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Analysis of Massive MIMO-Enabled Downlink Wireless Backhauling for Full-Duplex Small Cells

Hina Tabassum, Ahmed Hamdi Sakr, Ekram Hossain

arXiv:1511.05073v2cs.ITmath.IT

TL;DR

The network-level value of in-band full-duplex wireless backhauling remains unclear because access and backhaul links face multiple interference sources. This paper models downlink rate coverage in mixed-mode massive-MIMO wireless-backhauled small cells, and its results indicate that an appropriate mode mix and self-interference cancellation level are important for high coverage.

  • Problem

    The network-level performance and feasibility of in-band full-duplex wireless backhauling remain unclear amid self-interference and co-tier and cross-tier interference on access and backhaul links.

    Source: B. Motivation and Contributions · p. 2

  • Method

    The paper uses stochastic geometry to model downlink rate coverage in mixed in-band and out-of-band small cells, accounting for long-term backhaul channels and both long- and short-term access channels.

    Source: B. Motivation and Contributions · p. 2, §III · p. 5

  • Results

    Numerical results show that in-band backhauling is useful in some scenarios, while neither exclusively in-band nor exclusively out-of-band backhauling may be useful.

    Source: B. Motivation and Contributions · p. 2

  • Takeaways & Limitations

    A suitable proportion of out-of-band small cells and an appropriate self-interference cancellation value are crucial for obtaining high rate coverage.

    Source: §VIII · p. 15

Abstract

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Using tools from stochastic geometry, we develop a framework to model the downlink rate coverage probability of a user in a given small cell network (SCN) with massive MIMO-enabled wireless backhauls. The considered SCN is composed of a mixture of small cells that are configured in either in-band or out-of-band backhaul modes with a certain probability. The performance of the user in the considered hierarchical network is limited by several sources of interference such as the backhaul interference, small cell base station (SBS)-to-SBS interference and the SI. Moreover, due to the channel hardening effect in massive MIMO, the backhaul links experience long term channel effects only, whereas the access links experience both the long term and short term channel effects. Consequently, the developed framework is flexible to characterize different sources of interference while capturing the heterogeneity of the access and backhaul channels. In specific scenarios, the framework enables deriving closed-form coverage probability expressions. Under perfect backhaul coverage, the simplified expressions are utilized to optimize the proportion of in-band and out-of-band small cells in the SCN in closed-form. Finally, few remedial solutions are proposed that can potentially mitigate the backhaul interference and in turn improve the performance of in-band FD wireless backhauling. Numerical results investigate the scenarios in which in-band wireless backhauling is useful and demonstrate that maintaining a correct proportion of in-band and out-of-band FD small cells is crucial in wireless backhauled SCNs.

I. INTRODUCTION

The paper addresses the uncertain network-level value of in-band full-duplex wireless backhauling amid multiple interference sources. It develops a stochastic-geometry framework for mixed in-band and out-of-band small cells and finds that performance depends on selecting an appropriate mix and self-interference cancellation level.

I. INTRODUCTION

  • Wireless backhauling can reuse RAN spectrum, while full-duplex permits simultaneous transmission and reception in the same band but is limited by self-interference.The introduction contrasts wireless backhauling with wired, microwave, and millimeter-wave options and notes limited RAN spectrum availability.Source: §I · p. 1

A. Background Work

  • Earlier work examined backhaul interference management, backhaul delay, and full-duplex performance, including studies with ideal backhauls or restricted network settings.The cited work includes a massive-MIMO precoding study that ignores co-tier interference among small-cell base stations.Source: A. Background Work · pp. 1–2

B. Motivation and Contributions

  • The network-level gains of in-band full-duplex backhauling remain unclear because self-interference and co-tier and cross-tier interference affect access and backhaul links.The paper identifies a need to analyze when in-band backhauling may be beneficial relative to out-of-band backhauling.Source: B. Motivation and Contributions · p. 2
  • Using stochastic geometry, the paper models mixed-mode massive MIMO wireless backhauls and derives user downlink rate coverage while capturing different access- and backhaul-channel effects.It also gives closed-form expressions for specific scenarios and uses simplified expressions under perfect backhaul coverage to customize the mode proportion.Source: B. Motivation and Contributions · p. 2
  • Neither all-in-band nor all-out-of-band backhauling may be useful; numerical results stress choosing an appropriate mode mix, alongside suitable self-interference cancellation.The conclusion identifies the out-of-band proportion and self-interference cancellation as crucial to high rate coverage.Source: B. Motivation and Contributions · p. 2

C. Paper Organization and Notations

  • The paper organizes its analysis from system and channel models through SINR and rate-coverage derivations, mode customization, interference management, and numerical results.Its notation section defines Gamma distributions, special functions, probability density and cumulative distribution functions, and expectation.Source: C. Paper Organization and Notations · p. 3

A. Network Deployment Model

  • The deployment model places connector nodes, small-cell base stations, and users on independent homogeneous Poisson point processes, with users associating to the strongest-average-power small cell.Correlated connector-node and small-cell locations are not modeled because of analytical intractability.Source: A. Network Deployment Model · p. 3

B. Channel Model

The channel and backhaul model separates distance-dependent loss, shadowing, and fading from the modes used to serve small cells. It assumes massive-MIMO connector nodes with orthogonal pilots and zero-forcing beamforming, while distinguishing long-term backhaul effects from access-link fading.

1) Path-Loss:

  • Path loss for a generic link is distance raised to the negative path-loss exponent, with the exponent greater than 2.The notation uses the distance between generic network elements and denotes the path-loss exponent by β.Source: 1) Path-Loss · p. 3

2) Shadowing and Fading:

  • Links are subject to log-normal shadowing and Nakagami-m fading; the fading model includes Rayleigh fading at m = 1 and can approximate Rician fading.The displacement theorem permits shadowing to be handled through an equivalent Poisson point process when the relevant fractional moment is finite.Source: 2) Shadowing and Fading · p. 3

C. Backhaul Modes of Operation at SBSs

  • In-band mode uses one bandwidth-B band for access and backhaul, while a fair out-of-band comparison splits total bandwidth B equally between the two links.Out-of-band access uses 0.5B and backhaul uses 0.5B; using bandwidth B for each would instead consume 2B.Source: C. Backhaul Modes of Operation at SBSs · pp. 3–4

D. Massive MIMO-enabled Backhaul Model

  • Each connector node serves up to S single-antenna small-cell base stations using M antennas, with the massive-MIMO regime defined by 1 ≪ S ≪ M.The model assumes orthogonal pilots without pilot contamination and uses TDD channel reciprocity. Linear zero-forcing beamforming with equal power per backhaul stream mitigates intra-cell interference; backhaul rates concentrate on deterministic limits, and backhaul links experience long-term channel effects only.Source: D. Massive MIMO-enabled Backhaul Model · pp. 4–5

E. Load of CNs and Backhaul Access Probability of SBSs

The section models how CN load and limited backhaul streams affect SBS access, then defines normalized rate metrics and the performance, interference, and SINR framework for both backhaul modes.

E. Load of CNs and Backhaul Access Probability of SBSs

  • A CN may have more associated SBSs than its supported backhaul streams, so it randomly selects S SBSs when it cannot serve them all simultaneously.The number of associated SBSs is random; its PMF is approximated using a gamma-distributed Voronoi-cell area, under an independent PPP assumption.Source: E. Load of CNs and Backhaul Access… · p. 5

III. PERFORMANCE METRICS AND SINR MODEL OF IBFD AND OBFD TRANSMISSION MODES

  • The section characterizes interference sources and formulates access- and backhaul-link SINR for both IBFD and OBFD, supporting later rate-coverage analysis.Source: §III · p. 5

A. Performance Metrics

  • The analysis defines access- and backhaul-link rate metrics for IBFD and OBFD, and uses normalized rate (spectral efficiency) for evaluation.Normalized rate is obtained by dividing the rate equations by bandwidth B.Source: A. Performance Metrics · p. 5

1) Downlink rate coverage of an SBS in IBFD mode:

Rate coverage is determined by the access and backhaul requirements for each operating mode, while access SINR accounts for SBS interference and the IBFD backhaul transmissions that interfere with users.

1) Downlink rate coverage of an SBS in IBFD mode:

2) Downlink rate coverage of an SBS in OBFD mode:

1) Access link:

  • For an IBFD user, access SINR includes serving-SBS signal, co-tier and cross-tier interference, and thermal noise; distance to the serving SBS follows a Rayleigh distribution under the PPP model.Source: 1) Access link · p. 6
  • IBFD users also receive interference from SBSs receiving backhaul data and from CN backhaul transmissions, whose total power has no short-term fading because of channel hardening.The interfering SBS intensity uses a mean-load approximation based on E[Ns] = λs/λc and the stream limit S.Source: 1) Access link · p. 6

2) Backhaul link:

The backhaul-link model accounts for inter-cell interference and residual self-interference in IBFD, while the OBFD access-link interference intensity is specified through a mean-load approximation.

2) Backhaul link:

  • An IBFD SBS's backhaul SIR includes interference from other active SBSs, neighboring CNs, and residual self-interference tied to its own transmit power.The SI cancellation capability ξ is treated as constant for analytical convenience.Source: 2) Backhaul link · p. 6

1) Access link:

  • For OBFD access, interfering SBS intensity is modeled as (1 − q) min (λs/λc, S) λc using the mean-load approximation.Source: 1) Access link · p. 6

2) Backhaul link:

The analysis derives rate coverage by first obtaining interference Laplace transforms, then evaluating access and backhaul coverage for IBFD and OBFD, with OBFD treated as a special case in the link analyses.

IV. DOWNLINK RATE COVERAGE ANALYSIS OF IBFD/OBFD SBSS

  • The analytical framework derives co-tier and cross-tier interference transforms, then combines access- and backhaul-link coverage to obtain total user rate coverage in each mode.Source: §IV · p. 7

2) Backhaul link:

A. Rate Coverage Analysis: Access Links

B. Rate Coverage Analysis: Backhaul Links

The section derives backhaul-link rate coverage by characterizing interference and applying inversion to obtain coverage expressions. The OBFD case follows from the IBFD expression by changing the threshold and removing self-interference.

V. SIMPLIFIED RATE COVERAGE EXPRESSIONS: SPECIFIC SCENARIOS AND APPROXIMATIONS

The section simplifies access-link rate coverage under Rayleigh fading and approximates expressions for Gamma/Rayleigh fading. It also identifies how coverage sensitivities differ between IBFD and OBFD under perfect backhaul coverage.

A. Simplified Rate Coverage for Rayleigh Fading

B. Approximate Rate Coverage for Gamma/Rayleigh Fading

  • An approximation to the Gauss hypergeometric function further simplifies access-link coverage for Gamma and Rayleigh fading, with Rayleigh expressions given for both IBFD and OBFD.Source: B. Approximate Rate Coverage for… · p. 9
  • With perfect backhaul coverage, IBFD access coverage depends on CN/SBS powers and intensities, while OBFD is power-independent and becomes intensity-independent when average CN load is below S.Source: B. Approximate Rate Coverage for… · p. 9

C. Perfect Backhaul Coverage: Large Values of M

With ideal backhaul coverage, the paper derives closed-form choices of the in-band fraction q to maximize typical-user coverage or balance coverage across IBFD and OBFD SBSs. These choices support adapting the mode proportion to network conditions.

VI. BACKHAUL INTERFERENCE MITIGATION TECHNIQUES

The section proposes coordination and three approaches to address backhaul interference: distributed mode selection, interference rejection, and CN power control. Their mechanisms target interference affecting in-band backhauling and users.

VI. BACKHAUL INTERFERENCE MITIGATION TECHNIQUES

  • The motivation is that user-side backhaul interference can bottleneck in-band wireless backhauling, making CN–SBS coordination important to its potential performance gains.Source: §VI · p. 10

A. Distributed Backhaul-Aware IBFD/OBFD Mode Selection

  • The distributed rule selects IBFD when serving-SBS power sufficiently exceeds the strongest interfering CN power, and OBFD when that CN is comparable or stronger.The threshold τ can be chosen by user and trades rate coverage against backhaul interference; distributed decisions may degrade performance, especially if τ is not optimized.Source: A. Distributed Backhaul-Aware… · p. 10

B. Interference Rejection

  • With full CSI, CN precoding can null its interference at the user served by its associated SBS; the stated antenna requirement is M ≥ 2 × min(Ns, S).Source: B. Interference Rejection · pp. 10–11

C. Backhaul Interference-Aware (BIA) Power Control at CNs

VII. NUMERICAL AND SIMULATION RESULTS

Simulations examine downlink coverage across IBFD/OBFD proportions and SBS densities, validating the derived expressions. The results show that a suitable mode mix can balance SBS coverage, while coverage depends on mode share and interference.

A. Rate Coverage vs. Fraction of SBSs in IBFD/OBFD Mode

B. Rate Coverage vs. Intensity of SBSs

Rate coverage responds differently to SBS density, CN density, and SI cancellation across IBFD and OBFD modes. Distributed mode selection performs near-optimally at one tested density, but its threshold needs adjustment for higher densities.

B. Rate Coverage vs. Intensity of SBSs

  • As SBS intensity rises, OBFD coverage declines because co-tier interference grows at access and backhaul links, even after a CN reaches its support limit S.The selected S SBSs can still move closer to a CN as SBS intensity increases, sustaining co-tier interference.Source: B. Rate Coverage vs. Intensity of SBSs · p. 12
  • IBFD coverage first rises and then falls with SBS intensity, allowing the number of SBSs to be optimized for IBFD coverage.Initially, backhaul interference at a typical user is relatively small; beyond a point, it becomes more significant and coverage decreases.Source: B. Rate Coverage vs. Intensity of SBSs · p. 12
  • Higher CN intensity favors OBFD, whereas higher SBS intensity favors IBFD; the optimal SBS intensity for IBFD also increases with CN intensity.A higher CN intensity can provide stronger OBFD backhaul links, but increases backhaul interference in IBFD mode.Source: B. Rate Coverage vs. Intensity of SBSs · p. 13

C. Impact of SI Cancellation

  • Increasing SI cancellation improves IBFD coverage but leaves OBFD performance unchanged; sparse networks may require greater cancellation for IBFD gains over OBFD.For low SBS intensity, weak access links require high transmit power and consequently high SI cancellation; the authors identify OBFD-only mode as the right choice in such scenarios.Source: C. Impact of SI Cancellation · p. 13

D. Distributed Mode Selection

  • At SBS intensity λ′s = 50, distributed mode selection with τ = 10 achieves near-optimal performance, but that threshold is not optimal at higher SBS intensities.The authors state that τ therefore needs to be optimized for different network parameters.Source: D. Distributed Mode Selection · p. 13
  • Higher CN transmit power lowers the selected IBFD proportion q, while higher SBS intensity raises it.The reported trends reflect greater backhaul interference from higher CN power and the relative favoring of IBFD at higher SBS intensity.Source: D. Distributed Mode Selection · p. 13

E. Backhaul Interference Mitigation

Interference mitigation can improve typical-user rate coverage, with its gains depending on CN transmit power and SBS intensity. The framework also extends to pilot contamination and random scheduling.

E. Backhaul Interference Mitigation

F. Extensions to Include the Impact of Pilot Contamination

  • Pilot-contamination interference from CNs reusing pilots is modeled by thinning the CN PPP according to pilot-use probability.The reuse probability depends on the number of SBSs associated with a CN and the number of supported pilot sequences.Source: F. Extensions to Include the Impact of… · pp. 14–15
  • Pilot-contamination interference at IBFD and OBFD SBSs can be incorporated into the rate-coverage analysis using a Laplace transform.The analysis uses tools similar to those developed earlier in the paper.Source: F. Extensions to Include the Impact of… · p. 15

G. Random Scheduling at a Given SBS

  • For random or round-robin scheduling, the framework weights a user's normalized rate by its channel-access probability, 1/Nu, then averages over Nu.The number of users per SBS is modeled using the distribution for associated SBSs, with mean λu/λs.Source: G. Random Scheduling at a Given SBS · p. 15

VIII. CONCLUSION

  • High rate coverage depends on choosing an appropriate proportion of out-of-band small cells and an appropriate SI cancellation value.The conclusion also identifies multiple SBS antennas, opportunistic user service through CNs, and opportunistic scheduling as possible extensions.Source: §VIII · p. 15
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