Multicarrier Division Duplex (MDD)

• MDD is a duplexing paradigm that assigns disjoint uplink and downlink subcarrier groups to enable simultaneous bidirectional communication with minimal cross-link interference.
• It leverages FFT-based digital separation and channel reciprocity, allowing near real-time channel state updates that are crucial in high-mobility and massive MIMO scenarios.
• MDD supports scalable cell-free massive MIMO and THz fronthaul applications by employing advanced subcarrier and power allocation strategies to optimize spectral efficiency.

Multicarrier Division Duplex (MDD) is a duplexing paradigm in wideband orthogonal frequency-division multiplexing (OFDM) wireless systems, where uplink (UL) and downlink (DL) transmissions are allocated to mutually orthogonal subsets of subcarriers within the same frequency band and time slot. By partitioning the available spectrum into distinct subcarrier groups for UL and DL, MDD enables simultaneous bidirectional communication with minimal cross-link interference (CLI) and relaxed self-interference (SI) cancellation requirements compared to classical in-band full-duplex schemes. This structure leverages the natural channel reciprocity across both time and frequency domains and is particularly beneficial in high-mobility, cell-free, and massive MIMO deployments where channel aging and pilot contamination limit the performance of conventional time-division duplexing (TDD) (Arnold et al., 2018, Li et al., 2022, Li et al., 2022, Li et al., 2023, Li et al., 2022).

1. Fundamental Principles and System Architecture

MDD operates by splitting the total set of subcarriers $\mathcal{M}_{\text{tot}}$ into two disjoint subsets: one for UL traffic ($\mathcal{M}_{\text{UL}}$), and the other for DL traffic ($\mathcal{M}_{\text{DL}}$), such that $$\mathcal{M}_{\text{tot}} = \mathcal{M}_{\text{UL}} \cup \mathcal{M}_{\text{DL}}$$ and $$\mathcal{M}_{\text{UL}} \cap \mathcal{M}_{\text{DL}} = \emptyset$$. For OFDM-based massive MIMO, subcarrier partitioning can be realized using interlaced or grouped mappings (e.g., even indices for UL, odd for DL) (Arnold et al., 2018, Li et al., 2022). During each OFDM symbol period, users transmit on $\mathcal{M}_{\text{UL}}$ while receiving on $\mathcal{M}_{\text{DL}}$, and the base station (BS) reciprocates with appropriate transmit/receive roles.

At the signal level, digital-domain orthogonality induced by the FFT suppresses inter-directional interference between UL and DL streams. Any residual SI manifests predominantly as analog-domain leakage, which is substantially mitigated by path loss, moderate analog isolation (circulators, couplers), and owing to the uncorrelated aggregate behavior in large antenna (M) regimes (Arnold et al., 2018). In cell-free and distributed massive MIMO, APs and UEs communicate simultaneously on their respective subcarrier sets, enabling continuous CSI acquisition without guard periods, guard bands, or slot switching (Li et al., 2022, Li et al., 2022).

2. Channel Reciprocity and Channel Tracking

MDD exploits reciprocity both in the temporal (within coherence time $T_c$) and frequency (within coherence bandwidth $B_c$) domains. For adjacent or closely spaced subcarriers $n, n'$ with $|n-n'| \cdot \Delta f \leq B_c$, the physical channel response $H(f_n, t)$ is approximately equal, enabling instantaneous DL precoding using UL pilot measurements from neighboring subcarriers (Arnold et al., 2018, Li et al., 2022).

Mathematically, for an UL subcarrier $n \in \mathcal{M}_{\text{UL}}$, the corresponding neighboring DL subcarrier $n+1 \in \mathcal{M}_{\text{DL}}$ satisfies $h^{UL}_n[k] \approx h^{DL}_{n+1}[k]$. Channel estimates $\hat{h}^{UL}_n[k]$ can thus be directly applied for DL precoding on $n+1$, yielding virtually fresh channel state information at every OFDM symbol. This two-dimensional reciprocity enables channel tracking at rates determined by the OFDM symbol time $T_{\text{sym}}$, in contrast to the millisecond-scale update intervals in classic TDD (Arnold et al., 2018, Li et al., 2022).

MDD further facilitates continuous or event-driven UL pilot transmission, fully overlapping with DL data, and supports data-aided (decision-directed) channel tracking strategies (Li et al., 2022). These features collectively suppress channel aging effects in high-mobility environments where TDD pilot-based CSI rapidly becomes outdated.

3. Performance, Spectral Efficiency, and Power Allocation

The mutual subcarrier orthogonality in MDD renders inter-AP (IAI) and inter-UE (IMI) digital-domain interference negligible after FFT separation. Analysis of SINR expressions—under zero-forcing (ZF) or maximum ratio (MR) precoding/combining—shows SI components as additive Gaussian noise, significantly relaxed compared to in-band full duplex (IBFD) where SI cancellation requirements can exceed 130 dB (Li et al., 2022, Li et al., 2022).

Spectral efficiency (SE) optimization in MDD systems must account for the mixed-integer nature of subcarrier allocation, power allocation, and AP/MS association. Quadratic transform (QT) and successive convex approximation (SCA) algorithms, block coordinate ascent, or advanced heuristics (meta-heuristic clustering, subcarrier-set assignment) are employed to maximize rates under power constraints and QoS requirements (Li et al., 2022, Li et al., 2023). For cell-free architectures, graph neural network (GNN)-based power allocation can deliver near-optimal SE with dramatically reduced computational complexity, capturing the interactions between APs, MSs, and the interference structure inherent in large distributed MDD topologies (Li et al., 2022).

The following table summarizes key comparative results for MDD, TDD, and IBFD massive MIMO:

Scheme	SI Cancellation Requirement	Channel Aging	Typical SE (high Doppler)
TDD	N/A	Severe	Decays sharply as $f_D$ increases
IBFD	$>100$ dB (analog+digital)	None	Only competitive if SI cancellation is extreme
MDD	$60{-}80$ dB (analog)	Mild/None	Nearly flat with Doppler; robust

Data from (Li et al., 2022, Arnold et al., 2018, Li et al., 2022)

4. Hardware and Implementation Considerations

Effective realization of MDD depends on analog-domain SI suppression—isolations of $30{-}45$ dB at the BS with circulators/hybrid couplers, and $20{-}35$ dB at UEs—combined with FFT-based digital orthogonalization (Arnold et al., 2018). Carrier frequency offsets (CFO) between transmit/receive local oscillators introduce subcarrier-dependent phase rotations but can be corrected by pilot-based estimation and digital compensation (Arnold et al., 2018).

Subcarrier spacing must satisfy $\Delta f\cdot N_\text{gap} \leq B_c$ to ensure adjacent-subcarrier reciprocity within coherence bandwidth. Pilot density on UL subcarriers can be 100%, as pilots do not interfere with DL data, allowing CSI to be freshly updated each OFDM symbol (Arnold et al., 2018, Li et al., 2022).

At large BS antenna counts $M$, the desired UL signal power scales with $M$, while the aggregate SI remains approximately constant (uncorrelated across antennas), causing the per-antenna SI contribution to vanish as $M \to \infty$ (Arnold et al., 2018).

5. Applications in Cell-Free Massive MIMO and THz Fronthaul

MDD has been integrated into cell-free massive MIMO (CF-mMIMO) architectures, where geographically distributed APs simultaneously serve users over both UL and DL subcarriers. In such topologies, MDD enables (i) concurrent DL data and UL pilot/data, (ii) free cancellation of IAI and IMI at the digital stage, and (iii) robustness to rapid channel variations (Li et al., 2022, Li et al., 2022).

For two-tier fronthaul in industrial CF-mMIMO, MDD is used to partition the THz fronthaul spectrum into orthogonal subcarrier sets for CPU$\to$CAP and CAP$\to$AP links, enabling fully wireless fronthaul with performance comparable to wired solutions, especially with adequate bandwidth (Li et al., 2023). The frame structure allows three simultaneous streams: CPU$\to$CAP (THz, $\mathcal{M}_{CC}$), CAP$\to$AP (THz, $\mathcal{M}_{CA}$), and AP$\to$Device (sub-6 GHz), all occupying their respective orthogonal subcarrier sets. Network resource allocation (clustering, subcarrier assignment, power allocation) is cast as a mixed-integer nonconvex optimization, solvable via a combination of K-medoids, greedy subcarrier assignment, and iterative convex relaxation (Li et al., 2023).

Key outcomes in such architectures include elimination of guard times, enhancement in end-to-end rates, and dynamic adaptability in AP clustering for varying network scales.

6. Comparative Advantages and Limitations

MDD provides several intrinsic advantages over conventional TDD and IBFD:

• Channel Tracking: MDD supports per-OFDM-symbol channel updates, allowing much lower mean-squared channel estimation error—especially under high Doppler spread—versus TDD, where channel staleness increases sharply with delay between UL pilot and DL payload (Arnold et al., 2018, Li et al., 2022).
• Spectral Efficiency: Concurrent, mutual orthogonality of UL/DL operation in the frequency domain reduces the need for guard periods and maximizes use of the available spectrum (Li et al., 2022, Arnold et al., 2018).
• SI/CLI Management: The FFT-based digital domain separation lowers the SI suppression requirement to levels feasible with existing analog hardware, without the cross-link interference management challenges of IBFD (Li et al., 2022, Li et al., 2022).
• Scalability and Complexity: GNN-based solutions for resource allocation in large-scale cell-free deployments offer near-optimal SE with orders-of-magnitude lower complexity than traditional convex optimization (Li et al., 2022).

Limitations include:

• Residual SI: Finite analog-domain SI suppression may necessitate moderately large antenna counts or supplementary cancellation circuitry for optimal performance (Arnold et al., 2018, Li et al., 2022).
• CFO Sensitivity: Accurate CFO estimation and correction are required to prevent inter-subcarrier leakage (Arnold et al., 2018).
• Coherence Bandwidth Constraint: Frequency reciprocity across subcarriers is only valid if $B_c \gg \Delta f$; in strongly frequency-selective channels, grouping rather than strict interlacing may be mandated (Arnold et al., 2018).

7. Analytical Models and Optimization Frameworks

Spectral efficiency maximization in MDD systems is formulated as a mixed-integer nonconvex problem, due to power, subcarrier, and association constraints. The following algorithmic approaches are established:

• Quadratic Transform (QT) with Successive Convex Approximation (SCA): Transforms nonconvex log-sum-rate objectives into block-coordinate concave subproblems with auxiliary variables, enabling tractable convex optimization per iteration (Li et al., 2022, Li et al., 2022).
• Graph Neural Network (CF-HGNN): Utilizes meta-path message passing and adaptive embeddings for AP/MS nodes, capturing communication and interference relations, attention mechanisms, and scalable output to arbitrary network sizes. Unsupervised training maximizes SE, with per-user QoS constraints embedded via ReLU-penalty losses. Demonstrated to reach within 99% of QT-SCA SE at $10^{-4}\times$ runtime (Li et al., 2022).
• Dynamic AP Clustering and Subcarrier Assignment: For THz MDD fronthaul, K-medoids and greedy subcarrier-set assignment, together with iterative end-to-end rate maximization, maintain max-min fairness across dynamically reconfigurable multi-tier networks (Li et al., 2023).

Collectively, these constructs enable practical and near-optimal operation of MDD in next-generation cell-free, massive MIMO, and industrial wireless networks.