Modeling and Analyzing the Coexistence of Wi-Fi and LTE in Unlicensed Spectrum

I. INTRODUCTION

• The motivation is to use lightly used unlicensed spectrum for LTE carrier aggregation while preserving fair coexistence with incumbent Wi-Fi and meeting unlicensed-spectrum regulations.The introduction notes that licensed spectrum below 6 GHz is scarce and expensive, and that more than 400 MHz of generally lightly used unlicensed spectrum is available in the 5 GHz band.Source: §I · pp. 1–2

A. Related Work and Motivation

• Prior coexistence studies relied on time-consuming system-level simulations, while existing analytical approaches had limitations in representing random network effects or matching Wi-Fi throughput results.The paper identifies deterministic fluid models as unable to capture multipath fading and Wi-Fi random backoff, and notes that earlier stochastic-geometry analysis did not closely match simulated Wi-Fi throughput or investigate discontinuous transmission and LBT with random backoff.Source: A. Related Work and Motivation · pp. 2–3

B. Contributions

• The paper proposes a stochastic-geometry framework that derives and evaluates MAP, SINR coverage, DST, and rate coverage for three LTE coexistence scenarios.The scenarios are continuous transmission without protocol changes, fixed-duty-cycle discontinuous transmission, and LBT with random backoff.Source: B. Contributions · pp. 3–4
• Compared with Wi-Fi coexisting with another Wi-Fi network, continuous LTE transmission severely degrades Wi-Fi SINR coverage, DST, and rate coverage, while LTE remains relatively robust to Wi-Fi.The degradation is attributed to persistent LTE eNB transmissions.Source: B. Contributions · p. 4
• With fixed-duty-cycle LTE, Wi-Fi generally has better DST and rate coverage under synchronous than asynchronous muting, but short LTE duty cycles are needed to protect Wi-Fi in either case.Synchronous muting gives Wi-Fi a cleaner channel while LTE is muted; LTE has worse DST and rate coverage under synchronous muting because eNBs transmit simultaneously.Source: B. Contributions · p. 4
• Under LBT with random backoff, Wi-Fi achieves better DST and rate coverage than baseline when LTE uses equal access priority with more sensitive CCA (e.g., -82 dBm) or lower priority; LTE maintains acceptable rate coverage.Source: B. Contributions · p. 4

A. Spatial locations

• Wi-Fi APs and LTE eNBs are modeled as independent homogeneous Poisson point processes in a single unlicensed band.The networks use full-buffer downlink traffic, with low-power small-cell eNBs as the LTE setting.Source: A. Spatial locations · p. 5
• Users are modeled as homogeneous Poisson point processes, associate with their closest AP or eNB, and are analyzed through a typical user at the origin.The user intensity is assumed much larger than the AP/eNB intensity, so each access point or base station has a user to serve.Source: A. Spatial locations · p. 5

B. Propagation Assumptions

• Both networks use a free-space path-loss model and i.i.d. Rayleigh fading, while shadowing is neglected.The channel fading variables are exponentially distributed.Source: B. Propagation Assumptions · pp. 5–6

C. Modeling Channel Access for Wi-Fi

• For Wi-Fi AP xi, contenders are other Wi-Fi APs and LTE eNBs whose received powers at xi exceed Γcs and Γed, respectively; xi transmits when its independent [0,1]-uniform back-off timer is smaller than contenders’ timers.Source: C. Modeling Channel Access for Wi-Fi · p. 7

D. Definition of Performance Metrics

• The analyzed performance metrics include medium access probability (MAP) for tagged APs and eNBs, and SINR coverage probability for typical Wi-Fi and LTE users.The Wi-Fi and LTE SINR coverage probabilities are evaluated conditional on the tagged transmitter accessing the channel.Source: D. Definition of Performance Metrics · p. 7, PLF LW · p. 7, PWF W L · p. 7

PLF LW

• Wi-Fi SINR coverage probability gives the probability that the typical STA's SINR exceeds threshold T, describing its instantaneous link performance.The LTE coverage probability is likewise defined for the typical UE conditional on its tagged eNB transmitting.Source: PLF LW · p. 7, PWF W L · p. 7, PLF L · p. 7

PLF L

• Density of successful transmissions (DST) is the mean number of links per unit area that meet the decoding SINR requirement, counting only links whose tagged transmitter accesses the channel..Source: PLF L · p. 8
• Rate coverage is the probability that a tagged AP or eNB can support an aggregate data rate of threshold ρ.The definition accounts for the fraction of time the tagged transmitter accesses the channel; user-perceived rates can additionally account for each user's average resource fraction.Source: PLF L · p. 8
• Because the network point processes are stationary and isotropic, the analyzed metrics do not depend on the tagged AP's or eNB's angle.The tagged link angles are set to zero without loss of generality, and the corresponding distance distributions are specified in Table I.Source: PLF L · p. 8

A. Medium Access Probability

• The analysis models Wi-Fi access as blocked by an LTE contender or by a Wi-Fi contender with an earlier back-off timer.The paper notes that this access model is consistent with IEEE 802.11 specifications, while energy detection is typically based on total interference.Source: A. Medium Access Probability · p. 9
• For PPP-distributed transmitters, the paper treats its total-interference-based energy-detection model as reasonable because the total-interference tail approaches that of the strongest interferer and no closed-form distribution is known.The discussion also cites the relatively large energy-detection threshold and simulations as support.Source: A. Medium Access Probability · pp. 9–10
• Adding LTE reduces the typical Wi-Fi AP’s MAP by a factor of exp(−NL) relative to the Wi-Fi-only scenario, with degradation exponential in eNB intensity λL.The MAP expression uses NL and NW as defined in Table II.Source: A. Medium Access Probability · p. 10
• Below 100 eNBs/km², LTE has little effect on Wi-Fi MAP, but above 100 eNBs/km², additional eNBs significantly degrade it.The authors attribute the limited low-density effect to the high energy-detection threshold for LTE signals.Source: A. Medium Access Probability · p. 11, Figure 2 · p. 11

1) SINR Coverage Probability of Typical Wi-Fi STA:

• The Wi-Fi SINR estimate is reported as accurate, but its derivation approximates dependent Wi-Fi interferers as a non-homogeneous PPP because their interference transform is not known in closed form.The paper also reports that the LTE–Wi-Fi interference correlation is mostly captured through LTE’s statistical effect on Wi-Fi MAP.Source: 1) SINR Coverage Probability of… · pp. 12–13
• LTE’s continuous interference significantly degrades Wi-Fi STA SINR coverage, and the impact is greater at lower AP intensity.At fixed LTE intensity, coverage is worse for λW = 200 than for λW = 400; Fig. 3 presents the Wi-Fi coverage comparison.Source: Figure 3 · p. 13, 1) SINR Coverage Probability of… · p. 14

2) SINR Coverage Probability of Typical LTE UE:

• Wi-Fi AP transmissions reduce LTE coverage, with the effect increasing as AP intensity rises or the energy-detection threshold rises.The discussion identifies this effect as the third term in the LTE coverage expression.Source: 2) SINR Coverage Probability of… · p. 15
• LTE UE SINR coverage improves as eNB intensity increases or AP intensity decreases, and remains reasonable unless λL ≪ λW.Coverage with λW = 0 is an upper bound; Fig. 4 presents the LTE UE coverage results.Source: 2) SINR Coverage Probability of… · pp. 15–16, Figure 4 · p. 15
• The analysis considers Wi-Fi downlink traffic; performance with Wi-Fi uplink traffic is left to future work.The authors note that similar techniques could derive MAP and SINR coverage when uplink traffic exists.Source: 2) SINR Coverage Probability of… · p. 16

IV. LTE WITH DISCONTINUOUS TRANSMISSION

• LTE discontinuous transmission uses a duty cycle η, transmitting for a fraction η of time and remaining muted for 1 − η.The duty cycle may be fixed or adaptively adjusted based on Wi-Fi medium utilization.Source: §IV · p. 16
• The paper considers static muting patterns in which eNBs either mute synchronously or asynchronously.Under synchronous muting, eNBs transmit and mute at the same time; under asynchronous muting, neighboring eNBs can use shifted patterns.Source: §IV · p. 16

A. LTE with Synchronous Discontinuous Transmission Pattern

• Synchronous LTE DST is its active-time fraction η multiplied by the eNB density and LTE SINR coverage probability.The time-averaged rate coverage expressions are defined for Wi-Fi and LTE at rate threshold ρ.Source: A. LTE with Synchronous Discontinuous… · p. 17
• With synchronous muting, time-averaged Wi-Fi DST combines its LTE-on and LTE-off performance, weighted by η and 1 − η, respectively.Fig. 5 compares DST under synchronous and asynchronous muting.Source: A. LTE with Synchronous Discontinuous… · p. 17, Figure 5 · p. 18
• For synchronous muting, LTE achieves better DST and rate coverage when η increases.The paper defines time-averaged rate coverage as the fraction of APs or eNBs supporting aggregate data rate ρ, averaged over time.Source: A. LTE with Synchronous Discontinuous… · pp. 17–18

B. LTE with Asynchronous Discontinuous Transmission Pattern

• Independent LTE transmission with probability η makes the interfering eNBs a PPP of intensity ηλL.This activity model underlies the Wi-Fi MAP and performance expressions.Source: B. LTE with Asynchronous Discontinuous… · p. 18
• The section gives expressions for Wi-Fi DST and time-averaged rate coverage, and for LTE time-averaged DST during its active fraction η.The Wi-Fi DST expression is in (14); the text introduces the rate-coverage expression and LTE DST expression.Source: B. LTE with Asynchronous Discontinuous… · p. 18
• Reducing η improves Wi-Fi DST and rate coverage.The section attributes both improvements to the time-averaged performance expressions.Source: B. LTE with Asynchronous Discontinuous… · p. 18

C. Comparison of Synchronous and Asynchronous Muting Patterns

• Synchronous muting generally outperforms asynchronous muting for Wi-Fi rate coverage.The comparison uses λW = 400 APs/km2 and λL = 400 eNBs/km2.Source: C. Comparison of Synchronous and… · p. 19
• When all LTE eNBs are muted, Wi-Fi APs observe a much cleaner channel and therefore benefit more from LTE muting than under the asynchronous scheme.A synchronous muting pattern with an LTE transmission duty cycle within 33.3% to 50% is suggested to protect Wi-Fi.Source: C. Comparison of Synchronous and… · p. 19
• Asynchronous muting outperforms synchronous muting in LTE DST and rate coverage.Independent thinning of LTE interferers under asynchronous muting is stated as the relevant distinction.Source: C. Comparison of Synchronous and… · p. 19

A. LTE with Same Channel Access Priority as Wi-Fi when (a, b) = (0, 1)

• For equal-priority access, LTE senses interfering LTE and Wi-Fi neighbors at threshold ΓL and uses a random backoff timer; the analysis derives MAPs and approximate SINR coverage for both networks.Equal priority corresponds to (a, b) = (0, 1).Source: §V · p. 19, A. LTE with Same Channel Access… · pp. 20, 22, 23
• Under equal priority, Wi-Fi AP MAP decreases with the total number of Wi-Fi and LTE contenders, and LTE affects it similarly to an additional CSMA/CA network.The analogous network has intensity λL and transmit power PL.Source: A. LTE with Same Channel Access… · pp. 20–21
• Because the transmitting AP and eNB processes are dependent thinnings with generally unknown closed-form Laplace functionals, SINR coverage is approximated using independent non-homogeneous PPPs.The approximation is used for the interfering transmitters in the coverage analysis.Source: A. LTE with Same Channel Access… · p. 21

B. LTE with Lower Channel Access Priority as Wi-Fi when (a,b) = (1,2)

• For lower-priority access, the section derives STA and UE coverage using procedures from the preceding cases, with the conditional AP MAP obtained by setting λL = 0.The lower-priority setting uses (a, b) = (1, 2), so LTE backoff timers exceed Wi-Fi timers.Source: B. LTE with Lower Channel Access… · pp. 23–24
• With lower-priority LBT/BO, each Wi-Fi AP has the same MAP as without LTE, while eNBs defer to strong APs and play a role similar to APs under continuous LTE transmission.This is the section’s stated MAP-based protection result for Wi-Fi.Source: B. LTE with Lower Channel Access… · pp. 23–24

• Simulations validate the SINR approximations across LTE sensing thresholds and AP/eNB densities.Source: B. LTE with Lower Channel Access… · p. 25
• With lower LTE channel access priority, a less sensitive LTE threshold can provide Wi-Fi SINR performance similar to the same-priority case.Source: B. LTE with Lower Channel Access… · p. 25
• Wi-Fi and LTE achieve good overall SINR coverage when both use LBT and random backoff; a more sensitive LTE threshold improves both by reducing LTE interference.Source: Figure 7 · p. 25, B. LTE with Lower Channel Access… · p. 25

VI. PERFORMANCE COMPARISONS OF DIFFERENT COEXISTENCE SCENARIOS

• Wi-Fi has its worst DST performance when coexisting with LTE; it achieves similar DST with LTE-U at 50% duty or specified LAA settings, and better DST than the baseline under those mechanisms.The LAA options include the same channel access priority as Wi-Fi with (a,b) = (0,1), ΓL = −82 dBm, and (a,b) = (1,2), ΓL = −77 dBm.Source: §VI · pp. 26–27
• An LAA threshold of −62 dBm barely improves Wi-Fi DST over LTE, so the authors recommend a more sensitive threshold.Source: §VI · p. 27
• LTE DST is around 50% lower with LTE-U or LAA using sensitive sensing thresholds, mainly because eNB MAP decreases.Source: §VI · p. 27
• LTE-U is simpler and low-cost but can degrade LTE performance at low duty cycles and is feasible only in some regions or bands; LAA requires more complex LBT and random back-off.Source: §VI · p. 28
• With appropriate access priority and sensing threshold, LAA improves Wi-Fi DST and rate coverage over baseline while maintaining acceptable LAA rate coverage.The authors also state that LAA meets the global requirement for unlicensed-spectrum operation.Source: §VI · p. 28

VII. CONCLUSION

• The proposed stochastic-geometry framework is validated and complements ongoing system-level simulation studies of LTE-U and LAA.Source: §VII · pp. 28–29
• The framework analytically derives and numerically evaluates medium access probability, SINR coverage probability, density of successful transmissions, and rate coverage across three coexistence scenarios.Source: §VII · p. 28
• Wi-Fi performance is significantly degraded under continuous LTE without protocol changes, whereas duty-cycle, sensing-threshold, or channel-access-priority adjustments can make LTE a good neighbor.The conclusion contrasts continuous transmission with the listed coexistence features.Source: §VII · p. 28
• Future work would extend the single-band, full-buffer analysis to multiple bands with channel selection, non-full-buffer delay, mixed downlink/uplink traffic, and joint LBT/discontinuous transmission.Source: §VII · p. 29

APPENDIX A

• For a tagged transmitting AP, Appendix A derives another AP’s conditional MAP using Bayes’ rule, Slyvniak’s theorem, de-conditioning, and modified access indicators.The denominator and numerator of the conditional MAP expression are evaluated separately.Source: Appendix A · pp. 29–30

APPENDIX B

• Appendix B computes the per-AP hW quantity using Slyvniak’s theorem and the PPP probability generating functional, yielding result (19).Source: Appendix B · p. 30