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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='color:#1F497D'>I am forwarding the message below to the CCSDS Optical Communications Working Group on behalf of Bryan Robinson.<o:p></o:p></span></p><div><p class=MsoNormal><span style='color:#1F497D'>-Lena<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Franklin Gothic Book",sans-serif;color:#1F497D'><img width=196 height=42 id="Picture_x0020_1" src="cid:image002.png@01D0A1EA.6C6BAEC0" alt="cid:image002.png@01CE3AB5.294A2660"></span><span style='font-size:9.0pt;font-family:"Franklin Gothic Book",sans-serif;color:#595959'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Franklin Gothic Book",sans-serif;color:#595959'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Franklin Gothic Book",sans-serif;color:#595959'>Lena Braatz<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Franklin Gothic Book",sans-serif;color:#595959'>Associate<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Franklin Gothic Book",sans-serif;color:#595959'>Office 434-973-4453<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Franklin Gothic Book",sans-serif;color:#595959'>braatz_lena@bah.com<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><a href="http://www.boozallen.com/"><span style='font-size:9.0pt;font-family:"Franklin Gothic Book",sans-serif'>www.boozallen.com</span></a></span><span style='font-size:9.0pt;font-family:"Franklin Gothic Book",sans-serif;color:#595959'><o:p></o:p></span></p></div><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Robinson, Bryan - 0667 - MITLL [mailto:brobinson@ll.mit.edu] <br><b>Sent:</b> Friday, June 05, 2015 8:20 AM<br><b>To:</b> sls-opt@mailman.ccsds.org<br><b>Cc:</b> Edwards, Bernard L. (GSFC-5600); Braatz, Lena [USA]<br><b>Subject:</b> [External] Optical Homodyne References<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>At the last CCSDS optical communications working group telecon, there was a request for references that describe the performance of the optical homodyne channel and its capacity. Here are some recommendations:<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Example of BER and SNR calculation for the optical homodyne channel:<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>[1] J. R. Barry and E. A. Lee, “Performance of Coherent Optical Receivers”, Proc. IEEE, vol. 78, no. 8, pp. 1369-1394, 1990.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Channel capacity for homodyne channel:<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The channel capacity for the AWGN channel was first derived b C. Shannon:<o:p></o:p></p><p class=MsoNormal>[2] C. E. Shannon, “A Mathematical Theory of Communication”, Bell Syst. Tech. J., vol 27, pp. 623-656, 1948.<o:p></o:p></p><p class=MsoNormal>The result is also commonly derived in modern information theory / communications texts, such as:<o:p></o:p></p><p class=MsoNormal>[3] T. M. Cover and J. A. Thomas, “Elements of Information Theory”, Wiley, 2006.<o:p></o:p></p><p class=MsoNormal>[4] J. G. Proakis and M. Salehi, “Digital Communications”, McGraw-Hill, 2008.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The formulas for optical channel capacity that we have presented to the CCSDS working group may be obtained by substituting the SNR for the optical homodyne channel, shown in [1], into the formula for channel capacity for the discrete-time AWGN channel shown in [2]-[4].<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Bryan S. Robinson<o:p></o:p></p><p class=MsoNormal>Assistant Group Leader<o:p></o:p></p><p class=MsoNormal>Optical Communications Technology<o:p></o:p></p><p class=MsoNormal>MIT Lincoln Laboratory<o:p></o:p></p><p class=MsoNormal>781-981-7675 (office)<o:p></o:p></p><p class=MsoNormal>781-981-4129 (fax)<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>