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Characterizing Signal Propagation in an UrbanMesh Network
Marco FiorePolitecnico di Torino
Dipartimento di ElettronicaCorso Duca degli Abruzzi 24
10129 Torino, ItalyEmail: [email protected]
Anastasios Giannoulis, Edward KnightlyRice University
ECE Department6100 Main Street
Houston, TX, 77005Email: {agiannou,knightly}@rice.edu
Abstract— Wireless mesh networks are multi-hop radio net-works, envisioned to build the backbone of a future pervasivecommunication infrastructure. This paper presents the results ofa user access-oriented, hands-on investigation on the propertiesof signal propagation in a wireless mesh network deployed inHouston, Texas, USA.
I. I NTRODUCTION
Wireless mesh networks are usually composed of nodesequipped with one or more wireless network interfaces andcommunicating with each other in a multi-hop fashion. A smallportion of these nodes also features a wired Internet connec-tion, and acts as a gateway for the other nodes in the meshnetwork. The mesh infrastructure thus extends the surfacecoverage of the wired gateways by means of a fully wirelessbackbone. Existing standards, namely IEEE 802.11a/b/g, arecurrenty employed to realize urban mesh networks, and newones, like IEEE 802.11s and IEEE 802.16j, are under studyand available as drafts.
Mesh networks are rapidly emerging as one of the mostpromising solutions to the so calledlast mile problem. Pro-viding broadband internet access at lower deployment andmaintenance costs with respect to wired connections, the meshinfrastructure is being adopted all over the world by a numberof communities, whose nature ranges from small towns in ruralareas, which traditional wired telcommunications providershave no advantage in reaching with their networks, up to largemetropolis where a capillary diffusion of high-speed internetaccess is technically impracticable by means of optical fibersor other wired solutions.
As far as urban coverage is concerned, an increasing numberof universities is deploying city-wide mesh testbeds [1], andmore and more commercial solutions are made today avail-able to administrations willing to provide ubiquitous networkcoverage to their communities [2], [3], [4], [5].
While a lot of attention has been paid to multi-hop rout-ing, gateway selection, multi-radio exploitation and otherbackbone-oriented aspects of mesh networking, small analysisis currently available from the user access perspective. Inparticular, a key factor in providing a satisfactory serviceto network customers is to achieve complete coverage ofthe serviced urban area, by guaranteeing the presence of asufficiently strong wireless signal to end users.
Signal propagation has been studied in the field of wirelesscellular networks, often with the support of complex simu-lation tools, especially to predict the strength of the radiosignal generated by one antenna, when positioned at a givenlocation. The same problem, tackled within mesh networking,presents several differences with respect to the cellular casestudy. First, different ranges of frequencies, 2.4 (802.11b) to 5(802.11a) GHz instead of 900 (GSM) to 2100 (UMTS) MHzare employed, leading to reduced penetration capabilitiesofthe radio wave and intrinsically different results in an urbanscenario. Also, 802.11-based Access Points employ a muchlower transmission power, as 802.11 cards with transmit pow-ers of 200 mW are considered high-power, while GSM BaseStations usually reach transmit powers of several Watts in anurban deployment. Finally, the signal quality required fordataexchanges over a wireless channel is generally higher than thatneeded to perform high-quality voice calls, as the tolerancetoward errors and losses is much lower in the first case. Byconsidering all these factors together, it appears clear that meshnetworks present unique characteristics, which influence signalpropagation and the resulting network performance.
In this paper, we present the outcome of a measurement-driven study of the outdoor wireless signal propagation inan urban mesh network, as perceived by end users. In Sec-tion II we describe the network where our experiments wereconducted, while the methodology we followed is detailed inSection III. In Sections IV V VI the measurements resultsare discussed at different levels of detail, on a global, per-node and per-direction perspective, respectively. In Section VIIwe discuss about the confidence of our measurements, andSection VIII draws some conclusions.
II. N ETWORK ENVIRONMENT
The urban mesh network built and maintained by RiceUniveristy researchers [1] within theTechnology For All(TFA) [6] initiative in South-East Houston, Texas, representsthe ideal environment for our tests. This mesh network, whichwe will refer to asTFA networkin the remainder of this paper,consits of a 17-node multi-hop backbone originating at a singlegateway and providing wireless coverage to a surface of morethan 4 km2. The area is a low-income, densely populatedneighborhood, where the mesh infrastructure provides bothfree Internet access to the local population and an experimental
Fig. 1. TFA network map. The two violet nodes are equipped with tworadios, the second interfaces building a dedicated directional link on a differentchannel with respect to the backbone and access tiers. The rightmost violetnode is the mesh wired gateway.
testbed for Rice telecommunications research. The wirelessinfrastructure provides free, open internet access to guestusers, but local residents are incentivated to register theirrouters, or even to install mesh nodes, by means of higherbandwidth guarantees. Featuring today more than a thousandregistered users, that deployed in South-East Houston is a fullyoperational mesh network, thus perfectly modeling the real-world urban scenario we are interested in.
The mesh nodes of TFA network are equipped with aVIA x86-based 1 GHz processor mounted on a mini-ITXmotherboard and a 200 mW SMC 2532-B 802.11b PCMCIAwireless card. The hardware is housed in a waterproof en-closure and runs the LocustWorld mesh Linux distribution.Nodes communication range is enhanced by means of high-gain 16dBi antennas mounted on top of poles, at an averageheight of 6 m. Since most of the buildings in the area areone-storey houses, this deployment allows most nodes to beon line of sight with each other. Due to the single interfacelimitation, both the mesh backbone and the user access tieroccur on a single channel. A map of the current deploymentof the TFA network is presented in Fig. 1
III. M ETHODOLOGY
Due to the large surface covered by the TFA Network, themeasurements were conducted by driving around the targetneighborhood. This approach is (i) consistent with the scopeof our research, since all the results are relative to the outdoorscenario we want to investigate, and (ii) efficient, as it allowsus to cover the vaste area under examination at vehicularspeed, and thus to collect in a reasonable time the largeamounts of data necessary to a comprehensive study.
We employ basic off-the-shelf hardware during this ex-periment, namely a GPS receiver, an external antenna anda wireless network interface card (NIC), all connected toa laptop. The GPS receiver is essential to extract preciseinformation about the position of the vehicle during the testdrives. The antenna is a 7 dBi magnetic antenna, located ontop of the car. We choose this solution because we noticeda noticeable improvement - often more than 100% in termsof sensed APs - with respect to the 2 dBi antenna embeddedin the wireless card. The wireless NIC is an Orinoco Gold802.11b PCMCIA card. The support for theb standard is
sufficient to our purposes, as the whole target mesh network isbuilt of b-only capable nodes. NetStumbler [7], a well-knownAccess Points (APs) detection software, is used to record thesignal strenght of the different mesh nodes over the roadtopology. NetStumbleractively detects the APs by probingthem for beacon frames, thus providing a higher sampling ratewith respect topassivesolutions, where the channel is simplylistened to. The software also takes as an input the data fromthe GPS receiver and matches it with the network informationgathered from beacons reception. Custom VisualBasic scripts,running within NetStumbler, allow us to record informationas we move. The hardware and software setup is summarizedin Table I. Such configuration resembles that tipically usedfor wardriving, however in the context of our project we arenot interested in determining the presence and position of theAPs, but in collecting a whole range of data on the behaviorof the network physical level.
Wireless NIC Orinoco Gold 802.11bAntenna 7 dBi gain external magnetic antennaGPS receiver Garmin GPS 18Software NetStumbler 0.4.0 running custom VisualBasic scripts
TABLE I
COVERAGE MEASUREMENTS SETUP
The results presented in the remainder of this section arederived from data collected during 16 test drives in theneighborhood where the wireless mesh network is located.Each test drive has a duration between 15 and 90 minutes. Weconducted the measurements between the 15th of December,2006 and the 15th of February, 2007, at different hours ofthe day, between 10am and 6pm. Over such a span of time,we encountered different atmospheric conditions, from sunnyweather to clouds, fog and rain. Both fog and rain proved tonoticeably affect the wireless signal propagation at vehicularspeed, leading to results which could be hardly averagedwith the remainder of our data and which depicted selfstanding coverage scenarios. Since these conditions representan exception to the standard climate of the region, and sinceobtaining a significative collection of related data would haverequired an unpredictable amount of time, we decided to focuson sunny or partially clouded weather conditions, reflectingthe common case 95% of times, thus filtering out resultscollected in presence of fog and rain. We instead did not noticesignificative differences between statistics recorded at differenthours of the day.
IV. N ETWORK COVERAGE
The complete coverage map provided by the mesh networkover the road topology is depicted in Fig. 2. The figure clearlyproofs that the mesh network is able to provide outdoor userconnectivity to the whole area, without any noticeable gapwith respect to the planned covered surface. The best recordedSignal to Noise plus Interference Ratio (SINR) is on averageat least 20 dB all over the map, a value which should guaranteea sufficient transmission quality to end users, and raises toanaverage of 30 dB over half of the neighborhood roads, withpeaks of 60 dB in proximity of the some mesh nodes antennas.
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Fig. 2. Overall network coverage. In each surface unit of side .0001 decimal degrees (approximately 11.12m in latitude and 9.65m in longitude), the valuematches the average Signal to Noise plus Interference Ratio(SINR) of the mesh node for which the highest average SINR wasrecorded in that location.
Simlar maps for the average noise and for the highest aver-age received signal strength show a fairly uniform distributionof noise all over the topology, and, consistenly, values of thereceived signal strength which follow the same trend observedfor the SINR. The CDFs of SINR, noise and signal strength,in Fig. 3 confirm the analysis, depicting a steep distributionof the noise and analogous curves for the SINR and the signalstrength. We can thus consider the received signal strengthandthe SINR as equivalent indicators of the quality of the channel,as seen by the mobile user. The same plot also allows us toidentify in 10 dB circa the threshold SINR for a frame to becorrectly received and decoded by the wireless NIC, as therelative CDF is null for lower values.
The reason for these excellent converage results is clearwhen observing Fig. 4, showing the average number of meshnodes sensed in each location of the road topology. Only onthe outer regions of the coverage map the number of meshnodes sensed is around one, meaning that the area is coveredby a single mesh node. As we proceed towards the center ofthe coverage map, the number of available backbone nodesincreases, with peaks of 7 mesh nodes sensed on the areasaround the nodes marked as TFA and Melcher. The CDF of theaverage number of mesh nodes is shown in Fig. 5, evidencingthat around 45% of the network is covered at least two meshnodes and that over 20% of the surface three or more meshnodes overlap. The high number of mesh nodes sensed in manylocations of the road topology on the one hand leads, as seenbefore, to high SINR and absence of connectivity holes, but,on
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Fig. 3. CDFs of the highest average signal strength, the average noise andthe highest average SINR, for each surface unit. The latter refers to the scaleon the upper x-axis. The errorbars report the average standard deviation fromthe mean.
the other hand, determines a higher contention for the channel,as all mesh nodes operates at the same frequency, and thus areduced access time for associated end users.
The mesh nodes, though identical from the hardware pointof view, do not held similar performances when the signalstrength received by an end user is studied. The geographicalposition of the antennas and the urban morphology of thesurroundings play a key role in determining the quality of the
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0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Arberry
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Fennel
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Glover
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
YMCA
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Galveston
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Deady
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Quince
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Narcissus
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
MossRose
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Fig. 4. Average number of sensed mesh nodes. In each surface unit, the value is averaged over the number of unique-BSSID beacons received every second.Beacons are transmitted by each mesh node with higher frequency than one second, but, due to their broadcast nature, to the possibility of collisions andto the congestion of the network, the actual number of received beacons is highly reduced. Moreover, the GPS coordinatesare updated every second andtherefore a higher precision in mesh nodes sensing would have just resulted in multiple measurements in the same location. An average number of meshnodes lower than one implies that beacons from backbone nodes have not been received every second.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 1 2 3 4 5 6 7
Cu
mu
lati
ve
Dis
trib
uti
on
Fu
nct
ion
Average number of APs
Fig. 5. CDFs of the average number of mesh backbone nodes sensed in eachsurface unit.
connection an end user would experience when associated to abackbone node. As a consequence, the strongest average signalreceived at each location is not just a matter of distance fromthe mesh node. In Fig. 6, a different color is associated to eachmesh node and the road surface coloring matches that of themesh node for which the highest average SINR was detectedin each location. We refer to this figure asuser association
map, as it shows which mesh node a user would associatewith depending on his/her geographical position, given thehighest SINR metric that is the standard AP association metricimplemented in most wireless NICs drivers today. It is evidentthat mesh nodes do not cover equivalent surfaces, with somenodes, as those located at Milby and YMCA, have a muchbroader coverage than others, such as those marked as Marand Arberry. Fig. 7, depicting the percentage of coveredroad topology controlled by each mesh node, brings furtherevidence to the above statement, by showing that the node atMilby covers 20% of the network while that tagged as Marscores a mere 1% as network best node.
V. M ESH NODES DIVERSITY
The reason for the disparity between mesh nodes in theuser association map is understood through the analysis ofthe signal propagation for the different mesh nodes. In thefollowing, for the sake of readability, we will limit our analysisto three representative mesh nodes: Milby, a strong, high-coverage node; Fennel, a typical, intermediate-converagenode;and Mar, a weak, low-coverage node.
The SINR map for the node at Milby is shown in Fig. 8.The antenna is located on the top of one of the few two-storiesbuilding in the area, which is surrounded by wide roads at West(the four-lane Broadway Street, running along the North-Southaxis) and North-East (the McArthur highway), a courtyard
Fennell
MossRose
Deady
Galveston
Milby
Melcher
YMCA
Mar
TFA
Linden
Adrian
Soto
Alvarez
Arberry
Narcissus
Quince
Kernel
Glover
No signal
Hig
hes
t av
erag
e S
INR
(dB
)
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
MossRose
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Linden
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Alvarez
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Melcher
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Adrian
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Milby
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als) Kernel
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Mar
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Soto
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
TFA
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Arberry
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Fennel
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Glover
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
YMCA
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Galveston
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Deady
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Quince
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Narcissus
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
MossRose
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Fig. 6. User association map. In each surface unit, the colormatches that of the mesh node for which the highest average SINR was recorded.
0
10
20
30
40
50
60
Aver
age
SIN
R (
dB
)
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
MossRose
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Linden
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Alvarez
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Melcher
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Adrian
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Milby
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als) Kernel
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Mar
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Soto
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
TFA
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Arberry
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Fennel
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Glover
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
YMCA
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Galveston
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Deady
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Quince
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Narcissus
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
MossRose
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Fig. 8. Milby mesh node SINR map.
at East and one-storey buildings at South-East. The elevated position of the antenna and the presence of large unobstructed
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Fennell
MossR
ose
Deady
Galveston
Milby
Melcher
YM
CA
Mar
TFALinden
Adrian
SotoA
lvarez
Arberry
Narcissus
Quince
Kernel
Glover
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Cu
mu
lati
ve
Dis
trib
uti
on
Fu
nct
ion
Pro
bab
ilit
y D
ensi
ty F
un
ctio
n
PDFCDF
Fig. 7. Percentage of surface covered by each mesh node with the highestaverage SINR, and relative cumulative function.
areas favor the propagation of the signal, especially towardsthe North and South directions, which happen to be in directline of sight with the antenna.
The mesh node at Fennel represents the typical node de-ployment in the urban mesh under study, as it is located overa single-story building in the middle of a residential areas. Thebuilding hosting the antenna is surrounded by akin structuresand by a quite dense foliage. The SINR map, in Fig. 9, showsa uniform propagation of the signal in each direction, whichis consistent with the omogeneity of the urban morphologyaround the antenna. An improved signal reception seems tobe achieved toward West and along the North-South direction,as, again, the mobile user is in line of sight with the antenna.However, when compared to the Milby map, it is evident thatboth the received signal strength and the covered surface arenoticeably reduced by the presence of obstacles.
The equivalent plot for the node tagged as Mar, in Fig. 10,shows an even worse situation, as the signal appears to becomeweak a few tens of meters away from the antenna, and,consequently, the covered area is further reduced. The antennais again located on the roof of a single-story building, butis this time surrounded by dense foliage and slightly higherbuildings, especially in the South direction. Moreover, bylooking at both the nodes distribution and at Fig. 4, Marhappens to be in the middle of an area characterized by densemesh nodes presence. Of the surrounding nodes, many appearto have a better placement with respect to Mar, in terms ofheight (Melcher), lack of surrounding obstacles (Soto) andline of sight from roads (MossRose). Still, we can notice apreferred direction in the signal propagation, this time alongthe West-East axis, in correspondence of Narcissus Street,where the mobile user has the best line of sight to the Marantenna.
The different propagation dynamics associated to each ofthe aforementioned mesh nodes can be coarsely described withindependent shadowing models fitting our measurements. Theshadowing propagation model describes the exponential decayof signal strength with distance through the formula
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
-45
-40
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Sig
nal
str
eng
th (
dB
m)
Distance (m)
fitted shadowing modelone standard deviation range
two standard deviations rangethree standard deviations range
milby α=2.04065 σ=5.41116
Fig. 11. Fitting shadowing model for Milby. Measurements are representedby dots, while the symmetric curves trace the 1, 2 and 3 standard deviationintervals around the mean.
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
-45
-40
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Sig
nal
str
eng
th (
dB
m)
Distance (m)
fitted shadowing modelone standard deviation range
two standard deviations rangethree standard deviations range
fennel α=2.57023 σ=4.91577
Fig. 12. Fitting shadowing model for Fennel. Measurements are representedby dots, while the symmetric curves trace the 1, 2 and 3 standard deviationintervals around the mean.
Pr(x) = Pr(x0) − 10αlog
(
x
x0
)
+ ǫ
wherePr(x) is the predicted received power at distancex,expressed in dB, andα is a pathlossexponent, the higher itsvalue, the faster the decay of signal strength with distance.The distancex0 is a reference distance for which the receivedpower Pr(x0) is known, andǫ is a zero-mean normallydistributed random variable, which accounts for probabilisticdifferences between different measurements performed at thesame distance from the signal source. Since the antennas ofthe mesh nodes are identical, the diverse shadowing modelsare fully characterized by the values ofα andσǫ, the standarddeviation of the random variableǫ, a measure of the level ofscattering of points at a given distance from the mesh node.We fit by means of a nonlinear least-squares algorithm thetheoretical curve to our field measurements for each meshnode.
The results are shown in Fig. 11, Fig. 12 and Fig. 13 for
0
10
20
30
40
50
60
Aver
age
SIN
R (
dB
)
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
MossRose
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Linden
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Alvarez
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Melcher
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Adrian
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Milby
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als) Kernel
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Mar
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Soto
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
TFA
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Arberry
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Fennel
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Glover
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
YMCA
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Galveston
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Deady
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Quince
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Narcissus
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
MossRose
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Fig. 9. Fennel mesh node SINR map.
0
10
20
30
40
50
60
Aver
age
SIN
R (
dB
)
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
MossRose
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Linden
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Alvarez
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Melcher
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Adrian
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Milby
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als) Kernel
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Mar
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Soto
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
TFA
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Arberry
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Fennel
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Glover
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
YMCA
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Galveston
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Deady
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Quince
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
Narcissus
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Longitude(W 95 degrees decimals)
Lat
itude
(N 2
9 d
egre
es d
ecim
als)
MossRose
0.2730.2750.2770.2790.2810.2830.2850.2870.2890.2910.2930.295
0.699
0.700
0.701
0.702
0.703
0.704
0.705
0.706
0.707
0.708
0.709
0.710
0.711
0.712
0.713
0.714
0.715
0.716
Fig. 10. Mar mesh node SINR map.
Milby, Fennel and Mar, respectively. It can be noticed that the three mesh nodes show different behaviors, which result
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eng
th (
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Distance (m)
fitted shadowing modelone standard deviation range
two standard deviations rangethree standard deviations range
mar α=2.81935 σ=4.96188
Fig. 13. Fitting shadowing model for Mar. Measurements are representedby dots, while the symmetric curves trace the 1, 2 and 3 standard deviationintervals around the mean.
0
0.05
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Pro
bab
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ensi
ty f
un
ctio
n
Signal strength standard deviation from mean (dB)
Signal strength standard deviation from mean (σ)
milby α=2.04065 σ=5.41116fitted normal distribution
Fig. 14. PDF of measurements around the theoretical mean forMilby. Thecurve represents the fitting zero-mean normal distribution.
in significantly diverse fitting curves. As it could be espected,propagation from the node at Milby is distinguished by a lowerpathloss exponent, resulting in farther reach of the signal,while Mar measurements lead to a high pathloss exponentand reduced range. The shadowing model matching Fenneldata lies in the middle.
The analysis of the theoretical curves also show an elevatestandard deviation, as shown in Fig. 14, where the distributionof measured values around the theoretical mean for the Milbynodes is provided. The other two node under examination showthe same behavior. The flat shape of the matching normaldistribution is determined by the evident scattering of pointscollected at the same distance from each mesh node.
VI. CAPTURING SIGNAL DIRECTIVITY
The cause of the spread of signal strength received at a givendistance from the node lies only partially on the fast dynamicsinduced by multipath fading on the received signal power. Infact, the aggregation of data collected at the same distancebutat different angles with respect to the antenna position hasto
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Sig
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str
eng
th (
dB
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Distance (m)
milby 0o North
α=2.00617 σ=6.73044
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eng
th (
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milby 45o North
α=2.17618 σ=4.61868
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eng
th (
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milby 90o North
α=1.9001 σ=1.81778
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nal
str
eng
th (
dB
m)
Distance (m)
milby 135o North
α=2.35421 σ=3.02201
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Sig
nal
str
eng
th (
dB
m)
Distance (m)
milby 180o North
α=1.89911 σ=2.16462
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Sig
nal
str
eng
th (
dB
m)
Distance (m)
milby 225o North
α=2.14405 σ=1.70923
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Sig
nal
str
eng
th (
dB
m)
Distance (m)
milby 270o North
α=1.95013 σ=4.83024
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Sig
nal
str
eng
th (
dB
m)
Distance (m)
milby 315o North
α=2.30832 σ=1.55272
Fig. 15. Fitting shadowing models for Milby. Each subset of measurements,identified by a different color, groups data recorded withina 45 degree anglefrom the mesh node and is characterized by a different propagation curve.The subset are tagged after the angle of the secant of the region they belongto.
be blamed as the main factor for the high standard deviationmeasured.
The empirical proof is obtained by dividing the collecteddata into subsets, according to the angle of the location ofmeasurement with respect to the signal source position, andreapeating the shadowing propagation model fitting for eachsubset independently. To obtain the angle or azimut anglebetween the signal source and the measurement point, we firstcompute the altitude, i.e. the angle of the measurement pointabove the horizon, as
The result of the nonlinear regression on the pathlossexponent for each subset of measurements in shown in Fig. 15for the backbone node at Milby. The discretization angleused is of 45 degrees, thus dividing the space into eight sec-tions, with secants along the North-South, East-West, North-West/South-East and North-East/South-West axis. It appearsevident that the curve obtained in Fig. 11, fitting the wholedata set recorded for the Milby node, only provides an averageindication on the propagation of the signal generated by thesource. Instead, when considering the direction of the receivedsignal, the different dynamics of propagation, determinedbythe urban scenario, can be captured. In the case of the meshnode at Milby, the signal appears to have a much betterpropagation along the North-South and East-West directives,where the presence of roads in direct line of sight favors anunconstrained diffusion of the signal. Measurements collectedon other directions do not lead to analogous properties, asthe signal spread is obstructed by buildings. We notice thatseparating the direction of measurements reduces the standarddeviation for most data subsets, but still there are a fewcases in which the value ofσǫ appears elevate. Reducingthe discretization angle would probably solve the problem,asit would allow to identify more precise propagation models.Unfortunately, the constrained mobility we are forced to duringon-vehicle measurements limits the locations we can collectdata from and does not allow to gather sufficient informationto model the propagation within small angles from the signal
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Fig. 16. Average measured signal strength as a function of the angle with respect to and of the distance from the signal source. The curves represent therelative fitting theoretical models. The three plots refer,from the top to the bottom, to the mesh nodes located at Milby,Fennelm, Mar and Melcher
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Signal strength standard deviation from mean (dB)
Signal strength standard deviation from mean (σ)
adrian α=2.53018 σ=1.86265fitted normal distribution
Fig. 17. PDF of measurements around the theoretical mean forAdrian. Thecurve represents the fitting zero-mean normal distribution.
source.The impact of the direction of the signal is even more
evident when looking at Fig. 16, where not only the angle,but also the distance from the antenna originating the signal isdiscretized. Since, due to road topology constraints and limitedsignal propagation towards some directions, we cannot collectdata for each angle/distance couple, the same figure alsoshows, for every measurement angle, the theoretical shadowingmodel curve matching the empirical results. The conclusionsof the previous discussion are validated in this plot by thepresence of curves characterized by lower pathloss exponentsin the four cardinal directions and more steep when diagonaldirections are considered.
Similar plots for the mesh nodes at Fennel and Mar showa more uniform distribution of signal along the differentdirections, differences in the directions are present but lessevident, as the signal strength is on average much lower thanthat recorded for the Milby node. Always in Fig. 16, Fennelstill shows a better propagation towards the North-South axisand in the West direction, while Mar has a generally low signalwhich is however stronger along the East-West axis.
We also stress that the high standard deviation our mea-surements suffered from in the cases taken into considerationis not always present. Some mesh nodes experience a lowstandard deviation, as it is the case for the mesh nodereferred to as Adrian, in Fig. 17. However, even in this caseseparating the different directions holds surprising results, asshown in Fig. 18, where the empirical data is divided intosubset according to the measurement angle with respect tothe antenna location and the correspondent fitting shadowingmodels are presented. We can notice that the low deviation ofthe aggregated data can deceive to think that the propagationis uniform in all directions, while some trajectories are stillfavorable with respect to others. Of course, in the case ofAdrian, the relative difference is much smaller than for theprevious cases.
It is also true that, if Adrian represents a mesh node whosesignal propagation experiences reduced scattering phenomena,other nodes show spreading dynamics which are influenced
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Fig. 18. Fitting shadowing models for Adrian. Each subset ofmeasurements,identified by a different color, groups data recorded withina 45 degree anglefrom the mesh node and is characterized by a different propagation curve.The subset are tagged after the angle of the secant of the region they belongto.
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melcher 225o North
α=2.45057 σ=1.58877
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melcher 315o North
α=2.53969 σ=2.00646
Fig. 19. Fitting shadowing models for Melcher. Each subset of measurements,identified by a different color, groups data recorded withina 45 degree anglefrom the mesh node and is characterized by a different propagation curve.The subset are tagged after the angle of the secant of the region they belongto.
by the direction even more than those previously studied.As an example, the backbone node located at Melcher issurrounded by trees and buildings at North, West and South,but Keller Street, one of the main roads of the neighborhood,and the Ingrando Park nearby allow for an optimal diffusionof the signal towards East. Fig. 19 and Fig. 16 prove the highdirectionality of the signal generated by the Melcher node.
VII. M EASUREMENTSCONFIDENCE
As far as the confidency on the collected data is concerned,in Fig. 20 the CDF of the time spent in each location of theroad topology is shown. The curve shows how we spent 10seconds or less in 70% of the visited surface units. This couldseem a poor result after more than 20 hours of driving aroundthe neighborhood, but it must be considered that
• the overall number of visited surface units amouts to morethan 5200, all within the neighborhood, for a total road
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Fig. 20. CDF of the time spent in each surface unit, for all thevisited surfaceunits and only considering those location where at least onemesh node wassensed on average.
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Fig. 21. CDF of recorded SINR 95% confidence interval span, expressed asa percentage of the absolute estimated mean, for surface units where at least2, 4, 10 and 30 seconds were spent, respectively.
length exceeding 50km• by driving in real traffic conditions, we necessarily spent
more time at some locations, like large intersectionsregulated by traffic light or congestioned roads. Thepresence of surface units where we recorded data formore than 500 seconds confirms this scenario
• many outer locations have been visited during only one ottwo test drives, as they proved to be too far to be reachedby the network coverage
• when considering only locations where at least one meshnode is sensed on average, the mean measurement timeincreases, as shown in Fig. 20. The number of locationsvisited for less than 10 second is reduced to 50% in thiscase. Thus, many unfrequently visited locations corre-spond to areas helding no interest to our research, as theyare not covered by the TFA Network
• in the following we show that the collected data tend tobe consistent after a few seconds measurements.
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Fig. 22. CDF of standard deviation span, expressed as a percentage of theabsolute estimated mean, for surface units where at least 2,4, 10 and 30seconds were spent, respectively.
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Fig. 23. CDF of the number of sensed mesh nodes 95% confidence intervalspan, for surface units where at least 2, 4, 10 and 30 seconds were spent,respectively.
In Fig. 21, the distribution of the span of 95% confidenceintervals is shown, for different minimum measurement times.Obviously, the confidence interval is reduced as the numberof measurements increases, but we can notice that even with afew seconds of data collection the prediction on the value ofthe mean SINR appear quite reliable. A similar plot, depictingthis time the CDF of the standard deviation, is shown inFig. 22. The effect of multiple measurements has an evenlower impact on the computed deviation, since the only effectof the increasing number of measurements lies in the tendencyof the CDF to move towards a step function, as the bordercases due to too few measurements are removed.
The number of mesh nodes sensed in each location tendsto vary in a non negligible way, and the reason must besearched in the unreliability of the wireless medium and ofthe CSMA/CA broadcast that is used for beacon transmission.Not receiving a beacon from the same set of mesh nodesduring two measurements, at a same location and non neces-sarily subsequent, is an understandable behavior, which thoughgreatly affects the confidence interval of the number of sensed
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Average signal strengthAverage noiseAverage SINR
Fig. 24. CDFs of the average signal strength, the average noise and theaverage SINR, for the MossRose mesh node. The latter curve refers to thescale on the upper x-axis. The errorbars report the average 95% confidenceinterval.
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Fig. 25. CDFs of the average signal strength, the average noise and theaverage SINR, for the MossRose mesh node. The latter curve refers to thescale on the upper x-axis. The errorbars report the average standard deviationfrom the mean.
nodes, in Fig. 21. As the time spent in a location increases,the confidence interval is reduced but the difference betweena few seconds of measurements and one or more minutes ofdata collection is contained.
Finally, we comment on the confidence of the results fora single mesh node. We discuss here only one representativebackbone node, namely MossRose, but the similar results havebeen produced for all the nodes of the mesh network. InFig. 24 the CDFs of signal strength, noise and SINR for theMossRose node are shown. We are interested in the errorbars,representing 95% confidence intervals for each value. Theplots shows that, even if the confidence interval tends tobe large for some values, for which evidently we did nothave enough measurements, the trend of the curves is clear.Moreover, the intervals are reduced as the absolute value ofthe mean grows, which gives us more confidence about thoseresults we are actually interested in, and the standard deviation,depicted along with the same CDFs in Fig. 25, appears to have
an even smaller span around the mean.
VIII. C ONCLUSIONS
In this paper we presented the outcome of a measurementcampaign on RF signal propagation in an urban environment.A wardriving-like approach was adopted to collect data froma real-world mesh network deployed in Houston, Texas, USA.We first identified the general coverage properties of themesh network, and then characterized the differences of signalpropagation from diverse typologies of nodes. We stressed theimportance of directivity in reliably modeling 802.11 signalpropagation in an urban environment, and we also commentedon the confidence of the information we collected. We believethat these results can help future deployment of mesh nodesin the network under analysis, as well as provide interestingclues to urban mesh deployers in more generic case studies.
REFERENCES
[1] J. Camp, J. Robinson, C. Steger, E. Knightly, “Measurement Driven De-ployment of a Two-Tier Urban Mesh Access Network”, in Proceedingsof MobiSys 2006, Uppsala, Sweden, June 2006.
[2] Tropos Networks,http://www.tropos.com.[3] MeshDynamics,http://www.meshdynamics.com.[4] Strix Systems,http://www.strixsystems.com.[5] Firetide, http://www.firetide.com.[6] Technology For All,http://www.techforall.org[7] NetStumbler,http://www.netstumbler.com
