Skip to main content

Constellation Diagrams of M-ary QAM | M-ary Modulation

QAM

Unlike M-ary PSK, where the signal is modulated with different phase-shifted versions of the carrier, QAM varies both the phase and the amplitude levels. For instance:

QAM = ASK + PSK

QAM Constellation Example
In the figure above, 2 amplitude levels and 4 phase shifts are applied, resulting in a total of 2 * 4 = 8 constellation points.

Multilevel QAM

In M-ary QAM, groups of data bits are mapped to one of M possible amplitude and phase-shifted signals. By sending a single symbol that represents multiple bits, we can theoretically achieve a data rate that is log₂(M) times higher than a binary modulation scheme (like BPSK or BASK).

Instead of only modifying the phase, frequency, or amplitude of the RF signal, the RF carrier's phase (or frequency) is also altered. Since the envelope and phase offer two degrees of freedom, M-ary modulation methods convert baseband data into four or more different RF carrier signals. We refer to four carrier signals because a symbol is made up of two or more bits, and two bits can represent four distinct signals. Such modulation schemes are called M-ary modulation.

Depending on whether the amplitude, phase, or frequency is changed, the modulation is referred to as M-ary ASK, M-ary PSK, or M-ary FSK. Because M-ary modulation techniques increase bandwidth efficiency, they are appealing for use in bandlimited channels. Since a physical channel's bandwidth is always limited, a 16-QAM system, for instance, uses the channel log₂(16) = 4 times more effectively than a BASK system.

To transfer signals in the form of symbols and to enhance the bit rate, M-ary PSK and M-ary QAM are both utilized. You can obtain multiple prior data rates if you send a symbol rather than a single bit at a time. These M-ary modulation techniques are used to multiplex data.

  • 16-QAM ==> 4N ('data rate' is 4 times as compared to binary ASK, FSK, or PSK)
  • 32-QAM ==> 5N
  • 64-QAM ==> 6N
  • 128-QAM ==> 7N
  • 256-QAM ==> 8N

Constellation Diagram of 4-QAM (Transmitted)
Fig 1: Constellation Diagram of 4-QAM (Transmitted)

Constellation Diagram of 4-QAM (Received thru noisy channel)
Fig 2: Constellation Diagram of 4-QAM (Received through a noisy channel)

(Get MATLAB Code)

MATLAB Code for BER vs SNR for M-ary QAM

BER vs SNR for M-ary QAM

(Get MATLAB Code)

People are good at skipping over material they already know!

View Related Topics to







Contact Us

Name

Email *

Message *

Popular Posts

Theoretical BER vs SNR for binary ASK, FSK, and PSK

📘 Overview & Theory 🧮 MATLAB Codes 📚 Further Reading Theoretical BER vs SNR for Amplitude Shift Keying (ASK) The theoretical Bit Error Rate (BER) for binary ASK depends on how binary bits are mapped to signal amplitudes. For typical cases: If bits are mapped to 1 and -1, the BER is: BER = Q(√(2 × SNR)) If bits are mapped to 0 and 1, the BER becomes: BER = Q(√(SNR / 2)) Where: Q(x) is the Q-function: Q(x) = 0.5 × erfc(x / √2) SNR : Signal-to-Noise Ratio N₀ : Noise Power Spectral Density Understanding the Q-Function and BER for ASK Bit '0' transmits noise only Bit '1' transmits signal (1 + noise) Receiver decision threshold is 0.5 BER is given by: P b = Q(0.5 / σ) , where σ = √(N₀ / 2) Using SNR = (0.5)² / N₀, we get: BER = Q(√(SNR / 2)) Theoretical BER vs ...

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

📘 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. BER = (number of bits received in error) / (total number of tran...

Comparisons among ASK, PSK, and FSK | And the definitions of each

📘 Comparisons among ASK, FSK, and PSK 🧮 Online Simulator for calculating Bandwidth of ASK, FSK, and PSK 🧮 MATLAB Code for BER vs. SNR Analysis of ASK, FSK, and PSK 📚 Further Reading 📂 View Other Topics on Comparisons among ASK, PSK, and FSK ... 🧮 Comparisons of Noise Sensitivity, Bandwidth, Complexity, etc. 🧮 MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK 🧮 Online Simulator for ASK, FSK, and PSK Generation 🧮 Online Simulator for ASK, FSK, and PSK Constellation 🧮 Some Questions and Answers 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 Parameters ASK FSK PSK Variable Characteristics Amplitude Frequency ...

Constellation Diagrams of ASK, PSK, and FSK

📘 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 📚 Further Reading 📂 Other Topics on Constellation Diagrams of ASK, PSK, and FSK ... 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM 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...

UGC NET Electronic Science Previous Year Question Papers

Home / Engineering & Other Exams / UGC NET 2022: Previous Year Question Papers ... UGC-NET (Electronics Science, Subject code: 88) UGC Net Electronic Science Question Paper With Answer Key Download Pdf [December 2024] UGC Net Electronic Science Question Paper With Answer Key Download Pdf [June 2024] UGC Net Electronic Science Question Paper With Answer Key Download Pdf [December 2023] UGC Net Electronic Science Question Paper With Answer Key Download Pdf [June 2023] UGC Net Electronic Science Question Paper With Answer Key Download Pdf [December 2022] UGC Net Electronic Science Question Paper With Answer Key Download Pdf [June 2022] UGC Net Electronic Science Question Paper With Answer Key Download Pdf [December 2021] UGC Net Electronic Science Question With Answer Key Download Pdf [June 2020] UGC Net Electronic Science Question With Answer Key Download Pdf [December 2019] UGC Net Elec...

Theoretical vs. simulated BER vs. SNR for ASK, FSK, and PSK

📘 Overview 🧮 Simulator for calculating BER 🧮 MATLAB Codes for calculating theoretical BER 🧮 MATLAB Codes for calculating simulated BER 📚 Further Reading BER vs. SNR denotes how many bits in error are received for a given signal-to-noise ratio, typically measured in dB. Common noise types in wireless systems: 1. Additive White Gaussian Noise (AWGN) 2. Rayleigh Fading AWGN adds random noise; Rayleigh fading attenuates the signal variably. A good SNR helps reduce these effects. Simulator for calculating BER vs SNR for binary ASK, FSK, and PSK Calculate BER for Binary ASK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary FSK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary PSK Modulation Enter SNR (dB): Calculate BER BER vs. SNR Curves MATLAB Code for Theoretical BER % The code is written by SalimWireless.Com clc; clear; close all; % SNR v...

Power Spectral Density Calculation Using FFT in MATLAB

📘 Overview 🧮 Steps to calculate the PSD of a signal 🧮 MATLAB Codes 📚 Further Reading Power spectral density (PSD) tells us how the power of a signal is distributed across different frequency components, whereas Fourier Magnitude gives you the amplitude (or strength) of each frequency component in the signal. Steps to calculate the PSD of a signal Firstly, calculate the first Fourier transform (FFT) of a signal Then, calculate the Fourier magnitude of the signal The power spectrum is the square of the Fourier magnitude To calculate power spectrum density (PSD), divide the power spectrum by the total number of samples and the frequency resolution. {Frequency resolution = (sampling frequency / total number of samples)} Sampling frequency (fs): The rate at which the continuous-time signal is sampled (in Hz). ...

MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...

🧮 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 i...