两种基于自适应投影次梯度的多址MIMO非线性均衡算法设计

Design of Two Multi-Access MIMO Nonlinear Equalization Algorithms Based on Adaptive Projected Subgradient

摘要: 多输入多输出(MIMO)系统是现代通信技术的核心组成部分，其中多址MIMO信道的研究具有关键意义。在多址MIMO信道中，发射端与接收端的多天线配置虽有效提升了传输速率和系统容量，但信号传输过程中存在的多用户干扰等问题，导致信道呈现显著的非线性特性，这给MIMO系统的非线性均衡带来了极大挑战。现有基于自适应投影次梯度法的核自适应多元回归算法，虽能一定程度上应对上述问题，却存在稀疏处理能力不足、计算复杂度偏高的缺陷。为此，本文聚焦多址MIMO系统均衡需求，以QPSK调制信号为研究载体，提出两种算法。首先针对传统回归算法的参数耦合问题，引入二元分类思想，将信道均衡问题转化为信号类别判别问题，进而提出多址MIMO核自适应二元分类算法。该算法突破传统回归范式的桎梏，显著提升计算效率，验证了回归转分类思路的可行性。进一步针对该算法依赖核矩阵运算的瓶颈，引入随机傅里叶特征近似传统核计算，提出多址MIMO基于随机傅里叶特征的自适应二元分类算法。该算法实现非线性问题的线性化转换，进一步降低计算复杂度。两种算法通过复值信号预测向实部与虚部类别判别的转化，既保留了核方法对信道非线性的拟合能力，又规避了传统回归算法的参数耦合问题，为QPSK调制下的多址MIMO系统信号均衡提供了新的解决方案，奠定了实验基础。实验结果表明，所提两种算法相较于现有方法均显著提升计算效率，且后者进一步缩减字典规模。这一结果验证了算法的有效性与优越性。

Abstract: Multiple-Input Multiple-Output (MIMO) systems are a core component of modern communication technologies, among which the research on multiple-access MIMO channels holds critical significance. In multiple-access MIMO channels, the multi-antenna configurations at the transmitter and receiver effectively improve the transmission rate and system capacity; however, issues such as multi-user interference during signal transmission lead to significant nonlinear characteristics of the channel, posing great challenges to the nonlinear equalization of MIMO systems. Existing kernel adaptive multivariate regression algorithms based on the adaptive projection subgradient method can address the aforementioned issues to a certain extent, but they suffer from deficiencies, including insufficient sparse processing capability and high computational complexity. To this end, focusing on the equalization requirements of multiple-access MIMO systems and using QPSK-modulated signals as the research carrier, this paper proposes two algorithms. First, to address the parameter coupling issue of traditional regression algorithms, the concept of binary classification is introduced to convert the channel equalization problem into a signal class discrimination problem, thereby proposing a multiple-access MIMO kernel adaptive binary classification algorithm. This algorithm breaks the constraints of the traditional regression paradigm, significantly improves computational efficiency, and verifies the feasibility of the idea of converting regression to classification. Furthermore, to tackle the bottleneck of this algorithm that relies on kernel matrix operations, random Fourier features are introduced to approximate traditional kernel calculations, leading to the proposal of a multiple-access MIMO adaptive binary classification algorithm based on random Fourier features. This algorithm realizes the linearized transformation of nonlinear problems and further reduces computational complexity. By converting complex-valued signal prediction into class discrimination for the real and imaginary parts, both algorithms not only retain the fitting ability of kernel methods for channel nonlinearity but also avoid the parameter coupling problem of traditional regression algorithms, providing a new solution for signal equalization in multiple-access MIMO systems under QPSK modulation and laying the experimental foundation. Experimental results demonstrate that the two proposed algorithms significantly improve computational efficiency compared with existing methods, and the latter further reduces the dictionary size. This result verifies the effectiveness and superiority of the proposed algorithms.