智能反射表面（IRS）是未來無線通信的一項新興技術。 它由一個大型二維無源散射元件陣列組成，這些元件控制射頻波的電磁特性，以便反射信號在目標接收器上進行信號的相互干擾或相加，或者破壞性地相加以減少同通道干擾。
我們提出了IRS 輔助多輸入多輸出（MIMO）通信系統通道估計方法。我們將接收信號遵循平行因子 (PARAFAC) 可用於估計所涉及的張量模型，利用封閉式或迭代式的數學驗算法進行通道估計。
演算法分別為LSKPF、ALS，第一個方案的MIMO通道估計是利用的 Khatri-Rao積所分解的封閉式解決方案，通過利用 1 階矩陣(rank-1 matrix)解決通道估計的問題，而第二個方案是迭代交替估計方案，雖然第一個算法是代數並且不那麼複雜，第二個可以在更少的訓練參數的限制條件下進行運行。 提供了說明性的數值結果來評估所提出的通道估計方法的性能。
考慮到IRS本身無法獲得直接的信號數據，給上行鏈路的估計和無線通信系統中的下行鏈路通道帶來困難。 在本文中，我們研究了IRS輔助MIMO通信系統的通道估計問題。我們應用張量模型描述 IRS輔助 MIMO的聯級通道的通信系統，並使用交替最小二乘法（ALS）提取上行鏈路和下行鏈路通道的算法。 傳統上，ALS方法是易於理解和實施，但需要很多迭代收斂於循環迭代。在本文中，我們通過引入Line search優化傳統ALS算法，我們探討Line search ALS 演算法 (LSALS)可以有效減少迭代次數，並更能有效地找到最小值，之後並提出Simplified ALS演算法，透過將ALS內的矩陣算式進行簡化，藉此降低乘法複雜度。

Intelligent reflective surfaces (IRS) are an emerging technology for future wireless communications. It consists of a large two-dimensional array of passive scattering elements that manipulate the electromagnetic properties of radio-frequency waves,
We present two channel estimation methods that rely on a parallel factor (PARAFAC) tensor modeling of the received signals. The first one has a closed-form solution based on a Khatri-Rao factorization of the cascaded MIMO channel, by solving rank-1 matrix approximation problems, while the second on is an iterative alternating estimation scheme. The common feature of both methods is the decoupling of the estimates of the involved MIMO channel matrices (base station-IRS and IRS-user terminal), which provides performance enhancements in comparison to competing methods that are based on unstructured LS estimates of the cascaded channel.
Considering that irs itself cannot obtain direct signal data, it brings difficulties to the estimation of the uplink and the downlink channel in the wireless communication system. In this paper, we study the problem of channel estimation for IRS-assisted MIMO communication systems. We apply tensor models to describe IRS-assisted MIMO communication systems with concatenated channels, and use Alternating Least Squares (ALS) algorithms to extract uplink and downlink channels. Traditionally, ALS methods are easy to understand and implement, but require many iterations to converge to loop iterations. In this paper, we optimize the traditional ALS algorithm by introducing Line search. We discuss that the Line search ALS algorithm (LSALS) can effectively reduce the number of iterations and find the minimum value more effectively, and then propose the Simplified ALS algorithm. By combining ALS Simplify the matrix calculation in the matrix to reduce the complexity of the program.

[1] E. Basar, M. D. Renzo, J. D. Rosny, M. Debbah, M. S. Alouini, and R. Zhang, “Wireless communications through reconfigurable intelligent surfaces,” IEEE Access, vol. 7, pp. 116 753–116 773, Aug 2019
[2] C. Liaskos, S. Nie, A. Tsioliaridou, A. Pitsillides, S. Ioannidis, and I. F. Akyildiz, “A new wireless communication paradigm through software- controlled metasurfaces,” IEEE Communications Magazine, vol. 56, pp. 162–169, 2018
[3] C. Huang, A. Zappone, G. C. Alexandropoulos, M. Debbah, and C. Yuen, “Reconfigurable intelligent surfaces for energy efficiency in wireless communication,” IEEE Transactions on Wireless Communications, vol. 18, no. 8, p. 4157–4170, Aug 2019
[4] E. Basar, “Reconfigurable intelligent surface-based index modulation: A new beyond MIMO paradigm for 6G,” 2019, [Online]. Available : https://arxiv.org/abs/1904.06704
[5] J. Li and P. Stoica, "MIMO radar with colocated antennas," IEEE Signal Processing Magazine, vol. 24, no. 5, pp. 106–114, Sep. 2007.
[6] P. Stoica and A. Nehorai, "Performance study of conditional and unconditional direction-of-arrival estimation," IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 38, no. 10, pp. 1783–1795, Oct. 1990.
[7] T. G. Kolda and B. W. Bader, “Tensor decompositions and applications,” SIAM Review, vol. 51, no. 3, pp. 455–500, 200
[8] R. A. Harshman, “Foundations of the PARAFAC procedure: Models and conditions for an explanatory multimodal factor analysis,” UCLA Working Papers in Phonetics, vol. 16, pp. 1–84, 1970
[9] P. Comon, X. Luciani, and A. L. F. de Almeida, “Tensor decompositions, alternating least squares and other tales,” Journal of Chemometrics ,vol. 23, no. 7-8, pp. 393–405, 2009.
[10] L. Wei, C. Huang, G. C. Alexandropoulos and C. Yuen, "Parallel Factor Decomposition Channel Estimation in RIS-Assisted Multi-User MISO Communication," 2020 IEEE 11th Sensor Array and Multichannel Signal Processing Workshop (SAM), 2020, pp. 1-5, doi:10.1109/SAM48682.2020.9104305.
[11] Z. He and X. Yuan, "Cascaded Channel Estimation for Large Intelligent Metasurface Assisted Massive MIMO," in IEEE Wireless Communications Letters, vol. 9, no. 2, pp. 210-214, Feb. 2020, doi:10.1109/LWC.2019.2948632.
[12] F. Roemer and M. Haardt, “Tensor-based channel estimation and iterative refinements for two-way relaying with multiple antennas and spatial reuse,” IEEE Trans. Signal. Process., vol. 58, no. 11, pp. 5720–5735,Nov. 2010.
[13] Kui Yuan Zhang and Jianping Li; Er Jian Guo,” Research on channel estimation algorithm of MIMO relay system based on PARAFAC model”, “2017 6th International Conference on Reliability, Infocom Technologies and Optimization (Trends and Future Directions) (ICRITO)” 20-22 September 2017.
[14] T. L. Jensen and E. D. Carvalho, “An optimal channel estimation scheme for intelligent reflecting surfaces based on a minimum variance unbiased estimator,” 2019, [Online]. Available: https://arxiv.org/pdf/1909.09440
[15] Gilderlan T. de Araújo and André L. F. de Almeida,“PARAFAC-Based Channel Estimation for Intelligent Reflective Surface Assisted MIMO System”, 2020 IEEE 11th Sensor Array and Multichannel Signal Processing Workshop (SAM), 08-11 June 2020.