In this paper, we develop a unified framework for IRS-aided transceiver designs under general power constraints in multiple-input multiple-output (MIMO) systems which implement interference (pre-)subtraction via Tomlinson-Harashima precoding (THP) or Decision Feedback Equalization (DFE) technologies. Armed with majorization theory, two fundamental classes of performance criteria, namely K-increasing Schur-concave and Schur-convex functions of the logarithm of Mean Square Error (MSE) of the data stream, are investigated in depth. Firstly, we propose a simplified counterpart of the optimal transceiver design under general power constraints, with equivalence guaranteed by Pareto optimization theory and Lagrange duality. Moreover, the optimal semi-closed form solution to this simplified transceiver design can be attained using the modified subgradient method. Next, we prove that for any Schur-concave objective, the optimal nonlinear THP (DFE) design is in essence the linear precoding (equalization). For any Schur-convex objective, the optimal transceiver design results in individual data streams with equal MSEs, and thereby reduces to the Gaussian mutual information maximization based design. Based on the above conclusions, we further propose an efficient alternating optimization algorithm to decouple the optimization of the transmit precoder and the IRS reflection coefficients, where the classical successive convex approximation (SCA) technique is applied to fight against non-convex subproblems. From the low computational complexity perspective, a two-stage scheme is also developed inspired by the capability of the IRS in constructing favorable wireless links. Finally, numerical results show the global optimality of the modified subgradient method and the excellent performance of the proposed alternating optimization algorithm and two-stage scheme.

中文翻译：

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通过多数化理论进行统一 IRS 辅助 MIMO 收发器设计


在本文中，我们为多输入多输出 (MIMO) 系统中一般功率约束下的 IRS 辅助收发器设计开发了一个统一框架，该系统通过 Tomlinson-Harashima 预编码 (THP) 或决策反馈均衡实现干扰（预）消除（DFE）技术。借助多数化理论，深入研究了两类基本性能标准，即数据流均方误差 (MSE) 对数的 K 递增 Schur 凹函数和 Schur 凸函数。首先，我们提出了一般功率约束下最优收发器设计的简化对应方案，并由帕累托优化理论和拉格朗日对偶性保证了等效性。此外，使用改进的次梯度方法可以获得这种简化的收发器设计的最佳半封闭形式解决方案。接下来，我们证明对于任何 Schur 凹目标，最优非线性 THP（DFE）设计本质上是线性预编码（均衡）。对于任何 Schur 凸目标，最佳收发器设计会产生具有相等 MSE 的各个数据流，从而简化为基于高斯互信息最大化的设计。基于上述结论，我们进一步提出了一种有效的交替优化算法来解耦传输预编码器和IRS反射系数的优化，其中应用经典的逐次凸逼近（SCA）技术来对抗非凸子问题。从低计算复杂度的角度来看，受 IRS 构建有利无线链路能力的启发，还开发了两阶段方案。 最后，数值结果表明了改进的次梯度方法的全局最优性以及所提出的交替优化算法和两阶段方案的优异性能。