Skip to main content

Menu

Home 📘 Wireless Communication (Main Page) Constellation Diagrams BER vs SNR GMSK MSK Channel Impulse Response Modulation Schemes MIMO Technology OFDM MATLAB Machine Learning Contact
Login Try App

Theoretical BER vs SNR for m-ary PSK and QAM


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.

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

  1. MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, ...
  2. Theoretical vs. simulated (using MATLAB) BER vs. SNR for ASK, FSK, and PSK

People are good at skipping over material they already know!

View Related Topics to







Contact Us

Name

Email *

Message *

Popular Posts

Constellation Diagram of ASK in Detail

A binary bit '1' is assigned a power level of E b \sqrt{E_b}  (or energy E b E_b ), while a binary bit '0' is assigned zero power (or no energy).   Simulator for Binary ASK Constellation Diagram SNR (dB): 15 Run Simulation Noisy Modulated Signal (ASK) Original Modulated Signal (ASK) Energy per bit (Eb) (Tb = bit duration): We know that all periodic signals are power signals. Now we’ll find the energy of ASK for the transmission of binary ‘1’. E b = ∫ 0 Tb (A c .cos(2П.f c .t)) 2 dt = ∫ 0 Tb (A c ) 2 .cos 2 (2П.f c .t) dt Using the identity cos 2 x = (1 + cos(2x))/2: = ∫ 0 Tb ((A c ) 2 /2)(1 + cos(4П.f c .t)) dt ...
Read more

Periodogram in MATLAB

Step 1: Signal Representation Let the signal be x[n] , where: n = 0, 1, ..., N-1 (discrete-time indices), N is the total number of samples. Step 2: Compute the Discrete-Time Fourier Transform (DTFT) The DTFT of x[n] is: X(f) = ∑ x[n] e -j2Ï€fn For practical computation, the Discrete Fourier Transform (DFT) is used: X[k] = ∑ x[n] e -j(2Ï€/N)kn , k = 0, 1, ..., N-1 Here: k represents discrete frequency bins, f_k = k/N * f_s , where f_s is the sampling frequency. Step 3: Compute Power Spectral Density (PSD) The periodogram estimates the PSD as: S_x(f_k) = (1/N) |X[k]|² Where: S_x(f_k) represents the power of the signal at frequency f_k . The factor 1/N normalizes the power by the signal length. Step 4: Convert to Decibels (Optional) For visualization, convert PSD to decibels (dB): S_x dB (f_k) = 10 lo...
Read more

MATLAB Code for Rms Delay Spread

RMS delay spread is crucial when you need to know how much the signal is dispersed in time due to multipath propagation, the spread (variance) around the average. In high-data-rate systems like LTE, 5G, or Wi-Fi, even small time dispersions can cause ISI. RMS delay spread is directly related to the amount of ISI in such systems. RMS Delay Spread [↗] Delay Spread Calculator Enter delays (ns) separated by commas: Enter powers (dB) separated by commas: Calculate   The above calculator Converts Power to Linear Scale: It correctly converts the power values from decibels (dB) to a linear scale. Calculates Mean Delay: It accurately computes the mean excess delay, which is the first moment of the power delay profile. Calculates RMS Delay Spread: It correctly calculates the RMS delay spread, defined as the square root of the second central moment of the power delay profile.   MATLAB Code  clc...
Read more

Online Simulator for ASK, FSK, and PSK

Try our new Digital Signal Processing Simulator!   Start Simulator for binary ASK Modulation Message Bits (e.g. 1,0,1,0) Carrier Frequency (Hz) Sampling Frequency (Hz) Run Simulation Simulator for binary FSK Modulation Input Bits (e.g. 1,0,1,0) Freq for '1' (Hz) Freq for '0' (Hz) Sampling Rate (Hz) Visualize FSK Signal Simulator for BPSK Modulation ...
Read more

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 Paper 1 With Answer Key Download Pdf [Sep 2024] with full explanation UGC Net Electronic Science Question Paper With Answer Key Download Pdf [Sep 2024]  UGC Net Paper 1 With Answer Key Download Pdf [June 2023] with full explanation UGC Net Electronic Science Question Paper With Answer Key Download Pdf [December 2023] with full explanation 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] ...
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 Comparison among ASK, FSK, and PSK Parameters ASK FSK PSK Variable Characteristics Amplitude Frequency ...
Read more

5G Channel Estimation using Orthogonal Matching Pursuit (OMP)

5G Channel Estimation... For millimeter wave massive MIMO communication in 5G, we observe that the number of available multipath that avails communication is much smaller than the maximum connections possible between the transmitter(TX) and receiver(RX). Only a few MPCs reach at receiver with good received signal strength. For example, the number of strong MPCs that reaches the receiver is L and there is N transmitter antenna on the transmitter side and N number of antennas on the receiver side. So, from the channel matrix of the massive MIMO system, we can say the total number of available paths or connections between TX and RX is equal to, N X N or, N^(2) Now, L << N^(2) For simplicity, if the number of possible strong beams from the transmitter and receiver sides are NtBeams and NrBeams, then, L = NtBeams * NrBeams If we look up the massive MIMO channel matrix , then, H= Primarily, if the number of available MPCs to avail communication bet...
Read more

OFDM for 4G & 5G

📘 Overview 📘 Example: (OFDM using QPSK) 🧮 MATLAB Codes 🧮 Q & A and Summary 📚 Further Reading   Orthogonal Frequency Division Multiplexing When a signal with high bandwidth traverses through a medium, it tends to disperse more compared to a signal with lower bandwidth. A high-bandwidth signal comprises a wide range of frequency components. Each frequency component may interact differently with the transmission medium due to factors such as attenuation, dispersion, and distortion. OFDM combats the high-bandwidth frequency selective channel by dividing the original signal into multiple orthogonal multiplexed narrowband signals. In this way it, overcomes the inter-symbol interferences (ISI) issue. Block Diagram     ‘k’ indicates kth position in a input symbol N is the number of subcarriers   Example: (OFDM using QPSK) 1.        Input Parameters: N   Number of Input bits: 128 Number ...
Read more