Constellation Diagrams of ASK, PSK, and FSK

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.

This article will primarily discuss constellation diagrams, as well as what constellation diagrams tell us and the significance of constellation diagrams. Constellation diagrams can often demonstrate how the amplitude and phase of signals or symbols differ. These two characteristics lessen the interference between two signals or symbols.

Figure 1: Constellation diagrams of ASK, PSK, and FSK (Get MATLAB Code)

The constellation points for ASK, PSK, and FSK [↗] are located in a different pattern, and the distances between the constellation points vary. According to the above diagram, the distance between ASK constellation points is (√Eb -0) = √Eb (where Eb stands for energy per bit). From the above figure, you can also see the distances between constellation points for PSK and FSK are 2√Eb and √(2Eb), respectively. In a constellation diagram, if the distance between signaling points is less, then the probability of error (Pe) will be higher and vice versa.

Get MATLAB Code for ASK, FSK, and PSK

From the aforementioned, ASK is prone to bit errors due to the shorter distance between constellation points than others. PSK, on the other hand, will perform well in that situation. In real-world communication, we always prefer PSK if the channel is noisy. We prefer FSK for very high-frequency communication.

This illustration in Figure 1 above, known as a constellation diagram, graphically shows the complicated envelope of each potential symbol state. In a constellation diagram, the in-phase and quadrature components of the complex envelope are represented by the x- and y-axes, respectively. The spacing between the signals shows how diverse the modulation waveforms are on a constellation diagram, which also shows how well a receiver can distinguish between all potential symbols in the presence of noise. This concept will become more evident when you look at higher-order modulations like M-QAM, QPSK, M-PSK, etc. [Read More about M-QAM and M-PSK constellation diagrams] Unlike binary ASK, FSK, and PSK, where signal sets only consist of {0 and 1}, a signal set will contain many symbols.

MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK

(Get MATLAB Code for the above)

(Get MATLAB Code)

Energy per Bit required for Transmission of Binary Bits in ASK, FSK, and PSK Modulation Schemes

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How to estimate constellation points for real systems?

We know for real systems signal is received as a distorted and attenuated version of the actual transmitted signal. The nearest constellation point is assigned to the received bit or symbol. For example, to estimate the channel, we use an equalizer. The main function of an equalizer is to calculate the estimated channel from training bits/symbols. The training bits/symbols are known to the receiver. Non-linear equalizers are mostly used equalizers rather than linear equalizers.

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