Low-Complexity Hybrid Beamforming for Multi-Cell mmWave Massive MIMO: A Primitive Kronecker Decomposition Approach

TL;DR

This work tackles inter-cell interference in uplink multi-cell mmWave FD-MIMO by introducing a hybrid beamforming approach based on primitive Kronecker decomposition (PKD) with dynamic factor allocation. By decomposing steering vectors into many Kronecker factors and allocating factors to cancel inter-cell interference while maximizing desired-signal power, the analog beamformer can null strong interference in a reduced subspace, with the digital MMSE beamformer handling intra-cell interference. A low-complexity variant updates the analog beamformer only when AoAs change, and the authors derive a sufficient antenna configuration $MN = 2^{\Gamma + \lceil \log_2 K \rceil}$ to enable the proposed scheme, along with a detailed complexity analysis. Simulations show the proposed schemes closely approach the performance of an optimal digital MMSE benchmark with substantially lower complexity and hardware costs, and exhibit robustness to varying interference conditions, outperforming several benchmark hybrid schemes.

Abstract

To circumvent the high path loss of mmWave propagation and reduce the hardware cost of massive multiple-input multiple-output antenna systems, full-dimensional hybrid beamforming is critical in 5G and beyond wireless communications. Concerning an uplink multi-cell system with a large-scale uniform planar antenna array, this paper designs an efficient hybrid beamformer using primitive Kronecker decomposition and dynamic factor allocation, where the analog beamformer applies to null the inter-cell interference and simultaneously enhances the desired signals. In contrast, the digital beamformer mitigates the intra-cell interference using the minimum mean square error (MMSE) criterion. Then, due to the low accuracy of phase shifters inherent in the analog beamformer, a low-complexity hybrid beamformer is developed to slow its adjustment speed. Next, an optimality analysis from a subspace perspective is performed, and a sufficient condition for optimal antenna configuration is established. Finally, simulation results demonstrate that the achievable sum rate of the proposed beamformer approaches that of the optimal pure digital MMSE scheme, yet with much lower computational complexity and hardware cost.

Figures (6)

• Figure 1: An illustrative UPA receiving the data from the desired user $k$, interfered with user $p$ in an adjacent cell.
• Figure 2: An illustrative example of how to determine the optimal Kronecker factor for a given beamforming vector $\bm{f}_{\rm RF}(k)$. Although all three factors can effectively null the $i^{\rm th}$ inter-cell interference because the $i^{\rm th}$ factor $\bm{f}_{\psi\gamma}^{(i)}$ of the beamforming vector is orthogonal to the $i^{\rm th}$ factor $\bm{a}_{\psi\gamma}^{(i)}$ of the interference signal, $i = 1, 2, 3$, the 3rd factor $\bm{f}_{\psi\gamma}^{(3)}$ is preferred to $\bm{f}_{\psi\gamma}^{(1)}$ and $\bm{f}_{\psi\gamma}^{(2)}$, due to its capability of enhancing the desired signal (the distances $\rho_3 < \rho_1 < \rho_2$).
• Figure 3: Achievable sum rate versus Tx SNR (ISR = $0$ dB, $\Psi = 2$, $\Gamma_\psi = 1$, $M = 8$, and $N = 16$).
• Figure 4: Achievable sum rate versus Tx ISR (SNR = $20$ dB, $\Psi = 2$, $\Gamma_\psi = 1$, $M = 8$, and $N = 16$).
• Figure 5: Achievable sum rate versus column numbers of antenna array (SNR = $20$ dB, ISR = $0$ dB, $\Psi = 2$, $\Gamma_\psi = 1$, and $M = 8$).

Theorems & Definitions (6)

• Lemma 1: Kronecker Decomposition
• Definition 1: Primitive Kronecker Decomposition
• Lemma 2: The weak commutative law of Kronecker product
• proof
• Theorem 1
• proof