Differential Space-Time Block Coding for Phase-Unsynchronized Cell-Free MIMO Downlink

TL;DR

This work tackles the challenge of phase misalignment in downlink CF-mMIMO by introducing a differential space-time block coding (DSTBC) scheme that obviates the need for AP phase synchronization. It develops an amicable orth design-based DSTBC framework, proves phase-misalignment cancellation in the ML metric, and derives closed-form SINR expressions for both conventional and DSTBC CF-mMIMO systems. The analysis shows that DSTBC can restore performance close to fully synchronized operations, with significant BER gains and robust SE under phase uncertainty, particularly for small numbers of APs per user. The results indicate that DSTBC is a viable, low-complexity approach to enable scalable, phase-agnostic CF-mMIMO downlink in realistic synchronicity-limited deployments.

Abstract

In the downlink of a cell-free massive multiple-input multiple-output (CF-mMIMO) system, spectral efficiency gains critically rely on joint coherent transmission, as all access points (APs) must align their transmitted signals in phase at the user equipment (UE). Achieving such phase alignment is technically challenging, as it requires tight synchronization among geographically distributed APs. In this paper, we address this issue by introducing a differential space-time block coding (DSTBC) approach that bypasses the need for AP phase synchronization. We first provide analytic bounds to the achievable spectral efficiency of CF-mMIMO with phase-unsynchronized APs. Then, we propose a DSTBC-based transmission scheme specifically tailored to CF-mMIMO, which operates without channel state information and does not require any form of phase synchronization among the APs. We derive a closed-form expression for the resulting signal-to-interference-plus-noise ratio (SINR), enabling quantitative comparisons among different DSTBC schemes. Numerical simulations confirm that phase misalignments can significantly impair system performance. In contrast, the proposed DSTBC scheme successfully mitigates these effects, achieving performance comparable to that of fully synchronized systems.

Figures (6)

• Figure 1: Illustration of how the information matrix $\mathbf{C}^{t}_{k}$ is row-wise split among the AP serving UE $k$. The CPU assigns each row of matrix $\mathbf{C}^{t}_{k} \in \mathbb{C}^{L_k \times L_k}$ to an AP serving the UE $k$ via the mapping $m(l,k)$, with $l \in \mathcal{M}_k$. In this illustration, a matrix of dimension $\mathbf{C}^{t}_{k} \in \mathbb{C}^{4 \times 4}$ is considered. Thus, $\mathbf{C}^{t}_{k}$ is composed of four rows, each comprising a duration time of four symbols. To exemplify the meaning of the mapping $m(l,k)$, note that, since AP $7$ is assigned the fourth row of $\mathbf{C}^{t}_{k}$, it follows that $m(7,k) = 4$.
• Figure 2: Comparison of the per-UE DL SE of CF-mMIMO systems in the presence of phase misalignment effects by varying the value of $\alpha$ in \ref{['Eq:instantaneousSINR_2']} and \ref{['Eq:SINR_hardening_2']} from 0 to $\pi$. Eqs. \ref{['Eq:instantaneousSINR_2']} and \ref{['Eq:SINR_hardening_2']} refer to the upper and lower bounds, respectively. Parameters settings: $L = 40$, $K = 20$, $N = 4$ and $L_k = 8$.
• Figure 3: CDF of (a) BER (b) per-UE SE for conventional and DSTBC-based CF-mMIMO systems under varying phase misalignment levels. Parameters: $L = 100$, $K = 20$, $L_k = 2$, $N = 4$. Precoding scheme: P-MMSE.
• Figure 4: CDF of (a) BER (b) per-UE SE for conventional and DSTBC-based CF-mMIMO systems under varying phase misalignment levels. Parameters: $L = 100$, $K = 20$, $L_k = 4$, $N = 4$. Precoding scheme: P-MMSE.
• Figure 5: Average BER versus the modulation order. Parameters setting: $L = 40$, $K = 20$, $L_k = 2$, $N = 4$, and $\alpha = \pi$. Precoding scheme: P-MMSE.

Theorems & Definitions (7)

• Proposition 1
• Proposition 2
• Corollary 1
• Example : Orthogonal Code Matrices
• Lemma 1
• Proposition 3
• Proposition 4