16-QAM (16 Quadrature Amplitude Modulation) is a popular digital modulation scheme used in many communication systems, including Wi-Fi, cellular, and satellite communications. In this modulation technique, 16 different symbols are used to represent a 4-bit sequence.   1. What is Maximum Likelihood Detection? Maximum Likelihood (ML) Detection is a decision rule used in communication systems to detect the transmitted signal based on the received signal. The goal is to choose the symbol that maximizes the likelihood of observing the received signal, considering the noise in the system. In the context of 16-QAM , ML detection involves choosing the closest point in the 16-QAM constellation to the received signal, where the closeness is measured by the Euclidean distance.   2. 16-QAM Modulation 16-QAM uses both amplitude and phase to represent 16 different combinations of 4 bits. The constellation points are arranged in a grid, where each point co...

  Let's assume your original digital message bitstream is: 0, 0, 1, 0, 0, 0, 1, 0, 1, 1 In 4-QAM, we group them into pairs: (00), (10), (00), (10), (11). Your baseband symbols are: Symbol 1 (Bits 00): -1.00 - j1.00 Symbol 2 (Bits 10): 1.00 - j1.00 Symbol 3 (Bits 00): -1.00 - j1.00 Symbol 4 (Bits 10): 1.00 - j1.00 Symbol 5 (Bits 11): 1.00 + j1.00   To transmit these symbols over a wireless medium, we modulate this baseband signal onto a high-frequency carrier (e.g., 50 Hz). This process creates the passband signal , where the information is stored in the phase and amplitude of the sine wave. Fig 1: 4-QAM Baseband I and Q Components Fig 2: 4-QAM Passband Modulated Signal   In this example, the symbol rate is 5 symbols per second. Detailed Explanation 4-QAM Constellation Mapping In standard 4-QAM mapping, bits are converted to complex points on a grid: Bits...

📊 BER vs SNR 📡 Modulation 🧮 MATLAB 📘 Simulations Relationship Between Bit Error Rate (BER) and Signal-to-Noise Ratio (SNR) 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. Q-function / erfc (Click here) QPSK (Quadrature Phase Shift Keying) Transmits 2 bits per ...

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 🧮 4-QAM MATLAB 🧮 16-QAM MATLAB 🚀 Online Simulator 📂 Other Topics on Constellation Diagrams... ▼ 🧮 MATLAB Code for 4-QAM 🧮 MATLAB Code for 16-QAM 🧮 MATLAB Code for m-ary QAM 🧮 Simulator for m-ary PSK 🧮 Simulator for m-ary QAM 🧮 Overview of Energy per Bit (Eb / N0) 🧮 Simulator for ASK, FSK, and PSK Overview of QAM 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 variation in the message signal (or voltage variation). So, we may say that QAM is a combination of phase and amplitude modulation. Additionally, it performs better than ASK or PSK [↗] . In fact, any constellation for any type of modulatio...

🧮 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; snr_db = -5:2:25; 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) ber_psk_results(i, :) = berawgn(snr_db, 'psk', psk_orders(i), 'nondiff'); end for i = 1:length(qam_orders) ber_qam_results(i, :) = berawgn(snr_db, 'qam', qam_orders(i)); end figure; semilogy(snr_db, ber_psk_results(1, :), 'o-', 'LineWidth', 1.5, 'DisplayName', 'BPSK'); hold on; for i = 2:length(psk_orders) semilogy(snr_db, ber_psk_results(i, :), 'o-', 'DisplayName', sprintf('%d-PSK', psk_or...

🧮 Simulators 📘 Theoretical BER 💻 MATLAB Code 📚 Further Reading Interactive BER Calculator Calculate theoretical BER for m-ary PSK and QAM systems instantly. M-ary PSK Eb/No (dB) Modulation Order (M) --- M-ary QAM Eb/No (dB) Modulation Order (M) --- Bit Error Rate (BER) & BER Requirements by Application → ...

📘 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...