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Bardwell J.Math and physics for the 802.11 wireless LAN engineer.pdf
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of accurate transmission relative to noise and errors and adjusts its data transmission rate accordingly. This change in data rate is transparent to the user of the radio (except, of course, they may see

their files being transferred more slowly). Most 802.11 radio designers use more than simple signal strength measurements to determine when to shift to lower data rates.

A Challenging Beamwidth Question

The Professor and the Chauffeur are discussing 802.11 networking. The Chauffeur has been learning, little by little, as he has had to sit through the Professorʼs lectures many times. The Chauffeur makes the following statement:

The ideal situation would be to have a user who is inside the HPBW of the access point antenna and the access point inside the HPBW of the userʼs antenna.

The Chauffeur illustrates his thought with the following diagram:

Figure 4.21 The Client and the Access Point Are Within Each Other’s HPBW Zone

The Professor says, “Interesting idea, but Iʼm sorry to say that youʼre completely wrong.” The reason the Chauffeur is wrong is because the reciprocity theorem says that “If I can hear you, you can hear me (for the same input power).” Hence, if the client can hear the AP then the AP can hear the client, or vice versa. Considering the location of 802.11 client machines relative to the HPBW of the access point antenna is appropriate. Confirming that the access point is within the HPBW of the client antenna is unnecessary. This assumes, of course, that the client and the access point have the same input power to their respective antennae.

Signal Strength and Reduced Data Rate

As a general rule of thumb, when an 802.11 radio is receiving at less than -70 dBm the range is being approached where noise and environmental considerations are probably forcing the data rate to drop. Remember that the power is going to drop in alignment with the Inverse Square Law.

Assume that youʼre 10 feet away from the transmitting antenna of a typical access point rated at 100 mW which is 20 dBm. You measure the signal strength along the perpendicular center-line of the antenna (at the point of strongest signal). You find that the signal strength at this location is -10 dBm

Math and Physics for the 802.11 Wireless LAN Engineer

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Copyright 2003 - Joseph Bardwell

(which is, by the way, not unrealistic). If you now move up or down in space, to the point where you meet the extension of the HPBW angle, you can expect the measure -13 dBm (half of what was measured at the center-line). By the time you get 100 feet away from the antenna you can expect your signal strength reading (at the center-line) to fall to less than -60 dBm. Now itʼs time to be concerned about being outside the HPBW angle since youʼre only 10 dB away from dropping below -70 dBm. Fortunately, the area inside the HPBW angle has grown as you got further away from the apex of the angle and you may find that you simply canʼt position a receiver outside the HPBW when youʼre 100 feet away from the antenna.

Itʼs very important that you recognize that the preceding description assumed the measurement of - 60 dBm at a distance of 100 feet. While this is a plausible value for some interior environments it is not to be construed to be a generally applicable rule-of-thumb or suggested guideline. As they say in automobile advertisements “Your mileage may vary.”

We can use the basic trigonometric relationships to make some general comments about access point placement in 802.11 wireless networks. Consider a typical access point with a 1-wavelength antenna (roughly 12.5 cm). This dipole will have a HPBW of roughly 47º. Figure 4.22 (below) shows an access point mounted on a 9-foot high ceiling with a user sitting at their desk near the access point. The annotations on the right-hand side of the figure are explained following the figure.

Figure 4.22 User #1 Is Outside the Beamwidth Angle of the Access Point

The ceiling in the figure (above) is 9 feet high. The top of the userʼs desk, where their notebook computerʼs antenna is located, is 3 feet high. The antenna, then, is 6 feet below the ceiling. Because the access point is mounted at the ceiling line (point A) the ceiling forms the centerline of the beamwidth angle. The bottom half of the beamwidth angle is 23.5 degrees (below the horizontal). The tangent of 23.5 degrees is 0.4348 (obtained using a scientific calculator). The tangent is the ratio of the side opposite the angle to the side adjacent the angle (Law of Tangents). In this case, thatʼs the line CB (the 6 foot distance from ceiling to desktop) divided by the unknown distance from the wall, line AC. Rearranging the equation for the Law of Tangents to solve for the length of line AC yields: AC = CB / tangent or AC = 6 / 0.4348 and the answer (13.799) is rounded to 13.8 feet. User #1, therefore, is underneath the beamwidth angle and outside the 47O HPBW of the antenna. User #2 is beyond 13.8 feet from the wall and is inside the HPBW angle.

Math and Physics for the 802.11 Wireless LAN Engineer

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Copyright 2003 - Joseph Bardwell

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