Ai Xingxing, Zhao Jiayi, Zhang Hongtao, Sun Yong
ZTE Corporation, Algorithm Department, Wireless Product R&D Institute, Wireless Product Operation Division, Shenzhen 518057, China.
Key Laboratory of Universal Wireless Communications, Ministry of Education of China, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Sensors (Basel). 2022 Aug 19;22(16):6248. doi: 10.3390/s22166248.
Accurate channel state information (CSI) is important for MIMO systems, especially in a high-speed scenario, fast time-varying CSI tends to be out of date, and a change in CSI shows complex nonlinearities. The kernel recursive least-squares (KRLS) algorithm, which offers an attractive framework to deal with nonlinear problems, can be used in predicting nonlinear time-varying CSI. However, the network structure of the traditional KRLS algorithm grows as the training sample size increases, resulting in insufficient storage space and increasing computation when dealing with incoming data, which limits the online prediction of the KRLS algorithm. This paper proposed a new sparse sliding-window KRLS (SSW-KRLS) algorithm where a candidate discard set is selected through correlation analysis between the mapping vectors in the kernel Hilbert spaces of the new input sample and the existing samples in the kernel dictionary; then, the discarded sample is determined in combination with its corresponding output to achieve dynamic sample updates. Specifically, the proposed SSW-KRLS algorithm maintains the size of the kernel dictionary within the sample budget requires a fixed amount of memory and computation per time step, incorporates regularization, and achieves online prediction. Moreover, in order to sufficiently track the strongly changeable dynamic characteristics, a forgetting factor is considered in the proposed algorithm. Numerical simulations demonstrate that, under a realistic channel model of 3GPP in a rich scattering environment, our proposed algorithm achieved superior performance in terms of both predictive accuracy and kernel dictionary size than that of the ALD-KRLS algorithm. Our proposed SSW-KRLS algorithm with M=90 achieved 2 dB NMSE less than that of the ALD-KRLS algorithm with v=0.001, while the kernel dictionary was about 17% smaller when the speed of the mobile user was 120 km/h.
准确的信道状态信息（CSI）对于多输入多输出（MIMO）系统至关重要，特别是在高速场景中，快速时变的CSI往往会过时，并且CSI的变化呈现出复杂的非线性。核递归最小二乘（KRLS）算法为处理非线性问题提供了一个有吸引力的框架，可用于预测非线性时变CSI。然而，传统KRLS算法的网络结构会随着训练样本数量的增加而增长，导致在处理输入数据时存储空间不足且计算量增加，这限制了KRLS算法的在线预测。本文提出了一种新的稀疏滑动窗口KRLS（SSW-KRLS）算法，通过对新输入样本的核希尔伯特空间中的映射向量与核字典中的现有样本进行相关性分析来选择候选丢弃集；然后，结合其相应输出确定被丢弃的样本，以实现动态样本更新。具体而言，所提出的SSW-KRLS算法将核字典的大小维持在样本预算范围内，每次时间步需要固定的内存和计算量，纳入正则化并实现在线预测。此外，为了充分跟踪强烈变化的动态特性，在所提出的算法中考虑了遗忘因子。数值模拟表明，在3GPP丰富散射环境下的实际信道模型中，我们提出的算法在预测精度和核字典大小方面均比ALD-KRLS算法具有更优的性能。当移动用户速度为120 km/h时，我们提出的M = 90的SSW-KRLS算法比v = 0.001的ALD-KRLS算法的归一化均方误差（NMSE）低2 dB，而核字典小约17%。
