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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





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