Duplex: Bidirectional Operations in Communications

• Duplex is defined as a bidirectional or two-part operating principle enabling simultaneous or coordinated operations (e.g., full-duplex and half-duplex) in wireless communications and beyond.
• Adaptive schemes like α-duplex optimize overlapping uplink/downlink bands to balance rate gains against interference, demonstrating practical performance improvements.
• Emerging duplex applications span quantum state transfer, speech-to-speech interactions, optical instruments, and algebraic constructs, highlighting its versatile, multi-domain impact.

Duplex denotes a class of bidirectional or two-part operating principles in which transmission, interaction, or structure is organized across paired directions or paired components rather than a single one-way path. In wireless communications, duplexing specifies how uplink and downlink share time, frequency, antennas, or network topology; the associated design space includes half-duplex, full-duplex, dynamic TDD, FDD, partial-overlap schemes, and virtual or emulated full-duplex architectures (AlAmmouri et al., 2015). In more recent work, the same term also appears in duplex speech-to-speech interaction with simultaneous user and agent streams (Hu et al., 21 May 2025), two-way quantum state transfer through a spin chain (Wang et al., 2011), asymmetric absolute optical instruments built by splicing two lens halves (Peng et al., 2020), and duplex Hecke algebras of type $B$ defined through Hecke generators and additional symmetric-group data (Xie et al., 2023). Across these literatures, “duplex” denotes either simultaneous two-way operation or a two-part composition.

1. Wireless duplexing and its interference structure

In the wireless literature, the canonical contrast is between half-duplex and full-duplex. Half-duplex separates uplink and downlink in time or frequency, whereas full-duplex reuses the same time-frequency resource for simultaneous uplink and downlink, potentially doubling spectral efficiency at the link level (Goyal et al., 2014). The benefit is limited by self-interference at the transceiver and by cross-link interference between uplink and downlink transmissions across cells (Jr. et al., 2020).

A central result of stochastic-geometry analyses is that the uplink is especially vulnerable to downlink interference because BS transmit power is high while the uplink target received power is comparatively low. In the in-band $\alpha$-duplex formulation, full overlap can provide improved downlink rate gains of up to $97\%$, but this comes at the expense of uplink rate degradation of up to $94\%$ (AlAmmouri et al., 2015). System-level studies of multi-cell full-duplex and dynamic-TDD further identify cross-link interference, especially BS-to-BS interference in the uplink, as the remaining challenge once self-interference suppression is sufficiently strong (Jr. et al., 2020).

Duplexing constraints also appear in FDD massive MIMO through duplex-pattern reciprocity. Studies of practical user handsets report noticeable duplex pattern divergence across uplink and downlink bands; in a measured population of 16 commercial phones, only two phones showed no marked high pattern divergence in any band (Eggers et al., 2020). This makes duplexing not only a resource-allocation problem but also a radiation-pattern and cluster-illumination problem.

2. Adaptive, hybrid, and partial-overlap duplex schemes

A large part of recent duplex research replaces fixed mode selection with adaptive control. The $\alpha$-duplex scheme introduces a continuum between HD and FD by allowing uplink and downlink bands to overlap by $2\alpha B$, with $\alpha=0$ corresponding to HD and $\alpha=1$ to full overlap (AlAmmouri et al., 2015). For the Sinc$^2$–Sinc pulse pair, the effective cross-mode factor is nulled at $\alpha_{\rm sp}=0.2776$, and the scheme provides a simultaneous improvement of $\alpha$0 for the downlink rate and $\alpha$1 for the uplink rate (AlAmmouri et al., 2015). The same framework shows that the optimal overlap depends on the design objective rather than being universally equal to full overlap.

In opportunistic spectrum sharing, duplexing can be driven by a local success probability rather than a deterministic sensing threshold. The opportunity probability is defined as

$\alpha$2

and each node accesses the medium randomly with probability equal to its own OP (Kim et al., 2018). This directly induces a hybrid HD/FD rule for a communicating pair: if both nodes transmit, the pair operates in FD; if only one transmits, it operates in HD. For example, OP values $\alpha$3 and $\alpha$4 yield an FD probability of $\alpha$5, and the FPGA-based real-time prototype reports up to 4 times higher system throughput than conventional LTE-TDD (Kim et al., 2018).

A related received-power-based hybrid scheme for heterogeneous networks switches each user between HD and FD according to whether $\alpha$6 is above or below a tier-dependent threshold $\alpha$7 (Tang et al., 2016). The analytical and simulation results show that strong users are better FD candidates, weak users are better HD candidates, and the hybrid scheme outperforms fixed HD and fixed FD. The reported performance keeps a stable gain of roughly $\alpha$8 over conventional HD across different small-cell densities (Tang et al., 2016).

Other hybridizations combine classical duplex families. Dynamic time-frequency division duplex assigns separate uplink and downlink bands as in FDD, then shares each band dynamically between two users in a D-TDD fashion; the scheme doubles the diversity gain on both the corresponding BS–U1 and BS–U2 channels compared to existing duplexing schemes and requires only local BS–U1 and BS–U2 CSI rather than inter-cell interference knowledge (Razlighi et al., 2019). In multi-cell flexible-duplex OFDM networks, interference-aware algorithms SAFP and RMDI optimize worst-case QoS satisfaction rather than traffic matching alone; the reported gain is two-fold under a low level of traffic asymmetry and three-fold when traffic is highly asymmetric (Liao, 2017).

A common misconception is that full-duplex is uniformly superior once self-interference is controlled. Bidirectional ISAC provides a counterexample: because sensing echo is useful for sensing but harmful to communication, full-duplex may not always outperform half-duplex, especially in the sensing-prior regime or when the communication channel is line-of-sight-dominated (Wang et al., 2022).

3. Emulation and architectural decomposition of full-duplex operation

One response to the hardware difficulty of colocated full-duplex is to emulate it using coordinated half-duplex nodes. CoMPflex realizes a full-duplex base-station function with two wired-together and spatially separated half-duplex base stations, one serving uplink and the other serving downlink (Thomsen et al., 2015). A full-duplex base station is the special case of CoMPflex with separation distance zero (Thomsen et al., 2016). In a planar stochastic-geometry model, CoMPflex brings BSs closer to the mobile stations they serve while increasing the distance between a mobile station and interfering mobile stations, and this produces communication-reliability gains over the FD-BS baseline; the reported downlink success probability is about $\alpha$9 higher over most SINR thresholds (Thomsen et al., 2016). In the one-dimensional Wyner-style model, CoMPflex also improves sum-rate and energy efficiency, with the conclusion reporting about $97\%$0 to $97\%$1 normalized energy-efficiency improvement for large splitting distances and higher path-loss exponents (Thomsen et al., 2015).

Virtual full-duplex can also be created without simultaneous RF transmission and reception at the same node. Rapid on-off-division duplex assigns each half-duplex radio a random on-off signature over a frame; a node transmits during on-slots and receives during off-slots, so over one frame every node can transmit a message to peers and simultaneously receive a message from each peer (Guo et al., 2010). The half-duplex constraint is modeled as erasure of received samples during transmit slots rather than total inability to exchange data in the same frame. Under both OR-channel and Gaussian multiaccess analyses, RODD throughput is reported to be significantly larger than that of ALOHA (Guo et al., 2010).

At the relay level, X-duplex treats the duplex mode itself as a selectable resource. In a two-hop amplify-and-forward relay with two antennas, the relay adaptively chooses transmit and receive antenna roles and operates in either FD or HD mode to minimize symbol error rate (Li et al., 2017). The selected SINR is

$97\%$2

and the asymptotic diversity order satisfies $97\%$3 (Li et al., 2017). This mode-and-antenna adaptation reduces the high-SNR performance floor associated with residual self-interference and outperforms pure FD, pure HD, hybrid FD/HD, and RAMS in the reported comparisons (Li et al., 2017).

4. Physical-layer realization, scheduling, and self-interference cancellation

Practical full-duplex deployment depends on scheduling, power control, and cancellation rather than duplex mode selection alone. In small multi-cell systems with FD base stations and HD user equipment, a hybrid scheduler pairs uplink and downlink users only when full-duplex provides a throughput advantage and otherwise defaults to HD (Goyal et al., 2014). With practical self-interference cancellation, the proposed system achieves $97\%$4 throughput improvement in the downlink and $97\%$5 in the uplink in an indoor multi-cell scenario at $97\%$6 dB cancellation, and $97\%$7 in downlink and $97\%$8 in uplink in an outdoor multi-cell scenario at the same cancellation level (Goyal et al., 2014). The same study also shows that energy efficiency can deteriorate sharply under naive power allocation, so throughput gains do not imply bits-per-joule gains.

System-level macro-cell analyses reinforce the same point. Multi-cell full-duplex and dynamic-TDD are limited mainly by BS-to-BS cross-link interference in the uplink, and a low-complexity BSint receiver using BS-to-BS CSI and a ZF null can suppress the dominant interference source (Jr. et al., 2020). Under proper CLI management, the reported gains approach doubling: in low traffic, BSint variants provide about $97\%$9 gain over HD, and the overall conclusion is that full-duplex can almost double system throughput if cross-link interference is controlled (Jr. et al., 2020).

At the device level, compact full-duplex MIMO radios combine analog and digital cancellation. A $94\%$0 full-duplex MIMO prototype for D2D-underlaid cellular networks uses dual-polarized antennas with about $94\%$1 dB self-talk isolation and $94\%$2 dB cross-talk isolation, for roughly $94\%$3 dB total analog cancellation; the real-time digital canceller reaches about $94\%$4 dB, yielding about $94\%$5 dB combined cancellation (Chung et al., 2016). Implemented on an FPGA-based SDR platform with 20 MHz bandwidth, the prototype achieves about $94\%$6 throughput over half-duplex LTE SISO when transmit power is below 15 dBm and about $94\%$7 at 23 dBm (Chung et al., 2016).

Flexible-duplex deployment also requires nonlinear digital cancellation. Frequency-domain nonlinear SIC for IBFD and SBFD models PA nonlinearity and IQ imbalance through bases such as

$94\%$8

then selects only basis terms whose estimated interference power satisfies $94\%$9 (Kim et al., 4 Mar 2025). The algorithm uses an impulse-like pilot,

$\alpha$0

and is reported to offer lower complexity than conventional digital SIC while being directly applicable to OFDM flexible-duplex MIMO systems (Kim et al., 4 Mar 2025).

5. Duplex interaction in speech and quantum communication

In speech-to-speech modeling, duplex denotes simultaneous conversational streams rather than turn-based alternation. SALM-Duplex uses continuous user inputs and codec agent outputs with channel fusion to model simultaneous user and agent streams directly (Hu et al., 21 May 2025). The architecture employs a pretrained streaming encoder for user input, separate user and agent modeling, and a codec operating at $\alpha$1 kbps with 4 codebooks at 12.5 frames/s (Hu et al., 21 May 2025). The model is reported as the first duplex S2S model without requiring speech pretrain and the first openly available duplex S2S model with training and inference code (Hu et al., 21 May 2025). On reported barge-in benchmarks, UltraChat barge-in success is $\alpha$2 versus $\alpha$3 for Moshi, and Impatient barge-in success is $\alpha$4 versus $\alpha$5; the corresponding barge-in latencies are $\alpha$6 s versus $\alpha$7 s and $\alpha$8 s versus $\alpha$9 s (Hu et al., 21 May 2025).

In quantum communication, duplex describes simultaneous state transfer in opposite directions through a common spin chain. Alice and Bob each encode a qubit on opposite ends of an open $2\alpha B$0-site spin-$2\alpha B$1 chain evolving under the XY Hamiltonian

$2\alpha B$2

with the initial chain in the fully polarized ground state (Wang et al., 2011). The central finding is that transmission fidelity at each end can usually be enhanced by the presence of the second party. For a 10-site chain with $2\alpha B$3 and $2\alpha B$4, the reported maximum fidelity is $2\alpha B$5 when $2\alpha B$6 and $2\alpha B$7 when $2\alpha B$8 (Wang et al., 2011). For $2\alpha B$9, the peak time also shifts from about $\alpha=0$0 without Bob’s encoding to $\alpha=0$1 with it (Wang et al., 2011). In this setting, duplex operation enhances both fidelity and latency rather than introducing contention.

6. Duplex constructions in optics and algebra

Outside communication theory, “duplex” can denote an object assembled from two distinct but compatibly joined halves. A duplex Mikaelian lens is formed by splicing two half Mikaelian lenses with different periods, while a duplex Maxwell’s fish eye lens is obtained from it by the exponential conformal map

$\alpha=0$2

when the ratio of the two periods is rational (Peng et al., 2020). The standard Mikaelian profile is

$\alpha=0$3

and the duplex period is

$\alpha=0$4

The duplex Mikaelian lens has continuous translation symmetry but no mirror symmetry about the $\alpha=0$5-axis, whereas the duplex Maxwell’s fish eye lens has continuous rotational symmetry from $\alpha=0$6 to $\alpha=0$7 (Peng et al., 2020). These systems remain absolute optical instruments in geometric optics, but they exhibit caustics for off-axis sources and a Talbot self-imaging effect in the duplex Mikaelian case (Peng et al., 2020).

In representation theory, the duplex Hecke algebra of type $\alpha=0$8, denoted $\alpha=0$9, is a $\alpha=1$0-algebra generated by $\alpha=1$1 for $\alpha=1$2 and elements $\alpha=1$3 indexed by $\alpha=1$4 for $\alpha=1$5, with the type-$\alpha=1$6 Hecke relations

$\alpha=1$7

and the special braid relation

$\alpha=1$8

among its defining identities (Xie et al., 2023). The algebra admits natural tensor-space representations and participates in a Levi-type $\alpha=1$9-Schur-Weyl duality of type $^2$0. The main double-centralizer statements are

$^2$1

which identify the duplex Hecke algebra and the relevant Levi-type quantum group as mutual centralizers on tensor space (Xie et al., 2023).

Across these domains, duplex is not a single mechanism but a recurrent formal pattern. In wireless systems it marks simultaneous or partially overlapping uplink and downlink operation under self-interference and cross-link interference constraints; in speech and quantum models it denotes concurrent two-way interaction; in optics and algebra it denotes composite structures built from two coordinated halves (AlAmmouri et al., 2015). The term therefore retains a common core—paired directions or paired components—while its technical realization depends strongly on the surrounding mathematical or physical setting.