Power, Linearity, and Distortion Practical Power Topics Informational

How do I calculate the peak to average power ratio of a multi-carrier OFDM signal?

Calculating the peak-to-average power ratio (PAPR) of a multi-carrier OFDM signal determines the ratio between the maximum instantaneous power and the average power of the waveform, which directly determines the required power amplifier backoff. An OFDM signal is the sum of N independent subcarriers, each modulated with data. The peak power occurs when all subcarriers align in phase (constructive addition), and the average power is the sum of the individual subcarrier powers. The theoretical maximum PAPR is: PAPR_max = 10 x log10(N) dB, where N is the number of subcarriers. For 64 subcarriers (802.11a WiFi): PAPR_max = 18 dB. For 1200 subcarriers (LTE 20 MHz): PAPR_max = 30.8 dB. However: the probability of all subcarriers aligning perfectly is extremely small. The practical PAPR (at the 0.01% probability level, meaning the PAPR exceeds this value only 0.01% of the time) is approximately: PAPR_practical approximately 10-12 dB for most OFDM systems regardless of N (the PAPR distribution converges to approximately the same range for large N). This means the PA must be backed off by approximately 6-8 dB below its P1dB (or Psat) to handle the OFDM signal peaks without clipping, which significantly reduces the PA efficiency. A PA with 50% efficiency at Psat operates at approximately 15-20% efficiency at 7 dB backoff.

Category: Power, Linearity, and Distortion

Updated: April 2026

Product Tie-In: Power Amplifiers, Combiners, Loads

OFDM PAPR Calculation

PAPR is the fundamental challenge of OFDM and multi-carrier systems. It forces the PA to operate at a large backoff from its maximum power point, wasting most of the PA's power capability as heat.

PAPR Reduction Techniques

Clipping: Limit the signal peaks to a defined threshold. Simple but introduces in-band distortion and out-of-band spectral regrowth. Acceptable for a few dB of PAPR reduction (clip at 3-4 dB above average)
Crest factor reduction (CFR): More sophisticated than clipping. Uses peak cancellation: when a peak exceeds the threshold, a scaled copy of the peak waveform is subtracted from the signal. This reduces the peak while minimizing the in-band distortion. CFR can reduce PAPR by 3-5 dB
DPD + CFR: Combine CFR (to reduce PAPR) with digital pre-distortion (DPD, to linearize the PA at the reduced backoff). This approach is standard in modern 4G/5G base station transmitters, enabling PA operation at 3-5 dB backoff instead of 7-8 dB, recovering 3-5 dB of PA efficiency

OFDM PAPR Parameters

PAPR_max = 10log₁₀(N) [dB]
For N=256: PAPR_max = 24.1 dB (theoretical maximum)
PAPR (CCDF at 10⁻⁴): approximately 10-12 dB for large N
PA backoff = PAPR_practical - PA headroom
Efficiency at backoff: η(backoff) ≈ η_max × 10^(-backoff/10)
For η_max=50%, backoff=7dB: η ≈ 10%

Common Questions

Frequently Asked Questions

What PAPR do real standards specify?

WiFi 802.11a/g/n/ac (64-256 subcarriers): PAPR approximately 10-12 dB (at 10^-4 CCDF). LTE (300-1200 subcarriers): PAPR approximately 8-11 dB (with SC-FDMA uplink: approximately 6-8 dB, lower PAPR than OFDM). 5G NR (OFDM with CP-OFDM): PAPR approximately 10-13 dB (depending on bandwidth and modulation). DVB-T (1705 or 6817 subcarriers): PAPR approximately 12-15 dB.

Why does PAPR matter for battery life?

In mobile devices: the PA typically consumes 50-80% of the total transmit power. PAPR forces the PA to operate at backoff, reducing efficiency. For a Class-AB PA at 7 dB backoff: efficiency approximately 10-15% (vs. 40-50% at Psat). This means: the battery energy wasted as heat in the PA is 5-10× the useful RF output power. Reducing PAPR by 3 dB (using CFR or SC-FDMA) improves the PA efficiency by approximately 2× and extends the battery life proportionally. This is why LTE uses SC-FDMA (not OFDM) for the uplink.

What is EVM and how does it relate to PAPR?

EVM (Error Vector Magnitude) measures the modulation quality. When the PA clips the OFDM peaks: the modulation is distorted, increasing the EVM. The EVM must be below the standard's requirement: 802.11ac 256-QAM: EVM < -32 dB (2.5%). LTE 64-QAM: EVM < -8% (-22 dB). If the PAPR is not managed (insufficient backoff or no CFR): the EVM exceeds the requirement and the transmitted data has excessive bit errors. The PA backoff is set to maintain the required EVM under worst-case PAPR conditions.

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