Peak Regrowth

The finite impulse response (FIR) filter applied to suppress out-of-band emissions is the primary cause of peak regrowth. When a clipped signal passes through a filter, the time-domain convolution smears the sharp discontinuity created by clipping. If the filter's impulse response has significant sidelobes or a long duration, the energy removed from one peak is redistributed in time, constructively interfering with adjacent samples and causing new peaks to emerge above the clipping threshold. The filter length directly trades off spectral containment against regrowth severity.

The Clipping Ratio (CR)—the ratio of the maximum permitted amplitude to the RMS level of the unclipped signal—determines how frequently and severely peaks are truncated. A lower CR (more aggressive clipping) removes more energy from the signal, but creates steeper discontinuities at the clip boundary. These sharper transitions contain higher-frequency spectral components that are attenuated by the filter, causing greater energy redistribution and more pronounced regrowth. The relationship is nonlinear: halving the CR can more than double the regrowth magnitude.

The Complementary Cumulative Distribution Function (CCDF) of the original signal dictates the density and clustering of peaks. Signals with heavy-tailed envelope distributions—such as OFDM with a large number of subcarriers—exhibit frequent, closely spaced peaks. When multiple peaks are clipped within a time window shorter than the filter's impulse response length, the redistributed energy from each clipped peak overlaps and sums constructively. This peak clustering effect makes regrowth in dense multicarrier signals significantly harder to control than in sparse single-carrier waveforms.

A single stage of clipping and filtering rarely achieves the target PAPR due to regrowth. The standard solution is iterative clipping and filtering (ICF) , where the output of each filter stage is re-clipped to the target threshold. Each iteration removes a fraction of the regrown peaks, converging toward the desired PAPR. The trade-off is increased in-band distortion (EVM) and computational latency. Typical implementations use 3–5 iterations, with diminishing returns beyond that point as the signal approaches a stationary envelope distribution.

The shape of the filter's passband and stopband directly influences regrowth behavior. A filter with a sharp transition band (high Q) provides excellent spectral containment but requires a long impulse response, exacerbating time-domain energy spreading. Conversely, a filter with a gradual roll-off has a shorter impulse response and less regrowth, but allows more out-of-band emission. Modern CFR designs use optimized windowing functions (Kaiser, Chebyshev) or peak windowing techniques that apply a smooth time-domain window directly to each clipped peak, eliminating the need for a separate filter stage.

Peak windowing is an alternative to the clip-and-filter approach that directly addresses regrowth. Instead of hard-clipping and then filtering the entire signal, peak windowing detects each peak above the threshold and multiplies the surrounding samples by a pre-designed smooth window function (e.g., Gaussian, Kaiser, Hamming). The window is spectrally shaped to match the emission mask, so no separate filter is required. Because the window is applied locally to each peak, energy redistribution is confined to the immediate vicinity, significantly reducing regrowth compared to global filtering.

The fundamental iterative process that causes peak regrowth. Hard clipping truncates the signal envelope at a threshold, generating out-of-band spectral splatter. A subsequent low-pass filter removes this splatter but causes the filtered waveform's peaks to re-exceed the original clipping threshold. This necessitates multiple clipping-and-filtering stages to converge on the target PAPR.

The primary in-band distortion metric directly traded off against peak regrowth suppression. Aggressive clipping and filtering to eliminate regrowth introduces in-band distortion, measured as EVM. The iterative design must balance:

• EVM floor: Maximum allowable constellation distortion per 3GPP standards
• PAPR target: Required peak reduction for PA efficiency
• Regrowth tolerance: Acceptable residual peak exceedance after final filtering

A cascaded architecture designed explicitly to manage peak regrowth through progressive clipping. Each stage applies a clipping ratio (CR) slightly tighter than the previous, followed by filtering. This distributes the distortion across stages, allowing each filter to be less aggressive. The result is controlled ACLR and EVM while converging to the final PAPR target with minimal residual regrowth.

The out-of-band emission metric that filtering aims to protect, and which regrowth threatens. Peak regrowth after filtering indicates residual nonlinearity that still generates spectral splatter. The iterative clipping-and-filtering loop continues until the signal simultaneously meets:

• ACLR spec: Typically -45 dBc for adjacent channel
• Spectral mask: Regulatory emission limits vs. frequency offset
• PAPR target: Required crest factor reduction