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Advanced M-ary Modulation Simulator: Constellation, min dist, Efficiency, SER, EVM (RMS)


Advanced M-ary Communication Lab

Analytical & Statistical Performance of Digital Modulation

Theoretical Probability of Error (\(P_s\))
\[ P_s = Q\left(\sqrt{\frac{2 E_b}{N_0}}\right) \]
Efficiency2 bps/Hz
Min Dist (\(d_{min}\))1.41
Symbol Error1.2e-5
EVM (RMS)0.0%
Constellation Diagram
Noise PDF & Decision Tail

1. Geometric Mapping

Each point on the grid represents a unique bit sequence. As M increases, points are packed tighter.

2. Noise Contribution

The cloud around each point is AWGN. If the cloud overlaps a decision boundary, a bit flip occurs.

3. Error Probability

The Q-function measures the area of the tail that crosses into the wrong decision territory.

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