Duplex Gating: Enhancing Bidirectional Performance

• Duplex gating is a mechanism that selectively switches between full-duplex and half-duplex operations using power thresholds and interference metrics.
• It employs hybrid methods in heterogeneous networks, dynamic time slot allocation in mmWave systems, and reinforcement learning in flexible duplex frameworks.
• In medical sensing, sparse nested array scheduling leverages duplex gating to enhance Doppler ultrasound imaging while maintaining high frame rates.

Duplex gating refers to mechanisms that selectively enable or disable bidirectional (full-duplex) operations, transmissions, or measurements on wireless and sensing links at fine time, frequency, or spatial granularity, with the goal of optimizing spectral efficiency, interference, frame rate, or signal quality under practical device and environmental constraints. Across wireless heterogeneous networks, millimeter-wave relay systems, machine-learning-assisted flexible spectrum systems, and medical Doppler ultrasonography, duplex gating appears in power-threshold-based hybrid modes, dynamic per-link TDD, reinforcement-learning-driven transmission gating, and sparse scheduling of emission slots.

1. Power-Threshold-Based Duplex Gating in Heterogeneous Networks

In two-tier HetNets comprising macro and small-cell base stations (BSs), "hybrid duplex switching" implements duplex gating by using a received power threshold $\gamma_k$ per tier to determine if a user operates in full-duplex (FD) or half-duplex (HD) mode. Each user, after associating to the BS offering maximal long-term average downlink power $\xi = P_k D_k^{-\alpha}$, engages in FD operation (simultaneous DL/UL) if $\xi \geq \gamma_k$; otherwise, the user remains in HD, alternating: occupying either uplink or downlink in a time or frequency band. The design rationale is that under low received power, the accumulation of residual self-interference (RSI) plus cross-link and cross-tier interference degrades FD gains below those of HD; only at high enough $\xi$ can the doubled resource utilization advantage of FD outweigh its interference costs (Tang et al., 2016).

Spatial performance metrics are analytically derived by approximating the combined deployments (macro, small-cell BSs, users) as independent inhomogeneous Poisson point processes (PPP), valid under statistical homogeneity assumptions. Signal-to-interference-plus-noise ratio (SINR) distributions for both duplex modes and both channels are computed with Laplace functionals of the relevant interference point fields, accounting for RSI, cross-tier interference, and cell geometry. Closed-form per-user spectral efficiencies are integrated over the different operating regimes and network tiers.

2. Optimization and Algorithms for Duplex Gating

In the hybrid-duplex HetNet framework, the optimum choice of gating threshold $\gamma_k$ (or, equivalently, the number of FD users per cell) is cast as a nonlinear integer programming problem. The sum rate objective function is maximized over $\Delta_m$ (number of FD users in each BS $m$’s cell), subject to user power rankings. The combinatorial nature of cross-cell interference (since each FD user also acts as an interferer for its neighbors) renders direct optimization intractable for large $M,N_m$. A centralized greedy algorithm iteratively increases or decreases $\Delta_m$ in each cell, evaluating the total sum rate at each step until no further single-step improvement can be achieved. The threshold $\gamma_m$ is derived from the power rankings as the midpoint between the $\Delta_m$-th and $(\Delta_m+1)$-th users (Tang et al., 2016).

This approach closely approximates the maximizer for small networks (compared against exhaustive search), and efficiently converges in large-scale deployments within a moderate number of iterations.

3. Dynamic and Flexible Duplex Gating in Millimeter-Wave and RL-Assisted Systems

Per-link dynamic duplex gating in millimeter-wave (mmW) cellular relay systems leverages the strong directional isolation inherent in mmW propagation and high-gain antenna arrays. Here, time frames are slotted, and each node independently chooses to transmit (TX) or receive (RX) per subframe, so that each directed link $(i \to j)$ is "active" only if $i$ is in TX and $j$ in RX mode. This link-by-link flexibility enables dynamic time-domain duplexing (DTDD), adapting the DL/UL split locally within the overall network time-synchronization constraint (Ford et al., 2015).

The corresponding optimization is a mixed-integer program maximizing sum of proportional-fair utilities, constrained by half-duplex scheduling at each node, resource budgets, and per-link Shannon capacity determined by a constant-interference model (worst-case aggregate random beam interference). A recursive greedy algorithm exploits the tree-structured relay topology to allocate TX/RX modes in a decentralized yet globally utility-optimal way for each subtree, alternating DL and UL mode increments and performing local convex optimizations of bandwidth and rate assignments.

Simulation of DTDD vs. static globally-synchronized TDD shows throughput and cell-edge rate gains of 1.5–4.5× depending on network density and relay count, with especially significant uplink benefit due to elimination of static backhaul bottlenecks and local adaptation (Ford et al., 2015).

In reinforcement-learning-based flexible duplex systems, gating is controlled by a learned access threshold $\theta_t$ adapted in real time for each slot using online interference measurements. The gating decision $g_t$ is binary: transmission (FD mode) occurs if an "opportunity" value $OP_t$ computed from sensor data exceeds $\theta_t$; otherwise the transmitter remains silent. The RL agent, implemented on an FPGA-testbed, uses a REINFORCE policy-gradient update to maximize a reward composed of area spectral efficiency minus a self-interference penalty, directly linking duplex gating policy to physical resource performance (Kim et al., 2020). The gating decision logic is mapped to fast hardware for practical low-latency operation.

Key outcomes include up to 30% improvement in area spectral efficiency over static FD baselines, with RL policies adapting $\theta_t$ over $<1000$ slots.

4. Duplex Gating in Medical Sensing: Sparse Doppler Schedules

In duplex ultrasound, simultaneous acquisition of B-mode (structural) imaging and spectral Doppler (velocity) data is limited by the need to share slow-time transmission slots between wide-band B-mode and narrow-band Doppler pulses. Nested-array-based sparse sampling constructs a non-uniform, minimal-time schedule that fills all Doppler lags (in autocorrelation) with far fewer than $P$ pulses (the standard window length), using two interleaved subarrays with $N_1$ and $N_2$ pulses such that $N_2 (N_1+1)=P$. The optimal choice, when $P$ is a perfect square, is $N_\text{min}=2\sqrt{P}-1$, yielding dramatic improvement in B-mode frame rates for a fixed Doppler spectral resolution (Cohen et al., 2017).

Idle slots ($D = P - N$) are reallocated to B-mode transmission, so that frame rates rise by a factor proportional to $P/(P-N)$. Recovery of Doppler power spectra is accomplished either by folding and FFT (NEST, optimal for real-time) or via subspace methods (NESPRIT, for high precision in off-grid frequency estimation). Simulations and in vivo studies confirm that duplex gating through sparse schedules preserves Doppler fidelity while substantially increasing structural imaging rates—something infeasible in conventional uniform interleaving.

5. Analytical Trade-offs, Design Principles, and Practical Guidance

For power-thresholded duplex gating, theoretical analyses reveal several core trade-offs. With nonzero residual self-interference, pure FD operation (i.e., setting thresholds $\gamma_k=0$ everywhere) severely degrades SINR and uplink/downlink coverage due to compound interference effects; conversely, pure HD ($\gamma_k\to\infty$) squanders the spectral efficiency enabled by simultaneous bidirectional use. There exists an explicit intermediate optimal threshold, at which gains of 30–50% over either pure regime are observed, depending on network density, power, and cancellation prowess (Tang et al., 2016). Macro users are more sensitive to FD interference, while small-cell users accrue more FD benefit.

Dynamic per-link and RL-based gating approaches further generalize these insights, showing that locally and temporally adaptive gating schedules, whether determined by greedy optimization or policy-gradient learning, outperform static, global, or naive always-on policies under ever-present interference and load variability (Ford et al., 2015, Kim et al., 2020).

For medical duplex systems, nested sparse schedules formalize the minimal sampling rate required for perfect Doppler recovery, offering clear design guidelines: choose $P$ for desired Doppler resolution, solve for $(N_1,N_2)$ to minimize transmission count, and allocate freed slots to structural imaging.

Summary Table: Duplex Gating Mechanisms and Contexts

Application Domain	Gating Criterion	Optimization/Algorithm
Heterogeneous Networks	DL Power threshold $\gamma_k$	Nonlinear integer prog., greedy search (Tang et al., 2016)
mmWave Relay Networks	Per-link time slot TX/RX	Greedy recursive scheduler (Ford et al., 2015)
Sub-6 GHz RL Systems	Learned threshold $\theta_t$	Policy-gradient RL, FPGA gating (Kim et al., 2020)
Medical Doppler	Sparse nested array sampling	Integer minimization, FFT/eigen recovery (Cohen et al., 2017)

6. Implications and Practical Implementation

Duplex gating unifies resource allocation, interference management, and quality optimization under a single, selective-enablement paradigm. Setting and updating gating parameters can be managed at different temporal and spatial scales: cell-wise using long-term radio measurements in HetNets, per-link and per-subframe in mmWave, adaptively per slot by RL agents in flexible duplex scenarios, or by hardware-scheduled transmission tables in sensing.

A plausible implication is that further improvements in self-interference cancellation, real-time interference awareness, or cross-layer control can support even deeper integration of fine-grained duplex gating across radio, network, and application layers. Moreover, extensions to multi-user MIMO, network slicing, and joint sensing/communications regimes are direct avenues for future research.