Crest Factor Reduction (CFR)

The most fundamental CFR technique. The signal amplitude is hard-limited to a predefined threshold, which generates out-of-band spectral regrowth. A subsequent low-pass filter removes this distortion from adjacent channels.

• In-band distortion: Clipping introduces EVM degradation that cannot be filtered.
• Iterative clipping: Multiple clip-and-filter stages progressively shape the peak distribution.
• Filter complexity: Steep transition bands are required to preserve the corrected spectrum, increasing latency.

Instead of hard-clipping, detected peaks above a threshold are multiplied by a smooth windowing function (e.g., Gaussian, Kaiser, or raised-cosine). This shapes the clipping noise to concentrate its spectrum within the signal band.

• Spectral control: Windowing avoids the sharp discontinuities of hard clipping, significantly reducing ACLR regrowth.
• Peak regrowth: Overlapping correction pulses applied to adjacent peaks can cause new peaks to form, requiring iterative detection.
• Coefficient design: The window shape directly trades off EVM against out-of-band emissions.

A pre-computed cancellation pulse is added to the original signal in anti-phase at each detected peak location. The pulse is designed to cancel the peak while having a spectrum that fits within the transmit mask.

• Cancellation pulse library: Pulses are pre-designed to match the carrier configuration and stored in memory.
• Scaled addition: The pulse amplitude is scaled to exactly cancel the peak to the target threshold.
• Low computational load: Only requires addition operations at peak locations, making it suitable for high-speed FPGA implementation in massive MIMO systems.

A subset of OFDM subcarriers—called Peak Reduction Tones (PRTs)—are reserved and do not carry data. A specialized signal is computed on these reserved tones to cancel time-domain peaks without introducing in-band distortion or out-of-band emissions.

• EVM-free: Because PRTs are orthogonal to data tones, the data-bearing subcarriers experience zero in-band distortion.
• Data rate loss: Reserving tones reduces overall throughput, typically by 1-5%.
• Optimization problem: Finding the optimal PRT values is a convex optimization solved iteratively using techniques like the Signal-to-Clipping Noise Ratio (SCR) algorithm.

A nonlinear companding transform expands low-amplitude signals while compressing high-amplitude peaks, similar to companding in analog audio systems. The receiver applies the inverse transform to restore the original signal.

• μ-law and A-law: Standard companding curves adapted from speech processing.
• Receiver cooperation: Requires the receiver to know and apply the inverse decompanding function.
• Noise enhancement: Decompanding at the receiver amplifies channel noise along with the signal, creating a trade-off between PAPR reduction and BER performance.

Outer constellation points are dynamically moved outward within their decision regions to reduce peak magnitude. Since the points remain within correct decision boundaries, no side information is required at the receiver.

• Blind operation: The receiver demodulates normally without any knowledge of the extension.
• Margin exploitation: Only applicable to outer constellation points with room to move before crossing decision boundaries.
• Iterative projection: Points are adjusted iteratively in the frequency domain, with time-domain clipping constraints projected back, converging to a peak-reduced constellation.