Amplitude Shift Keying (ASK)

Theory:

Amplitude Shift Keying (ASK) is one of the simplest digital modulation techniques. In this method, a single carrier wave is switched ON or OFF to transmit binary symbols. The binary ASK system was an early form of digital modulation, used in wireless telegraphy. In a binary ASK system, binary symbol '1' is represented by transmitting a sinusoidal carrier wave of fixed amplitude A_c and fixed frequency f_c for the bit duration T_b. Binary symbol '0' is represented by switching off the carrier for T_b seconds. This signal can be generated simply by turning a sinusoidal oscillator's carrier ON and OFF according to the modulating pulse train, which is why this scheme is also known as On-Off Keying (OOK). The ASK signal can be generated by applying the incoming binary data and the sinusoidal carrier to the two inputs of a product modulator. The resulting output is the ASK wave.

In this modulation, binary '1' is represented by the presence of a carrier and binary '0' by the absence of a carrier.

ASK Transmitter:

Here, the electrical signal representation technique is ON-OFF coding. In which
1 => +V (positive voltage)
0 => 0 V (zero voltage)

ASK Receiver:

For the demodulation of ASK, a coherent detector is typically used. This involves correlating the received signal with the carrier wave.

• For binary '1' (carrier present): The output of the correlator (or matched filter) will be proportional to the amplitude of the received carrier, e.g., A_c * T_b / 2.
• For binary '0' (carrier absent): The output will be close to zero.

A threshold detector then compares this output to a predetermined threshold to decide whether a '1' or '0' was transmitted.

The receiver aims to differentiate between the presence and absence of the carrier to recover the original binary data.

Constellation Diagram of ASK

Figure: Constellation Diagram of Binary ASK

In the above figure, the reference axis corresponds to the normalized basis function φ₁(t) = √(2/T_b) cos(2Пf_ct) for 0 ≤ t ≤ T_b.

Distance of the '1' symbol from the origin is √(E_b). Energy of the '1' symbol = {√(E_b)}² = E_b.
Distance of the '0' symbol from the origin is 0. Energy of the '0' symbol = 0
Distance between signaling points, d₁₂ = √(E_b).
High-order Amplitude Shift Keying (ASK) refers to using a large number of amplitude levels to represent digital data. For instance, in binary ASK (BASK), there are two amplitude levels, usually represented as 0 and 1. High-order ASK can have more than two amplitude levels, such as 4, 8, 16, 64, etc.

Under different noise configurations

Let's explore ASK modulation under two common noise scenarios: AWGN (Additive White Gaussian Noise) and Rayleigh fading.

ASK Modulation with AWGN:

We've already discussed the effect of AWGN on ASK modulation in the previous response. The mathematical effect involves adding Gaussian-distributed noise to the modulated signal. The received signal y(t) is given by:
y(t) = x(t) + n(t)
Where:
x(t) is the modulated ASK signal.
n(t) is the AWGN.
The effect of AWGN is to add random variations to the amplitude of the signal, which can lead to erroneous detection of the transmitted symbols. The SNR (signal-to-noise ratio) plays a crucial role in determining the quality of demodulation, with higher SNR values leading to better performance.

ASK Modulation with Rayleigh Fading:

Rayleigh fading is a type of multipath fading that occurs in wireless communication channels. It's characterized by a random variation in the amplitude of the received signal due to constructive and destructive interference of multiple signal paths.

Mathematically, Rayleigh fading can be represented as a complex Gaussian random variable with zero mean and a certain variance. The received signal y(t) in the presence of Rayleigh fading can be represented as:
y(t) = h . x(t) + n(t)
Where:
h is the complex fading coefficient, representing the channel gain and phase shift.
x(t) is the modulated ASK signal.
n(t) is the noise

The fading coefficient h introduces random amplitude and phase variations to the signal. Due to the randomness of h, the received signal's amplitude will experience fluctuations, impacting the detection of transmitted symbols. The actual fading distribution might vary depending on the specific channel characteristics.

When ASK modulation is subjected to different noise configurations, the mathematical representation of the received signal changes. Under AWGN, Gaussian noise is added to the signal's amplitude. Under Rayleigh fading, the complex fading coefficient introduces random amplitude and phase variations. The performance of ASK modulation in these scenarios depends on the SNR for AWGN and the characteristics of the fading channel for Rayleigh fading.