Hi!
Thanks for sharing the details about your experiment. Could you please
write the packet size of your experiment?
Another question is what's the relationship between the packet size
and the number 23 in the formula of CpmModelC.nc. I remenber that
there is a former mail saying that the packet size is 28. Is number 23
simply substract 5 from 28?
Following is the formula:
PRR=(1-0.5*erfc(\beta_1*\sqrt{\frac{|SINR}-\beta_2|}{2}}))^{23*2}
~~23 is here.
Thanks in advance.
On 8/12/09, Yin Chen <[email protected]> wrote:
> On Tue, Aug 11, 2009 at 8:34 PM, Razvan Musaloiu-E.<[email protected]>
> wrote:
>> Hi!
>>
>> On Tue, 11 Aug 2009, Philip Levis wrote:
>>
>>>
>>> On Aug 7, 2009, at 1:27 PM, Razvan Musaloiu-E. wrote:
>>>
>>>> Hi!
>>>>
>>>> About 2 months ago, a commit [1] to CpmModelC.nc that eliminates the
>>>> problem of receiving packets (non-zero PRR) for negative SNR also made a
>>>> significant change to the hardcoded PRR/SNR curve. This was not
>>>> adequately
>>>> documented in the commit message and many people might not be aware of
>>>> this. Here is a plot that shows the differences:
>>>> http://bit.ly/znrwQ
>>
>> I made a mistake in the above graph. In Yin's data the SNR is actually
>> SINR. After accounting for this the new graph looks like this:
>> http://farm3.static.flickr.com/2456/3812438521_c08b3ec98e_o.png
>>
>> So the new curve is actually in agreement with Yin's data. :-)
>>
>>>> The points represent the data collected by Yin Chen, a member of our
>>>> lab.
>>>> In his tests the noise level was controlled by using a noise generator
>>>> so
>>>> it covers a wide range. Similar data was also reported by the following
>>>> paper:
>>>> http://portal.acm.org/citation.cfm?id=1460427
>>>>
>>
>> The conversion of SINR to SNR should also make this data in agreement with
>> the new curve.
>>
>>>> So there are reasons to believe that even the current curve we have in
>>>> the
>>>> tree is not the most accurate one. Caution is advised! :-)
>>
>> Considering that multiple datasets collected in very different ways are in
>> agreement now I think there are good reasons to believe the new curve is a
>> good one.
>>
>>>> [1]
>>>> http://hinrg.cs.jhu.edu/git/?p=tinyos-2.x.git;a=commit;h=afe96d7e2a3747bba450e3db88a89569a0ba53b6
>>>
>>> The methodology Yin used to collect the data set in the above figure is
>>> not
>>> appropriate for calculating SNR/PRR curves.
>>
>> I think it is. Here is a visual representation of the signal/noise space
>> explored by Yin's data:
>> http://farm4.static.flickr.com/3548/3812438643_bf272d9b56_o.png
>>
>> Only 12 receiving motes were used but multiple TX levels were used.
>> Here are two other views:
>>
>> SNR vs Signal
>> http://farm3.static.flickr.com/2448/3813253680_f72943d1a3_o.png
>>
>> SNR vs Noise
>> http://farm3.static.flickr.com/2623/3813253658_12aa32c68a_o.png
>>
>>> There are three separate issues, all of which have a common concern:
>>> averaging. While the data sets in the above paper are suitable for its
>>> conclusions, they have problems when it comes to simulation.
>>>
>>> 1) It combines many node pairs: each pair can have a different SNR/PRR
>>> curve.
>>> This is why an SNR of 3dB can have a PRR of 95% or 5%.
>>
>> Here is the SNR vs PRR for each node:
>> http://farm3.static.flickr.com/2607/3812438555_0199f0591d_o.png
>>
>> It seems that the overall shape of the curve stays the same and is only
>> shifted to the left or right. We should be able to simulate this using an
>> appropriate random variable. More experiments are needed to clarify
>> this.
>>
>>> 2) Signal is a not a controlled variable, and it is averaged. A lack of
>>> control means that it will vary due to environmental conditions, and the
>>> fact
>>> that it is averaged over received packets leads to sampling bias. It is
>>> not
>>> clear in the paper if the plot averages the RSSI of packets along a link
>>> or
>>> averages the per-packet SNR. Since N is considered to be constant (more
>>> on
>>> that below), the two are equivalent. But if the signal strength has
>>> variation, and you observe the SNR only of received packets, you can
>>> observe
>>> an SNR higher than the PRR would suggest.
>>>
>>> 3) Noise/interference are not controlled. Taking the average of N assumes
>>> that it is a gaussian variable; while N is, external interference I can
>>> disrupt this measurement. This might explain why the SNR/PRR curve is
>>> lower.
>>> E.g., if 10% of my packets have a high interference, my averaged N will
>>> go up
>>> significantly in a way that will lead the SNR curve to lead to incorrect
>>> conclusions.
>>
>> Yin has some plots that shows the variations of the signal and noise in
>> his data. I agree that both are legitimate concerns.
>
> Just to clarify a bit, the experiment used channel 26, and was
> conducted in a quiet office. So basically both the signal and noise
> RSSI were quite stable. Each data point in the SNR vs PRR graph is
> averaged over 250 packets. And for 90% of the data points, the
> standard deviations of the RSSI across the 250 packets is smaller than
> 0.8 dB, and almost all data points have std below 1 dB.
>
> -
> Yin
>
>>
>>> There are ways to give a sense of the degree of these methodological
>>> limitations. The spread of discrete points in the Figure is a good
>>> approach
>>> for 1). A plot of the S distribution could help with 2). A plot of the N
>>> distribution could help with 3).
>>>
>>> The current curve in TOSSIM was generated from a data set that Kannan
>>> collected using a variable attenuator, shielded cabling, and 2 micaZ
>>> motes.
>>> I've attached a plot of the associated data. The error bar along the
>>> X-axis
>>> is the standard deviation of signal strength. Using a variable attenuator
>>> and
>>> shielded cables leads these values to be very stable. The red bar shows
>>> the
>>> noise floor, which he calculated as the mode of RSSI readings taken when
>>> there were no transmissions. Since these were measured in a closed
>>> system,
>>> they are not affected by external interference.
>>
>> I did not know how was the data collected by Kannan. From your description
>> I understand that the noise was always constant (-96 dBm). Is this
>> correct? It also seems that in the experiment tested only a very small
>> number of distinct PRR values (I can only see only 4-5). It could be
>> possible to test a few more? More points in the -90 and -93 dBm would
>> paint a much clearer picture.
>>
>>> The prior curve was generated with an inferior data set, taken from an
>>> uncontrolled environment (such as Yin's).
>>
>> I think the experiments did by Yin are complementary to the one did by
>> Kannan because they explore the SNR when the noise is different from the
>> noise floor. I think this is very important because it's not so obvious
>> that the SNR vs PRR curve is the same for various noise levels (which is
>> exactly what CPM is relying on :-)).
>>
>> To reiterate what I said somewhere in the middle of this reply: the (at
>> least visual) agreement between three very different experiments (Kannan,
>> the Sensys 2008 paper and Yin) is an excellent indication that the new
>> curve is a good one. :D
>>
>> All the best!
>> Razvan ME
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>
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Liu Shucheng
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