了编码矩阵的列正交性假设。在第三种方法中，将交替最小二乘算法与对范德蒙德因子的校正相结合，以在发射器和接收器侧包含空间转向矢量，以从估计的信道估计多径参数。对接收器进行了复杂性分析，并建立了与信道估计有关的预期Cramer-Rao边界。