PaperlayerView exact revision on arXiv

Source-linked AI summary

Interference Management in 5G Reverse TDD HetNets with Wireless Backhaul: A Large System Analysis

Luca Sanguinetti, Aris Moustakas, Merouane Debbah

arXiv:1407.6481v4cs.ITmath.IT

TL;DR

The work addresses the challenge of increasing capacity and maintaining QoS while limiting the energy consumption of dense networks, where wireless backhaul can be a bottleneck. The authors analyze a reverse-TDD HetNet using BS MMSE reception and ZF or RZF precoding to serve MUEs and provide wireless backhaul under imperfect MUE CSI. SUE transmit power is 0.85 mW in the proposed HetNet versus up to 0.22 W in massive MIMO.

  • Problem

    The work addresses the challenge of increasing capacity and maintaining QoS while limiting the energy consumption of dense networks, where wireless backhaul can be a bottleneck.

    Source: §I · p. 1

  • Method

    The authors analyze a reverse-TDD HetNet using BS MMSE reception and ZF or RZF precoding to serve MUEs and provide wireless backhaul under imperfect MUE CSI.

    Source: §VII · p. 12

  • Results

    SUE transmit power is 0.85 mW in the proposed HetNet versus up to 0.22 W in massive MIMO.

    Source: §V · p. 10

  • Takeaways & Limitations

    The reported SUE power saving may prolong battery lifetime.

    Source: §V · p. 9

    The paper leaves scheduling for very-high-mobility MUEs and multi-cell analysis with limited cooperation as future work.

    Source: §VII · p. 12

Abstract

from arXiv · show

This work analyzes a heterogeneous network (HetNet), which comprises a macro base station (BS) equipped with a large number of antennas and an overlaid dense tier of small cell access points (SCAs) using a wireless backhaul for data traffic. The static and low mobility user equipment terminals (UEs) are associated with the SCAs while those with medium-to-high mobility are served by the macro BS. A reverse time division duplexing (TDD) protocol is used by the two tiers, which allows the BS to locally estimate both the intra-tier and inter-tier channels. This knowledge is then used at the BS either in the uplink (UL) or in the downlink (DL) to simultaneously serve the macro UEs (MUEs) and to provide the wireless backhaul to SCAs. A geographical separation of co-channel SCAs is proposed to limit the interference coming from the UL signals of MUEs. A concatenated linear precoding technique employing either zero-forcing (ZF) or regularized ZF is used at the BS to simultaneously serve MUEs and SCAs in DL while nulling interference toward those SCAs in UL. We evaluate and characterize the performance of the system through the power consumption of UL and DL transmissions under the assumption that target rates must be satisfied and imperfect channel state information is available for MUEs. The analysis is conducted in the asymptotic regime where the number of BS antennas and the network size (MUEs and SCAs) grow large with fixed ratios. Results from large system analysis are used to provide concise formulae for the asymptotic UL and DL transmit powers and precoding vectors under the above assumptions. Numerical results are used to validate the analysis in different settings and to make comparisons with alternative network architectures.

I. INTRODUCTION

The paper motivates a two-tier HetNet to combine massive-MIMO coverage with small-cell capacity and wireless backhaul, then develops reverse-TDD coordination and large-system power analysis under imperfect MUE channel estimates.

I. INTRODUCTION

  • The proposed HetNet combines a massive-MIMO macro tier for mobile UEs with small cells for low-mobility UEs and wireless backhaul, addressing backhaul as a bottleneck.The work analyzes power consumption while meeting target rates, with imperfect MUE CSI and large-system scaling.Source: §I · p. 1, A. Main contributions · pp. 1–2

A. Main contributions

  • The main contributions are a reverse-TDD protocol, asymptotic RZF precoding under imperfect MUE CSI, and large-system analysis of UL and DL power.The system also considers MMSE reception and ZF or RZF processing.Source: A. Main contributions · pp. 1–2

B. Comparison with related literature

  • Unlike, this work adds wireless backhaul and imperfect MUE CSI, and analyzes network power rather than average sum rate.It modifies the protocol to reverse TDD both between tiers and among SCAs.Source: B. Comparison with related literature · p. 2

II. SYSTEM MODEL

  • The model uses single-antenna SCAs and MUEs, with low-mobility SUEs around SCAs and MUEs assigned to groups by proximity to SCAs.Co-channel SCAs are grouped to maximize same-group separation and control interference.Source: A. Main contributions · p. 1, §II · pp. 2–3

A. Transmission protocol

  • In reverse TDD, the BS transmits in DL while SCAs operate in UL, and vice versa, with synchronized transmissions and reciprocal channels within the coherence time.The protocol supports wireless backhaul while serving MUEs and SUEs and uses geographic separation to counter interference.Source: A. Transmission protocol · p. 3

B. Channel Model and Assumptions

The channel model allows generic distance-dependent path loss and assumes imperfect channel estimates for MUEs but perfect channel knowledge for SCAs and SUEs. The UL analysis uses MMSE reception to characterize target-rate powers asymptotically, including how imperfect MUE CSI affects power and feasibility.

B. Channel Model and Assumptions

  • For MUEs, the channel model combines small-scale fading with distance-dependent path loss, kept generic as long as it decreases with distance and is bounded below.The same model is adopted for SCAs and SUEs.Source: B. Channel Model and Assumptions · p. 4
  • Only MUE channels have imperfect estimates; SCA and SUE channels are assumed perfectly known at the BS.The estimate-quality parameter ranges from perfect CSI at τ_i = 0 to uncorrelated CSI at τ_i = 1.Source: B. Channel Model and Assumptions · p. 4

III. LARGE SYSTEM ANALYSIS OF THE MACRO-TIER INTERFERENCE IN UL

  • The UL analysis uses an MMSE receiver to compute powers meeting target rates while accounting for MUE and SCA interference, including interference to SUEs in the other group.Geographical separation limits, but does not eliminate, interference from UL transmitters to SUEs.Source: §III · p. 4
  • In the large-system regime, the required UL powers reduce to solving for unique ξ and δ values determined by system parameters and SINR targets.Imperfect MUE CSI affects both quantities, and (ξδ)^−1 represents the fractional UL power increase for transmitters in R; powers diverge if the stated feasibility condition is unmet.Source: §III · pp. 5–6

IV. LARGE SYSTEM ANALYSIS OF THE MACRO-TIER INTERFERENCE IN DL

In the DL, the BS uses linear precoding to serve receivers in R while nulling interference toward SCAs in SB. Channel reciprocity lets it reuse UL estimates, with imperfect CSI for MUEs and perfect CSI for SCA channels.

IV. LARGE SYSTEM ANALYSIS OF THE MACRO-TIER INTERFERENCE IN DL

  • The BS sacrifices spatial degrees of freedom to serve receivers in R while nulling its interference toward SCAs in SB.The text says interference from UL transmissions in SB can reasonably be neglected because there are relatively few transmitting SUEs and they are geographically distant.Source: §IV · p. 6
  • Channel reciprocity lets the BS use UL channel estimates for DL transmissions, with imperfect CSI for MUEs and perfect knowledge of SCA channels.The assumed perfect knowledge covers both H(SB) and H(SR).Source: §IV · p. 6
  • Constraining the precoding matrix to the null space of H(SB) eliminates macro-tier interference at SCAs in SB under perfect knowledge of H(SB).The construction writes V = T(SB)F, then designs F using the composite channel estimate.Source: §IV · p. 6

A. Regularized Zero Forcing

The RZF design uses average channel attenuations and a regularization parameter to form the concatenated precoder. Its asymptotic power expression includes the cost of nulling interference toward SCAs.

A. Regularized Zero Forcing

  • The design uses average channel attenuations in Λ and scales ρ by N so that it converges to a constant as N and K grow.The concatenated matrix T(SB)F is called RZF.Source: A. Regularized Zero Forcing · p. 6
  • The use of average attenuations yields a closed-form expression for optimal ρ, although the cited single-tier optimality result does not apply under imperfect CSI and SCA nulling.The cited result concerns a single-tier MIMO downlink with perfect CSI and equal rate constraints.Source: A. Regularized Zero Forcing · p. 6
  • The asymptotic RZF power expression includes a regularization parameter whose optimum does not depend on the MUE CSI-error values.The factor 1 − cS accounts for interference nulling toward SCAs.Source: A. Regularized Zero Forcing · p. 6

B. Zero Forcing

The ZF design has a stricter feasibility condition than RZF under imperfect MUE CSI. The stated condition requires sufficient degrees of freedom relative to the network load and SCA nulling.

B. Zero Forcing

  • The cited passage states that 1 − cS − c(B + 1) > 0 must be satisfied, presenting it as a condition that follows from equation (32).Source: B. Zero Forcing · p. 7
  • RZF is more robust than ZF to imperfect CSI of MUEs.The same condition as for ZF must also be fulfilled in the UL.Source: B. Zero Forcing · p. 7

V. NUMERICAL RESULTS

Finite-network simulations evaluate transmit power across network architectures and channel-uncertainty settings. They report aggregate throughput and power costs, as well as rate and feasibility limits under imperfect CSI.

V. NUMERICAL RESULTS

  • Monte-Carlo simulations use 1,000 channel realizations and UE distributions for a BS with 128 antennas and 16 regularly gridded SCAs, with 128 active MUEs; τ² values 0.1 and 0.3 correspond to 15 and 50 km/h, respectively.The two sets R and B count 64 MUEs and 8 SCAs, with 8 MUEs near each SCA.Source: §V · pp. 7–8
  • MUE uplink power is essentially the same as in a wired-backhaul HetNet despite 3 bit/s/Hz wireless backhaul, while SCA downlink power is substantially reduced through shielding.SCA uplink power is close to that of SUEs in massive MIMO; SCA power shows mild dependence on MUE rate because increased MUE targets raise system interference.Source: §V · p. 8, Figure 5 · p. 8, Figure 6 · p. 8
  • RZF requires 0.1 W at the BS for a 2 bit/s/Hz target rate; at a 3 bit/s/Hz SUE target, HetNet SUE power is 0.85 mW versus 0.22 W in massive MIMO.The proposed HetNet requires marginally more BS power than massive MIMO, while its SUE power is substantially lower.Source: §V · p. 9, Figure 9 · p. 9
  • At τ²=0.3, RZF is more robust than ZF and can handle MUE target rates up to 1.75 bit/s/Hz, while both precoders' required power diverges as rates increase.The system becomes infeasible beyond an MUE target rate of approximately 1.5 bit/s/Hz in the cited uncertainty analysis.Source: §V · pp. 8–9, Figure 11 · p. 9
  • 4.8 Gb/s/km2 aggregate area throughput is achieved with total power consumption of 5.52 W UL and 6.05 W DL in the proposed HetNet.The comparison uses a MUE target rate of 1.5 bit/s/Hz and τ²=0.1.Source: §V · p. 10, Table II · p. 10

VI. DISCUSSIONS AND PERSPECTIVES

The section introduces discussion of mobility and other practical aspects of the proposed HetNet.

  • The discussion covers mobility and other practical aspects of the proposed HetNet.Source: §VI · p. 10

A. Impact of mobility

The analysis contrasts mobility’s limited effect on other users’ sum rates with its strong effect on transmit power when target rates must be met. It discusses rate reduction and CSI-free space-time coding as responses, with a rate–energy tradeoff for high-mobility users.

A. Impact of mobility

  • A single high-mobility MUE with rate requirements can substantially increase UL and DL transmit powers, unlike the per-user rate effect reported for sum-rate analysis.Source: A. Impact of mobility · p. 10
  • For high-mobility MUEs, lowering target rates can address channel-estimation error; alternatively, DL can serve them one at a time using space-time coding that requires no BS CSI.Source: A. Impact of mobility · p. 10

T2KST C

  • When STC and linear-precoding service times are comparable, STC-served MUE rates are reduced by a factor of K_STC; comparable spectral efficiencies instead require substantially more energy.Source: T2KST C · p. 10

B. Tradeoff between proximity effect and density of users

The discussion relates MUE–SUE separation and user density to uplink interference, and evaluates that relationship under simplifying assumptions. It notes that the analysis applies only to uniformly distributed MUEs.

  • For the Table II setting, average interference normalized to noise is 1.3×10^3, yet SUEs retain good average SINRs due to their proximity to SCAs.The interference depends on SCA radius, inter-SCA distance, and MUE density.Source: B. Tradeoff between proximity effect… · p. 10
  • Under the uniform-MUE assumptions, the analytical estimate E{I_K}/σ^2 ≈ 5.5 × 10^3 is of the same order as the numerical 1.3 × 10^3, supporting the approximation despite its simplifying assumptions.Source: B. Tradeoff between proximity effect… · p. 11
  • For d ≫ x̄, average interference is attributable mainly to the αd^2 MUEs at distances of order d, providing a way to assess the user-density–separation tradeoff.Source: B. Tradeoff between proximity effect… · p. 11
  • The analysis assumes uniformly distributed MUEs; nonuniform densities would require accounting for spatial variation when optimizing SCA locations.Source: B. Tradeoff between proximity effect… · p. 11

C. Impact of correlation at BS antennas

The paper reports low transmit power at substantial aggregate area throughput when CSI errors stay below critical values, while examining antenna correlation and dynamic TDD implications. Its correlated-channel analysis is more involved, and asynchronous macro-tier transmissions require a full-duplex BS.

C. Impact of correlation at BS antennas

  • For correlated BS antennas, deterministic equivalents require fixed-point equations and a K × K matrix inverse, while optimal RZF regularization requires numerical optimization.Source: C. Impact of correlation at BS antennas · p. 11
  • With the evaluated angular-spread settings, antenna correlation produces only a marginal required-power difference, and imperfect CSI has the same impact in correlated and uncorrelated cases.Source: C. Impact of correlation at BS antennas · p. 11

D. Dynamic UL-DL TDD

  • Dynamic TDD can be used within the small-cell tier, but asynchronous macro-tier transmissions require a full-duplex BS.Source: D. Dynamic UL-DL TDD · p. 12

VII. CONCLUSIONS

  • When critical imperfect-CSI values are not exceeded, the architecture achieves about 4.8 Gb/s/km2 aggregate area throughput on a 10 MHz band with about 6 W in both UL and DL.Source: §VII · p. 12
  • The paper identifies multi-cell analysis with limited BS cooperation and scheduling very-high-mobility MUEs without rate reductions as follow-up directions.Source: §VII · p. 12

APPENDIX

The appendix proves Lemma 1 using asymptotic results from and proves Lemma 2 by extending that analysis to include the projection matrix. The second proof also identifies the minimum-power choice of its parameter.

1) Proof of Lemma 1:

  • Lemma 1 applies asymptotic results from under the stated channel-correlation assumption and uses the Woodbury identity twice to evaluate a channel cross-term.The proof then uses τ_i = 0 for SCA channels when assembling the result.Source: 1) Proof of Lemma 1 · p. 12

2) Proof of Lemma 2:

  • Lemma 2 follows the steps of with the projection matrix T(SB) included, under a uniformly bounded spectral norm condition on T(SB).The proof notes that the relevant trace involving H(SB) equals S.Source: 2) Proof of Lemma 2 · p. 12
  • The minimum power is achieved when μ equals the target γ; substituting this choice yields equation (27), from which Lemma 2 follows.Source: 2) Proof of Lemma 2 · p. 13

Related papers

Loading 1407.6481v4…