Objective. This interactive simulation illustrates why peaks hurt in RF power amplifiers (PAs). OFDM signals have a high Peak-to-Average Power Ratio (PAPR). To avoid distortion, the PA must be backed off, which reduces efficiency. If the backoff is too small, clipping causes EVM degradation and spectral regrowth (shoulders in the spectrum), which can interfere with neighboring channels.

Setup. We use N_FFT = 256, 4× oversampling (1024-point IFFT), and 200 active subcarriers (center-aligned). You can switch QPSK, 16QAM, or 64QAM. The PA is modeled as hard clipping at a threshold set by the Input Backoff (dB). Lower backoff → more clipping → higher EVM and spectral regrowth; higher backoff → cleaner signal but lower efficiency.

Theory

PAPR. The peak-to-average power ratio (often expressed in dB) is the ratio of the largest instantaneous power to the mean; oversampling is used to catch inter-sample peaks:

Clipping. The PA clips at amplitude A set by the input backoff; for |x| > A it outputs A·x/|x| (hard clipping):

EVM & Spectral regrowth. Clipping distorts the signal, increasing EVM (Error Vector Magnitude) and causing spectral regrowth—energy “spilling” into guard bands. Shoulders in the spectrum graph indicate interference with neighboring channels.

Cross-shaped constellation. Under strong clipping, the received constellation (FFT of the clipped time-domain signal) often forms a “+” (cross) pattern: dense clusters along the I and Q axes. This is real OFDM compression behavior, not a plotting artifact. OFDM time-domain peaks tend to align near the I/Q axes (phase ≈ 0°, 90°, 180°, 270°). Magnitude clipping maps those peaks onto a circle; the resulting axis-biased distortion, seen in the frequency domain, pushes received symbols toward the axes and produces the cross. The exact pattern depends on backoff, modulation, and FFT size, but the underlying mechanism is what happens in real PAs when driven into compression.

Simulation

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

 

Usage

Use the Modulation dropdown (QPSK, 16QAM, 64QAM) and the Input Backoff (dB) slider (0–25 dB) to explore the trade-off. Presets: Extreme (0 dB) → no backoff, max clipping; High Distortion (2 dB); Balanced (7 dB); Clean / Low Eff (12 dB); No clipping (25 dB) → reference, minimal EVM. The top bar shows PAPR, EVM, and Efficiency. Time domain: green = original |x|, red dashed = clipped, orange = threshold. Spectrum: blue = original, red = clipped (shoulders = regrowth). Constellation: gray = original symbols, red = received after clipping. AM/AM: input vs output amplitude; green 1:1 line vs red saturation ceiling. CCDF: fraction of samples with |x| > level vs |x|; bin-based over time-domain amplitude; green = original, red = clipped.

Parameters

• N_FFT: 256. Oversampling: 4× (1024-point IFFT). Active subcarriers: 200 (center).
• Modulation: QPSK, 16QAM, or 64QAM. Higher-order modulations tend to have higher PAPR.
• Input Backoff (dB): 0–25 dB. Clipping threshold = √P_avg · 10^{−Backoff/20}.
• Efficiency: Proxy 100 − 3×Backoff (%), clamped 0–100.

Key Concepts

• PAPR = max|x|² / avg|x|² (dB). OFDM has high PAPR → PA backoff → efficiency loss.
• Clipping → EVM increase and spectral regrowth (shoulders in spectrum).
• EVM: RMS(error) / RMS(reference) over active subcarriers after FFT of clipped signal.
• Cross-shaped constellation: Under clipping, received points often cluster along the I and Q axes (“+” shape). This reflects real OFDM compression—axis-biased peaks and magnitude clipping—not a visual artifact.
• CCDF: Fraction of time-domain samples with |x| > level vs |x|. Bin-based histogram; green = original, red = clipped. Clipping caps the envelope → clipped tail drops at threshold.

Limitations

• Hard-clipping PA model. The amplifier is an ideal memoryless hard limiter. Real PAs have smooth AM/AM compression, AM/PM phase distortion, and memory effects (frequency-dependent behavior) that change EVM and regrowth.
• No PAPR-reduction techniques. The demo shows the problem, not the cures: clipping-and-filtering, tone reservation, SLM/PTS, companding, and DPD (digital pre-distortion) are not implemented.
• Single OFDM symbol, fixed FFT. N_FFT = 256 with 4× oversampling and 200 active subcarriers; results vary with FFT size, subcarrier count, and windowing, and no symbol-to-symbol averaging of CCDF is done.
• Efficiency is a proxy. "Efficiency = 100 − 3×Backoff%" is an illustrative linear proxy, not a real PA drain-efficiency curve (which depends on class, load-line, and Doherty/ET architecture).
• Idealized chain. No pulse shaping, cyclic prefix effects on spectrum, DAC/ADC quantization, I/Q imbalance, phase noise, or channel — only the clipping nonlinearity is modeled.
• No receiver correction. EVM is measured on the raw FFT of the clipped signal; equalization, decision-feedback, and coding that a real receiver would apply are out of scope.