Skip to main content
Login Home Wireless Communication Modulation MATLAB Beamforming Project Ideas MIMO Computer Networks

Theoretical BER vs SNR for m-ary PSK and QAM


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 efficient than BPSK, slightly higher BER at same SNR.

M-ary PSK (Phase Shift Keying)

  • Encodes multiple bits using M phases.
  • General BER expression is complex and depends on cos and sin terms.
  • Higher-order schemes (e.g., 8-PSK, 16-PSK) have higher BER for same SNR.

M-ary PSK is a modulation technique where each symbol represents log₂(M) bits by shifting the phase of a carrier. The phases are spaced evenly in a circle, and the distance between points decreases with higher M, making it more error-prone at low SNRs.

BER (approximate for large M and high SNR in AWGN):


BER ≈ (2 / log₂(M)) × erfc(√SNR × sin(Ï€ / M))
  • As M increases, spectral efficiency improves but BER performance degrades.
  • Gray coding is typically used to minimize BER.
  • Exact BER uses summation expressions, but approximations are common for analysis.

M-ary QAM (Quadrature Amplitude Modulation)

  • Uses both amplitude and phase variations.
  • BER: BER = (log₂(M)/2) × (1 - 1/√M) × erfc(√((3SNR)/(M - 1)))
  • Higher-order QAM (e.g., 16-QAM, 64-QAM) is more spectrally efficient, but BER increases with order.

Practical Considerations

  • AWGN Channel: Additive White Gaussian Noise affects the signal; SNR is key to system performance.
  • Simulation: SNR is varied to analyze BER behavior using tools like MATLAB.
  • Error Correction: Techniques like Forward Error Correction (FEC) help reduce BER.

Example

For a BPSK system in an AWGN channel:

Formula: BER = 0.5 × erfc(√SNR)

At SNR = 0 dB: BER ≈ 0.078649603525

Conclusion

Understanding the BER vs. SNR relationship is essential for designing efficient digital communication systems. Different modulation schemes provide trade-offs between spectral efficiency and BER performance.

 

Further Reading


People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

s

  Website: www.salimwireless.com
  Interests: Signal Processing, Telecommunication, 5G Technology, Present & Future Wireless Technologies, Digital Signal Processing, Computer Networks, Millimeter Wave Band Channel, Web Development
  Seeking an opportunity in the Teaching or Electronics & Telecommunication domains.
  Possess M.Tech in Electronic Communication Systems.


Contact Us

Name

Email *

Message *

Popular Posts

Comparing Baseband and Passband Implementations of ASK, FSK, and PSK

📘 Overview 🧮 Baseband and Passband Implementations of ASK, FSK, and PSK 🧮 Difference betwen baseband and passband 📚 Further Reading 📂 Other Topics on Baseband and Passband ... 🧮 Baseband modulation techniques 🧮 Passband modulation techniques   Baseband modulation techniques are methods used to encode information signals onto a baseband signal (a signal with frequencies close to zero), allowing for efficient transmission over a communication channel. These techniques are fundamental in various communication systems, including wired and wireless communication. Here are some common baseband modulation techniques: Amplitude Shift Keying (ASK) [↗] : In ASK, the amplitude of the baseband signal is varied to represent different symbols. Binary ASK (BASK) is a common implementation where two different amplitudes represent binary values (0 and 1). ASK is simple but susceptible to noise...
Read more

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. It is defined as,  In mathematics, BER = (number of bits received in error / total number of transmitted bits)  On the other hand, SNR ...
Read more

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

📘 Overview of QAM 🧮 MATLAB Code for m-ary QAM (4-QAM, 16-QAM, 32-QAM, ...) 🧮 Online Simulator for M-ary QAM Constellations 📚 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 QAM Unlike this, the M-ary PSK signal is modulated with a different phase-shifted version of the carrier signal and varying amplitude levels. Let me give an example for better comprehension. QAM = ASK +...
Read more

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...
Read more

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   Simulator for Calculating Bandwidth of ASK, FSK, and PSK The baud rate represents the number of symbols transmitted per second. Both baud rate and bit rate a...
Read more

MATLAB Code for Pulse Amplitude Modulation (PAM) and Demodulation

📘 Overview & Theory of Pulse Amplitude Moduation (PAM) 🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of Analog Signal and Digital Signal 🧮 Simulation results for comparison of PAM, PWM, PPM, DM, and PCM 📚 Further Reading 📂 Other Topics on Pulse Amplitude Modulation ... 🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of an Analog Signal (2) 🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of Digital data 🧮 Other Pulse Modulation Techniques (e.g., PWM, PPM, DM, and PCM)   Pulse Amplitude Modulation (PAM) & Demodulation of an Analog Message Signal 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 per...
Read more

Coherence Bandwidth and Coherence Time

🧮 Coherence Bandwidth 🧮 Coherence Time 🧮 Coherence Time Calculator 🧮 Relationship between Coherence Time and Delay Spread 🧮 MATLAB Code to find Relationship between Coherence Time and delay Spread 📚 Further Reading   Coherence Bandwidth Coherence bandwidth is a concept in wireless communication and signal processing that relates to the frequency range over which a wireless channel remains approximately constant in terms of its characteristics. coherence bandwidth is  The inverse of Doppler spread delay time, or any spread delay time due to fading in general.  The coherence bandwidth is related to the delay spread of the channel, which is a measure of the time it takes for signals to traverse the channel. The two are related by the following formulae: Coherence bandwidth = 1/(delay spread time) Or, Coherence Bandwidth = 1/(root-mean-square delay spread time) (Coherence bandwidth in Hertz) For instance, the coherence bandwidth is...
Read more

Definition of the Fourier Series

  1. Introduction Most of the phenomena studied in the domain of Engineering and Science are periodic in nature. For instance, current and voltage in an alternating current circuit. These periodic functions could be analyzed into their constituent components (fundamentals and harmonics) by a process called Fourier analysis. A Fourier series is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series. Fourier series is used to describe a periodic signal in terms of cosine and sine waves. In other words, it allows us to model any arbitrary periodic signal with a combination of sines and cosines.      Fig: Sine Wave       Fig: Triangular Wave    Fig: Sawtooth Wave      Fig: Square Wave   2. The common form of the Fourier series Sinusoidal functions are periodic over 2Ï€ angular distance. For a perio...
Read more