Web Simulation 

 

 

 

 

OFDM Cyclic Prefix Trade-off

Objective. This interactive simulation shows the Cyclic Prefix (CP) trade-off in OFDM: too little CP causes Inter-Symbol Interference (ISI) and destroys the signal; too much CP wastes capacity and reduces spectral efficiency. The goal is to find the "sweet spot" where CP is just long enough to cover the channel delay spread.

Setup. We use a simplified OFDM model: NFFT = 64, QPSK modulation. The channel has exponential-decay impulse response of length Delay Spread. The CP is prepended to each symbol; the receiver strips it and runs an FFT on the remaining NFFT samples. If the channel "tail" extends beyond the CP into the FFT window, we get ISI.

Sections

Theory

Channel & ISI. The channel impulse response h[n] has exponential decay over Delay Spread samples, normalized so Σ|h[n]|² = 1. The ISI energy is the fraction of channel energy whose taps fall after the CP and spill into the FFT window:

ISI = Σn ≥ NCP |h[n]|²      SINR = SNR / (1 + K·ISI)

where K is a penalty factor. From SINR follow the error metrics: EVM ∝ 1/√SINR, and a sigmoid on SINR gives a BLER (block-error) proxy.

Efficiency & Goodput. The CP is pure overhead, so spectral efficiency and useful throughput are:

η = NFFT / (NFFT + NCP)      Goodput = η·(1 − BLER)
The sweet spot: too short a CP lets ISI raise BLER (Goodput falls); too long a CP shrinks η (Goodput also falls). Peak goodput sits where NCP ≈ Delay Spread — just long enough to cover the channel tail, and no longer.

Simulation

The interactive simulator is below. Use the controls to explore the concepts described above.

Controls

16
10
20 dB
Efficiency: —
BLER: —
Goodput: —
Panel A: Time Domain (CP, Data, Tail)
Panel B: QPSK Constellation
Panel C: Overhead / Link Quality / Goodput

 

Usage

Use the Preset dropdown to load scenarios: High ISI (CP=4, Delay=20), Wasted Efficiency (CP=32, Delay=5), Optimal (CP=22, Delay=20). Adjust CP Length, Delay Spread, and SNR sliders to explore the trade-off. Run/Pause stops or resumes the animation; sliders and plots update even when paused. Show circular (CP loop) toggles the CP Loop View: a green "Perfect Cycle" when safe (Delay ≤ CP), or a red corrupted arc with "Broken Illusion!" when the tail exceeds the CP (ISI).

Panel A (Time Domain): Two tracks—original Symbol 1 (top) and delayed copy + Symbol 2 (bottom). Blue = CP, green = data; red = interference region. Waveforms overlay the blocks. When the tail enters the FFT window, "INTERFERENCE (ISI)!" appears; otherwise "SAFE". Panel B (QPSK Constellation): Ideal × marks and received points with real ISI distortion. EVM at the center is directly measured from the constellation (RMS error / RMS reference). Panel C shows Overhead, Link Quality, and Goodput bars; Goodput peaks when CP ≈ Delay Spread.

Parameters

Control

Range

Effect

CP Length

0–32 samples

Prepended to each symbol; longer CP reduces ISI but lowers efficiency

Delay Spread

0–48 samples

Length of the channel impulse response (exponential decay)

SNR

0–40 dB

Higher SNR improves link quality

Preset

High ISI / Wasted / Optimal

Loads a scenario; overrides sliders until you change them

Run/Pause

toggle

Toggles animation; sliders and plots still update when paused

Show circular (CP loop)

toggle

CP Loop View — green circle (safe) or red corrupted arc (ISI)

Key Concepts

  • Sweet spot: Set CP ≈ Delay Spread. Too little CP → ISI, high BLER, low Goodput. Too much CP → low efficiency, low Goodput.
  • Goodput = Efficiency × (1 − BLER). Efficiency = NFFT/(NFFT + NCP).
  • EVM: Measured from the constellation as RMS(error) / RMS(reference); dimensionless.

Limitations

  • Teaching model: SINR, EVM, and BLER come from simplified closed-form relations (penalty factor K, a sigmoid), not a full bit-level OFDM link simulation.
  • One exponential channel: the channel is a single exponential-decay impulse response. Real multipath profiles, fading over time, and Doppler are not modelled.
  • No synchronization errors: perfect timing and frequency sync are assumed; CFO, sampling offset, and phase noise (which also eat into the CP budget) are ignored.
  • Fixed NFFT and QPSK: 64-point FFT with QPSK only; other FFT sizes, modulations, and pilot/coding schemes are out of scope.