What is Crest Factor Reduction?

What is Crest Factor Reduction or CFR?

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- everything RF

Jul 9, 2022

Crest Factor Reduction (CFR) is a technique used to reduce the peak-to-average power ratio (PAPR) of the signal supplied to Power Amplifiers (PA) in a communication system. High peak-to-average power ratio (PAPR) is undesirable and is encountered in modern communication methods, such as Orthogonal Frequency Division Multiplexing (OFDM). CFR helps in increasing the efficiency of power amplifiers in communication systems.

Peak-to-average power ratio (PAPR) of a waveform is defined as the ratio of the peak amplitude squared (peak power) divided by the RMS value squared (average power). To further simplify, PAPR is the ratio of peak power to the average power of a signal, usually expressed in decibels (dB). A lower PAPR is desired for the good efficiency of the transmission system.

CFR is used to reduce PAPR by limiting the signal peaks sent to the power amplifier to a desired threshold value. Note that the CFR technique limits the signal peaks when the peaks exceed the specified threshold value, thereby, enhancing the efficiency of the power amplifier.

CFR techniques can be useful for improved linearization of the Pre-distorter + PA system, particularly when operating under a very high compression region of the amplifier. Pre-distorter is a module/device cascaded with the RF power amplifier (usually integrated with PA) in digital-pre-distortion (DPD). Digital-pre-distortion is a technique used to improve the linearity of the PA. A well-designed PA with CFR and DPD can achieve an efficiency of about 30% in a typical OFDM application.

Crest Factor Reduction Techniques

CFR can be implemented using various methods such as clipping, peak windowing, noise shaping, pulse injection, and peak cancellation.

Clipping

Clipping is the conventional method that clips the signal peak to achieve the desired PAPR. Figure 1 shows how clipping reduces the PAPR. 

Figure 1: Clipping CFR technique

Clipping leads to sharp corners in a clipped signal which, in turn, leads to an unwanted out-of-band emission. To reduce this unwanted emission, the clipped signal is passed via a low-pass filter. The major drawback of clipping and filtering (CAF) is the peak regrowth caused by filtering. The amount of peak regrowth is generally intractable. This is undesirable for a transmitter with a digital pre-distorter (DPD) as the DPD needs to strictly keep the peak below a predefined value to ensure that no signal sweeps into the saturation region of the PA. Hence, other CFR technique like peak cancellation and peak windowing are preferred to reduce PAPR. The clipping operation is mathematically expressed as follows.

Where x[n] is the input signal on which CFR is applied.

  • x[n] is the clipping signal
  • xclip[n] is the clipped signal
  • A is the threshold level determined by desired PAPR

Peak Windowing

Peak Windowing is a CFR technique that aims to provide a smooth peak signal with desired PAPR. In this technique, clipping is implemented by multiplying the original signal in the region of the peak with a windowing function, as shown in figure 2.

Figure 2: Peak Windowing CFR Technique

Peak Cancellation

Peak cancellation is a CFR technique that reduces the PAPR of a signal by subtracting spectrally shaped cancellation pulses from original input signal peaks that exceed a specified threshold. These cancellation pulses are designed to have a spectrum that matches that of the input signal and therefore introduce negligible out-of-band interference.

Figure 3: Showing peak cancellation pulses, original signal & threshold limit

 Figure 4: Showing peak cancellation pulse & signal before and after CFR

How Does PAPR Impact Power Amplifier Efficiency 

Power amplifiers are key components for the overall performance of communication systems, but they are inherently non-linear devices. The non-linearity of the PA leads to adjacent channel interference, violations of the out-of-band emissions standards mandated by regulatory bodies, and in-band distortion, which degrades the bit-error-rate (BER) and data throughput of the communication system. To reduce non-linearity, power amplifiers can be operated at a lower power level (i.e., “backed off”) so that it operates in a linear region.

Understanding signal peak and average

New transmission techniques like WCDMA and OFDM have higher peak-to-average power ratios (PAPR). A high PAPR means that the signal power fluctuated occasionally to a very large value; therefore, a large PAPR requires a higher power rating PA to linearly amplify the occasionally occurring peaks of the signal. So, the required power rating, and hence power consumption, and cost of the amplifier are proportional to the PAPR of the signal being amplified.

Let us assume that we need to transmit 50 W of power, on average, to provide RF coverage during high-traffic hours. If the transmit signal has a PAPR of 0 dB, we need an amplifier with a power rating of 50 W (able to output 50 W while operating linearly). However, if the signal has a PAPR of 3 dB, we will need an amplifier capable of 100 W to linearly amplify the occasionally occurring peaks of the signal. It means that after selecting PA with a power rating of 100 W of saturation power, we operate the PA at 50 W output power (keeping 50 W headroom to handle occasional occur peak power). Operating at such a large back-off reduces the efficiency of that PA.

As we know, for a high PAPR we require a high-power rating (high RF output power rating) amplifier to linearly amplify the signal. Amplifiers capable of delivering higher output powers requires a higher level of bias current at all times, which is reflected in the DC power consumption, even when the PA is not delivering high levels of output power (here, in this example, 100 W). So, while handling 50 W output power, the high level of bias current at all times leads to increased loss of DC power as heat. High DC power consumption while handling 50 W output, reduces the efficiency of PA. Hence, crest factor reduction (CFR) is used to improve power amplifier efficiency, reduce PA power rating requirement, and therefore, cost by reducing the PAPR.