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Hybrid Full-/Half-Duplex System Analysis in Heterogeneous Wireless Networks
Jemin Lee, Tony Q. S. Quek
TL;DR
The paper addresses how to analyze heterogeneous networks combining FD and HD access points while accounting for self-interference and network interference. It develops interference and throughput models for HDHNs, then shows when FD, HD, or tier-specific duplex choices provide higher throughput.
Problem
Existing FD analysis must account for self-interference together with network interference from randomly distributed FD nodes.
Method
The paper models multi-tier HDHNs, characterizes FD-cell interference, and derives HDHN throughput using AP density, self-IC capability, and transmission powers.
Results
FD achieves higher network throughput than HD for high self-IC capability and large AP density, while all-FD or all-HD operation outperforms mixing modes within a tier.
Takeaways & Limitations
Different tier networks operating in different duplex modes can improve total heterogeneous-network throughput.
Takeaways & Limitations
The paper identifies transmission-power control, MIMO FD throughput, network-interference cancellation, and secrecy as future HDHN research issues.
Abstract
from arXiv · showhide
Full-duplex (FD) radio has been introduced for bidirectional communications on the same temporal and spectral resources so as to maximize spectral efficiency. In this paper, motivated by the recent advances in FD radios, we provide a foundation for hybrid-duplex heterogeneous networks (HDHNs), composed of multi-tier networks with a mixture of access points (APs), operating either in bidirectional FD mode or downlink half-duplex (HD) mode. Specifically, we characterize the net- work interference from FD-mode cells, and derive the HDHN throughput by accounting for AP spatial density, self-interference cancellation (IC) capability, and transmission power of APs and users. By quantifying the HDHN throughput, we present the effect of network parameters and the self-IC capability on the HDHN throughput, and show the superiority of FD mode for larger AP densities (i.e., larger network interference and shorter communication distance) or higher self-IC capability. Furthermore, our results show operating all APs in FD or HD achieves higher throughput compared to the mixture of two mode APs in each tier network, and introducing hybrid-duplex for different tier networks improves the heterogenous network throughput.
I. INTRODUCTION
The paper motivates hybrid-duplex heterogeneous networks by combining FD and HD APs to improve spectral efficiency while accounting for self-interference and network interference. It develops throughput-based analysis to determine how network parameters and the FD-AP fraction affect performance.
- Motivation: FD radios enable bidirectional communication over the same temporal and spectral resources, potentially increasing link capacity and spectrum flexibility.
- Challenges: Self-interference is received from a node’s own transmission during simultaneous transmission and reception, making cancellation capability central to FD performance.
- Proposed framework: The paper proposes HDHNs comprising multi-tier networks with APs operating in bidirectional FD mode or downlink HD mode.
- Contributions: The analysis characterizes interference from distributed APs and users in FD-mode cells and derives HDHN throughput incorporating self-interference, AP density, and transmission powers.
- Contributions: The paper quantifies the FD-mode AP fraction that maximizes HDHN throughput according to self-IC capability and other network parameters.
II. HYBRID-DUPLEX HETEROGENEOUS NETWORK MODEL
This section introduces the HDHN model and characterizes the network interference generated within it.
- The section describes the HDHN model and characterizes its network interference.
A. Network Model
The model represents each tier with spatially distributed APs whose cells operate in HD or FD mode, while users associate through weighted pathloss and FD nodes retain residual self-interference after cancellation.
- Each of the K tiers distributes APs according to a homogeneous PPP, with each AP operating in downlink HD mode or bidirectional FD mode.
- HD-mode cells provide downlink communication, whereas FD-mode cells support simultaneous uplink and downlink communication.
- Users are distributed according to a homogeneous PPP and associate with APs using a weighted pathloss rule across tiers.
- The association framework includes nearest-AP and maximum-average-received-power rules as special cases.
- FD nodes experience residual self-interference after cancellation, while HD-mode nodes have zero self-interference because they do not transmit while receiving.
- The residual self-interference channel is modeled as a constant, although the framework can be extended to random self-IC capability.
B. Network Interference Characterization
The paper models FD-cell interference as combined AP and user interference, approximates user locations relative to interfering APs, and derives its Laplace transform for the HDHN analysis.
- The SIR is defined for a receiver communicating over a pathloss-and-Rayleigh-fading channel.
- Interference from an FD-mode cell includes contributions from both its AP and its associated user.
- Because the receiver-to-interfering-AP distance is assumed much larger than the AP-to-user separation, the associated user’s distance is approximated by the interfering AP’s distance.
- When AP and user transmission powers are equal, the combined fading-power term follows an Erlang distribution; unequal powers yield a hypo-exponential distribution.
- Lemma 1 gives the Laplace transform of the approximated interference from FD-mode cells in an ith-tier network.
- The approximation matches the non-approximated case well, especially in dense networks with large λFD.
III. HYBRID-DUPLEX HETEROGENEOUS NETWORK THROUGHPUT
This section analyzes successful transmission probability in HDHNs and uses it to define and derive HDHN throughput as a performance measure.
- The analysis first evaluates the successful transmission probability of HDHN nodes.
A. Successful Transmission Probability
The successful transmission probability is formulated for HD- and FD-mode nodes across network tiers, with target SIRs linked to target data rates and closed forms available only under special conditions.
- Target SIR values can be selected from target user and AP data rates using τu = 2Ru/W −1 and τa = 2Ra/W −1.Here, W is the communication bandwidth.
- Theorem 1 gives the successful transmission probability for an HD- or FD-mode node in each tier.The expression depends on transmitter and receiver transmission powers and tier-specific interference terms.
- Closed-form probabilities are provided for αi = 4, ∀i ∈K, or CFD_k(Pr) = 0.The general successful transmission probability is difficult to express in closed form outside these special cases.
- For perfect self-IC, CFD_k(Pr) = 0, closed-form FD-mode probabilities are available when αi = α > 2, ∀i ∈K.
- In HD mode, successful transmission probability excludes self-interference because CHD_k(Pr) = 0.
B. HDHN Throughput Analysis
This section defines HDHN throughput from successful transmitter–receiver pairs and analyzes how duplex-mode densities, transmission probabilities, self-IC, and interference shape network throughput.
- HDHN throughput measures the average successful data rate per unit area, in bits/sec/Hz/m2.Cell HDHN throughput instead normalizes total throughput by the average number of cells and uses bits/sec/Hz/cell.
- Closed-form HDHN throughput expressions are derived for special cases, including perfect self-IC and αi = 4, ∀i ∈K.
- The throughput combines HD-mode AP, FD-mode AP, and FD-mode user densities with their corresponding successful transmission probabilities.
- More FD-mode cells increase the number of transmitting nodes but also increase network interference, reducing successful transmission probabilities.
- With perfect self-IC, the throughput-maximizing FD-mode AP portion is p̂FD_k = 1 for every tier.This result holds for αk = α > 2 and equal user and AP target rates, Ru = Ra.
- Under perfect self-IC, operating all APs in FD mode maximizes throughput regardless of transmission power or AP spatial density.
IV. NUMERICAL RESULTS
The numerical results show how HDHN throughput varies with self-interference cancellation, AP density, transmission power, and duplex-mode allocation. FD is favored under higher density or stronger self-IC, while tier-wide and cross-tier mode choices determine maximum throughput.
- Throughput versus self-IC and density: Figures 3 and 4 evaluate network-1 throughput against self-IC capability and network-2 AP density under different duplex modes and AP powers.Figure 3 uses P_a,1 = 30 W, whereas Figure 4 uses P_a,1 = 9 W; simulation results in Figure 3 agree well with the analysis.
- Throughput versus self-IC and density: For large λ2 and low LdB,1, FD throughput exceeds HD throughput because increased interference makes self-interference less dominant while associated APs become closer.The density increase has opposing effects: it raises network interference but also shortens the communication distance.
- Throughput versus self-IC and density: When self-interference is small, FD throughput decreases with λ2 because increased network interference outweighs the benefit of shorter communication links; HD throughput also decreases with λ2.This behavior is reported for LdB,1 < −45 in Figure 4.
- FD-mode proportion: Throughput relative to the HD baseline increases with the FD-mode AP portion at high total AP density and decreases at low total AP density.The ratio S1/SHD is evaluated across AP-density ratios and FD-mode portions.
- FD-mode proportion: Operating all APs in either FD or HD achieves higher tier throughput than mixing the two modes within a tier.For Rλ,ij > 1, deploying FD-mode APs in all cells of network 1 achieves the maximum S1.
- Transmission power and self-IC: For Rλ,12 < 4, HD outperforms FD at LdB,1 = −30, whereas perfect self-IC reverses the comparison; increasing Pu,1 helps FD with perfect self-IC but hurts it at LdB,1 = −30.The results attribute these opposite power effects to whether reliable communication or residual self-interference primarily determines throughput.
- Cross-tier duplex allocation: The best two-tier duplex set is (FD, FD) for large Rλ,21, while the transition from HD to FD occurs at a smaller ratio in network 1 because it has better self-IC and lower Pu,1.The cell throughput is evaluated against Rλ,21 with λ1 = 10^-3.
- Cross-tier duplex allocation: For λt = 2 · 10^-3 and λt = 1 · 10^-2, the best duplex sets are respectively (FD, HD) and (FD, FD) across all λ1/λ2 ratios.The results indicate that total AP density determines the preferred duplex set more strongly than the AP-density ratio.
V. CONCLUSION
The paper develops an analytical foundation for hybrid-duplex heterogeneous networks and derives throughput while accounting for spatial AP distribution, self-interference cancellation, and network interference. Its results identify favorable duplex configurations for individual tiers and heterogeneous networks.
- V. CONCLUSION: The framework characterizes FD-mode network interference and derives HDHN throughput using AP spatial density, self-IC capability, and transmission powers.These factors are explicitly included in the HDHN analysis.
- V. CONCLUSION: Higher throughput is achieved by FD mode when HDHNs have high self-IC capability and large AP density.The conclusion associates larger AP density with the FD advantage.
- V. CONCLUSION: Operating all APs in either HD or FD is better for a tier than mixing the two duplex modes within that tier.
- V. CONCLUSION: Using different duplex modes across heterogeneous-network tiers can enhance total heterogeneous-network throughput.
B. Proof of Theorem 1
The proof derives the SIR CCDF by averaging over the associated-link distance and interference transforms under the network association rule. It also states a tractability approximation for an FD-mode interference case.
- B. Proof of Theorem 1: The SIR CCDF is obtained for Rayleigh fading channels and expressed using the distance D to the associated AP and the Laplace transform of interference.The distance distribution is then used to represent the CCDF.
- B. Proof of Theorem 1: The interference integral begins at the nearest unassociated AP distance because the association rule constrains competing AP locations.Campbell’s theorem is used in evaluating the resulting integral.
- B. Proof of Theorem 1: The analysis ignores cases where an FD-cell user is closer to another associated user than to its own AP because users generally transmit with lower power than APs.The approximation is introduced for analytical tractability.
C. Proof of Corollary 5
The corollary proof analyzes how the throughput changes with FD-mode probability and transmission power, then identifies the throughput-maximizing FD probability. Under equal AP densities, FD interference is no lower than HD interference.
- C. Proof of Corollary 5: The proof shows that the auxiliary functions c1(Pt) and c2(Pt) decrease with transmission power Pt.The ordering c1(Pt) ≤ c2(Pt) is also stated.
- C. Proof of Corollary 5: With equal AP densities, FD-mode interference is always at least as large as HD-mode interference.This comparison is used in the interference-transform analysis.
- C. Proof of Corollary 5: When user and AP transmit powers are equal, the relevant throughput component is zero and the result is unaffected by the FD-mode probability.
- C. Proof of Corollary 5: For a tier network, the throughput-maximizing FD-mode probability is the maximum permitted value, denoted ˆpFD_k.