Lab 8.10 — OFDM PAPR, clipping and spectral regrowth

Goal

Extend the OFDM mini-link with a transmitter-focused experiment that connects waveform statistics to real RF and fixed-point constraints:

• estimate the OFDM peak-to-average power ratio (PAPR) distribution;
• plot the complementary cumulative distribution function (CCDF);
• apply magnitude clipping at several A/RMS ratios;
• measure the resulting PAPR, EVM, BER and out-of-band energy;
• explain why digital back-off and peak dBFS matter before the AD9363 transmit path.

Why this lab matters

A QPSK constellation can look robust while the time-domain OFDM waveform still contains large peaks. Those peaks can cause fixed-point overflow, DAC clipping or RF power-amplifier compression. Reducing PAPR by hard clipping lowers the peaks, but it also increases EVM and spectral regrowth and can eventually create bit errors.

Processing chain

flowchart LR
    BITS[random bits] --> MAP[QPSK mapper]
    MAP --> ALLOC[subcarrier allocation]
    ALLOC --> IFFT[oversampled IFFT]
    IFFT --> CLIP[magnitude clipping]
    CLIP --> AWGN[AWGN]
    AWGN --> FFT[FFT]
    FFT --> METRICS[PAPR / EVM / BER / OOB]

Run

python blocks/block_08_modulation_and_synchronization/python/lab_8_10_ofdm_papr_clipping.py

Generated artifacts

docs/assets/lab810_ofdm_papr_ccdf.png
docs/assets/lab810_ofdm_clipping_tradeoff.png
docs/assets/lab810_ofdm_spectral_regrowth.png
docs/assets/lab810_ofdm_papr_metrics.json

Default experiment

• FFT=64;
• 52 occupied subcarriers;
• 4× oversampling for PAPR estimation;
• 4000 OFDM symbols for the CCDF;
• 300 OFDM symbols and 31,200 compared bits per clipping point;
• SNR = 24 dB;
• clipping ratios from 3.0 down to 0.7 times RMS amplitude.

With the deterministic default seed, the unclipped signal has roughly 7 dB median PAPR and about 10 dB at the 99th percentile. Severe clipping reduces average PAPR to about 1 dB, but raises EVM above 25%, increases out-of-band energy and produces nonzero BER.

Metrics and interpretation

• PAPR describes peak stress on the digital and RF path.
• EVM exposes in-band constellation distortion before BER necessarily changes.
• BER proves whether the digital decisions still work.
• Out-of-band/in-band power is a compact spectral-regrowth indicator; it is not a standards-compliant ACLR measurement.

This combination reinforces a key course rule: no single metric is sufficient. A waveform can have BER=0 while EVM and spectral quality are already degrading.

Clipping sweep (default run)

Clip level (x RMS)	PAPR	EVM	Bit errors / 31 200	Out-of-band / in-band
none	7.1 dB	2.8 %	0	−25.0 dB
2.0	6.1 dB	4.1 %	0	−24.3 dB
1.6	4.4 dB	7.6 %	0	−21.9 dB
1.3	3.1 dB	12.6 %	0	−18.9 dB
1.1	2.4 dB	17.0 %	0	−16.9 dB
0.9	1.6 dB	21.9 %	0	−14.9 dB
0.7	1.0 dB	26.9 %	2	−13.1 dB

Read down the columns: clipping buys PAPR, and the bill is paid first in EVM and out-of-band energy. Bits survive until EVM is about 27 %, because QPSK decisions only use signs; by then the spectral regrowth (12 dB worse than unclipped) would already fail any spectrum mask.

Exercises

1. Pick the clip level you would ship if the spectrum mask required out-of-band power at least 20 dB below in-band. What PAPR and EVM do you get?
2. Replace QPSK with 16-QAM on the subcarriers (see Lab 8.11). At which clip level do bit errors now appear, and why earlier?
3. The AD9363 DAC is 12 bits. How much digital back-off from full scale does the 99th-percentile PAPR (about 9.8 dB) require, and how many effective bits does that leave for the average signal?

Answers (checked by running the lab script)

1. Clip ratio 1.6: out-of-band power −21.8 dB below in-band, PAPR 4.4 dB (from 7.2 dB), EVM 7.7 %, BER 0. At 1.3 the out-of-band power is already −18.9 dB and fails the mask. Note that even unclipped the measurement reads −25 dB, set by the 24 dB SNR noise in the empty bins, so a −20 dB requirement is checked only 5 dB above that floor.
2. With 16-QAM bit errors appear at clip ratio 1.3 (BER 2.6e-4 at EVM 12.6 %) and reach 3.7e-2 at 0.7; QPSK stays at BER 0 down to 0.9 and shows its first errors only at 0.7 (EVM 27 %). The EVM is the same for both at each ratio; at equal average power the distance from a 16-QAM point to its nearest boundary is 2.2 times smaller than for QPSK (0.316 against 0.707), so it tolerates far less EVM.
3. The peak must fit in full scale, so the average sits 9.8 dB below it. At about 6 dB per bit that costs 9.8 / 6.02 ≈ 1.6 bits: the average signal sees roughly 10.4 effective bits of the 12, and its quantization SNR drops from about 74 to about 64 dB. This is the price of an OFDM waveform's PAPR in the DAC.

Report checklist

• Include the PAPR CCDF.
• Report median and 99th-percentile PAPR.
• Compare unclipped and clipped EVM.
• Report BER with the number of compared bits.
• Include the spectral-regrowth plot.
• Recommend a safe digital back-off strategy for a future AD9363 measurement.