Beam-Coherence-Aware Two-Stage Digital Combining for mmWave MU-MIMO Systems

Abstract

This paper considers a wideband millimeter-wave MIMO system with fully digital transceivers at both the base station and the user equipment (UE), focusing on mobile scenarios. To reduce the baseband processing burden at the UE, we propose a two-stage digital combining architecture, where the received signals are compressed from $K$ antennas to dimension $N_{\mathrm c}$ before baseband processing. The first-stage combining matrix exploits channel geometry and is updated on the beam-coherence timescale, which is longer than the channel coherence time, while the second stage is updated per channel coherence time. We develop a pilot-based channel estimation framework tailored to the proposed two-stage digital combining architecture, leveraging maximum likelihood estimation. Furthermore, we propose a time-domain method that exploits the finite delay spread to reconstruct the full channel from a reduced number of pilot subcarriers. Precoding and combining schemes are designed accordingly, and spectral efficiency expressions with imperfect channel state information are derived. Numerical results show that the proposed time-domain approach outperforms hybrid beamforming while reducing pilot overhead. We further demonstrate that the framework extends to multi-user MIMO and retains its performance advantages. These results highlight the potential of two-stage fully digital transceivers for future wideband systems.

Figures (8)

• Figure 1: A mmWave MIMO mobile system.
• Figure 2: The channel is approximately time-invariant in each block $\tau$, comprising all subcarriers $S$ and channel coherence time $\mathsf{T}_\mathrm{C}$. The compressed digital combining matrix must be updated at the larger time intervals called the beam coherence time $\mathsf{T}_\mathrm{B}$, which is $\mathfrak{t}$ times larger than $\mathsf{T}_\mathrm{C}$. $\mathsf{T}_{\mathrm{p}}$ denotes the pilot time, corresponding to the duration used for pilot transmission within a coherence interval.
• Figure 3: Block diagram of a mmWave SU-MIMO system employing fully digital precoding and a two-stage digital combining architecture. a) In the proposed setup, the first-stage combining matrix $\mathbf{Q}[\nu]$ reduces the signal dimension and occasionally accesses CSI across all $K$ antennas. The second-stage combining $\mathbf{W}[\tau,\nu]$ is updated frequently but has a reduced dimension $N_\mathrm{c} < K$. b) The BeammWave company utilizes the same structure for implementing its UE receiver chips.
• Figure 4: The NMSE vs SNR for frequency- and time-domain estimation of $\hat{\mathbf{H}}^{\mathrm T}[1,\nu]$.
• Figure 5: The average SE of SU-MIMO at different time instances when moving along a linear trajectory with speed $\upsilon=5$ m/s.