From 6009b3011cbbca65869a220230b85be392ec63c5 Mon Sep 17 00:00:00 2001 From: =?utf8?q?Nils=20Forss=C3=A9n?= Date: Thu, 12 Dec 2024 02:06:31 +0100 Subject: [PATCH] updated report --- .vscode/ltex.dictionary.en-US.txt | 4 + .vscode/ltex.disabledRules.en-US.txt | 1 + .vscode/ltex.hiddenFalsePositives.en-US.txt | 1 + report/images/PAM8.png | Bin 0 -> 8892 bytes report/images/PAM8_error.png | Bin 0 -> 25117 bytes report/images/PAM8_recv.png | Bin 0 -> 12259 bytes report/images/PSK8.png | Bin 0 -> 30320 bytes report/images/PSK8_error.png | Bin 0 -> 24307 bytes report/images/PSK8_recv.png | Bin 0 -> 34902 bytes report/images/QAM16.png | Bin 0 -> 13350 bytes report/images/QAM16_error.png | Bin 0 -> 26823 bytes report/images/QAM16_recv.png | Bin 0 -> 26407 bytes report/images/QPSK.png | Bin 0 -> 18783 bytes report/images/QPSK_error.png | Bin 0 -> 23473 bytes report/images/QPSK_hamming.png | Bin 0 -> 37846 bytes report/images/QPSK_recv.png | Bin 0 -> 23547 bytes report/main.aux | 54 +- report/main.fdb_latexmk | 157 +++- report/main.fls | 778 +++++++++++++++++++- report/main.log | 559 +++++++++++++- report/main.out | 8 + report/main.pdf | Bin 33821 -> 391247 bytes report/main.synctex.gz | Bin 890 -> 419697 bytes report/main.tex | 771 ++++++++++++++++++- 24 files changed, 2284 insertions(+), 49 deletions(-) create mode 100644 .vscode/ltex.dictionary.en-US.txt create mode 100644 .vscode/ltex.disabledRules.en-US.txt create mode 100644 .vscode/ltex.hiddenFalsePositives.en-US.txt create mode 100644 report/images/PAM8.png create mode 100644 report/images/PAM8_error.png create mode 100644 report/images/PAM8_recv.png create mode 100644 report/images/PSK8.png create mode 100644 report/images/PSK8_error.png create mode 100644 report/images/PSK8_recv.png create mode 100644 report/images/QAM16.png create mode 100644 report/images/QAM16_error.png create mode 100644 report/images/QAM16_recv.png create mode 100644 report/images/QPSK.png create mode 100644 report/images/QPSK_error.png create mode 100644 report/images/QPSK_hamming.png create mode 100644 report/images/QPSK_recv.png create mode 100644 report/main.out diff --git a/.vscode/ltex.dictionary.en-US.txt b/.vscode/ltex.dictionary.en-US.txt new file mode 100644 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 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 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=, 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z5@m=~;AAlWp5kUoO<9WsP_0+5tGbr1;@!W+;%oNp=Fe5oZ|cjgs`rQz^;`N>^GOH4;{u-7)Z;C1_ zszgmFkopelZU9U1M=;=;^5N42*p66r%jKOH5vReY(As|-FJH+Yqf z?MLnhaI!o!3CF^r(u zqK!;`2y<|rae${E3+~&jU$G}D?!$8QqvEb_5?MDCw_I_Mh6M%#*uG);pmptb&z4re z(%JfU5{uj7?$QBlMWZ8y5&^dj77~k=@8;z&qlsfhIY9c29^#jx-sPD~H2fBFZ3iZ;d zyGK1ac2Ds-$Iel@!MlIBQF_~}ger7y^}82NXC*d7KXqCzwS6TpJgu9<;C zkQ-#g;eil)G2S@si_HS6AK1NE+G}1cClZa{H)WNsA68i+FN-^QRSZT=kQ@A_Tx|2# QYPU|*|9mqzD9H-|0BO3jWB>pF diff --git a/report/main.tex b/report/main.tex index 6a5d4ed..d41b479 100644 --- 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} -- 2.30.2

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