Let's assume your original message signal is: 1, 0, 1, 1, 1, 0, 1, 1, 0, 1. If you want to modulate it using 4-QAM, then your baseband signal will be: 4-QAM Symbols (Real + jImag) Symbol 0: -1.00 + j-1.00 Symbol 1: 1.00 + j-1.00 Symbol 2: -1.00 + j-1.00 Symbol 3: 1.00 + j-1.00 Symbol 4: 1.00 + j1.00   Now, if you want to transmit them through a typical wireless medium, you need to modulate the baseband signal with a carrier frequency (in our case, 50 Hz). The resulting passband signal looks like this               In the above code, the symbol rate is 5 symbols per second.   Detailed explanation 4-QAM Constellation Points In typical normalized 4-QAM, each symbol is mapped to a complex number: Bits Symbol (I + jQ) 00 -1 - 1j 01 -1 + 1j 11 +1 + 1j 10 +1 - 1j Each point lies on a square centered at the origin with I and Q values either +1 or -1. ...

The relationship between Bit Error Rate (BER) and Signal-to-Noise Ratio (SNR) is a fundamental concept in digital communication systems. Here’s a detailed explanation: BER (Bit Error Rate): The ratio of the number of bits incorrectly received to the total number of bits transmitted. It measures the quality of the communication link. SNR (Signal-to-Noise Ratio): The ratio of the signal power to the noise power, indicating how much the signal is corrupted by noise. Relationship The BER typically decreases as the SNR increases. This relationship helps evaluate the performance of various modulation schemes. BPSK (Binary Phase Shift Keying) Simple and robust. BER in AWGN channel: BER = 0.5 × erfc(√SNR) Performs well at low SNR. QPSK (Quadrature Phase Shift Keying) Transmits 2 bits per symbol. BER: BER = 0.5 × erfc(√(SNR)) More spectrally effici...

MATLAB Script % This code is written by SalimWirelss.Com clc; clear all; close all; M = 4; % Number of levels after quantization / size of signal constellation k = log2(M); % Number of bits per symbol rng(1) % Assaining the value of seed integer N = 1000000; % Number of bits to process % Initialize SNR values and BER array snr_dB = -20:1:20; % SNR values in dB BER = zeros(size(snr_dB)); for snr_idx = 1:length(snr_dB) snrdB = snr_dB(snr_idx); InputBits = randi([0 1], 1, N); % Generating randon bits InputSymbol_matrix = reshape(InputBits, length(InputBits)/k, k); % Reshape data into binary k-tuples, k = log2(M) InputSymbols_decimal = bi2de(InputSymbol_matrix); % Convert binary to decimal for n = 1:N/k if InputSymbols_decimal(n) == 0 QAM(n) = complex(1,1); elseif InputSymbols_decimal(n) == 1 QAM(n) = complex(-1,1); elseif InputSymbols_decimal(n) == 2 QAM(n) = complex(1,-1); else QAM(n) = complex(-1,-1); end end % Transmission of 4QAM data over AWGN channel Y = awgn(QAM,...

MATLAB Script % This code is written by SalimWirelss.Com clc; clear all; close all; M = 4; % Number of levels after quantization / size of signal constellation k = log2(M); % Number of bits per symbol rng(10) % Assaining the value of seed integer N = 10000; % Number of bits to process % Initialize SNR values and BER array snr_dB = 0:1:20; % SNR values in dB BER = zeros(size(snr_dB)); for snr_idx = 1:length(snr_dB) snrdB = snr_dB(snr_idx); InputBits = randi([0 1], 1, N); % Generating randon bits InputSymbol_matrix = reshape(InputBits, length(InputBits)/k, k); % Reshape data into binary k-tuples, k = log2(M) InputSymbols_decimal = bi2de(InputSymbol_matrix); % Convert binary to decimal for n = 1:N/k if InputSymbols_decimal(n) == 0 QAM(n) = complex(1,1); elseif InputSymbols_decimal(n) == 1 QAM(n) = complex(-1,1); elseif InputSymbols_decimal(n) == 2 QAM(n) = complex(1,-1); else QAM(n) = complex(-1,-1); end end % Transmission of 4QAM data over AWGN channel Y = awgn(QAM, sn...

📘 Overview of QAM 🧮 MATLAB Code for m-ary QAM (4-QAM, 16-QAM, 32-QAM, ...) 🧮 Online Simulator for M-ary QAM Constellations (4-QAM, 16-QAM, 64-QAM, ...) 📚 Further Reading 📂 Other Topics on Constellation Diagrams of QAM configurations ... 🧮 MATLAB Code for 4-QAM 🧮 MATLAB Code for 16-QAM 🧮 MATLAB Code for m-ary QAM (4-QAM, 16-QAM, 32-QAM, ...) 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM 🧮 Overview of Energy per Bit (Eb / N0) 🧮 Online Simulator for constellation diagrams of ASK, FSK, and PSK 🧮 Theory behind Constellation Diagrams of ASK, FSK, and PSK 🧮 MATLAB Codes for Constellation Diagrams of ASK, FSK, and PSK   One of the best-performing modulation techniques is QAM [↗] . Here, we modulate the symbols by varying the carrier signal's amplitude and phase in response to the vari...

🧮 MATLAB Code for BPSK, M-ary PSK, and M-ary QAM Together 🧮 MATLAB Code for M-ary QAM 🧮 MATLAB Code for M-ary PSK 📚 Further Reading MATLAB Script for BER vs. SNR for M-QAM, M-PSK, QPSK, BPSK % Written by Salim Wireless clc; clear; close all; num_symbols = 1e5; snr_db = -20:2:20; psk_orders = [2, 4, 8, 16, 32]; qam_orders = [4, 16, 64, 256]; ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); for i = 1:length(psk_orders) psk_order = psk_orders(i); for j = 1:length(snr_db) data_symbols = randi([0, psk_order-1], 1, num_symbols); modulated_signal = pskmod(data_symbols, psk_order, pi/psk_order); received_signal = awgn(modulated_signal, snr_db(j), 'measured'); demodulated_symbols = pskdemod(received_signal, psk_order, pi/psk_order); ber_psk_results(i, j) = sum(data_symbols ~= demodulated_symbols) / num_symbols; end end for ...

📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 📚 Further Reading 📂 View Other Topics on M-ary QAM, M-ary PSK, QPSK ... 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR 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 ...

📘 Overview 🧮 Constellation Diagram of QPSK 🧮 What is the significance of M-ary PSK? 🧮 Constellation Diagram of 8-PSK 🧮 Constellation Diagrams of 16-PSK 🧮 MATLAB Code for M-ary PSK (e.g, 4, 8, 16, 32, 64, 128) 📚 Further Reading Constellation Diagrams QPSK, M-PSK, M-QAM ... What is the difference between Bit and Symbol in the perspective of transmission? Symbols use bandwidth more efficiently than bits. For example, in the case of QPSK, one symbol or signal waveform is represented by 2 bits. Hence symbol rate is one-half of the bit rate. As a result, it occupies half bandwidth compared to the BPSK waveform. We know the primary purpose of modulation [↗] is to multiplex data. Here multiplexing is done so that there is less interference between parallel data streams. Suppose there is a communication channel; we can transmit a single data stream simultaneously. But if we send a symbol instead of a bit, we can sen...