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SoftNull: Many-Antenna Full-Duplex Wireless via Digital Beamforming

Evan Everett, Clayton Shepard, Lin Zhong, Ashutosh Sabharwal

arXiv:1508.03765v2cs.IT

TL;DR

Many-antenna full-duplex systems need to reduce self-interference without relying on increasingly complex analog cancellation circuitry. SoftNull uses digital transmit beamforming and receiver cancellation, achieving higher sum rate than half-duplex in measured many-antenna settings.

  • Problem

    Many-antenna full-duplex requires an approach to self-interference suppression that avoids analog-cancellation complexity growing with antenna count.

  • Method

    SoftNull partitions transmit and receive antennas, then uses transmit beamforming to reduce self-interference while preserving effective antennas for downlink communication.

  • Results

    At DTx = 18, SoftNull achieves a sum rate 23% better than half-duplex, while remaining 15% below ideal full-duplex in a measured 72-antenna scenario.

  • Takeaways & Limitations

    SoftNull offers a way to enable many-antenna full-duplex with current base-station radios without additional analog-cancellation circuitry.

Abstract

from arXiv · show

In this paper, we present and study a digital-controlled method, called SoftNull, to enable full-duplex in many-antenna systems. Unlike most designs that rely on analog cancelers to suppress self-interference, SoftNull relies on digital transmit beamforming to reduce self-interference. SoftNull does not attempt to perfectly null self-interference, but instead seeks to reduce self-interference sufficiently to prevent swamping the receiver's dynamic range. Residual self-interference is then cancelled digitally by the receiver. We evaluate the performance of SoftNull using measurements from a 72-element antenna array in both indoor and outdoor environments. We find that SoftNull can significantly outperform half-duplex for small cells operating in the many-antenna regime, where the number of antennas is many more than the number of users served simultaneously.

I. INTRODUCTION

SoftNull is an all-digital approach to many-antenna full-duplex that reduces self-interference while preserving effective transmit dimensions for downlink data. Measurements evaluate when it can outperform half-duplex, with gains depending on propagation environment, path loss, and user count.

  • Motivation: Many-antenna full-duplex enables simultaneous downlink and uplink MU-MIMO, but analog self-interference cancellation becomes more complex as antenna counts increase.The paper targets systems using current TDD radios without additional analog cancellation components.
  • SoftNull design: SoftNull partitions the array into transmit and receive antennas and uses digital transmit beamforming to reduce self-interference rather than perfectly nulling every receive antenna.Its precoder minimizes total self-interference subject to preserving a specified number of effective antennas for downlink transmission.
  • Evaluation: The evaluation uses 3D self-interference channel measurements from a 72-element array across varied propagation environments to assess SoftNull against half-duplex and ideal full duplex.The stated goal is to identify conditions for outperforming traditional half-duplex and quantify proximity to ideal full-duplex performance.
  • Self-interference reduction: SoftNull’s self-interference reduction depends on scattering, with more scattering producing less suppression while outdoor low-scattering conditions require sacrificing only a few effective antennas.The passage specifically describes a 72-element array partitioned into 36 transmit and 36 receive antennas.
  • Data rate gains over half duplex: 12 users at 100 dB path loss yield a SoftNull data rate 12% less than half duplex, whereas 4 users at 85 dB path loss yield an improvement of more than 40%.The introduction attributes these differences to the greater self-interference reduction required at higher path loss and the greater effective-antenna cost of serving more users.

II. SYSTEM DEFINITION · III. SOFTNULL DESIGN

The system models a multi-user full-duplex base station that partitions its antennas between transmission and reception while focusing on self-interference. SoftNull adds a modular two-stage reduction process to conventional MU-MIMO, combining transmit beamforming with receiver-side digital cancellation.

  • II. SYSTEM DEFINITION: The base station serves KUp uplink and KDown downlink users using M antennas, partitioned into MTx transmitting and MRx receiving antennas with MTx + MRx ≤ M.Each traditional radio antenna can transmit or receive, but not both simultaneously.
  • II. SYSTEM DEFINITION: The received base-station signal is modeled through uplink, self-interference, and receiver-noise components, with HSelf ∈ CMRx×MTx representing self-interference.Hup ∈ CMRx×KUp is the uplink channel matrix, and zUp ∈ CMRx is receiver noise.
  • II. SYSTEM DEFINITION: The downlink model includes the downlink channel, uplink-to-downlink user interference, and receiver noise through HDown, HUsr, and zDown.HDown ∈ CKDown×MTx, HUsr ∈ CKDown×KUp, and zDown ∈ CKDown.
  • II. SYSTEM DEFINITION: The analysis assumes HUsr = 0 to focus on self-interference, while acknowledging that inter-node interference remains for future characterization of overall network rate.In half-duplex operation, the self-interference term is eliminated and the channel dimensions use all M antennas.
  • III. SOFTNULL DESIGN: SoftNull uses two stages: conventional MU-MIMO precoding and equalization, followed by self-interference reduction through transmit beamforming and digital cancellation.The modular design can be incorporated into existing MU-MIMO systems.
  • III. SOFTNULL DESIGN: The self-interference reduction stage combines a transmitter-side precoder that reduces self-interference with a receiver-side digital canceler that reduces residual self-interference.The design focuses on the SoftNull precoder because digital cancellation is considered well understood and existing techniques sufficient for practical use.
  • III. SOFTNULL DESIGN: A higher-layer operation determines the partitioning of transmit and receive antennas, MTx and MRx, based on network needs.SoftNull therefore treats antenna-role allocation as an input to the physical-layer design.

A. Precoder Design · 1) Standard MU-MIMO downlink precoder: · 2) SoftNull precoder:

The precoder design combines a standard MU-MIMO downlink precoder with a SoftNull precoder. SoftNull suppresses self-interference while preserving effective antennas for downlink transmission, and the standard precoder then serves users using the resulting effective channel.

  • A. Precoder Design: The downlink precoder has two stages: the standard MU-MIMO precoder P_Down followed by the SoftNull precoder P_Self.P_Self suppresses self-interference, while P_Down limits interference among users.
  • A. Precoder Design: The standard MU-MIMO precoder P_Down controls DTx effective antennas and aims to deliver each user mostly its intended signal.It also aims to minimize signal intended for other users.
  • 1) Standard MU-MIMO downlink precoder:: P_Down requires only the effective downlink channel, H_Eff = H_DownP_Self, rather than separate knowledge of the self-interference and downlink channels.H_Eff can be estimated directly using pilots transmitted and received along the DTx effective antennas.
  • 1) Standard MU-MIMO downlink precoder:: The standard MU-MIMO precoder uses a power constraint coefficient α(ZFBF).The supplied passage identifies α(ZFBF) as a power constraint coefficient.
  • 2) SoftNull precoder:: The SoftNull precoder reduces self-interference while preserving DTx effective antennas for standard MU-MIMO downlink transmission.It has DTx effective-antenna inputs and MTx physical-antenna outputs, and assumes knowledge of H_Self.
  • 2) SoftNull precoder:: SoftNull minimizes total self-interference power subject to preserving DTx effective antennas through orthonormal precoder columns.The constraint P^HP = I_DTx×DTx forces the DTx columns to be orthonormal.
  • 2) SoftNull precoder:: The closed-form SoftNull solution projects onto the DTx left singular vectors of H_Self associated with its smallest DTx singular values.This construction solves the stated optimization problem.
  • 2) SoftNull precoder:: SoftNull selects the DTx-dimensional subspace of the original transmit space C^MTx that presents the least self-interference to the receiver.For H_Self = UΣV^H, the singular values in Σ are ordered, and v^(i) denotes the ith column of V.

B. SoftNull Simulation Example · IV. CHANNEL MEASUREMENT SETUP

The simulation illustrates that SoftNull reduces self-interference by sacrificing effective antennas, while channel measurements use a 72-antenna platform across diverse environments and client placements. Together, these setups characterize array coupling and provide traces for evaluating SoftNull performance.

  • B. SoftNull Simulation Example: SoftNull reduces self-interference by sacrificing effective antennas in a 3 × 6 array with M = 18 and an even (9, 9) transmit–receive partition.The simulation uses half-wavelength antenna spacing and computes fields with a full-wave electromagnetic solver.
  • B. SoftNull Simulation Example: The simulation models vertically polarized patch antennas tuned to 2.4 GHz, with resonant dimension L = 48.7 mm and an air dielectric between patch and ground.The full-wave solver captures near-field effects and mutual coupling among transmit antennas.
  • B. SoftNull Simulation Example: With DTx = 9 = MTx, no effective antennas are sacrificed and all receive antennas experience very high self-interference.When DTx = 6, three effective antennas are given up for self-interference reduction.
  • IV. CHANNEL MEASUREMENT SETUP: SoftNull measurements use the ArgosV2 platform with 72 2.4 GHz patch antennas connected to 18 WARP v3 boards and four emulated mobile clients.The platform supports 72 base-station antennas for transmission or reception.
  • IV. CHANNEL MEASUREMENT SETUP: Measurements collected 20 MHz-wideband real self-interference channel traces for the 2D array across diverse environments.The measurement environments included an anechoic chamber, an outdoor open field, and a highly scattered indoor deployment.
  • IV. CHANNEL MEASUREMENT SETUP: The measured traces support analysis of coupling between base-station antennas, Tx/Rx partitions, and real-world performance with clients.Figure 6 reports coupling strength between antenna pairs, with element colors representing average channel strength from antenna i to antenna j.
  • IV. CHANNEL MEASUREMENT SETUP: For each deployment, four clients occupied three locations each, measuring both 72 × 72 self-coupling and 72 × 4 downlink/uplink channels.The dataset contains more than 12 million wideband channels and more than 40 GB of channel traces.

V. SOFTNULL EVALUATION · A. Antenna Array Partitioning · 1) Heuristic Partitions Considered:

The evaluation uses measured channel traces to study SoftNull across antenna partitions, propagation environments, and client data rates. For partitioning, the paper compares empirical heuristics rather than solving the computationally difficult combinatorial optimization problem.

  • V. SOFTNULL EVALUATION: Measured channel traces are used to evaluate SoftNull’s self-interference reduction and its dependence on antenna partitioning and propagation environment.The evaluation also studies uplink and downlink data rates against half-duplex and ideal full-duplex systems.
  • V. SOFTNULL EVALUATION: Anechoic-chamber results are omitted because they were very similar to outdoor results and provided no additional insight.The full datasets are available at.
  • A. Antenna Array Partitioning: Partitioning M antennas into MTx transmit and MRx receive antennas is computationally difficult because the antenna-set search is combinatorial.The paper therefore evaluates heuristic partitions using channel-measurement traces.
  • 1) Heuristic Partitions Considered:: SoftNull is expected to perform best when self-interference power is concentrated in fewer eigenchannels.Reduced transmitter-to-receiver angular spread increases signal correlation, making the first eigenvalues more dominant.
  • 1) Heuristic Partitions Considered:: The heuristic partitions are presented as Tx/Rx spatial arrangements, with blue denoting transmit antennas and red denoting receive antennas.The figure includes the Northwest-Southeast and interleaved arrangements.
  • 1) Heuristic Partitions Considered:: The interleaved partition is expected to be near worst-case because its receive antennas experience interference arriving at every possible angle.This tests whether minimizing angular spread is an effective heuristic.
  • 1) Heuristic Partitions Considered:: The study compares the deterministic interleaved partition with the average measured performance of 10, 000 randomly chosen partitions.The random-partition comparison provides an empirical reference for the heuristic choices.

2) Evaluation of the Heuristic Partitions: · B. Impact of scattering on self-interference reduction

In an anechoic-chamber evaluation of a 72-element array with a 36/36 transmit–receive split, contiguous heuristic partitions produced a better self-interference/effective-antenna tradeoff than random or interleaved partitions. Scattering strongly affected SoftNull: outdoor channels enabled stronger reduction, while indoor performance was worse and outdoor results varied substantially for small preserved-antenna counts.

  • 2) Evaluation of the Heuristic Partitions:: The contiguous partitions achieved a much better self-interference/effective-antenna tradeoff than random and interleaved partitions.Measurements used the 72-element rectangular array with (M_Tx, M_Rx) = (36, 36) in an anechoic chamber.
  • 2) Evaluation of the Heuristic Partitions:: At > 50 dB self-interference reduction, random partitioning preserved 6 effective antennas, whereas every contiguous partition preserved at least 16.The maximum number of effective antennas was 36.
  • 2) Evaluation of the Heuristic Partitions:: The East-West partition performed best among the considered partitions, consistent with its minimum angular spread between transmit and receive partitions.This result aligns with the stated heuristic for partition selection.
  • B. Impact of scattering on self-interference reduction: With all 36 effective antennas preserved, the East-West partition achieved only 20 dB passive self-interference suppression.The scattering comparison used the 72-element array and a (M_Tx, M_Rx) = (36, 36) East-West partition.
  • B. Impact of scattering on self-interference reduction: Indoor self-interference reduction was not nearly as good as outdoor reduction.The passage introduces this difference while comparing the tradeoff between self-interference reduction and preserved effective antennas.
  • B. Impact of scattering on self-interference reduction: Giving up 16 effective antennas and preserving D_Tx = 20 for downlink increased self-interference suppression to more than 50 dB.The result is reported for the scattering-environment comparison in Figure 9(a).
  • B. Impact of scattering on self-interference reduction: Outdoors, direct paths dominate backscattered paths, concentrating channel power in dominant modes that SoftNull avoids.SoftNull reduces self-interference by avoiding the (M_Tx − D_Tx) dominant modes of the self-interference channel.
  • B. Impact of scattering on self-interference reduction: For outdoor D_Tx = 12, self-interference reduction ranged from 62 dB to 90 dB for a given antenna.For small D_Tx, outdoor reduction varied more than indoor reduction.

C. Achievable rate gains over half-duplex · 1) Achievable rates for measured channels, K=4 clients:

For four clients, SoftNull trades effective downlink antennas for self-interference suppression and can outperform half-duplex on measured channels. Indoor performance peaks at a 62% gain over half-duplex, while sufficiently large path loss can eliminate the gain.

  • C. Achievable rate gains over half-duplex: SoftNull evaluates measured 72 × 72 self-interference, 72 × 4 downlink, and 4 × 72 uplink channels across 64 OFDM subcarriers.The measurements use channel 4, a 20 MHz band in the 2.4 GHz ISM band.
  • C. Achievable rate gains over half-duplex: A dynamic noise figure of 25 dB limits digital cancellation to no more than 25 dB, requiring remaining self-interference reduction through beamforming.SoftNull gives up effective antennas for downlink operation so they can reduce self-interference.
  • 1) Achievable rates for measured channels, K=4 clients:: The comparison uses four uplink and four downlink clients, with SoftNull’s achievable rates compared against half-duplex and ideal full-duplex.SoftNull preserves a selectable number of effective antennas while operating uplink and downlink simultaneously.
  • 1) Achievable rates for measured channels, K=4 clients:: Outdoors, downlink rate increases with DTx while uplink rate decreases, because more preserved antennas improve downlink beamforming but reduce self-interference suppression.At DTx = 12, self-interference is sufficiently suppressed that digital cancellation removes the remaining interference; larger DTx values mainly reduce downlink rate.
  • 1) Achievable rates for measured channels, K=4 clients:: Indoors, SoftNull outperforms half-duplex for all DTx values; at DTx = 14, it achieves a 62% gain over half-duplex while remaining 12% below ideal full duplex.The antenna partition must match both self-interference suppression needs and the users’ angular distribution.
  • 1) Achievable rates for measured channels, K=4 clients:: Indoor gains exceed outdoor gains despite weaker indoor self-interference reduction because indoor clients are closer, producing less path loss and stronger uplink signals.Indoor clients were 4-9 m from the array, whereas outdoor clients were 9-15 m away.
  • 1) Achievable rates for measured channels, K=4 clients:: At 100 dB path loss, SoftNull cannot outperform half-duplex outdoors for any DTx, while at 70 and 85 dB outdoor path loss it can significantly outperform half-duplex.Indoors at 100 dB path loss, the required antenna sacrifice harms the downlink rate.

D. Varying number of clients · VI. CONCLUSION

SoftNull’s client-scaling behavior reflects a tradeoff between spatial multiplexing and sacrificing effective antennas for self-interference suppression. The conclusion emphasizes that SoftNull can enable full-duplex with existing base-station radios by suppressing, rather than perfectly nulling, self-interference.

  • D. Varying number of clients: Adding clients creates spatial-multiplexing opportunities for both half-duplex and SoftNull, but SoftNull simultaneously has fewer effective antennas available for self-interference reduction.The client counts are assumed equal for uplink and downlink.
  • D. Varying number of clients: At 70 dB path loss, SoftNull performance increases through K ≤20, then declines because serving more clients causes prohibitive self-interference.For K > 20, SoftNull underperforms half-duplex.
  • D. Varying number of clients: At 85 dB path loss, SoftNull outperforms half-duplex when K ≤12.Higher path loss requires sacrificing more effective antennas to suppress self-interference and avoid swamping the uplink signal.
  • D. Varying number of clients: At 100 dB path loss, SoftNull underperforms half-duplex for every evaluated client count.The supplied passage states this result but does not include the remainder of the sentence describing the client-count range.
  • VI. CONCLUSION: SoftNull enables full-duplex operation with current base-station radios without requiring additional analog-cancellation circuitry.This is presented as a central opportunity of the SoftNull approach.
  • VI. CONCLUSION: The SoftNull precoder sacrifices the minimum number of effective antennas needed to sufficiently suppress self-interference rather than perfectly nulling it.The conclusion’s analysis is based on channels measured using a 72-element array.

APPENDIX A OPTIMAL PRECODER SOLUTION

Appendix A defines the optimal precoder through an optimization problem and then rewrites the optimization function using simple manipulations.

  • The optimal precoder is obtained as the solution to an optimization problem.
  • The appendix presents the precoder derivation by first stating the optimization-based solution and then reformulating its objective.
  • The optimization function is rewritten via simple manipulations.

P HHH

The SoftNull optimization is solved using Lagrange multipliers: feasible stationary solutions use distinct eigenvectors of the self-interference matrix, and the optimum selects those with the smallest eigenvalues. Equivalently, the transmit beamforming columns are right singular vectors associated with the smallest singular values of HSelf.

  • Optimization method: Problem (8) is a convex optimization problem with equality constraints and can therefore be solved using Lagrange multipliers.The Lagrangian and its gradient provide the stationarity conditions.
  • Stationary solutions: Feasible stationary solutions use DTx distinct eigenvectors of HSelf^HHSelf as the columns of P.Distinct eigenvectors satisfy P^HP = I_DTx×DTx while meeting the stationarity condition.
  • Optimal solution: The objective is minimized by selecting the eigenvectors corresponding to the DTx smallest eigenvalues of HSelf^HHSelf.The selected indices are P = {MTx − DTx + 1, ..., MTx}.
  • Optimal solution: The optimal beamforming columns are equivalently right singular vectors of HSelf corresponding to its DTx smallest singular values.This follows from the singular value decomposition HSelf = UΣV^H.

APPENDIX B RATE COMPUTATION DETAILS

The appendix computes ergodic uplink and downlink achievable rates from per-packet SINRs, averaging user rates across channel realizations and weighting schemes by their uplink/downlink activity. It explains that SoftNull’s lower SINRs can nevertheless yield higher rates than half-duplex through concurrent transmission, under idealized coding assumptions.

  • Rate computation: Ergodic achievable rates are computed from per-packet signal-to-interference-plus-noise ratios for half-duplex, SoftNull, and ideal full-duplex.The schemes are indexed as HD, SoftNull, and IdealFD.
  • Activity allocation: Full-duplex schemes keep uplink and downlink simultaneously active, whereas half-duplex separates them across time slots or frequency bands with an even allocation.For IdealFD, α(IdealFD)_Up = 1; half-duplex uses separate uplink and downlink resources.
  • Rate computation: Downlink and uplink rates sum user rates and average them over channel realizations.For downlink, SINR is measured for each downlink user and channel realization; uplink rates are computed analogously.
  • SoftNull versus half-duplex: SoftNull has lower uplink SINR from residual self-interference and lower downlink SINR from antennas sacrificed for suppression, but can still outperform half-duplex through concurrent operation.The concurrent uplink and downlink operation provides a multiplexing gain represented through SoftNull’s activity allocation.
  • Rate assumptions: The rate comparison assumes optimal channel codes achieving the ideal Shannon rate and codes extending across multiple channel realizations.These assumptions aim to compare systems fairly without tying results to a particular coding scheme or modulation rate.

APPENDIX C EXPLANATION AND EXAMPLE OF DYNAMIC RANGE

Limited dynamic range creates received-power-dependent noise that can swamp weak uplink signals in full-duplex systems. Increasing self-interference suppression can lower this noise floor enough for a useful uplink, while the required suppression increases with path loss.

  • Dynamic-range noise: Dynamic-range noise scales with received power from sources including A/D quantization, oscillator noise, and amplifier non-linearities.Thus, a fixed thermal-noise-floor model is accurate only at low SNR.
  • Full-duplex example: With 20 dB self-interference reduction, the dynamic-range noise floor remains too high for a useful uplink under the example’s 0 dBm transmission and 80 dB path loss.The desired uplink arrives at −80 dBm, while the dynamic-range noise floor is 40 dB below the received power level.
  • Full-duplex example: 50 dB self-interference reduction lowers the received power to −50 dBm and the dynamic-range noise floor to −90 dBm, enabling a positive uplink SNR after digital cancellation.This permits a useful uplink communication link alongside downlink transmission.
  • Dependence on path loss: 70 dB suppression, rather than 50 dB, is required for a 10 dB uplink SNR when path loss increases from 80 dB to 100 dB.The passage states that required self-interference suppression is proportional to path loss between the base station and users.
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