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(ฯ€ / 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

Calculation of SNR from FFT bins in MATLAB

๐Ÿ“˜ Overview ๐Ÿงฎ MATLAB Code for Estimation of SNR from FFT bins of a Noisy Signal ๐Ÿงฎ MATLAB Code for Estimation of Signal-to-Noise Ratio from Power Spectral Density Using FFT and Kaiser Window Periodogram from real signal data ๐Ÿ“š Further Reading   Here, you can find the SNR of a received signal from periodogram / FFT bins using the Kaiser operator. The beta (ฮฒ) parameter characterizes the Kaiser window, which controls the trade-off between the main lobe width and the side lobe level in the frequency domain. For that you should know the sampling rate of the signal.  The Kaiser window is a type of window function commonly used in signal processing, particularly for designing finite impulse response (FIR) filters and performing spectral analysis. It is a general-purpose window that allows for control over the trade-off between the main lobe width (frequency resolution) and side lobe levels (suppression of spectral leakage). The Kaiser window is defined...
Read more

Difference between AWGN and Rayleigh Fading

๐Ÿ“˜ Introduction, AWGN, and Rayleigh Fading ๐Ÿงฎ Simulator for the effect of AWGN and Rayleigh Fading on a BPSK Signal ๐Ÿงฎ MATLAB Codes ๐Ÿ“š Further Reading Wireless Signal Processing Gaussian and Rayleigh Distribution Difference between AWGN and Rayleigh Fading 1. Introduction Rayleigh fading coefficients and AWGN, or additive white gaussian noise [↗] , are two distinct factors that affect a wireless communication channel. In mathematics, we can express it in that way.  Fig: Rayleigh Fading due to multi-paths Let's explore wireless communication under two common noise scenarios: AWGN (Additive White Gaussian Noise) and Rayleigh fading. y = h*x + n ... (i) Symbol '*' represents convolution. The transmitted signal  x  is multiplied by the channel coefficient or channel impulse response (h)  in the equation above, and the symbol  "n"  stands for the white Gaussian noise that is added to the si...
Read more

Gaussian minimum shift keying (GMSK)

๐Ÿ“˜ Overview & Theory ๐Ÿงฎ Simulator for GMSK ๐Ÿงฎ MSK and GMSK: Understanding the Relationship ๐Ÿงฎ MATLAB Code for GMSK ๐Ÿ“š Simulation Results for GMSK ๐Ÿ“š Further Reading Dive into the fascinating world of GMSK modulation, where continuous phase modulation and spectral efficiency come together for robust communication systems! Core Process of GMSK Modulation Phase Accumulation (Integration of Filtered Signal) After applying Gaussian filtering to the Non-Return-to-Zero (NRZ) signal, we integrate the smoothed NRZ signal over time to produce a continuous phase signal: ฮธ(t) = ∫ 0 t m filtered (ฯ„) dฯ„ This integration is crucial for avoiding abrupt phase transitions, ensuring smooth and continuous phase changes. Phase Modulation The next step involves using the phase signal to modulate a high-frequency carrier wave: s(t)...
Read more

Simulation of ASK, FSK, and PSK using MATLAB Simulink

๐Ÿ“˜ Overview ๐Ÿงฎ How to use MATLAB Simulink ๐Ÿงฎ Simulation of ASK using MATLAB Simulink ๐Ÿงฎ Simulation of FSK using MATLAB Simulink ๐Ÿงฎ Simulation of PSK using MATLAB Simulink ๐Ÿงฎ Simulator for ASK, FSK, and PSK ๐Ÿงฎ Digital Signal Processing Simulator ๐Ÿ“š Further Reading ASK, FSK & PSK HomePage MATLAB Simulation Simulation of Amplitude Shift Keying (ASK) using MATLAB Simulink      In Simulink, we pick different components/elements from MATLAB Simulink Library. Then we connect the components and perform a particular operation.  Result A sine wave source, a pulse generator, a product block, a mux, and a scope are shown in the diagram above. The pulse generator generates the '1' and '0' bit sequences. Sine wave sources produce a specific amplitude and frequency. The scope displays the modulated signal as well as the original bit sequence created by the pulse generator. Mux is a tool for displaying b...
Read more

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

๐Ÿ“˜ Overview of QAM ๐Ÿงฎ MATLAB Code for m-ary QAM (4-QAM, 16-QAM, 32-QAM, ...) ๐Ÿงฎ Online Simulator for M-ary QAM Constellations ๐Ÿ“š Further Reading ๐Ÿ“‚ Other Topics on Constellation Diagrams of QAM configurations ... ๐Ÿงฎ MATLAB Code for 4-QAM ๐Ÿงฎ MATLAB Code for 16-QAM ๐Ÿงฎ MATLAB Code for m-ary QAM (4-QAM, 16-QAM, 32-QAM, ...) ๐Ÿงฎ Simulator for constellation diagrams of m-ary PSK ๐Ÿงฎ Simulator for constellation diagrams of m-ary QAM ๐Ÿงฎ Overview of Energy per Bit (Eb / N0) ๐Ÿงฎ Online Simulator for constellation diagrams of ASK, FSK, and PSK ๐Ÿงฎ Theory behind Constellation Diagrams of ASK, FSK, and PSK ๐Ÿงฎ MATLAB Codes for Constellation Diagrams of ASK, FSK, and PSK QAM Unlike M-ary PSK, where the signal is modulated with diffe...
Read more

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

๐Ÿ“˜ Overview ๐Ÿงฎ Simulator for calculating BER ๐Ÿงฎ MATLAB Codes for calculating theoretical BER ๐Ÿงฎ MATLAB Codes for calculating simulated BER ๐Ÿ“š 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...
Read more

Constellation Diagrams of ASK, PSK, and FSK

๐Ÿ“˜ Overview of Energy per Bit (Eb / N0) ๐Ÿงฎ Online Simulator for constellation diagrams of ASK, FSK, and PSK ๐Ÿงฎ Theory behind Constellation Diagrams of ASK, FSK, and PSK ๐Ÿงฎ MATLAB Codes for Constellation Diagrams of ASK, FSK, and PSK ๐Ÿ“š Further Reading ๐Ÿ“‚ Other Topics on Constellation Diagrams of ASK, PSK, and FSK ... ๐Ÿงฎ Simulator for constellation diagrams of m-ary PSK ๐Ÿงฎ 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

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

๐Ÿ“˜ Overview of BER and SNR ๐Ÿงฎ Online Simulator for BER calculation of m-ary QAM and m-ary PSK ๐Ÿงฎ MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... ๐Ÿ“š Further Reading ๐Ÿ“‚ View Other Topics on M-ary QAM, M-ary PSK, QPSK ... ๐Ÿงฎ Online Simulator for Constellation Diagram of m-ary QAM ๐Ÿงฎ Online Simulator for Constellation Diagram of m-ary PSK ๐Ÿงฎ MATLAB Code for BER calculation of ASK, FSK, and PSK ๐Ÿงฎ MATLAB Code for BER calculation of Alamouti Scheme ๐Ÿงฎ 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