Coverage and Rate Analysis of Super Wi-Fi Networks Using Stochastic Geometry
Neelakantan Nurani Krishnan, Gokul Sridharan, Ivan Seskar, Narayan Mandayam
CCoverage and Rate Analysis of Super Wi-FiNetworks Using Stochastic Geometry
Neelakantan Nurani Krishnan, Gokul Sridharan, Ivan Seskar, Narayan MandayamWINLAB, Rutgers University671 US Route 1 South, North Brunswick, NJ - 08902 { neel45, gokul, seskar, narayan } @winlab.rutgers.edu Abstract — Recent regulatory changes proposed by the Fed-eral Communications Commission (FCC) permitting unlicenseduse of television white space (TVWS) channels present new op-portunities for designing wireless networks that make efficientuse of this spectrum. The favorable propagation characteristicsof these channels and their widespread availability, especiallyin rural areas, make them well-suited for providing broadbandservices in sparsely populated regions where economic factorshinder deployment of such services on licensed spectrum. Inthis context, this paper explores the deployment of an outdoorWi-Fi-like network operating in TVWS channels, referredto commonly as a Super Wi-Fi network. Since regulationsgoverning unlicensed use of these channels allow (a) mountingfixed devices up to a height of 30 m and operation at transmitpowers of up to 4 W EIRP, and (b) operation at transmitpowers of up to 100 mW EIRP for portable devices, suchnetworks can provide extended coverage and higher rates thantraditional Wi-Fi networks. However, these gains are subject tothe viability of the uplink from the portable devices (clients)to the fixed devices (access points (AP)) because of tighterrestrictions on transmit power of clients compared to APs. Thispaper leverages concepts from stochastic geometry to study theperformance of such networks with specific focus on the effect of(a) transmit power asymmetry between APs and clients and itsimpact on uplink viability and coverage, and (b) the interplaybetween height and transmit power of APs in determining thenetwork throughput. Such an analysis reveals that (a) maximumcoverage of no more than 700 m is obtained even when APsare deployed at 30 m height, and (b) operating APs at transmitpower of more than 1 W is beneficial only at sparse deploymentdensities when rate is prioritized over coverage.
I. INTRODUCTIONIn light of rapidly growing mobile broadband traffic,providing additional spectrum is an important policy goal forspectrum regulators worldwide. With Internet of Things (IoT)and Machine to Machine (M2M) communications rising upthe horizon, there is a need for ubiquitous connectivity.Meeting these requirements, especially in rural areas, ischallenging because of geographic and monetary constraints.In this context, this paper investigates the viability of de-ploying an outdoor Wi-Fi-like network using television whitespace (TVWS) channels in rural/suburban areas for providingbroadband connectivity. Such a network is typically referredto as a Super Wi-Fi network [1].TVWS channels are unused TV channels that can beopportunistically used on a secondary basis in the absenceof primary transmissions. In the USA, these channels are 6
TABLE ITV
CHANNELS FOR SECONDARY USE
TV Channels Freq. Band Freq (MHz) Allowed Devices2 VHF 54-60 Fixed5-6 VHF 76-88 Fixed7-13 VHF 174-216 Fixed14-20 UHF 470-512 Fixed21-35 UHF 512-602 Fixed and Portable39-51 UHF 620-698 Fixed and PortableFig. 1. Availability of TVWS Channels in the USA as of 02/15/2017[3]. Except for the urban centers on either coasts, TVWS channels areabundantly available.
MHz wide and span from 54 MHz to 698 MHz. In particular,the channels in the 512-698 MHz range allow the secondarydevices to be either fixed or portable, as in Table I [1]. Asseen in Fig. 1, TVWS channels are known to be locallyunder-utilized, especially in rural/suburban areas. Further,the relatively low frequency of TVWS channels comes withsome significant advantages like lower path loss and betterwall penetration [2].The under-utilization of TVWS channels in rural areas,along with their favorable propagation characteristics, moti-vates investigating the feasibility of deploying outdoor SuperWi-Fi networks for broadband connectivity in such regionswhere providing access solutions continues to be exorbitantlyexpensive. In particular, this work envisions deploying alarge number of fixed wireless access points (APs) over arural/suburban area with channel access mediated by carrier a r X i v : . [ c s . I T ] A p r ABLE IIFCC
REGULATIONS ( MAXIMUM V ALUES ) FOR OPERATION IN
TVWS
CHANNELS
Fixed device height 30 mPortable device height 1.5 mFixed device EIRP 4 W (per channel)Portable device EIRP 100 mW (per channel) sense multiple access with collision avoidance (CSMA/CA)while adhering to TVWS regulations. This work comple-ments recent interest in utilizing TVWS channels for provid-ing backhaul solutions [4], [5] where a wide-area networkof cellular base stations over TVWS channels for backhaulis studied.To mitigate any potential impact on the primary users,secondary usage of TVWS channels is regulated by theFederal Communications Commission (FCC) in the USA.In particular, Table II specifies two important regulationsthat significantly impact the operation of a secondary Wi-Fi-like network—the first governs the maximum height ofsecondary devices and the second governs the maximumtransmit power. In particular, the regulations allow mountinga fixed device at a height of up to 30 m while also allowingit to operate at up to 4 W EIRP (Equivalent IsotropicallyRadiated Power)—thus permitting a much larger coveragearea when compared to a typical Wi-Fi AP that is mounted atmuch lower heights and is restricted to transmit at no morethan 100 mW EIRP. However, since the portable devicesare restricted to a much lower transmit power of 100 mW,an increase in downlink coverage from AP to client is notreciprocated by an equivalent increase in uplink coverage. Inother words, there may be scenarios where the uplink maynot be viable even though the downlink is. This presentsa major point of difference between the network underconsideration and traditional Wi-Fi networks.Given the crucial role played by uplink association requestand acknowledgment packets in determining AP-client asso-ciation and successful downlink transmissions, the significantdifference in operating parameters between APs and clientsmakes it extremely important to factor in uplink viability.Additionally, the potentially large downlink coverage canhave a detrimental impact on the AP transmission probabil-ities when using CSMA/CA. Thus, although an increase inAP transmit power and/or height might seem beneficial, theabove issues highlight the difficulty in choosing the right setof operating parameters for striking the right balance betweencoverage and throughput in such networks.With the broad goal of understanding the performance oflarge-scale outdoor Super Wi-Fi networks, this work usesconcepts from stochastic geometry to obtain an analyticalcharacterization of SINR coverage and rates. Tools fromstochastic geometry are used to first characterize the prob-ability of transmission of a Super Wi-Fi AP and subse-quently study the area spectral efficiency (ASE) of such anetwork as a function of (a) AP deployment density, (b) APheight, and (c) AP transmission power. Due to the unequal transmission powers between APs and clients, this analysisexplicitly requires the uplink to be viable when computingthe downlink throughput. It is primarily in this respect thatthe current work significantly differs from existing literatureon analyzing such networks [6]–[8].The results of this work show that it is not alwaysbeneficial to operate at high AP transmit power ( P AP ) andAP height ( h AP ). It is consistently observed across differentdeployment densities that operating at high P AP and h AP values leads to a sharp drop in probability of transmissionfor APs, in turn decreasing the ASE. At deployment densitiesof less than AP / km , ASE is maximized when P AP and h AP are close to 1 W and 1.5 m, respectively. At higherdeployment densities of APs / km , ASE is maximizedwhen P AP and h AP are close to 0.1 W and 1.5 m, respec-tively. On the contrary, for optimal coverage, maximizing h AP proves beneficial (note that coverage is determined byuplink viability and hence is independent of P AP ). Setting P AP greater than 1 W is observed to be useful only in sparsedeployment densities, when rate is prioritized over coverage,with APs mounted at less than 6 m height.The rest of the paper is organized as follows — relatedwork is presented in Section II, the system model andparameters involved in the analysis are described in Sec-tion III, characterization of the network throughput is givenin Section IV, a discussion of the results obtained is providedin Section IV and the concluding remarks are mentioned inSection VI. II. RELATED WORKThe release of TVWS channels for unlicensed use pro-moted active research in investigating the feasibility ofdeploying cognitive radio networks in these channels [9]–[12]. The possibility of using TVWS channels for Super Wi-Fi operation is explored extensively in [8], [13]–[16]. Theauthors of [14] propose to enhance the coverage of publicWi-Fi networks operating in 2.4 GHz by extending theiroperation to TVWS channels. The authors of [15] built aprototype for Super Wi-Fi (called White-Fi) networking andmodified the medium access control (MAC) protocol to fac-tor in spatial and temporal variations of TVWS channels. In[8], a quantitative study of Super Wi-Fi networks is providedand it is observed that TVWS is an attractive alternativefor providing connectivity in outdoor rural areas. A realworld deployment of Super Wi-Fi networks is presentedin [16] where the potential of using TVWS for bringingbroadband connectivity to unconnected areas is established.The issue of transmit power asymmetry in TVWS networkshas been studied in [17], albeit in a vehicular connectivityset up, in which the authors propose to extend the rangeof uplink from clients by using existing cellular paths.However, in the current work, rural areas are the targetenvironments and hence no form of connectivity is likelyto be preexistent. While these efforts provide the motivationto better utilize this technically and economically significantfrequency range, a theoretical study of the performance ofa large scale Super Wi-Fi network is not available to theest of our knowledge. Additionally, such an analysis shouldconsider the various regulatory constraints imposed on theoperating parameters, specifically transmission powers andheights, as described in Table II. The current work providesa theoretical framework to serve this purpose by employingconcepts from stochastic geometry.Among the first efforts to theoretically analyze traditionalWi-Fi networks were the analyses presented in [18] and[19] to accurately model the 802.11 protocol. While theseefforts captured finer aspects of the CSMA/CA protocol (e.g.,exponential backoff), spatial aspects of the wireless mediumare not modeled. Stochastic geometry provides a naturalframework to analyze wireless networks while retaining thespatial characteristics of signal propagation. The use ofstochastic geometry for modeling and analyzing wirelessnetworks started with the extensive analysis of ALOHA[20], [21]. In particular, [21] studies CSMA-based networksusing a Matern hard-core point processes where each APwas assumed to have a disc of fixed radius around itselfwithin which there are no other APs. A modification to thisanalysis that modeled the backoff procedure in CSMA/CAand included fading was presented in [6], [7], [22]. The basicframework of [6] to analyze CSMA/CA forms the foundationfor the current effort. Subsequent analysis of interferencedue to concurrent AP transmissions is modeled using themethodology proposed in [23], [24].A comprehensive overview of using stochastic geometryto model a wide variety of wireless networks is given in [25],[26]. The mathematical tools and theory of point processesused in the current analysis are presented in [27] and [28].III. SYSTEM MODELConsider a large set of APs whose locations are fixed anddrawn from a homogeneous Poisson point process (PPP)of intensity λ . The set of AP locations is given by Φ A = { x , x , ..., x k , ... } . The notation || ( x i − x j ) || is used torepresent distances between APs at two locations x i and x j .The APs are assumed to only serve clients located within itsVoronoi cell (provided the uplink from client to AP is viable),with client locations being uniformly distributed within theVoronoi cell. In such a setting, the distribution of AP-Clientdistance r (without factoring uplink viability) is given by f r ( r ) = 2 πλre − λπr . (1)It is assumed that all APs have at least one associatedclient to serve at any instance. The APs have access toone TVWS channel (6 MHz wide) and all APs contendto get access to this channel. APs are bound by TVWSregulations that govern fixed devices while the clients arebound by the regulations governing portable devices. Thus,while APs can transmit at any transmit power P AP ≤ ,the clients are assumed to transmit at P C = 0 . W. The APsare also assumed to be mounted at any height h AP ≤
30 m ,while clients are always assumed to be at m height.Isotropic antennas are assumed at both APs and clients. Theanalysis in this paper assumes a persistent downlink trafficand negligible uplink traffic. A. Radio Propagation Model
The power received at a point y from an AP located at x is given by P ( x , y ) = P AP ρ ( x , y ) F ( x , y ) , (2)where ρ ( x , y ) is the pathloss encountered by the transmis-sion between x and y , and F ( x , y ) is the fading coefficientbetween x and y . F ( x , y ) is modeled as an i.i.d. exponentialrandom variable with mean µ = 1 . The notation P( d ), ρ ( d ) and F( d ) are used when referring to received power, pathlossand fading coefficient between two generic locations that areat a distance ‘ d ’ from each other.Two different pathloss models are used to define AP-APand AP-Client transmission links. The two pathloss modelsare drawn from the dual-slope model specified in [29] forsuburban environments. This particular pathloss model ischosen as it is sensitive to transmitter and receiver heightsand is applicable to a wide range of sub-GHz frequencies.The dual-slope model is given by ρ ( x , y ) in dB = ρ LOS + 20 + 25 log (cid:16) dR bp (cid:17) , if d < R bp ρ LOS + 20 + 40 log (cid:16) dR bp (cid:17) , if d ≥ R bp (3)where • d is the distance between x and y , • ρ LOS is the line-of-sight pathloss (in dB), given by ρ LOS = (cid:12)(cid:12)(cid:12)(cid:12)
20 log (cid:18) λ πh t h r (cid:19)(cid:12)(cid:12)(cid:12)(cid:12) , (4) • R bp is the breakpoint distance (in meters), given by R bp = 1 λ (cid:115) (Σ − ∆ ) − + ∆ ) (cid:18) λ (cid:19) + (cid:18) λ (cid:19) . (5)The different parameters involved in the above model are • λ - wavelength (m), • h t - height of transmitting antenna (m), • h r - height of receiving antenna (m), • Σ = h t + h r , • ∆ = h t − h r .For modeling AP-AP transmissions, h t and h r are set to APantenna height h AP . For modeling AP-client transmissions, h t = h AP and h r = 1 m . B. Channel Contention Model
Channel access in the current network is governed byCSMA/CA. In CSMA/CA, an AP gets access to a channelwhen there are no other contending APs in its neighbor-hood (i.e., the channel is sensed to be idle), otherwise anexponential back-off procedure is initiated. The channel issensed to be idle when the received signal strength fromall neighboring APs is below the clear-channel-assessment(CCA) threshold. In conventional Wi-Fi networks, the CCAthreshold is typically set to -82 dBm and the same thresholdis used in the current work. . Uplink Viability
Uplink viability determines the ability of a client toassociate with a neighboring AP. If the association requestmessages from the client do not reach an AP, the clientcannot be served. This scenario may often occur in SuperWi-Fi networks as clients transmit at powers lower than APs.Note that even though uplink viability also affects the receiptof acknowledgment (ACK) packets from the client indicatingsuccessful downlink transmission, the assumption in thecurrent work is that once association is established betweenan AP-client pair, the channel remains time invariant. Thispaper defines uplink viability as follows.
Definition 3.1:
The uplink transmission between client y and its AP x is said to be viable if the received signal strengthfrom the client to the AP exceeds a certain threshold γ , i.e., P C ρ ( x , y ) G ( x , y ) > γ. (6)Note that channel reciprocity is not assumed and hence G ( x , y ) and F ( x , y ) are two independent random variables.In this paper, the threshold γ is set to be equal to theCCA threshold σ . Although the criterion (6) only accountsfor uplink packet detection and not successful decoding,it simplifies the subsequent analysis while retaining theessential characteristics of the network under consideration.Using the above definition, uplink viability is computedas p U ( r ) = P [ P C ρ ( x , y ) G ( x , y ) > γ ] = e − µγPCρ ( x , y ) . (7)where r = || x − y || is the distance between AP x and client y . In particular, coverage range of an AP is defined as thelargest AP-client distance d such that p U ( d ) ≥ . (8)where p U ( r ) is defined in (7). D. Transmission Model
The signal to interference-plus-noise ratio (SINR) ob-served at a client y and associated with an AP x is givenby SINR( x , y ) = ρ ( x , y ) N + (cid:80) z ∈ Φ T \ x I ( z , y ) (9)where • N is the noise variance, • Φ T is the set of concurrently transmitting APs, • (cid:80) z ∈ Φ T \ x I ( z , y ) is the cumulative interference at client y due to all concurrently transmitting APs except AP x .The transmitted data rate from AP x to client y is then givenby log (1 + SINR ( x , y )) .IV. THROUGHPUT MODELING AND ANALYSISThis section focuses on characterizing the performance ofthe network under consideration through metrics such as APtransmission probability and area spectral efficiency. Areaspectral efficiency is defined as the average throughput of an AP multiplied by the density of the AP deployment. It isassumed that all APs actively contend for the channel andwhen channel access is granted, use the channel for a fixedperiod of time to transmit to one of their associated clients.For an AP to serve a client the following three transmissionsmust be successfully received: (a) association request packetsat the AP, (b) transmission payload packets at the client,and (c) acknowledgment packets at the AP. Clearly, (a) and(c) both require uplink viability, and it is assumed thatas long as the uplink received signal strength exceeds thethreshold γ , both these transmissions are successful. Underthese assumptions, the probability of an AP serving a userat a distance r is equal to the probability of an uplink viableclient being located at a distance r and is given by f R ( r | I u = 1) = f R ( r ) P ( I u = 1 | R = r ) P ( I u = 1) , (10)where I u is a binary random variable indicating uplinkviability. In particular, I u = ( P C ρ ( r ) G ( r ) > γ ) , and P ( I u = 1 | R = r ) = P (cid:16) G ( r ) > γP C ρ ( r ) (cid:17) = e − µγPc ρ ( r ) . (11)Given the random deployment of APs and clients, theaverage throughput is computed over all possible AP andand client locations. In particular, when the AP has channelaccess and serves an uplink-viable client located at a distance r , the average throughput to that client is given by T ( r ) = E ( SINR | R = r ) [log(1 + SINR)] (12)where the expectation is over the distribution of SINRconditioned on the client being at a distance of r from theAP. Note that the SINR distribution is independent of uplinkviability.Thus, the average throughput of an AP after accountingfor the probability of transmission can be written as T = (cid:90) ∞ p T ( r ) T ( r ) f R ( r | I u = 1) dr (13)where p T ( r ) is the transmission probability of the APconditioned on serving a client that is at a distance of r .Just as the SINR distribution, p T ( r ) is also independent ofuplink viability.The rest of the section focuses on computing p T ( r ) and T ( r ) . The methodology adopted is similar to the frameworkpresented in [6], [7]. A. Probability of AP Transmission: p T ( r ) Probability of an AP transmitting is governed byCSMA/CA and the exponential backoff procedure. As pro-posed in [6], the exponential backoff procedure used by anAP when the channel is busy can be approximately modeledby tagging each AP in the Poisson field with an independentmark. This mark decides the backoff time of that AP.In particular, each AP x in Φ A is assigned an independentmark m x uniformly distributed in [0,1]. Defining the neigh-borhood of an AP x as N ( x ) = { y ∈ Φ A : P ( x , y ) > σ } , anP transmits if no other AP in its neighborhood has a smallermark than itself. Thus, the set of concurrently transmittingAPs can now be defined as Φ T = { x ∈ Φ A : m x < m y , ∀ y ∈ N ( x ) } . (14)This model captures the fact that CSMA/CA grants chan-nel access to that AP with minimal back-off time (equivalentto having lowest mark) among all APs in its neighborhoodand that an AP abstains from transmitting if another AP inits neighborhood is already transmitting.Note that this approximate model ignores collisions, theexponential nature of back-off, and the history of timers.Nevertheless, as shown by the authors in [6], through ns-2simulations, this model provides fairly accurate results.Without loss of generality, we focus on an AP locatedat the origin and denoted as AP . Let AP serve aclient y located at a distance r . Computing the transmissionprobability is equivalent to computing the probability thatamong the APs with a mark less that m , none of them arein the neighborhood, i.e., p T ( r ) = P ( m x ≥ m ∀ x ∈ N ( )) . (15)It can be shown using the results in [6], [7] that thetransmission probability, as defined above, can be computedas p T ( r ) = (cid:90) e − λm (cid:82) R \B ( y ,r ) S ( x ) d x dm (16) = 1 − e − λ (cid:82) R \B ( y ,r ) S ( x ) d x λ (cid:82) R \B ( y ,r ) S ( x ) d x (17)where B ( y , r ) is a ball of radius r with the client at its center(which by hypothesis cannot contain any AP other than AP ) and S ( x ) is the probability of AP detecting an AP at x . S ( x ) can be computed as S ( x ) = P [ P AP ρ ( , x ) F ( , x ) > σ ] = e − µσPAP ρ ( || x || ) (18)The expression in (17) can be computed in a straightfor-ward manner using standard numerical techniques. B. Average Throughput to a Client: T ( r ) Computing the average throughput delivered by an APto its associated client at a distance r requires determiningthe distribution of SINR at the client. This in turn requiresthe computation of the cumulative interference caused at theclient due to all other APs concurrently transmitting with AP . To compute the SINR distribution, the methodology usedin [7] is adopted.In particular, the complementary cumulative distributionfunction (CCDF) of SINR can be expressed using Laplacefunctionals and written as P (SINR( r ) > β ) = ψ I ( s ) ψ N ( s ) , (19)where s = µβP AP ρ ( r ) , and ψ I ( · ) and ψ N ( · ) are the Laplacefunctionals of the interference from other AP transmissionsand additive noise, respectively. Switching to a user-centric perspective by shifting theorigin to the location of client and assuming AP tonow be located at ( r, (in polar coordinates), (19) can beapproximated as P (SINR > β ) ≈ e − sN e − λ (cid:82) π (cid:82) ∞ r q ( b ( v,θ ))[ − φ F ( sρ ( v ))] vdvdθ (20)where s is as before, and • q ( d ) is the probability that two APs separated by adistance d transmit concurrently (computation of q ( d ) is given in Appendix I), • b ( v, θ ) = v + r − rvcos ( θ ) is the distance betweenthe serving AP at ( r, and a generic interfering APlocated at ( v, θ ) , • φ F - Laplace transform of the fading random variable φ F ( x ) = x as fading is exponentially distributed, • N - Thermal noise variance.Evaluating (20) at s = µβP AP ρ ( r ) using standard numericaltechniques yields the distribution of SINR at the client.Once the distribution of SINR is obtained, the expected ratedelivered by the AP can be computed as E [log(1 + SINR )]) where the expectation is computed over the distribution ofSINR.V. NUMERICAL RESULTS AND DISCUSSIONThis section presents the results obtained using themethodology outlined earlier and highlights key takeawayson the design of Super Wi-Fi networks. Some of the keyparameters used in the computations are given in Table III.
TABLE IIID
EPLOYMENT SET UP
Channel Center Frequency 600 MHzChannel Bandwidth 6 MHzNumber of channels 1AP distribution Homogeneous PPP of intensity λ AP Transmission Power Variable between 0.1 W and 4 WClient Transmission Power 0.1 WAP Height Variable between 1.5 m and 30 mClient Height 1 mPathloss Based on ITU-R P.1411-8Fading Exponentially distributed with mean 1CCA Threshold σ -82 dBmUplink Viability Threshold γ -82 dBmNoise Variance ( N ) -173.97 dBm / Hz Traffic model Persistent downlink
A. Validation of Methodology
To validate the proposed stochastic-geometry-based modelof Super Wi-Fi networks, results obtained using such anapproach are compared against simulation results obtainedusing OPNET, an industry-standard packet-based networksimulation tool [30].In particular, due to computational complexity of largescale simulations in OPNET and lack of in-built support forrate adaptivity, OPNET is used to simulate the performanceof a network with a single AP and a single client. Thisresult is then compared against results obtained using thestochastic-geometry-based model in a sparse deployment
100 200 300 400 500 600 700 800AP - Client distance (in m)024681012 A P T h r o u g h p u t i n M bp s P AP = 0.1 W, OPNETP AP = 0.1 W, SG - p U ≤ 1P AP = 0.1 W, SG - p U = 1 a) AP throughput vs. AP-client distance r for P AP = 0 . and h AP = 30 m A P T h r o u g h p u t i n M bp s P AP = 1 W, OPNETP AP = 1 W, SG - p U ≤ 1P AP = 1 W, SG - p U = 1 b) AP throughput vs. AP-client distance r for P AP = 1 W and h AP = 30 m Fig. 2. Results from stochastic-geometry-based models and OPNETsimulation. The plot with p U ≤ is for the case when uplink viabilityis probabilistic and the one with p U = 1 is when uplink is assumed to bealways viable. setup where effects of channel contention are minimized andthe AP transmissions can be assumed to be independent ofeach other.For the OPNET simulation h AP and P AP are set to 30 mand . W or 1 W, respectively. Due to lack of support forrate adaptivity, modulation-and-coding-scheme (MCS) indexwas varied manually to identify the best index for a givensetup. While the pathloss model used in OPNET is differentfrom the one listed Table III, the simulation tool is used as ameans of validating the stochastic geometry analysis devel-oped in this paper. Specifically, OPNET uses the SuburbanHata model, where the pathloss after substitution of h AP =30 m is given by ρ ( d ) = 124 . .
23 log( d ) , where d is inkm. For comparison, the stochastic-geometry-based model isalso set to use the Suburban Hata model with AP density setto 0.1 AP/km .Fig. 2 shows the plots of AP throughput (in Mbps) perchannel as a function of AP-client distance (in m) for threecases - (i) OPNET simulation, (ii) stochastic-geometry modelwhen uplink viability is factored in, and (iii) stochastic- geometry model under the assumption that uplink is alwaysviable. Note that in OPNET fading is not modeled, whichis evident from the abrupt fall in throughput at ∼ m inFig. 2b. It is seen from Fig. 2a that the current model closelyfollows the throughput obtained using OPNET. Further, eventhough uplink and downlink powers are the same in this case,factoring uplink viability produces more accurate resultswhen compared to the existing models for Wi-Fi networks.The impact of uplink viability is even more pronouncedin Fig. 2b. Note that the proposed model and the OPNETresults both indicate that clients beyond m are incapableof being served. At shorter distances, while restrictions onMCS indices cap the maximum throughput in OPNET, nosuch restriction is placed on the proposed model. Due tolack of fading in OPNET simulations, OPNET predicts largerthroughputs in the 400 m to 550 m range than the proposedmodel. It is clear that models that do not factor in uplinkviability are particularly inaccurate at larger distances andpredict much larger coverage than is realistically possible.These results along with the comparison in [6] against ns-2simulations further validate this model. B. Results on Throughput and Coverage Analysis
The section presents the projected performance of SuperWi-Fi networks from the perspective of (a) transmissionprobability, (b) coverage of an AP, and (c) area spectralefficiency (network throughput). A well-designed Super Wi-Fi network requires striking the right balance between all ofthe above three attributes.
1) Transmission Probability:
This section examines theimpact of AP transmit power ( P AP ) and height ( h AP ) on APtransmission probabilities at various deployment densities.Fig. 3 plots average p T as a function of h AP for threedifferent densities. The average is computed over all AP-client distances r and is given by ¯ p T = E r [ p T ( r )] = (cid:90) ∞ p T ( r ) f R ( r | I u = 1) dr. (21)Fig. 3 illustrates the interplay between P AP and h AP in deciding how often an AP transmits and as expected,transmission probabilities decrease with increasing density.Note that at densities ≤ AP/km and low antenna heights(1.5 to 3 m), transmit power does not play a significant rolein determining the transmission probability. Further, it is seenthat at higher transmission powers, ¯ p T drops significantly as h AP increases. For instance, at an AP deployment densityof 1 AP/ km , when P AP = 4 W , an AP transmits with aprobability of ≈ . when operated at a height of 1.5 m butthis probability drops below 0.1 when operated at a height of15 m. In fact, at high densities ( ≥ APs/km ), operating atany height above 3 m does not seem optimal. On the otherhand, given a target ¯ p T and deployment density, and multiple ( P AP , h AP ) pairs that meet the target ¯ p T , choosing the pairwith the highest AP height is advisable, as increasing APheight benefits both uplink and downlink, while increasing P AP only aids downlink, leading to greater asymmetry. Thus,when designing Super Wi-Fi networks, careful consideration .0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0AP Power (in W)0.00.20.40.60.81.0 P r o b a b ili t y o f A P T r a n s m i ss i o n h AP = 1.5 mh AP = 3.0 mh AP = 6.0 mh AP = 9.0 mh AP = 15.0 mh AP = 30.0 mAP Density = 0.1/km a) Low Density P r o b a b ili t y o f A P T r a n s m i ss i o n h AP = 1.5 mh AP = 3.0 mh AP = 6.0 mh AP = 9.0 mh AP = 15.0 mh AP = 30.0 mAP Density = 1/km b) Medium Density P r o b a b ili t y o f A P T r a n s m i ss i o n h AP = 1.5 mh AP = 3.0 mh AP = 6.0 mh AP = 9.0 mh AP = 15.0 mh AP = 30.0 mAP Density = 10/km c) High DensityFig. 3. Probability of transmission of an AP under different transmission powers P AP , heights h AP , and densities. U p li n k v i a b ili t y AP Height = 1.5 mAP Height = 3.0 mAP Height = 4.5 mAP Height = 6.0 mAP Height = 9.0 mAP Height = 15.0 mAP Height = 30.0 m a) Probability of uplink viability vs. AP-client distance r forvarious AP heights. P r o b a b ili t y t h a t a c li e n t i s n o t c o v e r e d AP Density = 0.1/km AP Density = 1/km AP Density = 10/km b) Probability that client does not find an AP to associate with;note that client always transmits at 0.1 W.Fig. 4. Effect of AP density and height on uplink viability and geographic client coverage. must be given to the choice of P AP and h AP , with particularattention paid to uplink-downlink asymmetry.
2) Coverage Analysis:
Unlike existing work on charac-terizing coverage by computing the probability that SINRexceeds a given threshold, this work defines coverage viauplink viability and determines a client to be in coverageif the uplink packets are received above the CCA threshold.When defined in this manner, coverage becomes independentof downlink transmit power. This alternate definition isparticularly appropriate for Super Wi-Fi networks whereclients are restricted to transmit at 0.1 W, but APs are allowedto transmit up to 4 W. Fig. 4a plots uplink viability p U as afunction of AP-client distance, assuming clients to transmitat 0.1 W. It can be observed that even at an AP height of30 m, uplink is no longer viable beyond 700 m. In fact,for users who are 400 to 700 m away, uplink is viable lessthan of times—further restricting the range of an APif reliable transmission is desired. This coverage limitationleads to large coverage gaps in a sparse deployment, as seen in Fig. 4b. Assuming clients to be uniformly distributed,Fig. 4b shows that at deployment densities of 1 AP/km ,over 50% of clients cannot associate with any AP. Thus,Super Wi-Fi networks with deployment densities less than 1AP/km are only able to provide localized coverage whiledensities greater than 10 APs/km are required to ensurepervasive coverage over a wide area.This observation is illustrated in Figs. 5a and 5b. Fig. 5ashows coverage and downlink range (defined analogous tocoverage range; determines channel contention radius) ina Super Wi-Fi network with λ = 0 . AP/km . APs areassumed to be at a height of 30 m and transmit at 4 W.It is clear that at such densities only localized coverage ispossible. Further, the figure also illustrates why operating at P AP = 4 W is not optimal even at such low AP deploymentdensities. High AP transmit powers lead to unnecessaryenlargement of the contention radius, causing a drop in ¯ p T and a potential decrease in network performance (as seenin the next subsection). Fig. 5b represents a Super Wi-Fi D i s t a n c e ( i n k m ) AP Density = 0.1/km a) P AP = 4 W, h AP = 30 m D i s t a n c e ( i n k m ) AP Density = 10/km b) P AP = 1 W, h AP = 10 mFig. 5. AP downlink and uplink coverage for different deployment densities; dotted black circle - downlink coverage, red circle - uplink coverage. A r e a Sp e c t r a l E ff i c i e n c y ( i n b / s / H z / k m ) 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 AP Density = 0.1/ km a) Low Density A r e a Sp e c t r a l E ff i c i e n c y ( i n b / s / H z / k m ) 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 AP Density = 1/ km b) Medium Density A r e a Sp e c t r a l E ff i c i e n c y ( i n b / s / H z / k m ) 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 AP Density = 10/ km c) High DensityFig. 6. Area Spectral Efficiency (ASE) under different transmission powers P AP , heights h AP , and deployment densities. network with λ = 10 APs/km , that is capable of providingpervasive coverage. Parameters h AP and P AP are set to1 W and 10 m, respectively. At this height more than 80%of the area is covered. Once again it is seen that highertransmit powers lead to a large contention radius that can bedetrimental to network performance.
3) Area Spectral Efficiency:
Throughput T of an AP isas defined in (13). Area spectral efficiency is the product T λ , and reflects the total number of bits transmitted over thewireless medium in a given area. The following discussion issplit into three cases, depending on the deployment density.Fig. 6a, plots performance of a very sparse deploymentwith a density of 0.1 AP/km . At such densities, onlylocalized coverage is possible and for each curve in Fig. 6a,the coverage characteristics remain the same. It is seen thatfor a fixed transmit power, ASE increases with decreasingheight, owing to reduced coverage area, thereby serving onlythose clients who are at a very close proximity to the AP. Onthe other hand, if h AP is held fixed, then ASE increases with transmit power at lower heights, but decreases when h AP exceeds 9 to 10 m. This observation can be attributed to thefact that at lower AP heights, AP transmission probabilitiesare only a weak function of P AP , and the gains in downlinkSINR do not get negated by a drop in ¯ p T , as is the case forhigher AP heights. In the case when maximum coverage issought by setting h AP to 30 m, each AP delivers close to40 Mbps over a 6 MHz TVWS channel when operating ata transmit power of 0.1 W. The key takeaway here is thatwhen seeking to maximize localized coverage (by setting h AP > m), increasing AP transmit power is unlikelyto yield better performance due to the sharp drop in APtransmission probability.Fig. 6b considers a medium deployment density of 1AP/km . Once again two different behaviors are seen de-pending on whether h AP exceeds 3 m or not. It is clear that h AP exceeding 10 m has a detrimental impact on networkperformance. Even at such densities, pervasive coverage isdifficult to achieve. When maximum coverage is sought, each ABLE IVS
UGGESTED CHOICE OF AP OPERATING PARAMETERS FOR DIFFERENTDEPLOYMENT DENSITIES
Priority → Max. coverage/AP Max. throughput/APSparse ( λ = 0 . ) (0.1 W, 30 m) (1 to 4 W, 1.5 to 3 m)Medium ( λ = 1 ) (0.1 W, 30 m) (1 to 4 W, 1.5 m)High ( λ = 10 ) (0.1 W, 10 to 30 m) (0.1 W, 1.5 m) D i s t a n c e i n k m s Distribution of Households - Sharon Springs in Wallace County, KS
Fig. 7. Distribution of households in Sharon Springs, Wallace County,Kansas according to 2010 US Census. Each circle represents a house.
AP delivers close to 12 Mbps per TVWS channel, with a totalof 120 Mbps/km .Fig. 6c considers a dense deployment scenario with adensity of 10 APs/km . In this case, it is possible to achievepervasive coverage when h AP exceeds 15 m. Unlike theprevious two cases, for a fixed h AP , ASE decreases withincreasing P AP suggesting that changes in ¯ p T plays a moreimportant role than changes in SINRs. Maximizing coverageis not as important as before, and setting 9 m ≤ h AP ≤
15 msuffices to ensure that more than 80% of the clients are undercoverage. When h AP = 9 m, an ASE of 240 Mbps/km overone TVWS channel can be achieved. The striking similaritybetween Fig. 3c and Fig. 6c suggests that this network isinterference limited where interference dominates over noiseand an increase in transmit power leads to an equal amountof increase in signal and interference strength, leaving SINRunchanged.The key takeaways from this section are summarized inTable IV where λ denotes the number of APs/km . Notethat pervasive coverage is achieved only at high deploymentdensity and when coverage per AP is prioritized. C. Network Planning for a Suburban use-case
This section explores a network plan for providing broad-band connectivity to a suburban region using results from theprevious discussion. The region of interest is Sharon Springsin Wallace County, Kansas, USA. Fig. 7 shows the distribu-tion of houses in Sharon Springs obtained from the recordsof 2010 US Census. There are around 400 households spreadout over an area of 3 km . Suppose each household is to be supported with a data rate of 10 Mbps, the required networkthroughput is × / Mbps/km . In this area,37 TVWS channels amounting to a total of 222 MHz arecurrently available (from Google spectrum database [3]).Consider deploying a Super Wi-Fi network with a deploy-ment density of 10 APs/km . With the objective of attaininga coverage probability of at least 75% and with the ease ofmounting antennas on street light poles in mind, AP heightis chosen to be h AP = 6 m. Using results from Fig. 6c,AP transmit power P AP is set to 0.1 W to obtain an ASEof 12 bps/Hz/km , translating to a network throughput of72 Mbps/km per TVWS channel. Thus, it is possible tomeet the demands of this suburban region using at most 18of the 37 available channels. Further network efficiency andbetter coverage can be achieved using a more careful APdeployment leading to a more economical use of availablebandwidth.These computations suggest that such a network can bea reasonable access alternative to satellite-based internetservice which tends to be the dominant means of connectivityin such rural areas. Backhaul services for the deployed APscan also be provided using TVWS channels as investigatedin [4], [5]. VI. CONCLUSIONThis paper uses a stochastic geometry analysis to study thefeasibility of utilizing TVWS channels to provide broadbandconnectivity in rural and under-served regions using a Wi-Fi-like network. Regulations on transmit power and antennaheight for both APs and clients present situations in whichthe downlink may be viable but the uplink from client toAP is not. The performance of such a network operating inTVWS channels is analyzed using stochastic geometry whileexplicitly factoring in uplink viability. Such an analysis isused to characterize AP transmission probabilities, coverage,and area spectral efficiency. These results show that operatingAPs at high transmit powers and heights is not alwaysbeneficial to the performance of the network, even at low APdeployment densities. It is however seen that APs deployedat higher heights significantly improve uplink viability. Thisexemplifies the rate-coverage trade-off in these networks.The choice of operating parameters for such a network willdepend on the desired balance between coverage and rate.ACKNOWLEDGMENTThis work is supported in part by a grant from theU.S. Office of Naval Research (ONR) under grant numberN00014-15-1-2168. A PPENDIX ID ERIVATION OF PROBABILITY OF CONCURRENT AP TRANSMISSIONS
Let AP x represent an AP that is at a distance d from AP . Then, q ( d ) represents the probability that AP and AP transmit at the same time, and can be written as q ( d ) = P , x Φ A { x ∈ Φ T | ∈ Φ T } = P , x Φ A { x ∈ Φ T , ∈ Φ T } P , x Φ A { ∈ Φ T } . (22)To compute the numerator of (22), let m and m x as themarks chosen by AP and AP x respectively and assume m < m x , without loss of generality. Denote z as a potentialinterferer. To compute the joint probability that both AP and AP x concurrently transmit, two ‘classes’ of APs needto be considered—those with mark m < m , distributed asa PPP of intensity λm , which prevent both AP and AP x from transmitting, and those with mark m < m < m x ,distributed as a PPP of intensity λ ( m x − m ) , which preventonly AP x from transmitting. Using these observations, thenumerator of (22) can be computed as P , x Φ A { x ∈ Φ T , ∈ Φ T } = 2(1 − e − µσPAP PL ( x ) ) (cid:90) (cid:20)(cid:90) m e − λ ( m x − m ) (cid:82) R S x ( z ) d z dm x (cid:21) × e − λm (cid:82) R S or x ( z ) d z dm (23)where − e − µσPAP ρ ( x , ) is the probability that AP x is notin the neighborhood of AP . The factor of two accountsfor the case when m x < m . S x ( z ) is the probability thatAP x senses the transmission of AP z and S or x ( z ) =1 − (1 − S x ( z ))(1 − S ( z )) is the probability that theinterfering AP z is sensed by at least one of AP or AP x .In a similar manner, the denominator of (22) can be com-puted as P , x Φ A { ∈ Φ T } = (cid:90) (cid:90) m x e − λm (cid:82) R S ( z ) d z dm + (cid:90) m x (1 − e − µσPAP PL ( x ) ) e − λm (cid:82) R S ( z ) d z dm dm x . (24)In the above expression, the first term considers the casewhen m < m x , where AP can transmit regardless ofwhether AP x is transmitting or not, while the second termsconsiders the case when m > m x , in which case, AP cantransmit only if the AP cannot sense AP x ’s transmissions.R EFERENCES[1] FCC, “US FCC Third Memorandum Opinion and Order.ET Docket No. 04-186, FCC 12-36,” accessed: 02-15-2017. [Online]. Available: http://hraunfoss.fcc.gov/edocs$ $public/attachmatch/FCC-12-36A1.pdf[2] A. B. Flores, R. E. Guerra, E. W. Knightly, P. Ecclesine, and S. Pandey,“IEEE 802.11 af: a standard for TV white space spectrum sharing,”
IEEE Commun. Mag.
Proc. IEEE Global Commun. Conf. (GLOBECOM) ,2010.[5] S. Pattar, N. Mandayam, I. Seskar, J. Chen, and Z. Li, “Rate OptimalBackhaul and Distribution using LTE in TVWS,” Society of CableTelecommunication Engineers, Tech. Rep., 2015.[6] H. Q. Nguyen, F. Baccelli, and D. Kofman, “A stochastic geometryanalysis of dense IEEE 802.11 networks,” in
Proc IEEE Int. Conf.Comput. Commun. (INFOCOM) , 2007, pp. 1199–1207. [7] G. Alfano, M. Garetto, and E. Leonardi, “New insights into thestochastic geometry analysis of dense CSMA networks,” in
Proc IEEEInt. Conf. Comput. Commun. (INFOCOM) , 2011, pp. 2642–2650.[8] L. Simi´c, M. Petrova, and P. M¨ah¨onen, “Wi-Fi, but not on steroids:Performance analysis of a Wi-Fi-like network operating in TVWSunder realistic conditions,” in
Proc. IEEE Int. Commun. Conf. (ICC) ,2012, pp. 1533–1538.[9] S. J. Shellhammer, A. K. Sadek, and W. Zhang, “Technical challengesfor cognitive radio in the TV white space spectrum,” in
Proc. IEEEInf. Theory Workshop (ITW) , 2009, pp. 323–333.[10] M. Mishra and A. Sahai, “How much white space is there?”
EECSDept, Univ. of California, Berkeley, Tech. Rep. UCB/EECS-2009-3 ,2009.[11] D. Makris, G. Gardikis, and A. Kourtis, “Quantifying TV whitespace capacity: a geolocation-based approach,”
IEEE Commun. Mag. ,vol. 50, no. 9, 2012.[12] J. van de Beek, J. Riihijarvi, A. Achtzehn, and P. Mahonen, “UHFwhite space in Europe - a quantitative study into the potential ofthe 470–790 MHz band,” in
Proc. IEEE Symp. on New Frontiers inDynamic Spectrum Access Networks (DySPAN) , 2011.[13] A. Stirling, “White Spaces the New Wi-Fi?”
International Journal ofDigital Television , vol. 1, no. 1, pp. 69–83, 2010.[14] S. Kawade and M. Nekovee, “Broadband wireless delivery using aninside-out TV white space network architecture,” in
Proc. IEEE GlobalCommun. Conf. (GLOBECOM) , 2011.[15] P. Bahl, R. Chandra, T. Moscibroda, R. Murty, and M. Welsh, “Whitespace networking with Wi-Fi like connectivity,”
SIGCOMM Comput.Commun. Rev. , vol. 39, no. 4, pp. 27–38, 2009.[16] S. Roberts, P. Garnett, and R. Chandra, “Connecting africa using theTV white spaces: from research to real world deployments,” in
Proc.IEEE Int. Workshop Local and Metropolitan Area Networks , 2015.[17] T. Zhang, S. Sen, and S. Banerjee, “Enhancing Vehicular Internet Con-nectivity using Whitespaces, Heterogeneity, and a Scouting Radio,” in
Proc. ACM Int. Conf. Mobile Syst., Applicat., and Services , 2014, pp.287–300.[18] F. Cali, M. Conti, and E. Gregori, “IEEE 802.11 wireless LAN:capacity analysis and protocol enhancement,” in
Proc IEEE Int. Conf.Comput. Commun. (INFOCOM) , vol. 1, 1998, pp. 142–149.[19] G. Bianchi, “Performance analysis of the IEEE 802.11 distributedcoordination function,”
IEEE J. Sel. Areas Commun. , vol. 18, no. 3,pp. 535–547, 2000.[20] F. Baccelli, B. Blaszczyszyn, and P. Muhlethaler, “An Aloha protocolfor multihop mobile wireless networks,”
IEEE Trans. Inf. Theory ,vol. 52, no. 2, pp. 421–436, 2006.[21] ——, “Stochastic analysis of spatial and opportunistic Aloha,”
IEEEJ. Sel. Areas Commun. , vol. 27, no. 7, pp. 1105–1119, 2009.[22] H. ElSawy and E. Hossain, “A modified hard core point processfor analysis of random CSMA wireless networks in general fadingenvironments,”
IEEE Trans. Commun. , vol. 61, no. 4, pp. 1520–1534,2013.[23] M. Haenggi and R. K. Ganti,
Interference in large wireless networks .Now Publishers Inc, 2009.[24] A. Hasan and J. G. Andrews, “The guard zone in wireless ad hocnetworks,”
IEEE Trans. Wireless Commun. , vol. 6, no. 3, pp. 897–906, 2007.[25] H. ElSawy, E. Hossain, and M. Haenggi, “Stochastic geometry formodeling, analysis, and design of multi-tier and cognitive cellularwireless networks: A survey,”
IEEE Commun. Surveys Tuts. , vol. 15,no. 3, pp. 996–1019, 2013.[26] M. Haenggi, J. G. Andrews, F. Baccelli, O. Dousse, andM. Franceschetti, “Stochastic geometry and random graphs for theanalysis and design of wireless networks,”
IEEE J. Sel. Areas Com-mun. , vol. 27, no. 7, pp. 1029–1046, 2009.[27] F. Baccelli and B. Blaszczyszyn,
Stochastic Geometry and WirelessNetworks, Volume II - Applications , ser. Foundations and Trends inNetworking: Vol. 4: No 1-2, pp 1-312. NoW Publishers. [Online].Available: https://hal.inria.fr/inria-00403040/file/FnT2.pdf[28] S. N. Chiu, D. Stoyan, W. S. Kendall, and J. Mecke,