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BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... What is Bit Error Rate (BER)? The abbreviation BER stands for bit error rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. It is defined as,  In mathematics, BER = (number of bits received in error / total number of transmitted bits)  On the other hand, SNR refers to the signal-to-noise power ratio. For ease of calculation, we commonly convert it to dB or decibels.   What is Signal the signal-to-noise ratio (SNR)? SNR = signal power/noise power (SNR is a ratio of signal power to noise power) SNR (in dB) = 10*log(signal power / noise power) [base 10] For instance, the SNR for a given communication system is 3dB. So, SNR (in ratio) = 10^{SNR (in dB) / 10} = 2 Therefore, in this instance, the s...
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MATLAB Code for Pulse Width Modulation (PWM) and Demodulation

   Pulse Width Modulation (PWM) MATLAB Script clc; clear all; close all; fs=30; %frequency of the sawtooth signal fm=3; %frequency of the message signal sampling_frequency = 10e3; a=0.5; % amplitide t=0:(1/sampling_frequency):1; %sampling rate of 10kHz sawtooth=2*a.*sawtooth(2*pi*fs*t); %generating a sawtooth wave subplot(4,1,1); plot(t,sawtooth); % plotting the sawtooth wave title('Comparator Wave'); msg=a.*sin(2*pi*fm*t); %generating message wave subplot(4,1,2); plot(t,msg); %plotting the sine message wave title('Message Signal'); for i=1:length(sawtooth) if (msg(i)>=sawtooth(i)) pwm(i)=1; %is message signal amplitude at i th sample is greater than %sawtooth wave amplitude at i th sample else pwm(i)=0; end end subplot(4,1,3); plot(t,pwm,'r'); title('PWM'); axis([0 1 0 1.1]); %to keep the pwm visible during plotting. %% Demodulation % Demodulation: Measure the pulse width to reconstruct the signal demodulated_signal = zeros(size(msg)); for i = 1:leng...
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Theoretical and simulated BER vs. SNR for ASK, FSK, and PSK

  BER vs. SNR denotes how many bits in error are received in a communication process for a particular Signal-to-noise (SNR) ratio. In most cases, SNR is measured in decibel (dB). For a typical communication system, a signal is often affected by two types of noises 1. Additive White Gaussian Noise (AWGN) 2. Rayleigh Fading In the case of additive white Gaussian noise (AWGN), random magnitude is added to the transmitted signal. On the other hand, Rayleigh fading (due to multipath) attenuates the different frequency components of a signal differently. A good signal-to-noise ratio tries to mitigate the effect of noise.  Calculate BER for Binary ASK Modulation The theoretical BER for binary ASK (BASK) in an AWGN channel is given by: BER  = (1/2) * erfc(0.5 * sqrt(SNR_ask));   Enter SNR (dB): Calculate BER BER vs. SNR curves for ASK, FSK, and PSK Calculate BER for Binary FSK Modulation The theoretical BER for binary FSK (BFSK) in a...
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Antenna Gain-Combining Methods - EGC, MRC, SC, and RMSGC

 There are different antenna gain-combining methods. They are as follows. 1. Equal gain combining (EGC) 2. Maximum ratio combining (MRC) 3. Selective combining (SC) 4. Root mean square gain combining (RMSGC) 1. Equal gain combining method We add the correlated data streams from different antennas in the equal gain combining method. Then we multiply the resultant data with (1/(number of antennas)) For example, for two antenna gain-combining  If the received symbols are y1 and y2, then  Equal combing gain, y_egc = 0.5 * (y1 + y2) 2. Maximum ratio combining method We multiply the individual data streams with weights in the maximum ratio combining method. More weightage is multiplied by those data streams with maximum {|h|^2}, where h denotes the channel impulse response. And less weightage is multiplied by those data streams with corresponding small value of  {|h|^2}.  Then we sum the data streams to improve SNR. In the case of Maximum Ratio Combining, if y1 an...
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Comparisons among ASK, PSK, and FSK | And the definitions of each

Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK    Comparisons among ASK, PSK, and FSK Comparison among ASK,  FSK, and PSK Performance Comparison: 1. Noise Sensitivity:    - ASK is the most sensitive to noise due to its reliance on amplitude variations.    - PSK is less sensitive to noise compared to ASK.    - FSK is relatively more robust against noise, making it suitable for noisy environments. 2. Bandwidth Efficiency:    - PSK is the most bandwidth-efficient, requiring less bandwidth than FSK for the same data rate.    - FSK requires wider bandwidth compared to PSK.    - ASK's bandwidth efficiency lies between FSK and PSK. Bandwidth Calculator for ASK, FSK, and PSK The baud rate represents the number of symbols transmitted per second Select Modulation Type: ASK...
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Constellation Diagrams of ASK, PSK, and FSK

BASK (Binary ASK) Modulation: Transmits one of two signals: 0 or -√Eb, where Eb​ is the energy per bit. These signals represent binary 0 and 1.    BFSK (Binary FSK) Modulation: Transmits one of two signals: +√Eb​ ( On the y-axis, the phase shift of 90 degrees with respect to the x-axis, which is also termed phase offset ) or √Eb (on x-axis), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  BPSK (Binary PSK) Modulation: Transmits one of two signals: +√Eb​ or -√Eb (they differ by 180 degree phase shift), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  Key Points For Binary Amplitude Shift Keying (BASK), binary bit '0' can be represented as lower level voltage or no signal and bit '1' as higher level voltage.  For Binary Frequency Shift Keying (BFSK), you can map binary bit '0' to 'j' and bit '1' to '1'. So, signals are in phase.  A phase shift of 0 degrees could represent a binary '1...
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MATLAB Code for Pulse Amplitude Modulation (PAM) and Demodulation

  Pulse Amplitude Modulation (PAM) & Demodulation MATLAB Script clc; clear all; close all; fm= 10; % frequency of the message signal fc= 100; % frequency of the carrier signal fs=1000*fm; % (=100KHz) sampling frequency (where 1000 is the upsampling factor) t=0:1/fs:1; % sampling rate of (1/fs = 100 kHz) m=1*cos(2*pi*fm*t); % Message signal with period 2*pi*fm (sinusoidal wave signal) c=0.5*square(2*pi*fc*t)+0.5; % square wave with period 2*pi*fc s=m.*c; % modulated signal (multiplication of element by element) subplot(4,1,1); plot(t,m); title('Message signal'); xlabel ('Time'); ylabel('Amplitude'); subplot(4,1,2); plot(t,c); title('Carrier signal'); xlabel('Time'); ylabel('Amplitude'); subplot(4,1,3); plot(t,s); title('Modulated signal'); xlabel('Time'); ylabel('Amplitude'); %demdulated d=s.*c; % At receiver, received signal is multiplied by carrier signal filter=fir1(200,fm/fs,'low'); % low-pass FIR fi...
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MIMO Communication in MATLAB

  The code below is an example of 2 X 2 MIMO.   MATLAB Code clc; clear all; close all; % MIMO System Parameters numTx = 2; % Number of transmit antennas numRx = 2; % Number of receive antennas numSymbols = 50; % Number of symbols to transmit % Generate random binary data data = randi([0, 1], numTx, numSymbols); % PSK Modulation (BPSK) modulatedSymbols = 1 - 2 * data; % BPSK modulation: '0' maps to +1, '1' maps to -1 % Precoding (Identity Matrix for demonstration) precodingMatrix = eye(numTx); % Transmit Signal transmitSignal = precodingMatrix * modulatedSymbols; % Channel (Rayleigh Fading Channel) H = (randn(numRx, numTx) + 1i * randn(numRx, numTx)) / sqrt(2); % Rayleigh fading channel % Received Signal receivedSignal = H * transmitSignal; % Demodulation demodulatedSymbols = H' * receivedSignal; % PSK Demodulation (BPSK) receivedData = demodulatedSymbols < 0; % Decision threshold at 0 Output       Fig 1: Original Message Bits         ...
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