Math lesson needed dBm

Being no mathematician, can anyone give a simple rule of thumb on how to
compute various dBm receive sensitivity specs at various speeds?

For example, if receive sensitivity is -87dBm at 11 Mbps, what will it
be at 1 Mbps?

Also, what is the practical range difference between a sensitivity rated
at -92dBm and one rated at -95dBm for say most Muni APs?

Finally, if a few small twig like branches obscure 90 degrees right of
the line of sight between my sighted AP can I guesstimate the degree
this will interfere with a good connection, for a small wubber duckey
antenna? and for a panel antenna? Guess I ask alot of (dumb) questions,
eh?

JDavidson <(E-Mail Removed)> hath wroth:

>Being no mathematician, can anyone give a simple rule of thumb on how to
>compute various dBm receive sensitivity specs at various speeds?

No. They're measured, not computed.

>For example, if receive sensitivity is -87dBm at 11 Mbps, what will it
>be at 1 Mbps?

That can't be done. It's not linear, changes with modulation method,
and is not very consistent between implimentations. There is also
considerable creativity in measurement setup. Some vendors include
the loss of the pigtail between the entenna connector and the board.
Some do not. Some just use the chipset vendors sensitivity figures,
without consideration for the circuitry between the antenna connector
and the chipset (i.e. diversity switch, board traces, bandpass filter,
matching network, etc).

Receiver sensitivity is the signal level at which one gets a 10E-5 BER
(bit error rate). Sometimes, the PER (packet error rate) at 10% is
used as it's easier to measure. The BER/PER is really a measure of
SNR (signal to noise ratio).

At such low signal levels, digital noise from the board, card, or
computer have a large effect on sensitivity. The same design, but on
a different board layout, will result in different receive
sensitivities.

Doing it backwards, the minimum signal to noise ratio (Eb/No) can be
calculated for different speeds at a BER = 10E-5.

Speed SNR(dB)
11 6.99
5.5 5.98
2 1.59
1 -2.92

54 24.6
48 24.1
36 18.8
24 17.0
18 10.8
12 9.0
9 7.8
6 6.0

There are quite a few articles on communications design under:
http://www.commsdesign.com

>Also, what is the practical range difference between a sensitivity rated
>at -92dBm and one rated at -95dBm for say most Muni APs?

That's easy. A 6dB improvement is good for doubling your range. 12dB
would be 4 times the range. 3dB is about 1.4 times the range.

improvment = 10^(dB/20) = 10^(3/20) = 1.4

For example, if your access point has the stock 2dBi vertical omni
rubber ducky antenna on it, and you replace it with a 7dBi aftermarket
omni rubber ducky antenna (in violation of FCC 15.204), the 5dB
increase in gain should yield a 1.8 time improvement in horizontal
range.

>Finally, if a few small twig like branches obscure 90 degrees right of
>the line of sight between my sighted AP can I guesstimate the degree
>this will interfere with a good connection, for a small wubber duckey
>antenna? and for a panel antenna?

The antenna doesn't matter. What's important is the type of tree,
thickness, and whether the tree clears the Fresnel Zone. 2.4GHz
wireless requires MORE than line of sight to operate. It requires
that at least 0.8 times the Fresnel Zone clearance at midpoint is
unobstructed. Anything inside the Fresnel Zone will create
diffraction effects and losses. See:
| http://www.terabeam.com/support/calc...esnel-zone.php
My guess(tm) is that you have more than just a few branches in the
way. If the range is considerable, you may need to elevate your
antenna as the Fresnel Zone may hit the ground.

>Guess I ask alot of (dumb) questions,
>eh?

Nope.

--
Jeff Liebermann (E-Mail Removed)
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558

Jeff Liebermann <(E-Mail Removed)> hath wroth:


>Doing it backwards, the minimum signal to noise ratio (Eb/No) can be
>calculated for different speeds at a BER = 10E-5.
>
> Speed SNR(dB)
> 11 6.99
> 5.5 5.98
> 2 1.59
> 1 -2.92
>
> 54 24.6
> 48 24.1
> 36 18.8
> 24 17.0
> 18 10.8
> 12 9.0
> 9 7.8
> 6 6.0

Duh. I forgot the punch line.

You can use this chart to guess how far you can go at different
speeds. For example, if you can get a tolerable connection at
36Mbits/sec, slowing down the speed to 12Mbits/sec will result in a:
18.8 - 9.0 = 9.8dB
improvment in S/N ratio. That's good for an:
10E(9.8/20) = 3.1
times increase in range.

Similarly, if you can get a solid but slow connection and you want
more speed, you can add an antenna and guess how fast you'll be able
to go. For example, an 18Mbit/sec connection, with perhaps a 12dB
increase in antenna gain, will yield a SNR of:
10.8 + 12 = 22.8dB
which is approximately the SNR of a 36Mbit/sec connection.

--
Jeff Liebermann (E-Mail Removed)
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558

Thanks again for a good answer. One day I'll go to enjuneering skul and
lurn all about this, :-)

Jeff Liebermann <(E-Mail Removed)> wrote in
news:(E-Mail Removed):

> Jeff Liebermann <(E-Mail Removed)> hath wroth:
>
>
>>Doing it backwards, the minimum signal to noise ratio (Eb/No) can be
>>calculated for different speeds at a BER = 10E-5.
>>
>> Speed SNR(dB)
>> 11 6.99
>> 5.5 5.98
>> 2 1.59
>> 1 -2.92
>>
>> 54 24.6
>> 48 24.1
>> 36 18.8
>> 24 17.0
>> 18 10.8
>> 12 9.0
>> 9 7.8
>> 6 6.0
>
> Duh. I forgot the punch line.
>
> You can use this chart to guess how far you can go at different
> speeds. For example, if you can get a tolerable connection at
> 36Mbits/sec, slowing down the speed to 12Mbits/sec will result in a:
> 18.8 - 9.0 = 9.8dB
> improvment in S/N ratio. That's good for an:
> 10E(9.8/20) = 3.1
> times increase in range.
>
> Similarly, if you can get a solid but slow connection and you want
> more speed, you can add an antenna and guess how fast you'll be able
> to go. For example, an 18Mbit/sec connection, with perhaps a 12dB
> increase in antenna gain, will yield a SNR of:
> 10.8 + 12 = 22.8dB
> which is approximately the SNR of a 36Mbit/sec connection.
>