Skip to main content
Home Wireless Communication Modulation MATLAB Beamforming Project Ideas MIMO Computer Networks Lab 🚀
Electronics Industry Wireless FORUM Work Hub Applications & Games Generate QR for Any Link Sitemap Generator (for Any Website) Play game Electrical & Electronics Calculator Contact Get Newsletter.
☰

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



1. 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 refers to the signal-to-noise power ratio. For ease of calculation, we commonly convert it to dB or decibels.  

2. What is Signal the signal-to-noise ratio (SNR)?

SNR = signal power/noise power
(SNR is a ratio of signal power to noise power)

SNR (in dB) = 10*log(signal power / noise power) [base 10]

For instance, the SNR for a given communication system is 3dB.
So, SNR (in ratio) = 10^{SNR (in dB) / 10} = 2
Therefore, in this instance, the signal power is twice as powerful as the noise power.

3. Comparison of BER vs. SNR for BPSK, QPSK, 8-PSK, 16-PSK, 32-PSK, D-BPSK, D-QPSK, 4-QAM, 16-QAM, and 64-QAM

                              
Get MATLAB Code (BER vs. SNR for 64 QAM, 16 QAM, 4 QAM, D-QPSK, D-BPSK, 32 PSK, 16 PSK, 8 PSK, QPSK, BPSK - are shown there. Probability of BER Error {10log10(Pb)} and SNR in dB {E0 / N0 - SNR per bit} are plotted there.)
 
Get MATLAB Code for QAM
Get MATLAB Code for m-ary QAM  
Get MATLAB Code for m-ary PSK 

We usually use modulation schemes for better efficiency of bandwidth. For example, if we use a binary PSK system and someone uses a QPSK system, you can see you are transmitting only one bit in a symbol, and the QPSK user shares 2 bits in a signal at a time. Mathematically, the QPSK data rate or bit will be twice as compared to binary PSK or BPSK.

Further, QAM modulation techniques are introduced, which are a combination of Amplitude modulation and PSK. Which shows better performance than only PSK. And most information technology and consumer companies have already adopted this modulation technique for high data rate communication.

For example, if we are using 4 QAM, then we can send 2 bits in a symbol where the data rate is twice as compared to binary PSK. For 16 QAM, we send 4 bits in a symbol where the data rate is 4 times as compared to BPSK.

Here in the above figure, for PSK, the phase of the carrier signal is shifted to represent data. Where is 8 PSK, 3 bits fit in each symbol? In 8 PSK, the distance between the constellation point is small compared to BPSK, and 4 PSK and Eb/No ratio (SNR per bit) has to become more significant to attain target BER. In the above figure, QAM performs better than PSK in normal SNR. But if the channel is extremely noisy, then we go for BPSK.

Modulation Techniques No of Bits in a Symbol
 BPSK  1
 QPSK  2
 8-PSK  3
 16-QAM  4
64-QAM 6

We use OFDM technology for practical communication systems, e.g., for 4G LTE. Data bits are first mapped using QAM and then fed to an inverse fast Fourier transform the system to modulate the data with multicarrier signals. The signal is transmitted thru an antenna. That's why OFDM is called the multicarrier modulation technique or MCM.

We frequently use BER vs. SNR graph to compare how one modulation scheme is better. For example, to maintain the same bit error rate (BER), we need less SNR in a typical PSK system than FSK, as PSK is less susceptible to noise than FSK.

On the other hand, the ASK system is more sensitive to noise than FSK and PSK.

So, if we arrange the above three modulation schemes as per their noise resistance, then we get,

PSK > FSK > ASK

[Read more about ASK, FSK, and PSK]

So, to maintain the same bit error rate (BER) in a communication process, we need to provide less Power (SNR) to a PSK system and more SNR to an ASK system.
 

5. BER vs SNR for m-ary PSK




6. BER vs SNR for m-ary QAM





 7. Theoretical BER vs SNR for Alamouti Scheme


Get MATLAB Code

5. Different approaches to calculate BER vs SNR

1. Theoretical BER vs. SNR: Using probability theories of BER vs. SNR. Example - ASK, FSK, PSK done before


 
 

[Click Here]
 

2. Adding AWGN noise at different SNR to the transmitted modulated signal and then plot the BER at different SNR values



[Click here to get MATLAB Code]
 


 


3. Calculate BER vs SNR from Channel Impulse Response





People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

profile

  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

BER vs SNR for ASK, FSK, and PSK

  BER vs. SNR denotes how many bits in error are received in a communication process for a particular Signal-to-noise (SNR) ratio. In most cases, SNR is measured in decibel (dB). For a typical communication system, a signal is often affected by two types of noises 1. Additive White Gaussian Noise (AWGN) 2. Rayleigh Fading In the case of additive white Gaussian noise (AWGN), random magnitude is added to the transmitted signal. On the other hand, Rayleigh fading (due to multipath) attenuates the different frequency components of a signal differently. A good signal-to-noise ratio tries to mitigate the effect of noise.  Calculate BER for Binary ASK Modulation The theoretical BER for binary ASK (BASK) in an AWGN channel is given by: BER  = (1/2) * erfc(0.5 * sqrt(SNR_ask));   Enter SNR (dB): Calculate BER BER vs. SNR curves for ASK, FSK, and PSK Calculate BER for Binary FSK Modulation The theoretical BER for binary FSK (BFSK) in an AWGN channel is g
Read more

BER performance of QPSK with BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc

   Compare the BER performance of QPSK with other modulation schemes (e.g.,  BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc) under similar conditions. MATLAB Code clear all; close all; % Set parameters for QAM snr_dB = -20:2:20; % SNR values in dB qam_orders = [4, 16, 64, 256]; % QAM modulation orders % Loop through each QAM order and calculate theoretical BER figure; for qam_order = qam_orders     % Calculate theoretical BER using berawgn for QAM     ber_qam = berawgn(snr_dB, 'qam', qam_order);     % Plot the results for QAM     semilogy(snr_dB, ber_qam, 'o-', 'DisplayName', sprintf('%d-QAM', qam_order));     hold on; end % Set parameters for QPSK EbNoVec_qpsk = (-20:20)'; % Eb/No range for QPSK SNRlin_qpsk = 10.^(EbNoVec_qpsk/10); % SNR linear values for QPSK % Calculate the theoretical BER for QPSK using the provided formula ber_qpsk_theo = 2*qfunc(sqrt(2*SNRlin_qpsk)); % Plot the results for QPSK semilogy(EbNoVec_qpsk, ber_qpsk_theo, 's-', &#
Read more

Difference between AWGN and Rayleigh Fading

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 signal through any type of channel (here, it is a wireless channel or wireless medium). Due to multi-paths the channel impulse response (h) changes. And multi-paths cause Rayleigh fading. 2
Read more

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

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 Performance Comparison: 1. Noise Sensitivity:    - ASK is the most sensitive to noise due to its reliance on amplitude variations.    - PSK is less sensitive to noise compared to ASK.    - FSK is relatively more robust against noise, making it suitable for noisy environments. 2. Bandwidth Efficiency:    - PSK is the most bandwidth-efficient, requiring less bandwidth than FSK for the same data rate.    - FSK requires wider bandwidth compared to PSK.    - ASK's bandwidth efficiency lies between FSK and PSK. Bandwidth Calculator for ASK, FSK, and PSK The baud rate represents the number of symbols transmitted per second Select Modulation Type: ASK FSK PSK Baud Rate (Hz):
Read more

Why is Time-bandwidth Product Important?

Time-Bandwidth Product (TBP) The time-bandwidth product (TBP) is defined as: TBP = Δ f ⋅ Δ t Δf (Bandwidth) : The frequency bandwidth of the signal, representing the range of frequencies over which the signal is spread. Δt (Time duration) : The duration for which the signal is significant, i.e., the time interval during which the signal is non-zero. The TBP is a measure of the "spread" of the signal in both time and frequency domains. A higher TBP means the signal is both spread over a larger time period and occupies a wider frequency range.     To calculate the period of a signal with finite bandwidth, Heisenberg’s uncertainty principle plays a vital role where the time-bandwidth product indicates the processing gain of the signal. We apply spread spectrum techniques in wireless communication for various reasons, such as interference resili
Read more

RMS Delay Spread, Excess Delay Spread and Multi-path ...

Signal Processing RMS Delay Spread, Excess Delay Spread, and Multipath... RMS Delay Spread, Excess Delay Spread, and Multipath (MPCs) The fundamental distinction between wireless and wired connections is that in wireless connections signal reaches at receiver thru multipath signal propagation rather than directed transmission like co-axial cable. Wireless Communication has no set communication path between the transmitter and the receiver. The line of sight path, also known as the LOS path, is the shortest and most direct communication link between TX and RX. The other communication pathways are called non-line of sight (NLOS) paths. Reflection and refraction of transmitted signals with building walls, foliage, and other objects create NLOS paths. [ Read More about LOS and NLOS Paths] Multipath Components or MPCs: The linear nature of the multipath component signals is evident. This signifies that one multipath component signal is a scalar multiple of
Read more

Constellation Diagrams of ASK, PSK, and FSK

Modulation ASK, FSK & PSK Constellation 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: +√Eb​ or -√Eb (they differ by 180 degree phase shift), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  This article will primarily discuss constellation diagrams, as well as what constellation diagrams tell us and the significance of constellation diagrams. Constellation diagrams can often demonstrate how the amplitude and phase of signals or symbols differ. These two characteristics lessen the interference between t
Read more