updated report

author Nils Forssén <nilfo359@student.liu.se>

Thu, 12 Dec 2024 01:06:31 +0000 (02:06 +0100)

committer Nils Forssén <nilfo359@student.liu.se>

Thu, 12 Dec 2024 01:06:31 +0000 (02:06 +0100)
author Nils Forssén <nilfo359@student.liu.se>
Thu, 12 Dec 2024 01:06:31 +0000 (02:06 +0100)
committer Nils Forssén <nilfo359@student.liu.se>
Thu, 12 Dec 2024 01:06:31 +0000 (02:06 +0100)
diff --git a/.vscode/ltex.dictionary.en-US.txt b/.vscode/ltex.dictionary.en-US.txt

new file mode 100644 (file)

index 0000000..06c9f2a
--- /dev/null
+++ b/.vscode/ltex.dictionary.en-US.txt
@@ -0,0 +1,4 @@
+AWGN
+QPSK
+hard-descision
+Forssén
diff --git a/.vscode/ltex.disabledRules.en-US.txt b/.vscode/ltex.disabledRules.en-US.txt

new file mode 100644 (file)

index 0000000..f734e20
--- /dev/null
+++ b/.vscode/ltex.disabledRules.en-US.txt
@@ -0,0 +1 @@
+ENGLISH_WORD_REPEAT_BEGINNING_RULE
diff --git a/.vscode/ltex.hiddenFalsePositives.en-US.txt b/.vscode/ltex.hiddenFalsePositives.en-US.txt

new file mode 100644 (file)

index 0000000..bdefe46
--- /dev/null
+++ b/.vscode/ltex.hiddenFalsePositives.en-US.txt
@@ -0,0 +1 @@
+{"rule":"MORFOLOGIK_RULE_EN_US","sentence":"^\\Qmystyle backgroundcolor=, commentstyle=, keywordstyle=, stringstyle=, basicstyle=, breakatwhitespace=false, breaklines=true, captionpos=b, keepspaces=true, showspaces=false, showstringspaces=false, showtabs=false, tabsize=2 style=mystyle\\E$"}
diff --git a/report/images/PAM8.png b/report/images/PAM8.png

new file mode 100644 (file)

index 0000000..cf2cfb8

Binary files /dev/null and b/report/images/PAM8.png differ
diff --git a/report/images/PAM8_error.png b/report/images/PAM8_error.png

new file mode 100644 (file)

index 0000000..abfcb5e

Binary files /dev/null and b/report/images/PAM8_error.png differ
diff --git a/report/images/PAM8_recv.png b/report/images/PAM8_recv.png

new file mode 100644 (file)

index 0000000..8c91d06

Binary files /dev/null and b/report/images/PAM8_recv.png differ
diff --git a/report/images/PSK8.png b/report/images/PSK8.png

new file mode 100644 (file)

index 0000000..488489a

Binary files /dev/null and b/report/images/PSK8.png differ
diff --git a/report/images/PSK8_error.png b/report/images/PSK8_error.png

new file mode 100644 (file)

index 0000000..32faf51

Binary files /dev/null and b/report/images/PSK8_error.png differ
diff --git a/report/images/PSK8_recv.png b/report/images/PSK8_recv.png

new file mode 100644 (file)

index 0000000..68b09d3

Binary files /dev/null and b/report/images/PSK8_recv.png differ
diff --git a/report/images/QAM16.png b/report/images/QAM16.png

new file mode 100644 (file)

index 0000000..5cfe663

Binary files /dev/null and b/report/images/QAM16.png differ
diff --git a/report/images/QAM16_error.png b/report/images/QAM16_error.png

new file mode 100644 (file)

index 0000000..2c2235e

Binary files /dev/null and b/report/images/QAM16_error.png differ
diff --git a/report/images/QAM16_recv.png b/report/images/QAM16_recv.png

new file mode 100644 (file)

index 0000000..a151525

Binary files /dev/null and b/report/images/QAM16_recv.png differ
diff --git a/report/images/QPSK.png b/report/images/QPSK.png

new file mode 100644 (file)

index 0000000..b8b5169

Binary files /dev/null and b/report/images/QPSK.png differ
diff --git a/report/images/QPSK_error.png b/report/images/QPSK_error.png

new file mode 100644 (file)

index 0000000..2e71c7c

Binary files /dev/null and b/report/images/QPSK_error.png differ
diff --git a/report/images/QPSK_hamming.png b/report/images/QPSK_hamming.png

new file mode 100644 (file)

index 0000000..67dd926

Binary files /dev/null and b/report/images/QPSK_hamming.png differ
diff --git a/report/images/QPSK_recv.png b/report/images/QPSK_recv.png

new file mode 100644 (file)

index 0000000..cb46895

Binary files /dev/null and b/report/images/QPSK_recv.png differ
diff --git a/report/main.aux b/report/main.aux

index d490c35e0aac6ff81dca8ddee3f265c044ef8c80..9865f8846e16aa30244b190de7a1cea85bb32d13 100644 (file)
--- a/report/main.aux
+++ b/report/main.aux
@@ -1,2 +1,54 @@
  \relax 
-\gdef \@abspage@last{2}
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\contentsline\oldcontentsline
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax 
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\@writefile{toc}{\contentsline {section}{\numberline {0.1}Laboratory Exercise 2}{1}{section.0.1}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {0.2}Laboratory Exercise 3}{1}{section.0.2}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {0.3}Laboratory Exercise 4}{1}{section.0.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {0.3.1}Student task 1: Generation of constellations}{1}{subsection.0.3.1}\protected@file@percent }
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces 8-PAM constellation}}{2}{figure.0.1}\protected@file@percent }
+\newlabel{fig:pam8}{{1}{2}{8-PAM constellation}{figure.0.1}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces QPSK constellation}}{2}{figure.0.2}\protected@file@percent }
+\newlabel{fig:qpsk}{{2}{2}{QPSK constellation}{figure.0.2}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces 8-PSK constellation}}{3}{figure.0.3}\protected@file@percent }
+\newlabel{fig:psk8}{{3}{3}{8-PSK constellation}{figure.0.3}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces 16-QAM constellation}}{3}{figure.0.4}\protected@file@percent }
+\newlabel{fig:qam16}{{4}{3}{16-QAM constellation}{figure.0.4}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Reception of 8-PAM modulated symbols through an AWGN channel.}}{4}{figure.0.5}\protected@file@percent }
+\newlabel{fig:pam8_recv}{{5}{4}{Reception of 8-PAM modulated symbols through an AWGN channel}{figure.0.5}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Reception of QPSK modulated symbols through an AWGN channel.}}{4}{figure.0.6}\protected@file@percent }
+\newlabel{fig:qpsk_recv}{{6}{4}{Reception of QPSK modulated symbols through an AWGN channel}{figure.0.6}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {0.3.2}Student task 2: Signal transmission through AWGN channel}{4}{subsection.0.3.2}\protected@file@percent }
+\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Reception of 8-PSK modulated symbols through an AWGN channel.}}{5}{figure.0.7}\protected@file@percent }
+\newlabel{fig:psk8_recv}{{7}{5}{Reception of 8-PSK modulated symbols through an AWGN channel}{figure.0.7}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Reception of 16-QAM modulated symbols through an AWGN channel.}}{5}{figure.0.8}\protected@file@percent }
+\newlabel{fig:qam16_recv}{{8}{5}{Reception of 16-QAM modulated symbols through an AWGN channel}{figure.0.8}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Symbol and bit error rate of 8-PAM modulated symbols through an AWGN channel for different SNR values.}}{6}{figure.0.9}\protected@file@percent }
+\newlabel{fig:pam8_error}{{9}{6}{Symbol and bit error rate of 8-PAM modulated symbols through an AWGN channel for different SNR values}{figure.0.9}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {0.3.3}Student task 3: Channel coding}{6}{subsection.0.3.3}\protected@file@percent }
+\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Symbol and bit error rate of QPSK modulated symbols through an AWGN channel for different SNR values.}}{7}{figure.0.10}\protected@file@percent }
+\newlabel{fig:qpsk_error}{{10}{7}{Symbol and bit error rate of QPSK modulated symbols through an AWGN channel for different SNR values}{figure.0.10}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Symbol and bit error rate of 8-PSK modulated symbols through an AWGN channel for different SNR values.}}{7}{figure.0.11}\protected@file@percent }
+\newlabel{fig:psk8_error}{{11}{7}{Symbol and bit error rate of 8-PSK modulated symbols through an AWGN channel for different SNR values}{figure.0.11}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Symbol and bit error rate of 16-QAM modulated symbols through an AWGN channel for different SNR values.}}{8}{figure.0.12}\protected@file@percent }
+\newlabel{fig:qam16_error}{{12}{8}{Symbol and bit error rate of 16-QAM modulated symbols through an AWGN channel for different SNR values}{figure.0.12}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {0.3.4}Report Questions}{8}{subsection.0.3.4}\protected@file@percent }
+\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Bit error rate of QPSK modulated symbols with and without Hamming code (7, 4) across different SNR values. }}{9}{figure.0.13}\protected@file@percent }
+\newlabel{fig:qpsk_hamming}{{13}{9}{Bit error rate of QPSK modulated symbols with and without Hamming code (7, 4) across different SNR values}{figure.0.13}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {.1}Code for Laboratory Exercise 4}{9}{section.Alph0.1}\protected@file@percent }
+\newlabel{app:code_lab4}{{.1}{9}{Code for Laboratory Exercise 4}{section.Alph0.1}{}}
+\gdef \@abspage@last{23}
diff --git a/report/main.fdb_latexmk b/report/main.fdb_latexmk

index 66f7b35bfd3d3d6f896e0c0805eb2c1dff44c7ae..ce88c42dae7374bb47c53795d0e3a578dd9488d7 100644 (file)
--- a/report/main.fdb_latexmk
+++ b/report/main.fdb_latexmk
@@ -1,8 +1,13 @@
  # Fdb version 3
-["pdflatex"] 1733785553 "/home/forssennils/TSKS35/report/main.tex" "main.pdf" "main" 1733785554
-  "/etc/texmf/web2c/texmf.cnf" 1705495666 475 c0e671620eb5563b2130f56340a5fde8 ""
-  "/home/forssennils/TSKS35/report/main.tex" 1733785553 150 1cbbd4a869f0404c60c43136e8864637 ""
+["pdflatex"] 1733965317 "/home/nils/kurser/TSKS35/report/main.tex" "main.pdf" "main" 1733965318
+  "/etc/texmf/web2c/texmf.cnf" 1718133671 475 c0e671620eb5563b2130f56340a5fde8 ""
+  "/home/nils/.texlive2021/texmf-var/fonts/pk/ljfour/jknappen/ec/tcrm1095.600pk" 1733953238 12644 f6a09bfc9317d07418ad465c0e240344 ""
+  "/home/nils/kurser/TSKS35/report/main.tex" 1733965317 27099 cea90a61dcbf70472bf973707bdfd655 ""
    "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 ""
+  "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/tcrm1095.tfm" 1136768653 1536 02c06700a42be0f5a28664c7273f82e7 ""
+  "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm" 1136768653 1328 c834bbb027764024c09d3d2bf908b5f0 ""
+  "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm" 1136768653 1324 c910af8c371558dc20f2d7822f66fe64 ""
+  "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi10.tfm" 1136768653 1528 abec98dbc43e172678c11b3b9031252a ""
    "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi12.tfm" 1136768653 1524 4414a8315f39513458b80dfc63bff03a ""
    "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi6.tfm" 1136768653 1512 f21f83efb36853c0b70002322c1ab3ad ""
    "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi8.tfm" 1136768653 1520 eccf95517727cb11801f4f1aee3a21b4 ""
@@ -11,22 +16,160 @@
    "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr17.tfm" 1136768653 1292 296a67155bdbfc32aa9c636f21e91433 ""
    "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr6.tfm" 1136768653 1300 b62933e007d01cfd073f79b963c01526 ""
    "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr8.tfm" 1136768653 1292 21c1c5bfeaebccffdb478fd231a0997d ""
+  "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr9.tfm" 1136768653 1292 6b21b9c2c7bebb38aa2273f7ca0fb3af ""
    "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy10.tfm" 1136768653 1124 6c73e740cf17375f03eec0ee63599741 ""
    "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm" 1136768653 1116 933a60c408fc0a863a92debe84b2d294 ""
    "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm" 1136768653 1120 8b7d695260f3cff42e636090a8002094 ""
+  "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmtt10.tfm" 1136768653 768 1321e9409b4137d6fb428ac9dc956269 ""
+  "/usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmtt9.tfm" 1136768653 764 c98a2af25c99b73a368cf7336e255190 ""
+  "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb" 1248133631 34811 78b52f49e893bcba91bd7581cdc144c0 ""
+  "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb" 1248133631 32080 340ef9bf63678554ee606688e7b5339d ""
    "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1248133631 35752 024fb6c41858982481f6968b5fc26508 ""
    "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb" 1248133631 32722 d7379af29a190c3f453aba36302ff5a9 ""
    "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr17.pfb" 1248133631 32362 179c33bbf43f19adbb3825bb4e36e57a ""
+  "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb" 1248133631 32726 0a1aea6fcd6468ee2cf64d891f5c43c8 ""
+  "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1248133631 32569 5e5ddc8df908dea60932f3c484a54c0d ""
+  "/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt9.pfb" 1248133631 29078 718ea4567ceff944262b0f5b0800e1d9 ""
+  "/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1461363279 71627 94eb9990bed73c364d7f53f960cc8c5b ""
+  "/usr/share/texlive/texmf-dist/tex/generic/atbegshi/atbegshi.sty" 1575674566 24708 5584a51a7101caf7e6bbf1fc27d8f7b1 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/bigintcalc/bigintcalc.sty" 1576625341 40635 c40361e206be584d448876bba8a64a3b ""
+  "/usr/share/texlive/texmf-dist/tex/generic/bitset/bitset.sty" 1576016050 33961 6b5c75130e435b2bfdb9f480a09a39f9 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/etexcmds/etexcmds.sty" 1576625273 7734 b98cbb34c81f667027c1e3ebdbfce34b ""
+  "/usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty" 1576625223 8371 9d55b8bd010bc717624922fb3477d92e ""
+  "/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty" 1583617216 6501 4011d89d9621e0b0901138815ba5ff29 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/infwarerr/infwarerr.sty" 1575499628 8356 7bbb2c2373aa810be568c29e333da8ed ""
+  "/usr/share/texlive/texmf-dist/tex/generic/intcalc/intcalc.sty" 1576625065 31769 002a487f55041f8e805cfbf6385ffd97 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/kvdefinekeys/kvdefinekeys.sty" 1576878844 5412 d5a2436094cd7be85769db90f29250a6 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/kvsetkeys/kvsetkeys.sty" 1576624944 13807 952b0226d4efca026f0e19dd266dcc22 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/ltxcmds/ltxcmds.sty" 1600895880 17859 4409f8f50cd365c68e684407e5350b1b ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pdfescape/pdfescape.sty" 1576015897 19007 15924f7228aca6c6d184b115f4baa231 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pdftexcmds/pdftexcmds.sty" 1593379760 20089 80423eac55aa175305d35b49e04fe23b ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex" 1601326656 992 855ff26741653ab54814101ca36e153c ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex" 1601326656 43820 1fef971b75380574ab35a0d37fd92608 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex" 1601326656 19324 f4e4c6403dd0f1605fd20ed22fa79dea ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex" 1601326656 6038 ccb406740cc3f03bbfb58ad504fe8c27 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex" 1601326656 6944 e12f8f7a7364ddf66f93ba30fb3a3742 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex" 1601326656 4883 42daaf41e27c3735286e23e48d2d7af9 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex" 1601326656 2544 8c06d2a7f0f469616ac9e13db6d2f842 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex" 1601326656 44195 5e390c414de027626ca5e2df888fa68d ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex" 1601326656 17311 2ef6b2e29e2fc6a2fc8d6d652176e257 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex" 1601326656 21302 788a79944eb22192a4929e46963a3067 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex" 1601326656 9690 01feb7cde25d4293ef36eef45123eb80 ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex" 1601326656 33335 dd1fa4814d4e51f18be97d88bf0da60c ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex" 1601326656 2965 4c2b1f4e0826925746439038172e5d6f ""
+  "/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex" 1601326656 5196 2cc249e0ee7e03da5f5f6589257b1e5b ""
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+  "/usr/share/texlive/texmf-dist/tex/latex/base/atveryend-ltx.sty" 1636758526 2462 754d6b31b2ab5a09bb72c348ace2ec75 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty" 1622581934 5157 f308c7c04889e16c588e78aa42599fae ""
    "/usr/share/texlive/texmf-dist/tex/latex/base/report.cls" 1636758526 23203 8fbc410e29d3fd675970d5f9698c9c11 ""
    "/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo" 1636758526 8464 74db94825c407b51399ca17d9bd38a3d ""
+  "/usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty" 1579991033 13886 d1306dcf79a944f6988e688c1785f9ce ""
+  "/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg" 1459978653 1213 620bba36b25224fa9b7e1ccb4ecb76fd ""
+  "/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg" 1465944070 1224 978390e9c2234eab29404bc21b268d1e ""
+  "/usr/share/texlive/texmf-dist/tex/latex/graphics-def/pdftex.def" 1601931164 19103 48d29b6e2a64cb717117ef65f107b404 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty" 1622581934 18399 7e40f80366dffb22c0e7b70517db5cb4 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty" 1636758526 7996 a8fb260d598dcaf305a7ae7b9c3e3229 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty" 1622581934 2671 4de6781a30211fe0ea4c672e4a2a8166 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty" 1636758526 4009 187ea2dc3194cd5a76cd99a8d7a6c4d0 ""
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+  "/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def" 1623096352 49890 0bb76a5b745d92e86aed6f3f93e334f0 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref-langpatches.def" 1623096352 1777 940b1aa83773bc035eb882e8d6842769 ""
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+  "/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty" 1612734870 13242 133e617c5eebffdd05e421624022b267 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def" 1623096352 14132 c9404e8e78123ef0d1007c34d1d6da51 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/hyperref/puenc.def" 1623096352 117004 86586f287ddfad919a0a4bd68934277a ""
+  "/usr/share/texlive/texmf-dist/tex/latex/kvoptions/kvoptions.sty" 1602274869 22521 d2fceb764a442a2001d257ef11db7618 ""
    "/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def" 1642022539 29921 f0f4f870357ebfb8fe58ed9ed4ee9b92 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg" 1279039959 678 4792914a8f45be57bb98413425e4c7af ""
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+  "/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty" 1601326656 989 c49c8ae06d96f8b15869da7428047b1e ""
+  "/usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty" 1601326656 339 c2e180022e3afdb99c7d0ea5ce469b7d ""
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+  "/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty" 1601326656 325 f9f16d12354225b7dd52a3321f085955 ""
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+  "/usr/share/texlive/texmf-dist/tex/latex/todonotes/todonotes.sty" 1622837691 20709 ec0ab3eaf79cba9afda8dd45da4e5c5b ""
+  "/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty" 1622581934 10214 00ce62e730d0cfe22b35e8f1c84949c7 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/url/url.sty" 1388531844 12796 8edb7d69a20b857904dd0ea757c14ec9 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty" 1635798903 56029 3f7889dab51d620aa43177c391b7b190 ""
+  "/usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty" 1605910342 4902 efb3d66683a2da2a232f71e3a571a899 ""
    "/usr/share/texlive/texmf-dist/web2c/texmf.cnf" 1644012257 39432 7155514e09a3d69036fac785183a21c2 ""
    "/usr/share/texmf/web2c/texmf.cnf" 1644012257 39432 7155514e09a3d69036fac785183a21c2 ""
-  "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1705498991 4379155 98693266ff65f58d9f98aff394de12d2 ""
-  "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1725191074 2798398 91599ecc289bf793f3583bd0ad1c8d6a ""
-  "main.aux" 1733785554 32 044b7f8fc9779af7531264e0c5c84b6d "pdflatex"
-  "main.tex" 1733785553 150 1cbbd4a869f0404c60c43136e8864637 ""
+  "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1718463222 4039853 4b50262017b063640542615eb9b76378 ""
+  "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1718463227 2030218 2488935e032bf0e163a8600bd7a6d40e ""
+  "images/PAM8.png" 1733951856 8892 42ae7ce607da7929b0a84f9d2a480cc5 ""
+  "images/PAM8_error.png" 1733958212 25117 eb991370b3c2360f877c507547e97cd0 ""
+  "images/PAM8_recv.png" 1733958197 12259 01a10ef224744882e9164497197360f9 ""
+  "images/PSK8.png" 1733951884 30320 9b4534fddf2449ab6a33fef9a5287285 ""
+  "images/PSK8_error.png" 1733952049 24307 455b81d89b55dc1c04cef3a5a7d91a43 ""
+  "images/PSK8_recv.png" 1733952035 34902 01b5e91324c6edd52e59a0edec4ef038 ""
+  "images/QAM16.png" 1733964975 13350 bc547e045417906ff59ea40642f2bff9 ""
+  "images/QAM16_error.png" 1733952074 26823 db8b91cff2d7761e8dca174451384ddc ""
+  "images/QAM16_recv.png" 1733952062 26407 a4c284f83ac0dc3d956477585888a468 ""
+  "images/QPSK.png" 1733951868 18783 d5b85652e43e91f1126201c8a1ffd3f4 ""
+  "images/QPSK_error.png" 1733952020 23473 3f431725e4102b382eb06a9205d0f440 ""
+  "images/QPSK_hamming.png" 1733963822 37846 8faca096f539d658c9a532496ab98348 ""
+  "images/QPSK_recv.png" 1733952001 23547 430c6871cfaeb5ccadb4f39f665b3fc0 ""
+  "main.aux" 1733965318 5634 1e7702ec1b36d8e6683fb60d549e50a6 "pdflatex"
+  "main.out" 1733965318 1704 776428b4b8c14b8a493168b6bf03206d "pdflatex"
+  "main.tex" 1733965317 27099 cea90a61dcbf70472bf973707bdfd655 ""
    (generated)
    "main.aux"
    "main.log"
+  "main.out"
    "main.pdf"
diff --git a/report/main.fls b/report/main.fls

index 4bd9bd78461c3a53b1ead6062d61f73375ea25fd..82650bc2ef80e2e277bee3d6c73ac4759a99aa2e 100644 (file)
--- a/report/main.fls
+++ b/report/main.fls
@@ -1,9 +1,9 @@
-PWD /home/forssennils/TSKS35/report
+PWD /home/nils/kurser/TSKS35/report
  INPUT /etc/texmf/web2c/texmf.cnf
  INPUT /usr/share/texmf/web2c/texmf.cnf
  INPUT /usr/share/texlive/texmf-dist/web2c/texmf.cnf
  INPUT /var/lib/texmf/web2c/pdftex/pdflatex.fmt
-INPUT /home/forssennils/TSKS35/report/main.tex
+INPUT /home/nils/kurser/TSKS35/report/main.tex
  OUTPUT main.log
  INPUT /usr/share/texlive/texmf-dist/tex/latex/base/report.cls
  INPUT /usr/share/texlive/texmf-dist/tex/latex/base/report.cls
@@ -22,6 +22,624 @@ INPUT /usr/share/texlive/texmf-dist/tex/latex/base/size11.clo
  INPUT /usr/share/texlive/texmf-dist/tex/latex/base/size11.clo
  INPUT /usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map
  INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr10.tfm
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty
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+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty
+INPUT /usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty
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--- a/report/main.tex
+++ b/report/main.tex
@@ -1,13 +1,780 @@
  \documentclass[11pt]{report}
  
-\title{This is my title}
+\usepackage{graphicx}
+\usepackage{listings}
+\usepackage{hyperref}
+\usepackage{xcolor}
+\usepackage{todonotes}
+
+\title{TSKS35: Information and Communications Engineering Lab Report}
  \author{Nils Forssén}
  \date{\today}
+\setlength{\parindent}{0cm}
+\setlength{\parskip}{0.3cm}
+
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codegray}{rgb}{0.5,0.5,0.5}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
+
+\lstdefinestyle{mystyle}{
+    backgroundcolor=\color{backcolour},   
+    commentstyle=\color{codegreen},
+    keywordstyle=\color{magenta},
+    stringstyle=\color{codepurple},
+    basicstyle=\ttfamily\footnotesize,
+    breakatwhitespace=false,         
+    breaklines=true,                 
+    captionpos=b,                    
+    keepspaces=true,                                 
+    showspaces=false,                
+    showstringspaces=false,
+    showtabs=false,                  
+    tabsize=2
+}
+\lstset{style=mystyle}
+
  
  \begin{document} 
  \maketitle
+\section{Laboratory Exercise 2}
+\section{Laboratory Exercise 3}
+\section{Laboratory Exercise 4}
+
+Exercise 4 is made up of 3 parts, student tasks, covering the following topics:
+\begin{itemize}
+    \item Generation of different constellations representing symbols to be used by a transmitter. 
+    \item Assigning gray codes to the symbols.
+    \item Transmission and reception of the symbols through an AWGN (Additive White Gaussian Noise) channel.
+    \item Comparison of the symbol/bit error rates of the different constellations.
+    \item Transmission and reception of encoded data using the Hamming code (7, 4) and comparison
+        of the symbol/bit error rates of the different constellations.
+\end{itemize}
+
+The code used to solve the tasks and generate all figures is included in the appendix\nobreakspace\ref{app:code_lab4}
+
+\subsection{Student task 1: Generation of constellations}
+
+The first task was to generate constellations for 8-PAM (Pulse-Amplitude Modulation), QPSK
+(Quadrature Phase Shift Keying), 8-PSK (Phase Shift Keying) and 16-QAM
+(Quadrature Amplitude Modulation). Gray encoding was also to be applied to
+the constellation.
+
+The generated constellations with gray codes are shown in figures~\ref{fig:pam8},~\ref{fig:qpsk},~\ref{fig:psk8} and~\ref{fig:qam16}.
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/PAM8.png}
+    \caption{8-PAM constellation}\label{fig:pam8}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/QPSK.png}
+    \caption{QPSK constellation}\label{fig:qpsk}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/PSK8.png}
+    \caption{8-PSK constellation}\label{fig:psk8}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/QAM16.png}
+    \caption{16-QAM constellation}\label{fig:qam16}
+\end{figure}
+
+\subsection{Student task 2: Signal transmission through AWGN channel}
+
+The second task was to generate $10^6$ randomized symbols using the constellations from 
+student task 1 and transmit them through an AWGN channel. The received symbols were then
+to be plotted and compared using the minimum distance method to the original symbols in order to determine the symbol and bit error rate.
+The error rate for the different modulations was then to be plotted for different values of SNR (Signal to Noise Ratio).
+
+The results for the transmission and reception of the symbols through the AWGN channel are shown in figures~\ref{fig:pam8_recv},~\ref{fig:qpsk_recv},~\ref{fig:psk8_recv} and~\ref{fig:qam16_recv}.
+Make note of the different values of SNR used in the plots.
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/PAM8_recv.png}
+    \caption{Reception of 8-PAM modulated symbols through an AWGN channel.}\label{fig:pam8_recv}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/QPSK_recv.png}
+    \caption{Reception of QPSK modulated symbols through an AWGN channel.}\label{fig:qpsk_recv}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/PSK8_recv.png}
+    \caption{Reception of 8-PSK modulated symbols through an AWGN channel.}\label{fig:psk8_recv}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/QAM16_recv.png}
+    \caption{Reception of 16-QAM modulated symbols through an AWGN channel.}\label{fig:qam16_recv}
+\end{figure}
+
+The results for the symbol and bit error rates for the different constellations are shown
+in figures~\ref{fig:pam8_error},~\ref{fig:qpsk_error},~\ref{fig:psk8_error} and~\ref{fig:qam16_error}.
+The SNR was varied from -20 to 20 dB in steps of 2 dB.
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/PAM8_error.png}
+    \caption{Symbol and bit error rate of 8-PAM modulated symbols through an AWGN channel for different SNR values.}\label{fig:pam8_error}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/QPSK_error.png}
+    \caption{Symbol and bit error rate of QPSK modulated symbols through an AWGN channel for different SNR values.}\label{fig:qpsk_error}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/PSK8_error.png}
+    \caption{Symbol and bit error rate of 8-PSK modulated symbols through an AWGN channel for different SNR values.}\label{fig:psk8_error}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.6\textwidth]{images/QAM16_error.png}
+    \caption{Symbol and bit error rate of 16-QAM modulated symbols through an AWGN channel for different SNR values.}\label{fig:qam16_error}
+\end{figure}
+
+\subsection{Student task 3: Channel coding}
+
+The thirds task was to generate $4 * 10^6$ randomized information bits, encode them using
+the Hamming code (7, 4) and transmit them using QPSK or 4-QAM modulation through an AWGN channel.
+The received symbols were then to be decoded back into information bits using the hard-descision method.
+The bit error rate for the Hamming-encoded transmission was then to be compared the bit error rate of
+a transmission of the same information bits without any channel coding.
+
+The QPSK modulation technique was used to compare the coded transmission against the raw data transmission
+and the result is shown in figure~\ref{fig:qpsk_hamming}. This time the SNR was varied from -20 to 10 dB in steps
+of 2 dB and the plot displays a logarithmic scale for the y-axis to better show the difference between the two transmissions.
+
+\begin{figure}
+    \centering
+    \includegraphics[width=0.8\textwidth]{images/QPSK_hamming.png}
+    \caption{Bit error rate of QPSK modulated symbols with and without Hamming code (7, 4) across different SNR values. }\label{fig:qpsk_hamming}
+\end{figure}
+
+\subsection{Report Questions}
+
+Answers for the report-questions of Laboratory Exercise 4.  
+
+\begin{itemize}
+    \item \textbf{What are the difference between one- and two-dimensional constellations?
+        What is the difference between amplitude and phase modulations?
+        Observe and describe the constellations.}
+
+        This is my answer
+    \item \textbf{What is the purpose of Gray encoding? What is the difference between symbol 
+        error rate and bit error rate after applying Gray coding?}
+
+        This is my answer
+
+    \item \textbf{Comment on the difference on the symbol error rate for different modulation
+         schemes, what are the advantages and disadvantages of those?}
+
+         This is my answer
+
+    \item \textbf{What is the purpose of channel coding?}
  
+        This is my answer
+\end{itemize}
  
+\appendix
+\section{Code for Laboratory Exercise 4}\label{app:code_lab4}
+\begin{lstlisting}[language=Python]
+    # %% 
+    import numpy as np
+    import matplotlib.pyplot as plt
+    import scipy as stats
+    from scipy.fftpack import fft, rfft, irfft, fftfreq, rfftfreq
+    import scipy.signal
+    from scipy.stats import norm, expon
+    import math
+    
+    def diff_letters(a,b):
+        return sum ( a[i] != b[i] for i in range(len(a)) )
+    
+    # %%
+    # Create constellations
+    
+    M = 8
+    first = (2 - 1 - M)
+    last = (16 - 1 - M)
+    PAM8 = np.linspace(first, last, 8)
+    
+    M = 4
+    QPSK = [[math.cos(2* math.pi * m / M), math.sin(2 * math.pi * m / M)] for m in range(M)]
+    
+    M = 8
+    PSK8 = [[math.cos(2 * math.pi * m / M), math.sin(2 * math.pi * m / M)] for m in range(M)]
+    
+    M = 4
+    first = (-3)
+    last = (3)
+    PAM4 = np.linspace(first, last, 4)
+    QAM16 = []
+    for i in PAM4:
+        for j in PAM4:
+            QAM16.append([i, j])
+    
+    # %%
+    # Assign gray codes: 
+    
+    g_PAM8 = {format(k, '03b'): i for k, i in zip([0, 1, 3, 2, 6, 7, 5, 4], PAM8)}
+    
+    g_QPSK = {format(k, '02b'): i for k, i in zip([0,1,3,2], QPSK)}
+    
+    g_PSK8 = {format(k, '03b'): i for k, i in zip([0, 1, 3, 2, 6, 7, 5, 4], PSK8)}
+    
+    g_QAM16 = {format(k, '04b'): i for k, i in zip([0, 1, 3, 2, 4, 5, 7, 6, 12, 13, 15, 14, 8, 9, 11, 10], QAM16)}
+    
+    # %%
+    # Plot constellations
+    
+    # PAM-8
+    plt.figure(figsize=(4, 1))
+    plt.title("PAM-8 modulation, gray coding")
+    plt.plot(PAM8, [0]*8, 'o')
+    plt.yticks([])
+    plt.xticks(PAM8)
+    plt.grid(True)
+    for (k, s) in g_PAM8.items():
+        plt.text(s, 0, k)
+    
+    # QPSK
+    x = [x for x, y in QPSK]
+    y = [y for x, y in QPSK]
+    
+    circle_x = np.linspace(0, 2*np.pi, 100)
+    
+    plt.figure(figsize=(4, 4))
+    plt.title("QPSK modulation, gray coding")
+    plt.plot(np.cos(circle_x), np.sin(circle_x), color="orange")
+    plt.plot(x,y,'o', color="blue")
+    plt.xticks(x)
+    plt.yticks(y)
+    plt.grid(True)
+    for (k, s) in g_QPSK.items():
+        plt.text(*s, k)
+    
+    # PSK8
+    x = [x for x, y in PSK8]
+    y = [y for x, y in PSK8]
+    
+    plt.figure(figsize=(4, 4))
+    plt.title("PSK-8 modulation, gray coding")
+    plt.plot(np.cos(circle_x), np.sin(circle_x), color="orange")
+    plt.plot(x,y,'o', color="blue")
+    plt.xticks(x, rotation=45)
+    plt.yticks(y)
+    plt.grid(True)
+    for (k, s) in g_PSK8.items():
+        plt.text(*s, k)
+    
+    # QAM16
+    x = [x for x, y in QAM16]
+    y = [y for x, y in QAM16]
+    
+    plt.figure(figsize=(4, 4))
+    plt.title("QAM16")
+    plt.plot(x,y,'o')
+    plt.xticks(x)
+    plt.yticks(y)
+    plt.grid(True)
+    for (k, s) in g_QAM16.items():
+        plt.text(*s, k)
+    
+    # %%
+    # Transmission through AWGN channel
+    
+    num_symbols = 10**6
+    SNR_list = np.linspace(-20, 20, 21)
+    
+    # %%
+    # PAM8 transmission
+    
+    symbol_error_rate = []
+    bit_error_rate = []
+    
+    symbols = np.random.randint(0, len(PAM8), size=(num_symbols))
+    
+    PAM8_symbols = np.zeros(num_symbols, dtype=int)
+    for i, s in enumerate(symbols):
+        PAM8_symbols[i] = PAM8[s]
+    
+    for SNR_dB in SNR_list:
+    
+        SNR_linear = 10**(SNR_dB / 10)
+    
+        signal_power = np.mean(np.abs(PAM8_symbols)**2)
+        noise_power = signal_power / SNR_linear
+    
+        noise = noise_power * np.random.normal(0, 1, len(PAM8_symbols))
+        rx_signal = PAM8_symbols + noise
+    
+        distances = np.zeros(len(PAM8), dtype=float)
+        detected_symbols = np.zeros(num_symbols, dtype=int)
+        for i, r in enumerate(rx_signal):
+            for j, s in enumerate(PAM8):
+                distances[j] = np.linalg.norm(r - s)
+                
+            detected_symbols[i] = PAM8[np.argmin(distances)]
+            
+        errors = 0
+        bit_errors = 0
+        for i in range(num_symbols):
+            if PAM8_symbols[i] != detected_symbols[i]:
+                errors += 1
+                code = ""
+                expected_code = ""
+                for k, v in g_PAM8.items():
+                    if v == PAM8_symbols[i]:
+                        expected_code = k
+                    elif v == detected_symbols[i]:
+                        code = k
+                    
+                    if code != "" and expected_code != "":
+                        break
+                        
+                bit_errors += diff_letters(code, expected_code)
+            
+        SER = errors / num_symbols
+        
+        BER = bit_errors / num_symbols
+    
+        # Make the plot for specific SNR_dB
+        if SNR_dB == 20:
+            plt.figure(figsize=(4, 1))
+            plt.title("Recieved symbols, PAM-8 modulation (SNR_dB = 20)")
+            plt.plot(rx_signal, np.zeros(num_symbols), 'o', color="red")
+            plt.plot(PAM8, [0]*len(PAM8), 'o', color="blue")
+            plt.yticks([])
+            plt.xticks(PAM8)
+            plt.grid(True)
+            for (k, s) in g_PAM8.items():
+                plt.text(s, 0, k)
+    
+                
+        symbol_error_rate.append(SER)
+        bit_error_rate.append(BER)
+    
+    # Final curve plot
+    plt.figure(figsize=(4, 4))
+    plt.title("PAM-8 modulation error rate")
+    plt.plot(SNR_list, symbol_error_rate, 'o-', color="blue")
+    plt.plot(SNR_list, bit_error_rate, 'o-', color="red")
+    plt.xlabel("SNR (dB)")
+    plt.ylabel("Error rate")
+    plt.legend(["Symbol error rate", "Bit error rate"])
+    
+    # %%
+    # QPSK transmission
+    
+    symbol_error_rate = []
+    bit_error_rate = []
+    
+    symbols = np.random.randint(0, len(QPSK), size=(num_symbols))
+    
+    QPSK_symbols = np.zeros((num_symbols, 2), dtype=float)
+    for i, s in enumerate(symbols):
+        QPSK_symbols[i] = QPSK[s]
+    
+    for SNR_dB in SNR_list:
+    
+        SNR_linear = 10**(SNR_dB / 10)
+    
+        signal_power = np.mean(np.abs(QPSK_symbols)**2)
+        noise_power = signal_power / SNR_linear
+    
+        noise = noise_power * np.random.normal(0, 1, size=(num_symbols, 2))
+        rx_signal = QPSK_symbols + noise
+    
+        distances = np.zeros(len(QPSK), dtype=float)
+        detected_symbols = np.zeros((num_symbols, 2), dtype=float)
+        for i, r in enumerate(rx_signal):
+            for j, s in enumerate(QPSK):
+                distances[j] = np.linalg.norm(r - s)
+                
+            detected_symbols[i] = QPSK[np.argmin(distances)]
+        
+        errors = 0
+        bit_errors = 0
+        for i in range(num_symbols):
+            if QPSK_symbols[i][0] != detected_symbols[i][0] or QPSK_symbols[i][1] != detected_symbols[i][1]:
+                errors += 1
+                code = ""
+                expected_code = ""
+                for k, v in g_QPSK.items():
+                    if v[0] == QPSK_symbols[i][0] and v[1] == QPSK_symbols[i][1]:
+                        expected_code = k
+                    elif v[0] == detected_symbols[i][0] and v[1] == detected_symbols[i][1]:
+                        code = k
+                    
+                    if code != "" and expected_code != "":
+                        break
+                        
+                bit_errors += diff_letters(code, expected_code)
+            
+        SER = errors / num_symbols
+        
+        BER = bit_errors / num_symbols
+        
+        # Make the plot for specific SNR_dB
+        if SNR_dB == 10:
+            r_x = [x for x, y in rx_signal]
+            r_y = [y for x, y in rx_signal]
+    
+            x = [x for x, y in QPSK]
+            y = [y for x, y in QPSK]
+    
+            plt.figure(figsize=(4, 4))
+            plt.title("Recieved symbols, QPSK modulation (SNR_dB = 10)")
+            plt.plot(np.cos(circle_x), np.sin(circle_x), color="orange")
+            plt.plot(r_x, r_y, 'o', color="red")
+            plt.plot(x,y,'o', color="blue")
+            plt.xticks(x, rotation=45)
+            plt.yticks(y)
+            plt.grid(True)
+            for (k, s) in g_QPSK.items():
+                plt.text(*s, k)
+            
+        symbol_error_rate.append(SER)
+        bit_error_rate.append(BER)
+    
+    # Final curve plot
+    plt.figure(figsize=(4, 4))
+    plt.title("QPSK modulation error rate")
+    plt.plot(SNR_list, symbol_error_rate, 'o-', color="blue")
+    plt.plot(SNR_list, bit_error_rate, 'o-', color="red")
+    plt.legend(["Symbol error rate", "Bit error rate"])
+    plt.xlabel("SNR (dB)")
+    plt.ylabel("Error rate")
+    
+    # %%
+    # PSK8 transmission
+    
+    symbol_error_rate = []
+    bit_error_rate = []
+    
+    symbols = np.random.randint(0, len(PSK8), size=(num_symbols))
+    
+    PSK8_symbols = np.zeros((num_symbols, 2), dtype=float)
+    for i, s in enumerate(symbols):
+        PSK8_symbols[i] = PSK8[s]
+    
+    for SNR_dB in SNR_list:
+    
+        SNR_linear = 10**(SNR_dB / 10)
+    
+        signal_power = np.mean(np.abs(PSK8_symbols)**2)
+        noise_power = signal_power / SNR_linear
+    
+        noise = noise_power * np.random.normal(0, 1, size=(num_symbols, 2))
+        rx_signal = PSK8_symbols + noise
+    
+        distances = np.zeros(len(PSK8), dtype=float)
+        detected_symbols = np.zeros((num_symbols, 2), dtype=float)
+        for i, r in enumerate(rx_signal):
+            for j, s in enumerate(PSK8):
+                distances[j] = np.linalg.norm(r - s)
+                
+            detected_symbols[i] = PSK8[np.argmin(distances)]
+        
+        errors = 0
+        bit_errors = 0
+        for i in range(num_symbols):
+            if PSK8_symbols[i][0] != detected_symbols[i][0] or PSK8_symbols[i][1] != detected_symbols[i][1]:
+                errors += 1
+                code = ""
+                expected_code = ""
+                for k, v in g_PSK8.items():
+                    if v[0] == PSK8_symbols[i][0] and v[1] == PSK8_symbols[i][1]:
+                        expected_code = k
+                    elif v[0] == detected_symbols[i][0] and v[1] == detected_symbols[i][1]:
+                        code = k
+                    
+                    if code != "" and expected_code != "":
+                        break
+                        
+                bit_errors += diff_letters(code, expected_code)
+            
+        SER = errors / num_symbols
+        
+        BER = bit_errors / num_symbols
+        
+        # Make the plot for specific SNR_dB
+        if SNR_dB == 10:
+            r_x = [x for x, y in rx_signal]
+            r_y = [y for x, y in rx_signal]
+    
+            x = [x for x, y in PSK8]
+            y = [y for x, y in PSK8]
+    
+            plt.figure(figsize=(4, 4))
+            plt.title("Recieved symbols, PSK-8 modulation (SNR_dB = 10)")
+            plt.plot(np.cos(circle_x), np.sin(circle_x), color="orange")
+            plt.plot(r_x, r_y, 'o', color="red")
+            plt.plot(x,y,'o', color="blue")
+            plt.xticks(x, rotation=45)
+            plt.yticks(y)
+            plt.grid(True)
+            for (k, s) in g_PSK8.items():
+                plt.text(*s, k)
+            
+        symbol_error_rate.append(SER)
+        bit_error_rate.append(BER)
+    
+    # Final curve plot
+    plt.figure(figsize=(4, 4))
+    plt.title("PSK-8 modulation error rate")
+    plt.plot(SNR_list, symbol_error_rate, 'o-', color="blue")
+    plt.plot(SNR_list, bit_error_rate, 'o-', color="red")
+    plt.legend(["Symbol error rate", "Bit error rate"])
+    plt.xlabel("SNR (dB)")
+    plt.ylabel("Error rate")
+    
+    # %%
+    # QAM16 transmission
+    symbol_error_rate = []
+    bit_error_rate = []
+    
+    symbols = np.random.randint(0, len(QAM16), size=(num_symbols))
+    
+    QAM16_symbols = np.zeros((num_symbols, 2), dtype=float)
+    for i, s in enumerate(symbols):
+        QAM16_symbols[i] = QAM16[s]
+    
+    for SNR_dB in SNR_list:
+    
+        SNR_linear = 10**(SNR_dB / 10)
+    
+        signal_power = np.mean(np.abs(QAM16_symbols)**2)
+        noise_power = signal_power / SNR_linear
+    
+        noise = noise_power * np.random.normal(0, 1, size=(num_symbols, 2))
+        rx_signal = QAM16_symbols + noise
+    
+        distances = np.zeros(len(QAM16), dtype=float)
+        detected_symbols = np.zeros((num_symbols, 2), dtype=float)
+        for i, r in enumerate(rx_signal):
+            for j, s in enumerate(QAM16):
+                distances[j] = np.linalg.norm(r - s)
+                
+            detected_symbols[i] = QAM16[np.argmin(distances)]
+        
+        errors = 0
+        bit_errors = 0
+        for i in range(num_symbols):
+            if QAM16_symbols[i][0] != detected_symbols[i][0] or QAM16_symbols[i][1] != detected_symbols[i][1]:
+                errors += 1
+                code = ""
+                expected_code = ""
+                for k, v in g_QAM16.items():
+                    if v[0] == QAM16_symbols[i][0] and v[1] == QAM16_symbols[i][1]:
+                        expected_code = k
+                    elif v[0] == detected_symbols[i][0] and v[1] == detected_symbols[i][1]:
+                        code = k
+                    
+                    if code != "" and expected_code != "":
+                        break
+                        
+                bit_errors += diff_letters(code, expected_code)
+            
+        SER = errors / num_symbols
+        
+        BER = bit_errors / num_symbols
+        
+        # print("errors: ", errors)
+        # print("QAM16 Symbol error rate (SER): ", SER)
+        
+        # Make the plot for specific SNR_dB
+        if SNR_dB == 20:
+            r_x = [x for x, y in rx_signal]
+            r_y = [y for x, y in rx_signal]
+    
+            x = [x for x, y in QAM16]
+            y = [y for x, y in QAM16]
+    
+            plt.figure(figsize=(4, 4))
+            plt.title("Recieved symbols, QAM-16 modulation (SNR_dB = 20)")
+            plt.plot(r_x, r_y, 'o', color="red")
+            plt.plot(x,y,'o', color="blue")
+            plt.xticks(x)
+            plt.yticks(y)
+            plt.grid(True)
+            for (k, s) in g_QAM16.items():
+                plt.text(*s, k)
+            
+        symbol_error_rate.append(SER)
+        bit_error_rate.append(BER)
+    
+    # Final curve plot
+    plt.figure(figsize=(4, 4))
+    plt.title("QAM-16 modulation error rate")
+    plt.plot(SNR_list, symbol_error_rate, 'o-', color="blue")
+    plt.plot(SNR_list, bit_error_rate, 'o-', color="red")
+    plt.legend(["Symbol error rate", "Bit error rate"])
+    plt.xlabel("SNR (dB)")
+    plt.ylabel("Error rate")
+    
+    # %%
+    # Hamming code
+    
+    def hamming_encode(data):
+        if len(data) % 4 != 0:
+            raise ValueError("input data multiple of 4")
+    
+        G = [[1, 0, 0, 1, 0, 1, 1],
+             [0, 1, 0, 1, 0, 1, 0],
+             [0, 0, 1, 1, 0, 0, 1],
+             [0, 0, 0, 0, 1, 1, 1]]
+        
+        encoded_data = []
+        for k in range(0, len(data), 4):
+            block = data[k:k+4]
+            for i in range(7):
+                sum = 0
+                for j in range(4):
+                    sum += block[j] * G[j][i]
+                encoded_data.append(sum  % 2)
+            
+        return encoded_data
+    
+    def hamming_decode(recieved_data):
+        if len(recieved_data) % 7 != 0:
+            raise ValueError("Recieved data length mult of 7")
+        
+        H = [[1, 0, 1, 0, 1, 0, 1],
+             [1, 1, 0, 0, 1, 1, 0],
+             [1, 1, 1, 1, 0, 0, 0]]
+        
+        decoded_data = []
+        for k in range(0, len(recieved_data), 7):
+            block = recieved_data[k:k+7]
+            syndrome= []
+            for i in range(3):
+                syndrome_sum = 0
+                for j in range(7):
+                    syndrome_sum += block[j] * H[i][j]
+                syndrome.append(syndrome_sum % 2)
+            error_pos = sum([2 ** i for i, bit in enumerate(syndrome) if bit])
+            if error_pos > 0:
+                block[7-error_pos] ^= 1
+            decoded_data.extend([block[0], block[1], block[2], block[4]])
+        return decoded_data
+    
+    num_data_bits_by_4 = 10**6
+    
+    data = np.zeros(4 * num_data_bits_by_4)
+    for i in range(4 * num_data_bits_by_4):
+        data[i] = np.random.randint(0, 2)
+    
+    encoded = np.array(hamming_encode(data))
+    
+    ber_encoded = []
+    ber_plain = []
+    
+    QPSK_symbols_encoded = np.array([g_QPSK[str(int(block[0])) + str(int(block[1]))] for block in encoded.reshape(int(len(encoded) / 2), 2)])
+    QPSK_symbols_plain = np.array([g_QPSK[str(int(block[0])) + str(int(block[1]))] for block in data.reshape(int(len(data) / 2), 2)])
+    
+    num_symbols_encoded = len(QPSK_symbols_encoded)
+    num_symbols_plain = len(QPSK_symbols_plain)
+    
+    SNR_list = np.linspace(-20, 10, 16)
+    
+    # Encoded QPSK transmission
+    for SNR_dB in SNR_list:
+    
+        SNR_linear = 10**(SNR_dB / 10)
+    
+        signal_power = np.mean(np.abs(QPSK_symbols_encoded)**2)
+        noise_power = signal_power / SNR_linear
+    
+        noise = noise_power * np.random.normal(0, 1, size=(num_symbols_encoded, 2))
+        rx_signal = QPSK_symbols_encoded + noise
+    
+        distances = np.zeros(len(QPSK), dtype=float)
+        detected_symbols = np.zeros((num_symbols_encoded, 2), dtype=float)
+        for i, r in enumerate(rx_signal):
+            for j, s in enumerate(QPSK):
+                distances[j] = np.linalg.norm(r - s)
+                
+            detected_symbols[i] = QPSK[np.argmin(distances)]
+        
+        recv = []
+        for i in range(num_symbols_encoded):
+            code = ""
+            for k, v in g_QPSK.items():
+                if v[0] == detected_symbols[i][0] and v[1] == detected_symbols[i][1]:
+                    code = k
+                    break
+            
+            for char in code:
+                recv.append(int(char))
+                    
+        decoded = np.array(hamming_decode(recv))
+        
+        bit_errors = np.sum(data != decoded)
+        BER = bit_errors / num_symbols_encoded
+            
+        ber_encoded.append(BER)
+    
+    # Plain QPSK transmission
+    for SNR_dB in SNR_list:
+    
+        SNR_linear = 10**(SNR_dB / 10)
+    
+        signal_power = np.mean(np.abs(QPSK_symbols_plain)**2)
+        noise_power = signal_power / SNR_linear
+    
+        noise = noise_power * np.random.normal(0, 1, size=(num_symbols_plain, 2))
+        rx_signal = QPSK_symbols_plain + noise
+    
+        distances = np.zeros(len(QPSK), dtype=float)
+        detected_symbols = np.zeros((num_symbols_plain, 2), dtype=float)
+        for i, r in enumerate(rx_signal):
+            for j, s in enumerate(QPSK):
+                distances[j] = np.linalg.norm(r - s)
+                
+            detected_symbols[i] = QPSK[np.argmin(distances)]
+        
+        recv = []
+        for i in range(num_symbols_plain):
+            code = ""
+            for k, v in g_QPSK.items():
+                if v[0] == detected_symbols[i][0] and v[1] == detected_symbols[i][1]:
+                    code = k
+                    break
+            
+            for char in code:
+                recv.append(int(char))
+                    
+        bit_errors = np.sum(data != np.array(recv))
+        BER = bit_errors / num_symbols_plain
+            
+        ber_plain.append(BER)
+    
+    plt.figure(3)
+    plt.semilogy(SNR_list, ber_encoded, 'o-', label="With hamming")
+    plt.semilogy(SNR_list, ber_plain, 's-', label="Without encoding")
+    plt.title("Bit error rate for QPSK communication with and without encoding")
+    plt.xlabel("SNR (dB)")
+    plt.ylabel("Bit error rate")
+    plt.legend()
+    plt.grid(True)
+    plt.show()    
+\end{lstlisting}
  
-ölksjadf
  \end{document}
author	Nils Forssén <nilfo359@student.liu.se>
	Thu, 12 Dec 2024 01:06:31 +0000 (02:06 +0100)
committer	Nils Forssén <nilfo359@student.liu.se>
	Thu, 12 Dec 2024 01:06:31 +0000 (02:06 +0100)
.vscode/ltex.dictionary.en-US.txt	[new file with mode: 0644]	patch \| blob
.vscode/ltex.disabledRules.en-US.txt	[new file with mode: 0644]	patch \| blob
.vscode/ltex.hiddenFalsePositives.en-US.txt	[new file with mode: 0644]	patch \| blob
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report/images/PAM8_recv.png	[new file with mode: 0644]	patch \| blob
report/images/PSK8.png	[new file with mode: 0644]	patch \| blob
report/images/PSK8_error.png	[new file with mode: 0644]	patch \| blob
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report/images/QAM16.png	[new file with mode: 0644]	patch \| blob
report/images/QAM16_error.png	[new file with mode: 0644]	patch \| blob
report/images/QAM16_recv.png	[new file with mode: 0644]	patch \| blob
report/images/QPSK.png	[new file with mode: 0644]	patch \| blob
report/images/QPSK_error.png	[new file with mode: 0644]	patch \| blob
report/images/QPSK_hamming.png	[new file with mode: 0644]	patch \| blob
report/images/QPSK_recv.png	[new file with mode: 0644]	patch \| blob
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report/main.fdb_latexmk		patch \| blob \| history
report/main.fls		patch \| blob \| history
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report/main.out	[new file with mode: 0644]	patch \| blob
report/main.pdf		patch \| blob \| history
report/main.synctex.gz		patch \| blob \| history
report/main.tex		patch \| blob \| history