Interactive Fundamental Channel Estimation Simulator

Fundamental Channel Estimation

Experiment with how a wireless channel (h) distorts a known pilot signal (x) and how we recover it.

Noise Level (Variance): 0.10

Channel Magnitude (|h|): 1.0

Channel Phase (degrees): 45°

Actual Channel (h):

Estimated Channel (ĥ):

Estimation Error:

Formula: y = hx + n | ĥ = mean(y/x)

1. Received Signal (y)

Notice the rotation (phase shift) and scaling (magnitude) compared to the original pilot at (1,0).

2. Equalized Signal (y / ĥ)

After dividing by our estimate ĥ, the points should cluster back around (1,0).

How the Simulator Works

The Workflow

1. Transmit (x): We send a known "Pilot" symbol (1 + 0j).
2. Distort (h): The channel rotates and scales the signal.
3. Contaminate (n): Random noise is added to the signal.
4. Estimate (ĥ): The receiver calculates the channel by comparing y to x.
5. Recover: We divide the received signal by the estimate to "undo" the distortion.

The Math

1. Received Signal:
y = h ⋅ x + n

2. Least Squares Estimate:
ĥ = mean(y / x)

3. Equalization (Recovery):
xest = y / ĥ

*Since our pilot x = 1, the math simplifies to ĥ = mean(y).