Capacity Achieving by Diagonal Permutation for MU-MIMO channels

TL;DR

This paper introduces a low-complexity algorithm for MU-MIMO precoding that achieves capacity similar to Dirty Paper Coding by exploiting permutation properties, significantly reducing computational complexity.

Contribution

It demonstrates the equivalence of DPC and HOGMT precoding in 2-D channels and proposes a linear permutation-based method for efficient precoding order optimization.

Findings

Achieves capacity with 20 dB lower complexity for 5 users.

Provides a linear permutation-based implementation of DPC.

Reduces the need for factorial complexity in precoding order selection.

Abstract

Dirty Paper Coding (DPC) is considered as the optimal precoding which achieves capacity for the Gaussian Multiple-Input Multiple-Output (MIMO) broadcast channel (BC). However, to find the optimal precoding order, it needs to repeat N! times for N users as there are N! possible precoding orders. This extremely high complexity limits its practical use in modern wireless networks. In this paper, we show the equivalence of DPC and the recently proposed Higher Order Mercer's Theorem (HOGMT) precoding[1][2] in 2-D (spatial) case, which provides an alternate implementation for DPC. Furthermore, we show that the proposed implementation method is linear over the permutation operator when permuting over multi-user channels. Therefore, we present a low complexity algorithm that optimizes the precoding order for DPC with beamforming, eliminating repeated computation of DPC for each precoding order. Simulations show that our method can achieve the same result as conventional DPC with about 20 dB lower complexity for N = 5 users.