Coverage and Rate Analysis of Super Wi-Fi Networks Using Stochastic Geometry

Coverage and Rate Analysis of Super Wi-Fi Networks Using Stochastic Geometry Neelakantan Nurani Krishnan, Gokul Sridharan, Ivan Seskar, Narayan Mandayam WINLAB, Rutgers University North Brunswick, NJ, USA 3/9/2017 Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 1

Introduction Motivation Questions to ponder over.. How can TV White Spaces (TVWS) be used to provide extensive broadband connectivity to rural/under-served areas? Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 2

Introduction Motivation Questions to ponder over.. How can TV White Spaces (TVWS) be used to provide extensive broadband connectivity to rural/under-served areas? How do regulations imposed by FCC affect network performance (particularly transmit power and deployment height restrictions)? Given a region of interest, what should be the - 1 deployment density, 2 transmit power, and 3 deployment height of base stations to achieve reasonable performance? Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 2

Introduction Motivation Problem Statement Objective - Analyze the coverage and rate performance of outdoor Super Wi-Fi networks in the context of providing wireless connectivity to rural areas What is Super Wi-Fi? - Wi-Fi-like networks operating in TVWS bands What is super about Super Wi-Fi? - TVWS frequencies have excellent propagation characteristics including low pathloss, and wall penetration losses Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 3

Introduction TVWS basics TVWS Availability TV Channels Freq. Band Freq (MHz) Allowed Devices 2 VHF 54-60 Fixed 5-6 VHF 76-88 Fixed 7-13 VHF 174-216 Fixed 14-20 UHF 470-512 Fixed 21-35 UHF 512-602 Fixed and Portable 39-51 UHF 620-698 Fixed and Portable 0 From Google spectrum database (as of 02/16/2017) Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 4

Introduction FCC Regulations FCC Regulations AP Client Fixed device height Portable device height Fixed device EIRP Portable device EIRP 30 m 1.5 m 4 W (per channel) 100 mw (per channel) Table 1: Regulations governing secondary access of TVWS bands Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 5

Introduction FCC Regulations Transmit Power Asymmetry P AP = 4 W, h AP = 30 m, P C = 100 mw, h C = 1 m Black dotted circles - downlink coverage, Red circles - uplink coverage AP Density = 0.1/km 2 AP Density = 10/km 2 10 4.0 Distance (in km) 8 6 4 Distance (in km) 3.5 3.0 2.5 2.0 1.5 2 1.0 0.5 0 0 2 4 6 8 10 Distance (in km) 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Distance (in km) Downlink coverage - Distance till AP transmission power > Threshold DL Uplink coverage - Distance till client transmission power > Threshold UL Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 6

Introduction Objectives Objectives Analyze the coverage and rate performance of a Super Wi-Fi network as a function of the following quantities: 1 density of AP distribution (λ) 2 AP transmit power (P AP ) 3 AP height (h AP ) 4 power asymmetry (uplink viability) Tool - Stochastic Geometry Methodology Model AP distribution as a homogeneous Poisson point process (PPP) and analytically characterize coverage and area spectral efficiency (ASE) of the network Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 7

Introduction Notations Notations and Definitions Φ A - Set of AP locations - Homogeneous PPP λ - Intensity of PPP (Density of AP deployment) in per km 2 σ - CCA Threshold ρ(x, y) - Pathloss between points x and y G(x, y) - Fading between points x and y P AP - AP transmit power P C - Client transmit power Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 8

Performance Characterization Throughput Modeling Modeling of CSMA Each point x in Φ A will be assigned an independent mark t x uniformly distributed in [0,1] representing the back-off time The subset of concurrently transmitting APs - Φ T = {x Φ A : t x < t y, y N (x)} Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 9

Performance Characterization Throughput Modeling Now into Math The throughput of an AP averaged out over all AP - uplink viable client distances r is given by - T = E r (T (r)) = f R (r I u = 1) = f R(r)P(I u=1 R=r) P(I u=1) f R (r) = 2πrλe λπr2 I u = 1( P C ρ(r) G(r) > γ) }{{} Received power at AP from client 0 T (r) }{{} f R (r I u = 1) }{{} dr Throughput of AP at r AP-Client distance distribution ( = P(I u = 1 R = r) = P G(r) > ) γ P C ρ(r) = e µγ P C ρ(r) Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 10

Performance Characterization Throughput Modeling Math continued.. T (r) - throughput of the tagged AP conditioned on r = Product of : 1 transmission probability of AP conditioned on r : p T (r) 2 expected rate at the client associated with the tagged AP : (E[log 2 (1 + SINR)]) T = = 0 0 T (r)f R (r I u = 1)dr p T (r)e[log 2 (1 + SINR)]f R (r I u = 1)dr Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 11

Numerical Results Numerical Results and Discussion Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 12

Numerical Results Analysis Setup Key Parameters and Range of Values Channel Center Frequency 600 MHz Channel Bandwidth 6 MHz Number of channels 1 AP distribution Homogeneous PPP of intensity λ AP Transmission Power Variable between 0.1 W and 4 W Client Transmission Power 0.1 W AP Height Variable between 1.5 m and 30 m Client Height 1 m Pathloss Based on ITU-R P.1411-8 Fading Exponentially distributed with mean 1 CCA Threshold σ -82 dbm Uplink Viability Threshold γ -82 dbm Noise Variance (N 0 ) -173.97 dbm/hz Traffic model Persistent downlink Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 13

Numerical Results Pathloss Model Pathloss Modeling (ITU-R P.1411-8) Model is dual-slope and is a function of transmitter/receiver antenna heights ( ρ LOS + 20 + 25 log d R ρ(x, y) in db = bp ), if d < R bp ( ρ LOS + 20 + 40 log d R bp ), if d R bp ρ LOS is the line-of-sight pathloss (in db), given by ( ) ρ LOS = λ 2 20 log 8πh t h r R bp is the breakpoint distance (in meters), given by R bp = 1 ( ) λ 2 ( ) λ 4 (4h t h r ) λ 2 4(h 2 t + h2 r) + 2 2 Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 14

Numerical Results Pathloss Model Two Pathloss Models To obtain R bp and ρ LOS : AP - AP interaction - Use h t = h r = h AP AP - Client interaction - Use h t = h AP and h r = h C Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 15

Numerical Results Validation of Model Why Stochastic Geometry? Analytical characterizations using stochastic geometry give flexibility in changing operating parameters without re-running long simulations Our model is validated with OPNET (industry-standard packet-level simulator) 16 Results from stochastic geometry-based models and OPNET simulation. The plot with p U 1 is for the case when uplink viability is probabilistic and the one with p U = 1 is when uplink is assumed to be always viable AP Throughput in Mbps 14 12 10 8 6 4 2 P AP = 1 W, OPNET P AP = 1 W, SG - p U 1 P AP = 1 W, SG - p U = 1 0 0 200 400 600 800 1000 AP - Client distance (in m) Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 16

Numerical Results Probability of AP Transmission Probability of AP Transmission AP Density = 0.1/km 2 AP Density = 1/km 2 AP Density = 10/km 2 1.0 1.0 1.0 h AP = 1.5 m h AP = 3.0 m Probability of AP Transmission 0.8 0.6 0.4 0.2 h AP = 1.5 m h AP = 3.0 m h AP = 6.0 m h AP = 9.0 m h AP = 15.0 m h AP = 30.0 m Probability of AP Transmission 0.8 0.6 0.4 0.2 h AP = 1.5 m h AP = 3.0 m h AP = 6.0 m h AP = 9.0 m h AP = 15.0 m h AP = 30.0 m Probability of AP Transmission 0.8 0.6 0.4 0.2 h AP = 6.0 m h AP = 9.0 m h AP = 15.0 m h AP = 30.0 m 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 AP Power (in W) Figure 1: Low deployment density 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 AP Power (in W) Figure 2: Medium deployment density 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 AP Power (in W) Figure 3: High deployment density Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 17

Numerical Results Area Spectral Efficiency Downlink Area Spectral Efficiency AP Density = 0.1/km 2 AP Density = 1/km 2 AP Density = 10/km 2 Area Spectral Efficiency (in b/s/hz/km 2 ) 1.2 1.0 0.8 0.6 0.4 0.2 h AP = 1.5 m h AP = 3.0 m h AP = 6.0 m h AP = 9.0 m h AP = 15.0 m h AP = 30.0 m Area Spectral Efficiency (in b/s/hz/km 2 ) 12 10 8 6 4 2 h AP = 1.5 m h AP = 3.0 m h AP = 6.0 m h AP = 9.0 m h AP = 15.0 m h AP = 30.0 m Area Spectral Efficiency (in b/s/hz/km 2 ) 80 70 60 50 40 30 20 10 h AP = 1.5 m h AP = 3.0 m h AP = 6.0 m h AP = 9.0 m h AP = 15.0 m h AP = 30.0 m 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 AP Power (in W) Figure 4: Low deployment density 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 AP Power (in W) Figure 5: Medium deployment density 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 AP Power (in W) Figure 6: High deployment density Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 18

Numerical Results Uplink Viability Effect of Uplink Viability Uplink viability 1.0 0.8 0.6 0.4 0.2 AP Height = 1.5 m AP Height = 3.0 m AP Height = 4.5 m AP Height = 6.0 m AP Height = 9.0 m AP Height = 15.0 m AP Height = 30.0 m Probability that a client is not covered 1.0 0.8 0.6 0.4 0.2 AP Density = 0.1/km 2 AP Density = 1/km 2 AP Density = 10/km 2 0.0 0 200 400 600 800 1000 AP-Client distance (in m) Figure 7: Probability of uplink viability vs AP-client distance r for various AP heights 0.0 0 5 10 15 20 25 30 AP Height (in m) Figure 8: Probability that client does not find an AP to associate with; note that P C = 0.1 W always Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 19

Numerical Results Suggested Choice Prescription for AP Operating Parameters Priority P AP h AP Rate 1-4 W 1.5-3 m Coverage 0.1 W 30 m Low AP density (0.1/km 2 ) Priority P AP h AP Rate 1-4 W 1.5 m Coverage 0.1 W 30 m Medium AP density (1/km 2 ) Priority P AP h AP Rate 0.1 W 1.5 m Coverage 0.1 W 10-30 m High AP density (10/km 2 ) Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 20

Numerical Results Example Scenario Sharon Springs, Kansas Distribution of Households - Sharon Springs in Wallace County, KS 2 1.5 Distance in kms 1 0.5 0 0 0.5 1 1.5 Distance in kms Figure 9: Obtained from 2010 US Census (Each circle represents a household) Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 21

Numerical Results Sharon Springs, KS Sharon Springs - Network Specifications Data Rate Requirements Number of households - 400 in an area of 3 km 2 Data requirement of each house - 10 Mbps = Total network throughput = 1330 Mbps/km 2 Channel Availability Availability of TVWS channels in Sharon Springs from Google spectrum database - h AP > 6m Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 22

Numerical Results Sharon Springs, KS Sharon Springs - Network Design Deployment density = 10 APs/km 2 Assuming coverage probability of 75% suffices, set h AP = 6m (from fig. 12) For this choice of h AP, choose P AP which yields the highest ASE from fig. 8-10 In this case, P AP = 0.1 W with ASE = 12 b/s/hz/km 2 Channel throughput = 72 Mbps/km 2 37 channels = Use 18 of the available Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 23

Conclusion Key Takeaways Concluding Remarks FCC regulations on height and transmit power of fixed/portable devices lead to asymmetry in downlink and uplink coverage Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 24

Conclusion Key Takeaways Concluding Remarks FCC regulations on height and transmit power of fixed/portable devices lead to asymmetry in downlink and uplink coverage Analytically characterized the coverage and rate performance of outdoor Super Wi-Fi networks by leveraging tools from Stochastic Geometry Albeit permitted by FCC, operating APs at high transmit power and height is not meritorious even at densities as low as 1/10 km 2 Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 24

Backup slides BACKUP SLIDES Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 25

Throughput Characterization Probability of Transmission of AP Probability of Transmission of an AP T = 0 p T (r)e[log 2 (1 + SINR)]f R (r I u = 1)dr Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 26

Throughput Characterization Probability of Transmission of AP Probability of Transmission of the Tagged AP p T (r) = 1 0 e λat 0 R 2 \B(y,r) S(x)dx dt 0 = 1 e λa R 2 \B(y,r) S(x)dx λ a R 2 \B(y,r) S(x)dx S(x) is the probability of AP at 0 to sense another AP located at x: S(x) = P[ P (0, x) > σ] = P[P }{{} AP ρ(0, x) G(0, x) > σ] Power received at 0 from x Intuitive Reasoning The intensity of PPP of APs that can potentially prevent AP at 0 from transmitting is λ a t 0 (mark < t 0 ). This PPP is further thinned by S(x) which is location-dependent. Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 27

Throughput Characterization Distribution of SINR SINR Distribution and Expected Rate Computation T = 0 p T (r)e[log 2 (1 + SINR)]f R (r I u = 1)dr Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 28

Throughput Characterization Distribution of SINR SINR Distribution - Preliminaries Signal part in SINR = P AP ρ(r)g (where the AP-Client distance is r) = Straight forward result Noise part in SINR = ktb 106 dbm at B = 6 MHz Interference part in SINR - Not a trivial computation as this quantity depends on: 1 Probability of Transmission of AP 2 Distribution of interfering APs around the tagged APs which implicitly depends on the CCA threshold σ 3 Fading coefficient 4 Pathloss Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 29

Throughput Characterization Distribution of SINR Distribution of SINR Interfering APs form an in-homogeneous PPP, the local intensity of which depends on distance x from the tagged AP Laplace Transform of SINR, 2π ψ I+N (s) = ψ I (s)ψ N (s) e λa 0 r h(b(ρ,θ),λ a)[1 ϕ F (sp l(ρ))]ρdρdθ e sn0 ϕ F - Laplace Transform of the fading random variable; ϕ F (x) = 1 1+x as fading is exponentially distributed Evaluation of equation (1) at s = µβ P AP ρ(r) yields P[SINR > β] (1) Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 30

Throughput Characterization Expected Rate Expected Rate Determination From the CDF of SINR, the expected rate can be computed as: Expected Rate = E[log 2 (1 + SINR)] Neelakantan (Neel) (WINLAB) DySPAN 17 3/9/2017 31