Full Duplex Modeling for Wireless Systems

• Full Duplex Modeling (FDM) is a framework that enables simultaneous bidirectional communication over shared resources by mathematically characterizing self-interference and cross-link interference.
• It employs advanced techniques such as stochastic geometry, adaptive algorithms, and Markov chains to model interference and optimize resource allocation.
• FDM underpins diverse applications from wireless communications and cellular networks to dialogue systems, driving innovations in capacity doubling and real-time processing.

Full Duplex Modeling (FDM) refers to mathematical, algorithmic, and architectural frameworks that characterize systems capable of simultaneous, bidirectional transmission and reception over the same physical resource, typically in the context of wireless, networked, or dialogue-based applications. The core challenge in FDM is the accurate and tractable representation of self-interference (SI), cross-link/multi-user interference, and the resultant trade-offs in performance, resource allocation, and algorithmic complexity. FDM underpins a variety of domains, including wireless communications, physical-layer network coding, stochastic geometry for cellular topology, digital dialogue agents, information dissemination models, and hardware impairment mitigation.

1. System and Signal Modeling Foundations

FDM systems are defined by the concurrent operation of transmitter and receiver chains at the same node. In canonical wireless models, every FD node consists of a transmit RF chain and a receive RF chain, both operating on a shared frequency band. The baseband signal at a receiver must account for:

• Desired remote signals from other network nodes
• Residual self-interference (SI) from the node's own transmitter
• Inter-node interference (cross-link, multi-user, inter-cell) arising from concurrent transmissions

Mathematically, the received signal $r[n]$ at node $i$ comprises: $$r_i[n] = h_{ij}\,s_j[n] + \kappa_i h_{ii}\,s_i[n] + w_i[n],$$ where $h_{ij}$ models the fading channel from node $j$ to $i$, $\kappa_i$ is the SI cancellation coefficient ($0\leq \kappa_i\leq 1$), $h_{ii}$ captures the SI channel, $s_j[n]$ and $s_i[n]$ are the transmitted symbols, and $w_i[n]$ is Gaussian noise (Tedik et al., 2013, Kim et al., 8 Feb 2024).

In multi-cell settings, composite models include additional interference terms from neighboring base stations (BS), user equipments (UE), and D2D pairs, as seen in

$$\mathrm{SINR}_{\rm DL} = \frac{P_{\rm BS}\,h_0\,r_0^{-\alpha}}{I_{\rm DL}^{(c)} + I_{\rm UL}^{(c)} + \sigma^2}$$

(Kundu et al., 2020, AlAmmouri et al., 2015). Fractional power control (FPC) and topology constraints are often modeled via stochastic geometry (PPP, Matérn cluster process), yielding closed-form spatial PDFs and tractable Laplace transforms for interference.

2. Self-Interference Characterization and Cancellation

Self-interference is the defining technical limit for full-duplex operation, necessitating specialized modeling and cancellation techniques. SI arises from direct coupling, reflections, and nonidealities within the transceiver hardware. Its pre-cancellation power is

$P_{\rm SI,in} = P_{\rm tx}\,|h_{\rm SI}|^2,$

and post-cancellation residual is

$$P_{\rm SI,res} = P_{\rm tx}\,|h_{\rm SI}|^2 \cdot (1 - C_{\rm SIC}),$$

with $C_{\rm SIC}$ denoting the aggregate cancellation capability (analog, digital, hybrid stages) (Kim et al., 8 Feb 2024).

In advanced hardware-aware models, SI encompasses:

• I/Q modulator imbalance and PA nonlinearities (memory-polynomial expansion) (Anttila et al., 2014)
• Multidimensional RF cancellation matrices for MIMO arrays
• Near-field LOS channel sparsity in mmWave systems, expressed as $$H_{SI}(n,m) = \rho\,e^{-j2\pi r_{nm}/\lambda}/r_{nm}$$ (Xiao et al., 2017)

Digital cancellation typically follows spatio-temporal regression over basis signals derived from transmit waveforms, fitting polynomial and memory terms using LS or adaptive algorithms (Anttila et al., 2014). Beamforming-based SI nulling further exploits spatial sparsity for hardware-constrained mmWave arrays, with optimization over steering domains and projection onto constant-amplitude (CA) constraint sets.

3. Interference, SINR, and Capacity Analysis

FDM frameworks formalize all dominant interference mechanisms:

• Cross-link interference (CLI): concurrent UL→DL transmissions leak to unintended receivers
• Inter-cell interference (ICI): neighboring BSs/UEs inject additional noise
• Mutual interference in multi-hop, small-cell, D2D scenarios: aggregate PPP models, exclusion zones, and path-loss exponents

The general SINR at a receiver under FDM is: $$\mathrm{SINR} = \frac{\text{desired signal power}}{\text{SI} + \text{CLI} + \text{ICI} + \text{noise}}$$ (Jr. et al., 2020, AlAmmouri et al., 2015).

Closed-form capacity or rate expressions often leverage the Shannon bound,

$R = BW \cdot \log_2(1 + \mathrm{SINR}),$

and stochastic-geometry integrals. For example, ergodic rate for D2D FD links can be written as

$$R_\chi = \int_0^\infty \mathbb{P}(\mathrm{SIR}_\chi > e^t-1)\,dt$$

(Ali et al., 2016). Error rate and outage probability derivations use Rayleigh (or Rician) fading models, exponential interference distributions, and Laplace transforms for aggregate interference.

In physical-layer network coding, FD allows relay nodes to operate on symbol-wise XORs, doubling spectral efficiency compared to half-duplex and yielding theoretical BER floors dependent on residual SI coefficients (Tedik et al., 2013).

4. Resource Allocation, Scheduling, and MAC Protocols

Full-duplex modeling at the system level requires resource allocation and scheduling algorithms adapted to new interference regimes. Techniques include:

• Back-pressure weighted scheduling: sums per-link queue-weighted rates, exploiting FD opportunities when differential queues justify simultaneous transmissions (Xu et al., 2018)
• Joint UE selection with hybrid timeslot assignment: scheduling FD timeslots when advantageous, otherwise defaulting to HD (Goyal et al., 2014)
• Geometric programming (GP): nonconvex power control problems solved via iterative monomial approximations (Goyal et al., 2014, Xu et al., 2018)
• Contention-based MAC (CSMA/CA): Markov chain models extended for FD operation, yielding closed-form steady-state throughput and collision probabilities, quantifying hidden-terminal mitigation (Doost-Mohammady et al., 2015)

Resource allocation schemes often must balance throughput, fairness (e.g., proportional-fair utility), and energy efficiency.

Table: MAC-Level Modeling Elements in Full Duplex Wireless

Element	Model/Technique	Reference
Scheduling algorithm	Back-pressure, Greedy	(Xu et al., 2018)
Power allocation	GP, monomial approx.	(Goyal et al., 2014)
MAC contention	Discrete Markov chain	(Doost-Mohammady et al., 2015)
Fairness objective	Proportional fair	(Goyal et al., 2014)

5. Applications in Communication and Dialogue Systems

FDM is realized across diverse application domains:

• Cellular FD (macro-cell, small cell): sum-rate doubling possible with sufficient SI/CLI suppression and optimal scheduling (Jr. et al., 2020, Xu et al., 2018)
• Device-to-Device (D2D) FD: stochastic geometry shows network SE gains—up to 64%—provided mode selection and power control are tuned and SI cancellation is adequate (Ali et al., 2016)
• Millimeter-wave (mmWave) FD: spatial sparsity in SI channels enables array-based SI mitigation via analog and digital beamforming; multi-user scenarios leverage hybrid precoding and chain-doubling (Xiao et al., 2017)
• Physical-layer network coding (PNC): direct gain in throughput via FD operation at relays and ML detection with network-coded symbols (Tedik et al., 2013)
• Multi-tier cellular networks: $\alpha$-duplex spectrum sharing models balance SINR degradation vs. bandwidth increase, establishing critical SI cancellation thresholds for UE operation (AlAmmouri et al., 2015)
• Dialogue agents: full-duplex modeling in spoken dialogue requires continuous, synchronous inference over overlapping input/output streams, periodic synchronization tokens, anticipatory generation algorithms, and multi-stage training over synthetic and real-world speech (Veluri et al., 23 Sep 2024, Lin et al., 30 Jul 2025)
• Social network information dissemination: game-theoretic FDM yields unique Nash equilibria in bidirectional, feedback-rich exchanges, modeling rapid knowledge convergence and small-world emergence (Zinoviev et al., 2010)

6. Measurement, Simulation, and Benchmarking Techniques

Evaluation of FD systems is conducted via rigorous simulation and benchmarking frameworks:

• Monte Carlo simulations: error rates, SINR, and throughput under iid fading and noise (Tedik et al., 2013, Xu et al., 2018)
• 3D ray-tracing: accurate propagation modeling for multi-cell FD systems, capturing multipath, CLI, ICI, and system-level interaction (Kim et al., 8 Feb 2024)
• Automated speech overlap benchmarks: Full-Duplex-Bench v1.5 defines controlled scenarios, categorizes agent behaviors, and quantifies timing, prosodic, and speech quality metrics (Lin et al., 30 Jul 2025)
• Human MOS studies: direct evaluation of dialogue system meaningfulness and naturalness in full-duplex settings (Veluri et al., 23 Sep 2024)
• Analytical Markov chains: exact throughput calculation for FD MACs with varying topology, node density, and protocol parameters (Doost-Mohammady et al., 2015)

Benchmarking is increasingly modular and extensible, allowing insertion of new metrics, scenarios, and agent models.

7. Key Insights, Limitations, and Future Directions

• Ideal SI suppression can approach 120 dB, but interference from other links (CLI, ICI, UE-UE, BS-BS) is typically the bottleneck before FD reaches theoretical doubling of capacity (Jr. et al., 2020, Jr. et al., 2020, Xiao et al., 2017).
• Multi-tier and multi-cell FD systems require flexible modeling of topology (PPP, cluster process), coordinated scheduling, and advanced resource control—partial FD often outperforms pure FD in realistic UL-limited regimes (AlAmmouri et al., 2015, Kundu et al., 2020).
• FD UEs add marginal rate gains relative to FD BSs + HD UEs, unless multi-user diversity is high and SI attenuation exceeds critical thresholds (AlAmmouri et al., 2015).
• In dialogue agents, full-duplex modeling enables unprecedented synchronicity and overlap handling, but latency, chunk alignment, and model anticipation remain open performance constraints (Veluri et al., 23 Sep 2024, Lin et al., 30 Jul 2025).
• Game-theoretic FDM offers analytic insights into information dissemination and network topology properties, explaining rapid convergence and small-world statistics (Zinoviev et al., 2010).
• Comprehensive FDM must integrate PHY-layer impairment models, interference-limited MAC scheduling, network-level simulation, and application-layer performance criteria (Kim et al., 8 Feb 2024).

A plausible implication is that future FDM will increasingly leverage machine learning for interference suppression and resource allocation across hardware, channel, and higher protocol layers, seek tighter cross-layer integration, and continuously enlarge benchmarking domains to cover multimodal, real-time, and cross-disciplinary applications.