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On the Spectral Efficiency of Full-Duplex Small Cell Wireless Systems
Dan Nguyen, Le-Nam Tran, Pekka Pirinen, Matti Latva-aho
TL;DR
Full-duplex small-cell systems promise higher spectral efficiency but must manage self-interference and co-channel interference. The paper jointly designs beamformers, relaxes the rank constraints, and proposes iterative MAXDET- and SDP-based methods for the remaining nonconvex problem. Numerical experiments show substantially higher spectral efficiency than half-duplex when self-interference cancellation is efficient.
Problem
Full-duplex small-cell spectral-efficiency gains require evaluation in reference systems because self-interference and co-channel interference complicate practical operation.
Method
The paper applies rank relaxation to joint spectral-efficiency maximization and uses D.C.-based and SPCA-based iterative algorithms producing MAXDET and SDP subproblems.
Results
Full-duplex spectral efficiency is remarkably larger than half-duplex under 3GPP LTE small-cell setups when self-interference cancellation is efficient.
Takeaways & Limitations
Full-duplex transmission is a promising technique for improving spectral efficiency in small-cell wireless communication systems.
Takeaways & Limitations
The full-duplex system's uplink performance is significantly reduced, potentially becoming worse than half-duplex because of large self-interference.
Abstract
from arXiv · showhide
We investigate the spectral efficiency of full-duplex small cell wireless systems, in which a full-duplex capable base station (BS) is designed to send/receive data to/from multiple halfduplex users on the same system resources. The major hurdle for designing such systems is due to the self-interference at the BS and co-channel interference among users. Hence, we consider a joint beamformer design to maximize the spectral efficiency subject to certain power constraints. The design problem is first formulated as a rank-constrained optimization one, and the rank relaxation method is then applied. However the relaxed problem is still nonconvex, and thus optimal solutions are hard to find. Herein, we propose two provably convergent algorithms to obtain suboptimal solutions. Based on the concept of the difference of convex functions programming, we approximate the design problem by a determinant maximization program in each iteration of the first algorithm. The second method is built upon the sequential parametric convex approximation method, which allows us to transform the relaxed problem into a semidefinite program in each iteration. Extensive numerical experiments under small cell setups illustrate that the full-duplex system with the proposed algorithms can achieve a large gain over the half-duplex one.
I. INTRODUCTION
Full-duplex can use downlink and uplink transmissions simultaneously on the same frequency, but self-interference and co-channel interference make practical gains uncertain. The paper addresses this gap with joint beamformer optimization and two iterative solution methods.
- Full-duplex enables downlink and uplink channels to operate simultaneously in the same time slot and frequency band.
- Self-interference from transmit to receive antennas is the crucial implementation barrier for full-duplex systems.
- The paper evaluates full-duplex gains for a full-duplex BS communicating with half-duplex users under reference small-cell scenarios.
- Joint beamformer design maximizes total spectral efficiency under power constraints, but the rank-constrained formulation and its relaxed version remain difficult to solve globally.
- Two iterative local optimization algorithms address the relaxed problem using difference-of-convex structure and sequential convex approximations.
- Under 3GPP LTE small-cell specifications, full-duplex transmissions are superior to conventional half-duplex when self-interference is efficiently canceled.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system uses a full-duplex BS to serve separate downlink and uplink user sets on the same frequency band. Its spectral-efficiency maximization couples beamforming, self-interference, co-channel interference, and power constraints in a nonconvex rank-constrained problem.
- A full-duplex BS simultaneously communicates with KD downlink and KU uplink single-antenna users over the same frequency band.
- The BS has N = NT + NR antennas, with NT used for downlink transmission and NR dedicated to uplink reception.
- Linear beamforming is used downlink, while MMSE-SIC decoding is used uplink; SI denotes self-interference and CCI denotes co-channel interference.
- Downlink and uplink transmissions are coupled by co-channel interference and self-interference, motivating joint beamformer design for total spectral-efficiency maximization.
- The SEMax problem imposes a BS sum-power constraint and per-user uplink power constraints while requiring rank-one downlink covariance matrices.
- Dropping the rank-one constraints yields a relaxed problem that remains nonconvex and is difficult to solve globally.
III. PROPOSED BEAMFORMER DESIGNS
The relaxed beamformer-design problem remains nonconvex after rank relaxation, so the paper develops iterative reformulations to obtain tractable numerical solutions.
- The relaxed problem remains nonconvex after rank constraints are dropped, making globally optimal solutions difficult and computationally expensive to obtain.
- The proposed algorithms reformulate the relaxed problem into iterative tractable optimization problems of differing complexity.
A. Iterative MAXDET-based Algorithm
The first algorithm exploits the difference-of-concave structure of spectral efficiency to iteratively solve MAXDET approximations. Its objective is a convergent lower bound, but convergence may yield only a locally optimal solution of the relaxed problem, followed by randomization when rank one is not obtained.
- The system spectral efficiency is expressed as a difference of two jointly concave functions of the design variables.
- At each iteration, the concave component is replaced by an affine first-order majorization, producing a convex approximation over the original convex constraints.
- The resulting objective is a lower bound on full-duplex spectral efficiency, and its MAXDET updates monotonically increase that bound until convergence.
- Convergence is guaranteed because the lower bound increases while spectral efficiency remains bounded above by the power constraints.
- The algorithm may converge to a locally optimal solution of the relaxed problem; randomization extracts rank-one beamformers when necessary.
- MAXDET solvers are less flexible than SDP solvers, making solver choice a practical limitation despite the algorithm's convex subproblems.
B. Iterative SDP-based algorithm
The second algorithm uses SPCA and reformulations to approximate the relaxed beamformer problem by an SDP at every iteration. It converges to a KKT point while offering access to a broader class of efficient SDP solvers, although added slack variables can increase worst-case complexity.
- The method transforms the relaxed problem into a semidefinite program at each iteration using SPCA and suitable reformulations.
- The MAXDET approach can be slower or experimentally supported through SDP-based successive approximation, limiting its flexibility relative to the SDP formulation.
- Introducing auxiliary and slack variables converts product and nonconvex constraints into tractable linear, SOC, and iteratively convexified forms.
- The SPCA approximations use convex upper estimates and matching first derivatives to support local convergence of the iterative procedure.
- The algorithm terminates after convergence and can apply the same randomization procedure as Algorithm 1 to extract rank-one solutions.
- Algorithms 1 and 2 produce solution sequences converging to KKT points of their respective relaxed problems.
- Although added slack variables may raise worst-case complexity, the SDP formulation enables use of solvers such as SEDUMI and MOSEK.
A. Convergence and Complexity Comparison
The experiments compare convergence and runtime under i.i.d. and realistic channel models with specified transmit-power and self-interference settings. Algorithm 1 generally converges in fewer iterations, while Algorithm 2 can finish faster because it supports faster SDP solvers.
- The complexity and convergence experiments use both i.i.d. Gaussian channels and a realistic channel model.
- The simulations set BS and uplink-user powers to 20 dBW in the i.i.d. case and 10 dBm in the realistic case.
- Residual self-interference is parameterized at −30 dB for the first case and −100 dB for the second case.
- Algorithm 1 generally requires fewer iterations to converge because it searches for an improved solution over the whole feasible set at each iteration.
- Algorithm 2 can use faster SDP solvers such as SeDuMi or MOSEK, whereas Algorithm 1 relies on the comparatively limited MAXDET solver ecosystem.
- Algorithm 2 has a lower per-iteration solving time and consequently a smaller total solving time than Algorithm 1 in the reported comparisons.
B. Spectral Efficiency Performance
The simulations evaluate full-duplex spectral efficiency against half-duplex performance under LTE small-cell settings, varying self-interference, topology, transmit power, and co-channel interference. Full-duplex gains depend strongly on effective self-interference cancellation and user separation.
- Self-interference sensitivity: 45.6% and 55% total SE gains are reported for full-duplex over half-duplex under substantially suppressed self-interference.The comparison is made for two transmit-power constraint settings in the scenario of Fig. 3(a).
- Self-interference sensitivity: At σ2 SI = −55 dB, half-duplex outperforms full-duplex for both transmit-power constraint settings.Full-duplex requires at least 75 dB or 83 dB of self-interference cancellation, depending on the power setting, to achieve better downlink and uplink SE.
- Interference effects: When uplink self-interference is high, joint optimization reduces uplink transmit power, lowering CCI and improving the downlink contribution to total SE.The uplink SE can become extremely low, causing total full-duplex SE to be determined mostly by downlink transmission.
- Transmit-power effects: Smaller maximum transmit powers produce higher full-duplex SE gains because they reduce both self-interference and co-channel interference.The effect is reported in the average gain comparison of Fig. 4(c).
- Interference effects: When uplink and downlink users are close, full-duplex downlink performance can fall below half-duplex; CCI therefore requires control for deployment.In the reported setup, this occurs especially when dCCI < 64.82 m.
- Interference effects: Accounting for CCI improves the proposed design over the scheme without CCI modeling, yielding 2 bits/s/Hz higher total SE for approximately 60% of simulated topologies when KD = 3 and KU = 2.The comparison uses 1000 random topologies and averages total SE over 500 random channel realizations per topology.
V. CONCLUSION AND FUTURE WORK
The paper develops a full-duplex beamforming scheme for simultaneous downlink and uplink transmission and evaluates its spectral-efficiency performance in small-cell settings. It reports substantially higher spectral efficiency than half-duplex operation, while identifying self-interference, co-channel interference, and fairness as continuing concerns.
- The proposed scheme jointly maximizes downlink and uplink spectral efficiency under power constraints for a full-duplex BS serving multiple half-duplex users.
- The design uses two iterative approaches: one based on Frank-Wolfe and MAXDET programs, and another based on SPCA and SDPs.
- The evaluation includes spectral efficiency versus uplink-to-downlink-user distance and CDFs over 1000 random topologies.
- Numerical experiments under 3GPP LTE small-cell setups show remarkably larger spectral efficiency for full-duplex than half-duplex operation when self-interference cancellation is efficient.
- Future work targets improved self-interference cancellation, co-channel-interference-aware scheduling, fairness mechanisms, and switching between full- and half-duplex modes.
APPENDIX PROOF OF CONVERGENCE
The appendix establishes convergence of both iterative algorithms by showing monotonic, bounded objective sequences and convergence to points satisfying the relaxed problem’s KKT conditions. The proof uses tight first-order approximations and convex-program optimality conditions.
- The affine majorization is tight at the current iterate and has matching gradients, providing the key approximation properties for Algorithm 1.
- Algorithm 1 produces a nondecreasing objective sequence bounded above by the transmit-power constraints, so the sequence converges.
- Strict concavity of log det on the positive-definite domain and compact convex feasibility yield convergence of the iterates to an accumulation point.
- Slater’s condition holds for each convex subproblem, making its KKT conditions necessary and sufficient for subproblem optimality.
- At convergence, the approximation gradients can be replaced by the original gradients, and the resulting equations are the KKT conditions of the relaxed problem.
- Algorithm 2 follows the same convergence logic: its update preserves feasibility, makes the objective nondecreasing, and leads to a KKT point.