Coverage in mmWave Cellular Networks with Base station Cooperation

I. INTRODUCTION

• Unlike prior mmWave coverage analysis that omitted blockage, this work incorporates blockage alongside interference when deriving coverage probability.The cited prior analysis also found that narrower beams increase coverage by reducing beam overlap and interference.Source: §I · pp. 2–3
• The analysis builds on stochastic-geometry studies of mmWave blockage and microwave joint-transmission CoMP, adding directionality, blockage, and improved fading to the mmWave cooperation setting.The related mmWave work modeled LOS and NLOS links according to link length; the microwave CoMP work considered users served by base stations with strongest average received power.Source: §I · p. 3
• The paper studies base-station cooperation as a way to decrease signal outage in heterogeneous mmWave cellular systems.Its stochastic-geometry model incorporates realistic mmWave channel characteristics, directional gains, and blockage.Source: §I · p. 4
• Coverage probabilities are derived for a single-antenna typical user, incorporating blockage, interference, and Rayleigh, Nakagami, or no fading.The joint distribution of cooperating base stations relative to the typical user is also derived in the presence of blockage.Source: §I · p. 4

A. Network Model

• The network model places each tier's base stations in an independent two-dimensional homogeneous Poisson point process with tier-specific density and transmit power.Coverage is studied for a typical user at the origin.Source: A. Network Model · p. 5

B. Simplified Clustered Channel Model

• The channel model uses a clustered representation between base stations and the typical user, with one cluster assumed for simplicity.The paper also assumes cooperating base stations beam-steer toward the user using phase-shifter vectors, while the receiver applies a single processing vector.Source: §I · p. 4, B. Simplified Clustered Channel Model · p. 6, CHANNEL VARIABLES FROM THE INTERFERING… · p. 7

C. Received Signal at the Typical User

• The user’s cooperating set T provides the strongest average received power, while the received signal separates desired cooperating transmissions from interference.The transmitted signals and receiver noise are also specified in the model.Source: C. Received Signal at the Typical User · p. 9

D. Beam steering

• Cooperating base stations jointly send the same data and beam-steer toward the typical receiver, with independent, zero-mean, unit-variance transmitted symbols.The model assumes perfect beam steering to the typical receiver.Source: D. Beam steering · pp. 9–10

E. Decoding

• A single combining vector decodes the scalar symbol; path-angle CSI is assumed perfect, but the performance is an upper bound under the more realistic imperfect-angle case.The stated decoder can use RF phase shifters; near-optimal hybrid combining is left for future algorithm development.Source: E. Decoding · p. 10

F. Output Signal

• The output-signal description defines Ωφ as cos(φ) and uses normalized antenna separation; the instantaneous SINR follows from that signal model.Source: F. Output Signal · pp. 10–11, G. SINR Expression · p. 11

G. SINR Expression

• Coverage derivations address Rayleigh fading, blockage, Nakagami fading on direct cooperating links, and no small-scale fading on those links.The stated cases assume a single-antenna receiver; extending them to multiple receiver antennas is future work.Source: G. SINR Expression · pp. 11–12

H. Performance Analysis

• Fig. 2 presents two-tier coverage probability with two cooperating base stations; Example 1 compares n=2 with n=1 and considers different antenna counts.The figure uses the parameters in Table V.Source: Figure 2 · p. 13, H. Performance Analysis · p. 13

I. Numerical Results

• Cooperation raises coverage by almost 11% at T = 5 dB for Nt = 8, 16, and by 10% at T = 10 dB for Nt = 32, 64.The comparison is against no base-station cooperation; the reported coverage also increases with the number of base-station antennas.Source: §I · p. 13

A. Network model

• Each tier is modeled as an independent homogeneous PPP, with LOS probability e^(-β_k r) and distinct LOS and NLOS pathloss exponents.The blockage parameter β_k sets the average LOS range to 1/β_k.Source: A. Network model · p. 14

B. Performance Analysis

• Theorem 2 gives typical-user coverage for a K-tier network with blockage and n jointly transmitting base stations, updating the intensity and cooperating-base-station distance distribution.The theorem assumes a single-antenna user and ULA base stations with Nt antennas.Source: B. Performance Analysis · p. 15

C. Numerical Results

• Cooperation increases coverage in dense mmWave networks, where more LOS interferers make interference stronger and cooperation adds serving base stations.The paper contrasts this with scenarios where cooperation produces no substantial increase.Source: C. Numerical Results · p. 15
• Only approximately 0.05 coverage gain is reported with cooperation in the 250 m-radius tier at β = 0.02; higher transmit power without cooperation gives higher coverage.The authors attribute the small gain to high blockage and the greater distance, hence lower received power, of cooperating base stations in the less dense tier.Source: C. Numerical Results · p. 17, Figure 4 · p. 17
• An approximately 11% coverage increase is reported at T = 10, 15 dB in the dense-tier example.That example uses a 50 m average tier radius and Nt = 64.Source: C. Numerical Results · pp. 17–18, Figure 5 · p. 18

IV. COVERAGE PROBABILITY WITH NAKAGAMI FADING AND BLOCKAGE

• For cooperating links, the analysis considers Nakagami fading while retaining Rayleigh fading on interfering links, and derives coverage upper bounds.A second bound evaluates the network without interference, treating coverage as the probability that SNR exceeds the threshold.Source: §IV · pp. 18–19

A. Performance Analysis

• Theorem 3 gives an upper bound on typical-user coverage with blockage and Nakagami fading on the jointly transmitting base stations’ channel gains.The bound applies to a K-tier network with n cooperating ULA base stations.Source: A. Performance Analysis · p. 19
• For n = 1, the coverage expression is exact rather than an upper bound; the text also identifies a route to exact coverage using the true signal Laplace transform.The exact-coverage remark refers to replacing the lower-bound signal Laplace transform with the true one.Source: A. Performance Analysis · p. 19
• Corollary 4 gives an upper bound on coverage when interference is absent, using Nakagami fading on the cooperating channel gains.The example evaluates this bound alongside the bound that includes interference.Source: A. Performance Analysis · p. 20, B. Numerical Results · pp. 20–21

B. Numerical Results

• With β = 0.025 and average LOS range 40 m, the plotted curves with and without interference almost exactly overlap for both Rayleigh and Nakagami fading.The example compares m = 3 Nakagami fading with m = 1 Rayleigh fading for two cooperating base stations.Source: B. Numerical Results · pp. 20–21, Figure 6 · p. 21

V. COVERAGE PROBABILITY WITH NO SMALL SCALE FADING

• The section analyzes the same network model with cooperating channel gains assumed to experience no fading, an assumption motivated by directional transmission and receivers outside rich-scattering environments.Source: §V · p. 21

A. Numerical Results

• In the one-tier example, the no-cooperation, double-transmit-power curve is close to the two-cooperator, half-transmit-power curve, suggesting a power increase drives the gain in that noise-limited network.The passage says this observation also holds when cooperating gains are Rayleigh faded.Source: A. Numerical Results · p. 22
• At threshold T = 5 dB, the increase with CoMP and no small-scale fading exceeds the 5% increase for Rayleigh-distributed channel gains, indicating larger gains without serving-base-station small-scale fading.Source: A. Numerical Results · p. 23
• At T = 10, cooperation increases coverage by 16% without small-scale fading and almost 12% with Rayleigh fading in a network that is not noise limited.Source: A. Numerical Results · p. 23

VI. CONCLUSIONS

• Coverage probabilities are derived for the typical user with directionality, blockage, interference, and Rayleigh or Nakagami fading; results suggest cooperation rivals no cooperation especially in dense networks without fading on cooperating gains.The authors identify multi-antenna typical receivers and beam-steering errors as future work.Source: §VI · pp. 23–24

APPENDIX A

• The analysis differs from the cited framework by including multiple transmit antennas and interference dependent on independently uniform path angles.Source: Appendix A · p. 24

A. Distribution of Strongest Base stations

• The appendix derives the joint distribution of the two strongest base stations from the first station's distribution and a conditional distribution, then generalizes to n cooperating stations.Source: A. Distribution of Strongest Base… · pp. 24–25

B. Derivation of Coverage Probability

• Coverage derivation rewrites desired signal power using cooperating-base-station normalized pathlosses and evaluates interference through its Laplace transform, including a piecewise-linear beamforming-gain approximation for easier numerical evaluation.Source: B. Derivation of Coverage Probability · pp. 25–27
• The derivation assumes interfering path angles and beam-steering angles are independent and uniform over [−π, +π], making directional-cosine variables random.Source: B. Derivation of Coverage Probability · p. 26

A. Intensity and Intensity Measure

• The process Θ is formed from the tier processes, whose intensities are denoted λk(v).Source: A. Intensity and Intensity Measure · p. 27
• Pathloss takes values α1 and α2 with probabilities e^(-βk v) and 1 − e^(-βk v), respectively.Source: A. Intensity and Intensity Measure · p. 27
• The mapping theorem is used to obtain the intensity and intensity measure for each tier.Source: A. Intensity and Intensity Measure · pp. 27–28

A. Proof of Theorem 3

• The proof switches direct links to Nakagami fading with shape m and scale θ = 1 while keeping interfering links Rayleigh faded.Source: A. Proof of Theorem 3 · p. 28
• The desired-signal upper bound has |hi|^2 distributed as Gamma(nm, 1/m), with Laplace transform (1 + s/m)^(-nm).Source: A. Proof of Theorem 3 · p. 28
• The coverage calculation uses the interference Laplace transform with intensity λ(v) and the Laplace transform of noise.Source: A. Proof of Theorem 3 · pp. 28–29

• The no-interference coverage probability is given by (23) with LI(s) = 1.Source: B. Proof of Corollary 4 · p. 29
• A pole of order nm in the integrand allows Q to be solved using contour integration and its residue.Source: B. Proof of Corollary 4 · p. 29
• The proof rewrites f(z), then substitutes the functions in (45) to express the integral I.Source: B. Proof of Corollary 4 · p. 29