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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Hello Jon,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Thank you for the presentation and the simple APD model. The algebra is OK.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">In the proposed model the observations are homogeneous to number of photons by bit. It might be easier, as Nicolo suggested,
to use in the simulations observations that are defined in power (watt). I added in the back-up slides (slides 9 and 10) the model in power as well. The correspondence between the two is simply ns=Rres/q*Ps*Ts.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><u><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">I have a request</span></u><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">:
since we are going to do all the simulations again, <b>I would like to ask that people compute the mutual information in their simulations</b>. It is not complicated to do, and requires only few lines to be added in the code. Attached is a short note that
describes how to compute mutual information.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Concerning the simulations at 1.22 Mbps, we have used with the colleagues from the French riviera observatory an APD to
receive a 1Mbps signal, that had the following parameters:<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l1 level1 lfo2"><![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">-<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Data sheet:<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Noise Equivalent Power : 0.12 pW/√Hz @ M = 10<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Rres (1550 nm) = 0.95 A/W<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Electrical filter: tchebychef 5<sup>th</sup> order @ 2MHz<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">RT = 47 kΩ,
<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">M = 30 : APD amplification gain that was chosen<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">G_Ampli = 10 (transimpedance gain)<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">T_opt = 0.9: optical transmission lens before APD<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Responsivity [Volt/Watt] from datasheet= Rres* RT* M* G_Ampli* T_opt=</span><span lang="EN-US">
</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">1.2E7<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l1 level1 lfo2"><![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">-<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Measurements<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Responsivity [Volt/Watt] measured =1E7<o:p></o:p></span></p>
<p class="MsoListParagraph" style="margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2">
<![if !supportLists]><span lang="EN-US" style="font-size:11.0pt;font-family:"Courier New";color:#1F497D;mso-fareast-language:EN-US"><span style="mso-list:Ignore">o<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Measured TIA noise spectral density = 0.045 pW/√Hz => 0. 45 pW*RT/ Responsivity = 2.1 E-16 A/√Hz<o:p></o:p></span></p>
<p class="MsoListParagraph"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoListParagraph"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Note1: the APD was thermo-cooled at -20°C<o:p></o:p></span></p>
<p class="MsoListParagraph"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Note2: with the same APD but an electric filter bandwidth of 16MHz the measured TIA noise spectral density was
0.2 pW/√Hz (closer to the datasheet)<o:p></o:p></span></p>
<p class="MsoListParagraph"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Kind Regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US">Geraldine<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">De :</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> SLS-OPT <sls-opt-bounces@mailman.ccsds.org>
<b>De la part de</b> Jon Hamkins via SLS-OPT<br>
<b>Envoyé :</b> mercredi 22 avril 2020 18:16<br>
<b>À :</b> Nicolo Mazzali (external) <Nicolo.Mazzali@esa.int><br>
<b>Cc :</b> SLS-OPT@mailman.ccsds.org<br>
<b>Objet :</b> Re: [SLS-OPT] [EXTERNAL] Re: O3K channel model<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p>Thanks, Nicolò. Yes, there is more than one way to do this, and we could have expressed things in terms of received watts. The approach we took was to simplify the mean and variance expressions and use as few parameters as possible. In this way, the mean
depends only on rho (the fade) and ns (the mean number of absorbed photons per signal slot). This makes it intuitively related to the photon counting model, and allows straightforward plotting using photons/bit, which is the common metric by which to measure
optical coding performance.<o:p></o:p></p>
<p>One can do things in watts, and translate to n_s, if you find that more intuitive. We didn't find that as convenient, however. For example, if we had expressed the model so that the mean signal was Ps in incident watts, and used that as the free parameter
in the simulations, the variance expressions would include an eta/ (h nu) term, which would require knowing the frequency and quantum efficiency. That's not a problem, but it is two more parameters than are needed in the formulation we suggested. We think
it may be more easier to run simulations with the normalized model, and then plug in these other parameters later if you want to plot vs. received watts for an APD with a specific responsivity (or quantum efficiency and frequency).<o:p></o:p></p>
<p>Anyway, that was our thinking.<o:p></o:p></p>
<p> ----Jon<o:p></o:p></p>
<div>
<p class="MsoNormal"><strong>Jon Hamkins</strong><br>
Lead Technologist<br>
33 | Communications, Tracking, and Radar Division<br>
<strong>O</strong> 818-354-4764 | <strong>M</strong> 626-658-6220 <br>
<br>
<strong>JPL</strong> | jpl.nasa.gov <o:p></o:p></p>
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<p class="MsoNormal">On 4/22/2020 12:28 AM, Nicolo Mazzali (external) wrote:<o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Arial",sans-serif">Dear Jon,
</span><br>
<br>
<span style="font-size:10.0pt;font-family:"Arial",sans-serif">Thanks for summarizing the channel model and the parameters' values.</span>
<br>
<span style="font-size:10.0pt;font-family:"Arial",sans-serif">In principle we are fine with them, but we would like to understand the motivation for having all the powers (i.e., the signal power and noise variances) normalized as dimensionless quantities, instead
of having them in watts - which is probably more intuitive, at least from an engineering point of view. Could you please confirm that this is indeed the case and elaborate a bit on your choice?</span>
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<span style="font-size:10.0pt;font-family:"Arial",sans-serif">Thanks a lot in advance!</span>
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<span style="font-size:10.0pt;font-family:"Arial",sans-serif">Kind regards, </span><o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt"><b><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:gray">Modis for ESA - European Space Agency</span></b><span style="font-family:"Tms Rmn",serif">
</span><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:#00A1E0"><br>
<br>
Nicolò Mazzali, PhD </span><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:gray"><br>
Communication Systems & Technologies Engineer</span><span style="font-family:"Tms Rmn",serif">
</span><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:gray"><br>
<br>
Telecommunications Section (TEC-ESC)</span><span style="font-family:"Tms Rmn",serif">
</span><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:gray"><br>
Radio Frequency Systems Division (TEC-ES)</span><o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt"><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:gray">Directorate of Technology, Engineering & Quality (D/TEC)<b><br>
<br>
<br>
ESTEC</b><br>
Keplerlaan 1, PO Box 299<br>
NL-2200 AG Noordwijk, The Netherlands</span><u><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:#0082BF"><br>
</span></u><a href="mailto:nicolo.mazzali@esa.int"><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:#0082BF">nicolo.mazzali@esa.int</span></a><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:gray"> |
</span><a href="http://www.esa.int/"><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:#8F8F8F">www.esa.int</span></a><span style="font-size:8.0pt;font-family:"Verdana",sans-serif;color:gray"><br>
T +31 71 56 53215</span><o:p></o:p></p>
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<span style="font-size:9.0pt;font-family:"Arial",sans-serif;color:#5F5F5F">From: </span><span style="font-size:9.0pt;font-family:"Arial",sans-serif">"Jon Hamkins via SLS-OPT"
<a href="mailto:sls-opt@mailman.ccsds.org"><sls-opt@mailman.ccsds.org></a></span>
<br>
<span style="font-size:9.0pt;font-family:"Arial",sans-serif;color:#5F5F5F">To: </span><span style="font-size:9.0pt;font-family:"Arial",sans-serif"><a href="mailto:SLS-OPT@mailman.ccsds.org">"SLS-OPT@mailman.ccsds.org"</a>
<a href="mailto:SLS-OPT@mailman.ccsds.org"><SLS-OPT@mailman.ccsds.org></a></span>
<br>
<span style="font-size:9.0pt;font-family:"Arial",sans-serif;color:#5F5F5F">Date: </span><span style="font-size:9.0pt;font-family:"Arial",sans-serif">15/04/2020 17:20</span>
<br>
<span style="font-size:9.0pt;font-family:"Arial",sans-serif;color:#5F5F5F">Subject: </span><span style="font-size:9.0pt;font-family:"Arial",sans-serif">[SLS-OPT] O3K channel model</span>
<br>
<span style="font-size:9.0pt;font-family:"Arial",sans-serif;color:#5F5F5F">Sent by: </span><span style="font-size:9.0pt;font-family:"Arial",sans-serif">"SLS-OPT"
<a href="mailto:sls-opt-bounces@mailman.ccsds.org"><sls-opt-bounces@mailman.ccsds.org></a></span>
<o:p></o:p></p>
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Attached is the O3K channel model we discussed yesterday. It also contains a suggestion for how to state the O3K coding performance. I welcome your comments. If we can agree to the model in the next week or so, each agency may be able to begin simulating
with it and discuss some initial results at the May teleconferences. <br>
A few notes: <o:p></o:p></p>
<ul type="disc">
<li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
I am suggesting we study 10 Gsps, 78.125 Msps, and 1.22 Mbps, since those include the highest and lowest data rates and one in the middle.
<o:p></o:p></li><li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
I don't have a good suggestion for the TIA noise density at 1.22 Msps. Dirk, would you be able to supply a number?
<o:p></o:p></li><li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
I have algebraically simplified the expressions for the means and variances. You can compare the model to the expressions Dariush presented on yesterday (p. 5), and check my algebra.
<o:p></o:p></li><li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
I have included the fading parameter as well. Just set rho=1 if you want no fading.<o:p></o:p></li></ul>
<p class="MsoNormal" style="margin-bottom:12.0pt"> ----Jon <br>
-- <b><br>
Jon Hamkins</b><br>
Lead Technologist<br>
33 | Communications, Tracking, and Radar Division<b><br>
O</b> 818-354-4764 | <b>M</b> 626-658-6220 <br>
<b><br>
JPL</b> | jpl.nasa.gov [attachment "2020-04-15-O3K-channel-model.pptx" deleted by Nicolo Mazzali/estec/ESA]
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