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: N_FFT = 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 N_FFT samples. If the channel "tail" extends beyond the CP into the FFT window, we get ISI.

Theory

Channel & ISI. The channel impulse response h[n] has exponential decay over Delay Spread samples, normalized so Σ|h[n]|² = 1. ISI energy is the sum of |h[n]|² for n ≥ N_CP: taps that fall after the CP spill into the FFT window. SINR = SNR / (1 + K·ISI) with a penalty factor K; EVM ∝ 1/√SINR. A sigmoid on SINR gives a BLER (block error) proxy.

Efficiency & Goodput. Efficiency η = N_FFT/(N_FFT + N_CP). Goodput = η·(1 − BLER). When CP is too short, ISI raises BLER and Goodput drops; when CP is too long, η drops and Goodput also drops. The sweet spot is CP ≈ Delay Spread.

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

• 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 (dB): 0–40 dB. Higher SNR improves link quality.
• Preset: High ISI, Wasted Efficiency, or Optimal. Overrides sliders until you change them.
• Run/Pause: Toggle animation. Sliders and plots still update when paused.
• Show circular (CP loop): Dynamic CP Loop View—green circle (safe) or red corrupted arc (ISI)—reacts to CP and Delay Spread.

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 = N_FFT/(N_FFT + N_CP).
• EVM: Measured from the constellation as RMS(error) / RMS(reference); dimensionless.