Theoretical BER vs SNR for binary ASK and FSK

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Theoretical BER vs SNR for binary ASK and FSK

Theoretical Ber vs SNR for Amplitude Shift Keying (ASK)

The theoretical bit error rate (BER) for binary Amplitude Shift Keying (ASK) as a function of the signal-to-noise ratio (SNR) can be derived using the following expression:

Where:

Q(x) is the Q-function, which is the tail probability of the standard normal distribution.

SNR is the signal-to-noise ratio.

N0 is the noise power spectral density.

For a binary ASK system in an additive white Gaussian noise (AWGN) channel, the SNR is usually expressed in terms of the energy per bit 𝐸𝑏 and the noise power spectral density 𝑁0 :

Where Eb/N0 is the SNR and in mathematics Q(x) = 0.5 * erfc(x/√2)

This expression shows that the BER decreases as the SNR increases, meaning that a higher SNR leads to better performance (lower BER) for binary ASK.

Theoretical BER vs SNR for Frequency Shift Keying (FSK)

Formulae for bit error rate (BER) of binary FSK is

Where Q is the Q function

In mathematics Q(x) = 0.5 * erfc(x/√2)

So, theoretical BER for binary FSK will be

Where:

Q(x) is the Q-function.

Eb is the energy per bit.

N0 is the noise power spectral density.

erfc(x) is the complementary error function.

Fig: Theoretical BER vs SNR for Binary ASK Modulation

Fig: Theoretical BER vs SNR for Binary FSK Modulation

Similarities:

For both ASK and BFSK, the BER decreases as the SNR increases, indicating better performance at higher SNR values.

The formulas for BER in both cases involve the complementary error function, indicating that they follow similar trends, though the constants and scaling factors differ slightly.

MATLAB Code for theoretical BER vs SNR for BASK

MATLAB Code for theoretical BER vs SNR for BFSK

Also read about

[1] Theoretical BER vs SNR for binary PSK (BPSK)

[2] Constellation Diagrams of ASK, FSK, and PSK

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