Power Delay Profile Demo

Power delay profile demo

Pick a power delay profile (PDP), then read off the mean excess delay μτ, the RMS delay spread στ and the coherence bandwidth Bc. The second plot shows the frequency correlation |R(Δf)| of the channel — stretch the PDP in delay and watch the coherence bandwidth shrink by the same factor.

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Chooses the shape of P(τ). Only the controls for the selected model are shown.
Logarithmic slider, 10 ns to 5 µs. For the exponential PDP this is both μτ and στ.
Excess delay of the echo. The first ray sits at τ = 0.
Echo power relative to the first ray. 0 dB = equal rays (largest στ for a given τ2).
Illustrative 3GPP-like shapes, not the exact TR 38.901 tables. For the standardized TDL-A to TDL-E tables use the 3GPP TDL calculator.
Separate fields with comma, space or colon; separate taps with a new line or a semicolon. Up to 64 taps. Delays are shifted so the earliest tap is at 0.
Stretches all delays by one factor so the table has the στ set by the slider above — the same trick 3GPP uses (“DS scaling”). Shape is kept.
Makes ΣP(τk) = 1. Off: the strongest tap is 1. Changes the vertical axis only — μτ, στ and Bc are power-normalized by definition.
dB view reveals weak late taps that are invisible on a linear axis.
Compared with Bc to judge flat vs frequency-selective fading. Drawn as a purple dashed line on the correlation plot.
Mean excess delay μτ —
RMS delay spread στ —
Max excess delay (taps within 30 dB of peak) —
Bc ≈ 1 / (5 στ)  (correlation ≈ 0.5) —
Bc ≈ 1 / (2π στ)  (conservative) —
Bc measured from this PDP at |R| = 0.5 —
W / Bc (using 1 / (5 στ)) —
Verdict for this bandwidth —
Check —

Power delay profile P(τ)

Pin a channel, then change τrms or the taps to see στ and Bc move in opposite directions.

Frequency correlation |R(Δf)| = |Σ Pk e−j2πΔfτk| / ΣPk

Longer delay spread, narrower coherence bandwidth: choose Exponential, press “Pin current channel as reference”, then drag τrms from 100 ns to 1 µs. στ grows 10×, Bc falls to one tenth, and the grey reference curve in the lower plot stays much wider than the live blue one.

Two-ray fading nulls: choose Two-ray, set the power to 0 dB. |R(Δf)| now oscillates as |cos(πΔfτ2)| and hits zero every 1/τ2 in Δf — the deep notches of a two-path channel. Lower the echo power and the notches shallow out.

Full write-up: Power delay profile article. Next in the path: scattering function and TDL modeling.

Controls explained

PDP model
Exponential — the classic smooth-decay model P(τ) = (1/τrms) e−τ/τrms, sampled at τrms/10 up to 8 τrms; ideal curve drawn dashed. Two-ray — a direct ray plus one echo. Custom — any discrete tapped-delay-line table, e.g. a 3GPP-style profile.
τrms slider
Exponential model: the RMS delay spread itself (μτ equals it too). Custom model with scaling on: the target στ to which all tap delays are stretched. Hidden in Two-ray and in Custom without scaling.
Second-ray delay and power
Two-ray only. With relative power fraction a = P2/(P1+P2) the exact result is στ = τ2 √(a(1−a)), which peaks at τ2/2 for equal rays.
Tap preset and tap table
Each line is “excess delay in ns, power in dB”. Powers are relative, so only differences matter. Edit the text freely; the preset menu switches to “Edited by you”.
Scale delays to target στ
Multiplies every delay by σtarget/σcurrent. Powers are unchanged. This is how one standardized shape is reused for “short”, “normal” and “long” delay-spread scenarios.
Normalize total power
Rescales the displayed P(τ) so the taps sum to 1. The moments are ratios, so they do not change.
Vertical scale
Linear or dB (relative to the strongest tap, floor −40 dB).
Signal bandwidth W
Your signal’s bandwidth. If W is much smaller than Bc the fading is effectively flat across the signal; if W exceeds Bc different parts of the band fade differently (frequency-selective), which is when equalization or OFDM is needed.
Pin / Clear reference
Stores the current channel and overlays its |R(Δf)| in grey so you can compare two delay spreads directly. The reference is not saved in the shareable link.

How to use this demo

A power delay profile tells you how the average received power is spread over excess delay. Everything in the results panel is a moment of that profile: the mean excess delay μτ is its centre of mass, and the RMS delay spread στ is its standard deviation. The lower plot is the Fourier transform of the PDP — the frequency correlation function — and the frequency at which it falls to about one half is the coherence bandwidth.

Two rules of thumb are shown. Bc ≈ 1/(5στ) is the classic estimate for correlation about 0.5. Bc ≈ 1/(2πστ) is the more conservative figure; for an exponential PDP it is where |R| has dropped to about 0.71. The exact 0.5 crossing for an exponential PDP is √3/(2πστ) ≈ 0.28/στ, and the panel measures it for whatever profile you choose. The numbers differ by small constants, but they all scale as 1/στ: ten times the delay spread, one tenth of the coherence bandwidth.

Try a few starting points: exponential, 100 ns, exponential, 1 µs, equal-power two-ray, 500 ns, and two clusters scaled to 300 ns.

Read next

FAQ

Which coherence-bandwidth rule should I use? Use 1/(5στ) when you care about the band over which the channel gain stays correlated above about 0.5, and 1/(2πστ) for a more cautious figure. Both are approximations tied to a specific correlation level and PDP shape; the measured value in the panel is the one that belongs to your profile.

Why does normalizing the power not change στ? The moments divide by the total power ΣP(τk), so multiplying the whole profile by a constant cancels. Only relative powers matter.

Are the custom presets the standardized 3GPP profiles? No. They are illustrative tap tables with the same character as 3GPP TDL models. Use the 3GPP TDL calculator for the standardized tables and delay-spread scaling.

Why does the two-ray correlation never settle? A two-ray PDP has a sharp structure in delay, so its Fourier transform is periodic in frequency with period 1/τ2. Coherence bandwidth is then a poor summary: the channel has deep nulls separated by 1/τ2 no matter what στ suggests.