Skip to main content

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


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.  

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 if SNR is 3dB.


Simulator for BER in M-ary PSK

Simulator for BER in M-ary QAM


Explore Signal Processing Simulations

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. But sometimes, FSK is often a better choice than PSK for very noisy and long-distance communications — especially when noncoherent detection, low complexity, or phase-unstable channels are involved.

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.
 

1. BER vs SNR for m-ary PSK




2. BER vs SNR for m-ary QAM






 3. BER vs SNR for ASK, FSK, and PSK

 
 
 
 
 
 
 

 
 
 
 
 
 

4. Theoretical BER vs SNR for Alamouti Scheme


Get MATLAB Code

 

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


 
 

 

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



 


 


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

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

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...

Constellation Diagrams of ASK, PSK, and FSK

📘 Overview 🧮 Online Simulator for constellation diagrams of ASK, FSK, and PSK 🧮 Theory 🧮 MATLAB Codes 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM 📚 Further Reading 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.    Simulator for BASK, BPSK, and BFSK Constellation Diagrams ...

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

📘 Overview 🧮 Multipath Components or MPCs 🧮 Excess Delay spread 🧮 Power delay Profile 🧮 RMS Delay Spread 🧮 Simulator for Calculating RMS Delay Spread 🧮 Why is there significant multipath in the case of very high frequencies? 🧮 Why RMS Delay Spread is essential for wireless communication? 🧮 Why the Power Delay Profile is essential? 🧮 MATLAB Codes 📚 Further Reading 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 direc...

MATLAB Code for Pulse Amplitude Modulation (PAM) and Demodulation

📘 Overview & Theory 🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of an Analog Signal 🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of an Analog Signal (2) 🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of Digital data 🧮 Simulation results for comparison of PAM, PWM, PPM, DM, and PCM 🧮 Other Pulse Modulation Techniques (e.g., PWM, PPM, DM, and PCM) 📚 Further Reading   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 period 2*pi*fm (sinusoidal wave signal) c=0.5*square(2*pi*fc*t)+0.5; % square wave with period 2*pi*fc s=m.*c; % modulated signal (multiplication ...

Relationship between Gaussian and Rayleigh distributions

📘 Introduction, Gaussian Distribution, Relationship Between Gaussian and Rayleigh Distribution 🧮 How to mitigate Rayleigh fading? 🧮 Equalizer to reduce Rayleigh Fading (or Multi-path Effects) in MATLAB 🧮 MATLAB Code for Effects of AWGN and Rayleigh Fading in Wireless Communication 🧮 Simulator for the effect of AWGN and Rayleigh Fading on a BPSK Signal 📚 Further Reading Wireless Signal Processing Gaussian and Rayleigh distributions ...   The Rayleigh distribution in classical fading models (like wireless communication) arises from modeling the real and imaginary parts of a complex baseband signal as independent, zero-mean Gaussian random variables — under specific assumptions . 1. Gaussian Distribution  The Gaussian distribution has a lot of applications in wireless communication. Since noise in wireless communication systems is unpredictable, we frequently assume that it has a Gaussian distribution...

Difference between AWGN and Rayleigh Fading

📘 Introduction, AWGN, and Rayleigh Fading 🧮 Simulator for the effect of AWGN and Rayleigh Fading on a BPSK Signal 🧮 MATLAB Codes 📚 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...

MATLAB Codes for Various types of beamforming | Beam Steering, Digital...

Beamforming Techniques MATLAB Codes for Beamforming... The mathematical [↗] and theoretical aspects of beamforming [↗] have already been covered. We'll talk about coding in MATLAB in this tutorial so that you may generate results for different beamforming approaches. Let's go right to the content of the article. In analog beamforming, certain codebooks are employed on the TX and RX sides to select the best beam pairs. Because of their beamforming gains, communication created through the strongest beams from both the TX and RX side enhances spectrum efficiency. Additionally, beamforming gain directly impacts SNR improvement. Wireless communication system capacity = bandwidth*log2(1+SNR) bits/s. Thus, the capacity or overall throughput of the system increases. MATLAB Script %Written by Salim Wireless %Visit www.salimwireless.com for study materials on wireless communication %or, if you want to learn how to code in MATLAB clear all;...