Use MSE convergence, estimated filter shape, and stability map to find fast but stable adaptation.
Parameters
Step size μ
-
Coefficient update strength.
Tap count
tap
Length of the estimated FIR filter.
Input power
-
Mean power of the reference signal.
Observation noise
dB
Noise mixed into the error signal.
Plant drift
%
Time variation of the unknown system.
While paused, move the sliders to update the result instantly.
Results
0
Iteration n
—
Instant error e(n)
—
MSE [dB]
—
Step size μ
Live LMS convergence animation
Stability check (known solution)
Loading μ…
Model and equations
$$w(n+1)=w(n)+\mu e(n)x(n)$$
LMS is computationally light, but too large a step size destabilizes the update. Higher input power and more taps lower the stable step-size limit.
How to read it
The MSE plot checks whether convergence is fast and non-oscillatory.
The filter view shows whether tap length can represent the unknown path.
The map shows danger when input power increases.
Learn Adaptive Filter LMS by dialogue
🙋
When reading Adaptive Filter LMS, where should I look first? Moving Step size μ changes both the plots and the result cards.
🎓
Start with Misadjustment, but do not treat the number as the whole answer. Use MSE convergence to confirm the assumed state, then read Estimated filter shape for the distribution or trend. The MSE plot checks whether convergence is fast and non-oscillatory.
🙋
I can see why Step size μ changes Misadjustment. How should I judge the influence of Tap count?
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Move Tap count in small steps and watch Convergence samples. That reveals which term is controlling the result. LMS is computationally light, but too large a step size destabilizes the update. Higher input power and more taps lower the stable step-size limit. A single operating point is not enough; sweep the realistic scatter range.
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What is LMS stability map for? It feels like the ordinary curve already tells the story.
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LMS stability map is for finding boundaries where the condition becomes risky or margin collapses quickly. The filter view shows whether tap length can represent the unknown path. In Early design of echo or noise cancellers, the important question is often what happens after a small change, not only the nominal value.
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So if Misadjustment is within the target, can I accept the condition?
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Treat this as a first-pass review. It helps with Checking LMS step-size limits and Baseline comparison before NLMS or RLS, but final decisions still need standards, measured data, detailed analysis, and vendor limits. The map shows danger when input power increases.
Practical use
Early design of echo or noise cancellers.
Checking LMS step-size limits.
Baseline comparison before NLMS or RLS.
FAQ
Start with Misadjustment and Convergence samples. Then use MSE convergence to confirm the assumed state and Estimated filter shape to read distribution or bias. The MSE plot checks whether convergence is fast and non-oscillatory
Move Step size μ alone, then move Tap count by a comparable amount and compare the change in Misadjustment. LMS stability map shows combinations where margin or performance changes quickly.
Use it for Early design of echo or noise cancellers. Instead of trusting a single point, widen the input range and check whether Misadjustment keeps enough margin before moving to detailed analysis.
LMS is computationally light, but too large a step size destabilizes the update. Higher input power and more taps lower the stable step-size limit. Final decisions still require standards, measured data, detailed analysis, and vendor limits.
How to Use
Set step size (mu) between 0.001 and 0.1; smaller values reduce misadjustment but slow convergence.
Configure filter taps (order) from 4 to 64; higher tap counts increase computational load and steady-state MSE floor.
Adjust input power (0.5 to 5.0 watts) and noise level (−40 to 0 dBm); observe how stability margin compresses with aggressive step sizes and high power.
Monitor convergence samples and misadjustment percentage; run simulation and compare against theoretical bounds for your tap configuration.
Worked Example
Configure a 16-tap FIR adaptive filter with mu=0.02, input power=2.5, noise=−35 dB, plant drift 8% (this tool's output formulas). Convergence takes about 80 samples, misadjustment is about 29.8%, the stability margin is about 60%, and the MSE floor settles at about −32.5 dB. Increasing mu to 0.04 halves convergence to 40 samples but raises misadjustment to about 45.6% and lowers the stability margin to about 20%. This trade-off reflects fundamental LMS convergence-tracking behavior in time-varying channels.
Practical Notes
For 4G/5G channel estimation, use mu=0.01–0.03 with 32+ taps to suppress multipath without excessive noise amplification.
Plant drift (time-varying impulse response) increases optimal step size; monitor stability margin to avoid divergence in non-stationary channels.
Misadjustment scales with tap count and input power; halving mu typically reduces misadjustment by 75% but requires 4× more convergence samples.
Noise floor dominates MSE when mu is very small; balance step size against noise level for best steady-state performance in practice.