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FIGURE 13-8: Calculating the Earth™s curvature.
Chapter 13 ” Create a Long-Distance Wi-Fi Link

The Theorem of Pythagoras states that if a triangle has sides of length a,b,c, with sides a,b
enclosing an angle of 90 degrees (“right angle”), then a2 b2 c2. By the way, a right angle can
be defined here as the angle formed when two straight lines cross each other in such a way that
all four angles produced are equal.

Fresnel Zone Calculations
As mentioned earlier in this chapter, the Fresnel zone™s radius at the point where the ends of
the ellipse peak out, or the midpoint, should be free and clear to provide adequate signal
strength. A rule of thumb is to keep blockage under 40 percent, but transmission loss is immi-
nent if there™s any obstruction of the Fresnel zone.
In your long distance Wi-Fi design you should calculate the Fresnel zone to determine
height and placement of your antennas to ensure there will be no hindrance. It™s also impor-
tant to consider physical obstacles and their relation to the time of year. For example, during
the warm seasons leaves will sprout again and over time young trees could grow into the
zone as well.
For purposes of performing Fresnel zone calculations let™s look at a real world example and
factor in the potential obstacles. The formula we will use to calculate the Fresnel zone radius
is shown in Figure 13-9, where f is frequency in GHz, d1 (distance from transmitting antenna
to mid-point) and d2 (distance from receiving antenna to mid-point) represent the statute
miles, and h is the radius in feet.

For best transmission results you should keep the link path of the Fresnel zone at least 60 percent
free from obstruction.

For an example scenario, we surveyed the following specifications:

The distance between endpoint antennas is 9.5 miles.
L2 / 8R or y 9.52 / 8(3958) or y
The curvature of Earth is y 90.25 / 31664 miles;
therefore y 15 feet.
The highest mid-point obstacle is a one-story building at 22 feet.
The frequency in GHz is 2.4.

B f 1d1 d2 2
h 72.1

FIGURE 13-9: Fresnel zone formula, where f is the
frequency in GHz, d1 and d2 represent the statute
miles, and h is the radius in feet.
314 Part IV ” Just for Fun

Using the Fresnel zone formula, we simply follow these steps to calculate the radius of the mid-
point ellipse:

1. Divide 9.5 by 2 to get the d 1 and d 2 values: 9.2 / 2 4.6.
2. Multiply d 1 d2 4.6(4.6) 21.16.
3. Multiply the total distance by frequency or f (d 1 d2) 2.4(9.5) 22.8.
4. Divide the value from Step 2 by the value from Step 3 or (d1 d2) /
f (d1 d2) 21.16 / 22.8 0.928.
5. Take the square root of the value in Step 4 (as 0.928) 0.963.
6. Multiply the value from Step 5 by 72.1 to get h 72.1(.963) 69.4 feet, which is the
radius of the mid-point Fresnel zone ellipse.

That™s it! Simply factor in the height of the obstacles and you have the antenna height for this
long-distance Wi-Fi link in feet: 69.4 (15 22) 106.4. However, remember the 40 per-
cent blockage rule from earlier in this section? If necessary, you could reduce the height of the
antennas by further multiplying by 0.6, which accommodates 60 percent signal transmission
strength (with 40 percent blockage). By doing so, the final antenna height would decrease to
106.4(0.6) 63.8 feet.
Following are some popular ways you can improve the line-of-sight between end point antennas:

Raise the antenna mounting point on the existing structure.
Build a new structure, that is, a radio tower, that is tall enough to mount the antenna.
Increase the height of an existing tower.
Locate a different mounting point, such as another building or tower, for the antenna.
Cut down problem trees.

Budgeting Your Wireless Link
Now that you™ve made calculations to work around obstacles and accommodate Fresnel zone
radius requirements, it™s time to calculate whether or not the signal strength for your equip-
ment will meet the receiver™s signal threshold. This process is called link planning or link bud-
geting and involves several variables, all of which we™ll cover in this section.
We™ll break a WLAN link into the following elements:

Effective transmitting power: transmitter power (dBm) cable and connector loss (dB)
antenna gain (dBi)
Propagation loss [dB] : free space loss (dB)
Effective receiving sensibility: antenna gain (dBi)”cable loss (dB)”receiver sensitivity (dBm)
Chapter 13 ” Create a Long-Distance Wi-Fi Link

With regard to the specific equipment you plan on or are considering using, check the specifi-
cation sheets or contact the manufacturers™ technicians for the values mentionedearlier. Also,
for more accurate results taking into account the different transmitting and receiving properties
at both ends of the link, link budgeting should be performed in both directions. Moving for-
ward let™s break down each element and detail its individual components.

The link budget formula is actually not too difficult. Basically, to pre-suppose a positive connec-
tion, the transmitting power propagation loss receiving sensibility must be greater than
zero. A strong link, on the other hand, should have a 20 dB margin.

Effective Transmitting Power
The effective transmitting power consists of the transmitter power, cable, and connector loss,
and antenna gain. For simplicity, let™s look at each individual component:
The transmitter power (in watts or milliwatts) can be expressed on a logarithmic scale relative
to 1 milliwatt in dBm (deci-Bell relative to one milliwatt). Therefore, the output is compared
to one milliwatt: (1 dBm 10 log10(P / 0.001)); (P in watts).

To convert watts to dBm: 10 log (watts 1000) dBm
To convert dBm to watts: 10(dBm / 10) / 1000 watts. (Note: 10 to the (dBm / 10) power
is the inverse log of (dBm / 10))

For cable and connector loss, be sure to account for the cable length when calculating cable
loss and don™t forget to add the (negative) value for the connector. Cable manufacturers will
supply the cable and connector loss you can expect for a given frequency. A very nice cable
loss calculator is available at the Times Microwave Web site:
Antenna gain is important as it defines the antenna pattern with regard to where the far field is
strongest and weakest and in the middle, and by how much. Antenna gain is normally given in
decibels over an isotropic antenna (dBi). It™s the power gain in comparison to a hypothetical
isotropic (all directions equal) antenna. If your antenna specifications express gain in dBd, you
should add 2.14 to obtain the corresponding gain in dBi, since it™s compared to a dipole
antenna. We specify maximum antenna gain in terms of dBi.

There™s an excellent discussion about antenna gain on the Web at this address:

Propagation Loss
Propagation loss (PL) can be simply defined as loss of a wave in free space. Technically it is
defined as the signal attenuation between transmit (TX) and receive (RX) antennas due to the
316 Part IV ” Just for Fun

PLFS 1d2 10n log10 a b
l 2

FIGURE 13-10: Path loss in an ideal free-space path.

TX to RX separation and multipath (scattering). Basic transmission loss is given by the fol-
lowing formula: PL(dB) Pt(dB) Pr(dB) Gt(dB) Gr(dB), where Pt is the transmitted
power, Pr is the received power, Gt is the transmit antenna gain, and Gr is the receive antenna
gain. An ideal free space (FS) path (no ground reflection, no multipath) has a path loss which
is proportional to the square (n 2) of the separation d, where l is the wavelength, as shown
in Figure 13-10.
This typically represents the minimum path loss and serves as a lower limit. Values of n on the
order of 4 are more representative of realistic, cluttered environments.

For more information on path loss, visit the following Web page: www.wireless.

Effective Receiving Sensibility
The first two components of effective receiving sensibility, antenna gain (in dBi) and cable loss
(in dB), were covered previously. Therefore, we™ll only touch upon the third component, namely
receiver sensitivity (in dBm).
Receiver sensitivity is one of the vital specifications of any receiver. Whether measured as a sig-
nal to noise ratio, SINAD, or noise figure it is essential that any receiver has a sufficient level of
sensitivity. In other words to achieve a required bit rate, the receiver power threshold on the
card connector must be up to par. Otherwise, there will be a noticeable decrease in perfor-
mance. This specification is provided by the manufacturer; however, some of the most common
values are indicated in Table 13-2.

Table 13-2 Common Client Adapter Receive Sensitivity
Client Adapter dBm at 11 Mbps dBm at 5.5 Mbps dBm at 2 Mbps dBm at 1 Mbps

Orinoco PC-Card 82 87 91 94
Cisco Aironet 350
PC-Card 85 89 91 94
Edimax USB Client 81 n/a n/a n/a
Belkin Router/
Access Point 78 n/a n/a n/a
Chapter 13 ” Create a Long-Distance Wi-Fi Link

You will notice that the lower bandwidth commitment (towards the right of Table 13-2)
increases receive sensitivity. For an ultra-reliable, but slightly slower link, try setting your hard-
ware to a maximum of 1 Mbps.

Putting It All Together
Don™t be overwhelmed by the formulas and calculations required for link budgeting. If you™re
not comfortable with the mathematics, there™s an automated online calculator at More importantly, link planning can
save your time and money when you make equipment purchasing decisions. Calculating a link
budget beforehand will allow you to change components (based on their component values) to
better score in a positive margin.
To recapitulate, you can assume a positive signal connection by taking the combined
values from the transmitting power, propagation loss, and receiving sensibility with a
final value greater than zero. A strong link, on the other hand, should have a margin
of 20 dB. Therefore, referring back to our example scenario, we surveyed the following

The distance between endpoint antennas is 9.5 miles.
The curvature of Earth is y L2/8R or y 9.52 / 8(3958) or y 90.25 / 31664 miles;
therefore y 15 feet.
The highest midpoint obstacle is a one-story building at 22 feet.
The frequency in GHz is 2.4.
Using the Fresnel zone formula, we calculated 69.4 feet; which is the radius of the mid-
point Fresnel zone ellipse between antennas over our line-of-sight.
After factoring in the height of surveyed obstacles, we found the antenna height for this
long-distance Wi-Fi link should be 106.4 feet.

So based on the link budgeting factors, considering obstacles, and accommodating the Fresnel
zone radius following (also depicted in Figure 13-11) is a synopsis of a realistic long-distance
link experimental design:

Antenna height on each end: 106.4 feet
Antenna type on each end: 21 dBi Parabolic Dish Directional Antenna
Cabling on each end: Just enough low loss cabling to ensure the greatest distance

You might assume that in order to double the distance of your long-distance Wi-Fi link, you
would simply double the signal power, yet this is not the case. When dealing with long-distance
Wi-Fi links you must first understand that wireless signal strength degrades as the square of the
distance covered. Doubling the distance of your long-distance Wi-Fi link will require 22, or four
times the power, which is represented by a 6 dB gain.
318 Part IV ” Just for Fun

21 dBI Parabolic Dish Directional Antenna

106.4 feet

9.5 miles

FIGURE 13-11: An experimental long-distance Wi-Fi bridge design based on our example
survey results.

Cabling the Antenna
Begin by measuring the distance from your computer to your outside antenna location. Be sure
to choose a route that will protect your coax run and allow easy upgrading. Use a long exten-
sion cord to simulate your coax and help make the measurement more realistic. Try to keep the
coax cable run as short as possible to minimize the RF power loss, and avoid sharp bends,
which can damage the coax, or in some cases, change the coax™s impedance. Next, choose a
high quality brand of coax and cut it to that distance, plus about one meter extra, for slack.
Avoid the low-quality, high-loss cable such as RG-58, CB or TV/satellite coax. The LMR
series from Times Microwave is highly recommended. The coax you choose must have a 50
ohms impedance. Any other impedance, such as 75 ohms, may cause too much loss for this

Use of the 75 ohms hard-line used in cable TV service might be possible, though some experi-
mentation will be required. You may also be able to pick up very high-quality, hard-line coax
from cellular phone or broadcast installations. They usually give the spool end runs (the last 15
meters or so) away for free or even throw it away because it™s of no use to them. The connectors
for commercial hard-line are very expensive and hard to make, so remember that.

Prepare the coax for installation of the two N plugs on each end. You™ll need a suitable brand of
N-type connectors due to the large center conductor if you use LMR-400. The RF Industries
RFN-1006-PL N-Connector is a good brand. You may also need to route your coax before ter-
minating the N-Connectors if it has to run through small diameter holes. Take your time
installing the connectors. See Chapter 1 for more instructions on building your cable.
After attaching the connectors, wrap some 3 M Scotch Super 33 electrical tape, or equivalent
stretchy tape, around the bottom of the connector and a few centimeters of coax. Pull the tape
as tight as possible to help make the connector waterproof. If your antenna is going to be
exposed directly to heavy rain or high humidity, you may want to consider wrapping the con-
nection with some self-fusing silicone tape (Radio Shack part number 64-2336).
Next, route your coax to your outside antenna. Secure the cable to keep it from flopping around
in the wind or from people pulling on it. Leave a small loop of coax where it enters the building.
Chapter 13 ” Create a Long-Distance Wi-Fi Link

This will act as a drip loop and will keep rain from seeping into your building. You may also at
this time want to install a quality brand of inline coax lightning protection. PolyPhaser is one
such protector. Refer to the documentation on the proper grounding techniques that will be
required for lightning protectors to work properly.
Connect the cable up to your antenna™s connector jack. Wrap some Coax Seal, Mastic tape, or
any other pliable waterproof tape around the connector and then also wrap all that with Super
33 electrical tape. Secure the wrapped connector against the antenna mast.

When using rubberized Coax Seal or Mastic tape, don™t apply the tape to the connector directly,
you™ll just end up with a mess. Instead, wrap the connection with electrical tape and then wrap
the Coax Seal around the tape, sealing any small holes. This will save you a lot of hassle when
you have to remove the connection.

For onsite testing, you may wish to obtain a proper pigtail to connect your computer to the
N-type connector on the cable. You may also want to make some type of stress relief holder to
support the weight of the coax and adapter. For more information on connectors and cabling
see Chapters 1 and 2 or visit the Web at:˜pa0hoo/

Testing and Troubleshooting
Now that your link is installed, you should give it a nice going over with some common testing
tools. Also, use the network as you actually would on a regular basis. That is, download e-mails,
surf the Web, transfer files, and so on.
In setting up your actual link, proper planning needs to take place beforehand because you and
the person who will be helping you will be quite some ways apart and it may be difficult to
communicate, not to mention exchange extra parts.
On the day of your test, you should create a “pre-link checklist” before leaving for the site.
Forgetting equipment or other necesities can mean the difference between spending the day
surfing the net or sitting in traffic.
A typical pre-link checklist includes the following.(Note: there should be two of everything on
this list because there are two nodes required.)

Laptop computer
Extra laptop battery or power inverter with 12-volt adapter
Wireless adapter
Access point or bridge
Directional antenna”panel, grid, Yagi, dish
Temporary mounting solution”tripod, lightstand, or something similar
320 Part IV ” Just for Fun

Cellular phone or handheld radio
Spotting scope or binoculars
GPS or a good map

Keep yourself organized and stick to the checklist, and you can leave the aspirin at home. Always
remember to bring more than one pigtail per node, as their fragile end connectors are prone to
breaking, and you may be many, many miles from a replacement. Extra batteries for your laptop,
in addition to a power inverter, also will ensure success because a laptop on a single charge will
clearly not be sufficient for a full day of testing.

Making the Link
After you reach the site, survey the initial area to find a spot with good line-of-sight to the
intended direction of the link. Setting up the antenna, tripod, access point/bridge, and laptop
should be a very simple and standard procedure. Connect all of the subsequent hardware and
run a program that measures signal-to-noise ratio (SNR) such as NetStumbler. (See Chapter 6
for more on NetStumbler.) You will be able to detect the reception of a beacon frame, and then
use the SNR measurment for link tuning. You will need to adjust and fine tune the direction of
the antenna to achieve optimum signal strength. Make sure you do this in coordination with
the person in control of the other end of the link to ensure precision and accuracy. Make
adjustments on one side at a time.
Once you feel that you have optimized the wireless link quality to your satisfaction, confirm the
success of your project by testing the network transport over the wireless link.
Set up a continuous connection to the far-side computer. Adjust the settings on both comput-
ers to enable communication between them. It will depend on your network topology, but you
can often insert a laptop on either end and configure them for direct communication to each
other. If your wireless radios are also routers, you will need to configure the computers to par-
ticipate on each side of the network.
Once your network settings are configured as needed, a good first test is to ping the remote com-
puter over the wireless link. (Your pal on the other end should also do this and other steps with
your computer.) Run the Command Prompt and enter ping -t ip_address. The -t option
tells ping to keep going forever. If the link doesn™t work at this point, jump to the Troubleshooting
section below. Ping should resolve the address and start replying once a second. This will help
show you the link quality but it won™t measure throughput or continuous connectivity.

Sometimes a stray DHCP server may give you the wrong address and send your traffic over an
Internet connection away from the wireless link. If this happens, you will be able to surf the Web,
but you will not be able to connect to the computer on the other end of the wireless link.
Perform a tracert ip_address command to the far-side computer. Tracert will report on
which devices are routing your network traffic.

Next, use the link as it will actually be used on a daily basis. If you will be surfing the Web and
checking e-mail, do that. If it will be used for videoconfereincing or voice-over-IP (VoIP), try
Chapter 13 ” Create a Long-Distance Wi-Fi Link

that, too. Watch streaming videos, copy files back and forth to each other, and so on. You could
also try using Microsoft NetMeeting to send video or transfer files acrosss the link. Basically,
you want to exercise the link in any way you can.
While doing these link excercises, insert some attentuation into the system to simulate a low
signal condition. The “Go/NoGo Tester” from Wireless Info Net ( is a
neat, simple way to test how your link will perform on a bad day. Just plug this loss-inducing
barrel connector into your cabling and see if the link stays up. If the link dies, you need to care-
fully reconsider the components comprising the network. Check antenna selection, cable
lengths, connector quality, radio sensitivity, and of course antenna direction and physical aim.
Once you have accomplished these tasks and kept the link up and running, you have success-
fully designed and deployed your own long-distance Wi-Fi link.

Even when you™ve planned carefully, there can still be troubleshooting issues that may arise
when establishing a wireless connection of this type. The most common troubleshooting prob-
lems are something that most wireless users will experience at some time or another.
Broadly, problems arise in one of two areas: the wireless connection and network settings.

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