Low-Complexity Inverse Matrix Mini-Batch Gradient Descent for MIMO Equalization and Precoding

As the size of base station antenna arrays continues to grow, even with linear processing algorithms, the computational complexity and power consumption required for massive MIMO equalization or precoding (EoP) matrix computation increase exponentially. This paper proposes an inverse matrix minibatch gradient descent (IM-MBGD) method for MIMO EoP. The proposed method leverages minibatch gradient descent to compute the pseudo-inverse of the Gram matrix instead of directly calculating the EoP matrix. Since the pseudo-inverse matrix has significantly lower dimensions compared to the EoP matrix, this approach effectively reduces computational complexity and accelerates convergence. Based on our convergence analysis, to further minimize the iteration time and improve the accuracy of the EoP matrix, we optimize the IM-MBGD method using a finite-alphabet neighborhood search. The finite-alphabet search performs neighborhood optimization to achieve the optimal solution. Compared to state-of-the-art alphabet-based equalizers, our proposed method achieves a 14-fold reduction in computational complexity for EoP matrix calculation. Furthermore, in terms of storage and the overall equalization process, our method reduces overhead by 80% compared to linear equalizers.