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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.

BER = (number of bits received in error) / (total number of transmitted bits)

On the other hand, SNR refers to the Signal-to-Noise Ratio. For ease of calculation, we commonly convert it to decibels (dB).

What is Signal-to-Noise Ratio (SNR)?

SNR is defined as the ratio of signal power to noise power, and is often expressed in dB:

SNR = signal power / noise power

In dB, the formula becomes:

SNR (in dB) = 10 * log10(signal power / noise power)

For instance, an SNR of 3 dB means the signal power is twice as strong as the noise power.

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Simulator for BER in M-ary PSK

Simulator for BER in M-ary QAM


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Comparison of BER vs. SNR for Various Modulation Techniques

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

BER vs. SNR Graph
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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 that you are transmitting only one bit in a symbol, whereas the QPSK user shares 2 bits in a symbol at a time. Mathematically, the QPSK data rate or bit will be twice as compared to binary PSK (BPSK).

Further, QAM modulation techniques are introduced, which combine Amplitude Modulation and PSK, showing better performance than PSK alone. This technique is widely adopted in information technology and consumer electronics for high data-rate communication.

For example, in 4 QAM, we can send 2 bits in a symbol, resulting in a data rate twice as high as BPSK. Similarly, for 16 QAM, we send 4 bits in a symbol, making the data rate 4 times higher than BPSK.

In the figure above, PSK modulates the phase of the carrier signal to represent data. In 8 PSK, 3 bits fit into each symbol. However, in 8 PSK, the distance between constellation points is smaller than in BPSK and 4 PSK, which means that a higher Eb/No ratio (SNR per bit) is needed to achieve the target BER. While QAM performs better than PSK in normal SNR, BPSK is preferred in extremely noisy channels.

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

OFDM technology is used in practical communication systems such as 4G LTE. In this system, data bits are mapped using QAM and then processed by an inverse FFT to modulate the data with multicarrier signals, which are transmitted through an antenna. OFDM is called the multicarrier modulation technique (MCM).

We frequently use BER vs. SNR graphs to compare how different modulation schemes perform. For example, to maintain the same BER, PSK requires less SNR than FSK because PSK is less susceptible to noise. However, FSK may be better than PSK for very noisy and long-distance communications, especially with noncoherent detection or low complexity systems.


1. BER vs SNR for m-ary PSK

MATLAB code example for m-ary PSK
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2. BER vs SNR for m-ary QAM

BER vs SNR for m-ary QAM
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