Peak_Cancellation_Crest_Factor_Reduction_Reference_Design.pdf

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Peak_Cancellation_Crest_Factor_Reduction_Reference_Design xlinx的PC-CFR设计详细说明，教你如何用matlab搭建PC-CFR，可以用搭建的PC-CFR生产设计代码

XAPP1033 (v1.0) December 5, 2007 www.xilinx.com 1

of their respective owners.

Summary This application note provides designers with a highly optimized solution for Crest Factor

Reduction (CFR) that can be adapted to meet the needs of multiple air interfaces with minimum

effort. The system-level performance of the Peak Cancellation method of CFR is shown to be

better than other methods such as Peak Windowing and Noise Shaping. In addition, the Peak

Cancellation method can be implemented more efficiently than the other methods, resulting in

reduced overall cost.

Accompanying this application note are design files and test vectors for quickly evaluating the

performance of the reference design within MATLAB®. Instructions on how to integrate the

reference design into a larger system design are included. Design files are available for both

Virtex™-4 and Virtex-5 device architectures.

Introduction The wireless industry is currently following an aggressive drive to reduce Capital Expenditure

(CapEx) and Operating Expenditure (OpEx). Different dynamics can affect both of these to a

lesser or greater extent. If a typical base station is broken down into its constituent components,

it is estimated that an average of 40 to 60 percent of the overall CapEx cost is incurred with the

radio cards. Since the radio shelf contains the power amplifiers, the radio portion of the design

is also responsible for much of the OpEx incurred during the lifetime of the site. This is largely

due to the low efficiency of the power amplifiers when operating in a highly linear region.

The OpEx cost is directly related to the power amplifier efficiency in the base station. Currently,

a very small proportion of the DC power consumed by the base station is converted to radiated

energy. The efficiency at which a power amplifier may be operated is a function of the

transmitted signal. 3G signals have a high Peak to Average Power Ratio (PAPR) or Crest

Factor. This imposes significant operating restrictions on the power amplifier. In order to handle

the peaks, it is heavily backed off from its most efficient operating point. To increase efficiency,

CFR algorithms can be used to decrease the PAPR of the transmitted signal prior to it entering

the power amplifier. By doing so, the power amplifier can operate with less back off, and thus

increased efficiency. Another method of improving the efficiency of the power amplifier is to use

Digital Pre-Distortion (DPD). Rather than use digital signal processing to reduce the dynamic

range of the transmitted signal (CFR), DPD is used to linearize the power amplifier itself. DPD

is outside the scope of this document, but its reference is included as a widely used method of

amplifier efficiency improvement.

In multi-carrier systems, such as WCDMA, TD-SCDMA and CDMA2000, the PAPR of the

signal can be higher than in single carrier systems. In addition, the implementation of some

CFR methods, such as Noise Shaping, are costly for multi-carrier systems. The peak

cancellation CFR (PC-CFR) technique outlined in this application note is very well suited to

multi-carrier systems, and can even be applied to radios where multiple standards may be

required in the same radio transmission spectrum.

This application note also illustrates the dramatic reduction in dynamic power between

generations of FPGAs. This allows designers the ability to determine how much additional cost

savings can be made when evaluating both Power Supply and Heatsinking needs of traditional

chassis-mounted equipment and Remote Radio Head (RRH) applications.

Application Note: Virtex-5 and Virtex-4 Family

XAPP1033 (v1.0) December 5, 2007

Peak Cancellation Crest Factor Reduction

Reference Design

Authors: Ed Hemphill, Steve Summerfield, George Wang, and Dave Hawke

Description of Algorithm

XAPP1033 (v1.0) December 5, 2007 www.xilinx.com 2

Description of

Algorithm

This section gives an overview of the PC-CFR algorithm followed by detailed descriptions of

each main step in the algorithm. See

OFDM for Wireless Multimedia Communications

for an

overview of PAPR reduction techniques, including peak cancellation [Ref 1].

Algorithm Overview

The peak cancellation method of CFR reduces the peak to average power ratio (PAPR) of a

signal by subtracting spectrally shaped pulses from signal peaks that exceed a specified

threshold. The cancellation pulses are designed to have a spectrum that matches that of the

CFR input signal and therefore introduce negligible out-of-band interference. In general, the

CFR input signal and cancellation pulses are complex, and the peak search (described in

“Peak Detection,” page 4) is carried out on the signal magnitude.

Because the signals are complex, each cancellation pulse must be rotated to match the phase

of the corresponding signal peak. The peak magnitude of a given cancellation pulse is set

equal to the difference between the corresponding signal peak magnitude and the desired

clipping threshold. This method reduces the signal peak magnitudes to the threshold value

while preserving the signal phase.

Figure 1 illustrates the peak cancellation process in the time domain. The top plot shows a

section of the input signal magnitude. The horizontal line overlaid on the plot indicates the

clipping threshold. Any peak that exceeds this threshold is a candidate for cancellation. The

middle plot shows the magnitude of the cancellation pulse that is to be subtracted from the

input signal. The bottom plot shows the magnitude of the output signal after subtracting the

cancellation pulse from the input signal.

Figure 2 illustrates the characteristics of the peak cancellation method in the frequency domain

for a typical multi-carrier configuration. The power spectral density (PSD) of the input signal is

overlaid with the PSD of the cancellation pulse signal, also referred to as the clipping noise. The

cancellation pulse illustrated in Figure 1 has frequency domain content as illustrated in

Figure 2. In the case of a single carrier, the cancellation pulse would look much smoother. The

X-Ref Target - Figure 1

Figure 1:

Time Domain View of Peak Cancellation

0 100 200 300 400 500 600 700 800 900 1000

x 10

CFR Input Signal Magnitude

Magnitude

0 100 200 300 400 500 600 700 800 900 1000

x 10

Cancellation Pulse Magnitude

Magnitude

0 100 200 300 400 500 600 700 800 900 1000

x 10

CFR Output Signal Magnitude

Time (Samples)

Magnitude

Description of Algorithm

XAPP1033 (v1.0) December 5, 2007 www.xilinx.com 3

somewhat noisy appearance of the cancellation pulse in the time domain is consistent with the

non-symmetric multi-carrier spectrum in the frequency domain.

The peak cancellation method is similar to the noise shaping method of CFR that is described

in XAPP921c,

High Density WCDMA Digital Front End Reference Design

[Ref 3]. In noise

shaping, the signal is clipped and then subtracted from the original to produce a clipping noise.

The clipping noise is filtered to confine its spectrum to that of the input signal. The spectrally

shaped clipping noise is then subtracted from the original input signal to produce a PAPR

reduced signal with minimal out-of-band degradation.

Whereas the noise shaping method filters all samples of the clipping noise, the peak

cancellation method filters only the peak samples of the clipping noise. Treating the peak

samples as discrete delta functions allows the convolution to be replaced by a simple scaling of

the filter impulse response. This results in less signal distortion because the time domain

spread at the filter output is smaller compared to the noise shaping method. Because the

filtering of the signal peaks is implemented via simple scaling of the filter impulse response, the

computational burden is greatly reduced.

Algorithm Details

Figure 3 shows a block diagram of the PC-CFR algorithm. Peaks in the input signal are

detected and cancelled to produce a reduced PAPR signal. The peak detect block works on the

signal magnitudes to produce a peak location indicator along with magnitude and phase

information for each peak. The difference between the peak magnitudes and the clipping

threshold is generated by the peak scaling block. The magnitude difference is combined with

the phase information to produce the complex weighting that is used to scale the cancellation

pulse coefficients. The scaling and summation of a limited number of cancellation pulses

replaces the more computationally intense convolution that is used in the noise shaping

method.

Throughout this application note, it is assumed that there are four cancellation pulse generators

(CPGs) per iteration, which is a convenient choice for four clocks per sample. There is no

inherent limitation to the algorithm regarding the number of CPGs per iteration. Choosing the

number of CPGs to match the number of clocks per sample is done for hardware

efficiency.Each CPG outputs an unscaled version of the cancellation pulse waveform aligned

X-Ref Target - Figure 2

Figure 2:

Frequency Domain View of Peak Cancellation

-15 -10 -5 0 5 10 15

-20

100

PSD of Clipping Noise

Frequency (MHz)

Signal

Noise

Description of Algorithm

XAPP1033 (v1.0) December 5, 2007 www.xilinx.com 4

with a peak location. Each CPG can cancel only one peak at a time. The length of the

cancellation pulse combined with the number of CPGs determines the rate at which signal

peaks can be cancelled. The allocator block controls the distribution of CPGs to incoming

peaks. When a new peak is detected, the allocator assigns an available CPG to the

cancellation of that peak. If all CPGs are busy when a new peak is detected, it will not be

cancelled. Multiple iterations of the algorithm are necessary to eliminate the peaks that were

not cancelled during an earlier pass of the algorithm. The final step in the algorithm is to

subtract the summation of the CPG outputs from a delayed version of the input signal.

Peak Detection

There are multiple ways to define a signal peak. One common method defines a peak as any

sample that has magnitude greater than its neighboring samples. This method has the

advantage that it is simple to implement and results in a fixed delay from the detection of the

peak to the peak location. However, it has the disadvantage that it may result in the detection of

many local peaks in a single over-threshold region. Attempting to cancel many closely spaced

peaks at once can lead to constructive interference of the cancellation pulses and leads to peak

regrowth. Moreover, the allocation of CPGs will be less than optimal because a cluster of peaks

may consume all the CPG resources.

An alternate method of detecting peaks is based on finding the highest peak within an over-

threshold region. This has the advantage that only one peak is detected per over-threshold

region thus reducing the effects of peak regrowth and improving the CPG allocation statistics.

This method is illustrated in Figure 4. Note that multiple peaks exist in the second over-

threshold region, but only the highest peak is selected for cancellation. The disadvantage of

this method is the variable delay from the peak location to the detection of the peak. This is

because the algorithm must wait for the signal to cross below the clipping threshold before

declaring the highest peak in that region. The length of the delay is a function of the signal

characteristics and ratio of sampling rate to occupied bandwidth. The maximum delay from

signal peak to threshold crossing increases as the ratio of sampling rate to occupied bandwidth

increases.

Performance can be improved by using a detection threshold that is slightly higher than the

desired clipping threshold. This allows the algorithm to ignore peaks that are just barely

crossing the threshold and focus on peaks that exceed the threshold by some delta. The main

reason this provides improvement is the fact that some peak regrowth occurs, which can result

in many near threshold peaks. Allocating CPG resources to these small peaks during a second

X-Ref Target - Figure 3

Figure 3:

Block Diagram of PC-CFR Algorithm

Peak

Detect

Peak

Scaling

Reduced

PAPR

Signal

High

PAPR

Signal

Allocator

CPG #1

Peak

Locations

CPG #2

CPG #3

CPG #4

Sum

Mag

Phase

Delay

Description of Algorithm

XAPP1033 (v1.0) December 5, 2007 www.xilinx.com 5

iteration would provide minimal PAPR reduction with the risk of missing larger peaks that were

not cancelled during the first iteration.

Peak Scaling

The peak scaling step in the algorithm determines the complex scaling applied to the

cancellation pulse coefficients for each peak. The magnitude of the scaling is equal to the

difference between the signal peak and the clipping threshold. The phase is set equal to that of

the signal peak. Mathematically this is expressed in Equation 1.

Equation 1

In this equation, α is the complex scaling value, |x| is the magnitude of the signal peak, γ is the

clipping threshold, and θ is the phase of the signal peak.

Allocator

The allocator controls the assignment of CPG resources to the task of canceling incoming

peaks. During startup, all CPGs are available. When the first peak arrives, the allocator assigns

the first CPG to cancel it and then tags that CPG as being allocated. Once allocated, a CPG

becomes unavailable for the length of the cancellation pulse (in samples). When subsequent

peaks arrive, the allocator steps through the status of each CPG and assigns the first one

available. Peaks that arrive when all CPGs are currently busy will not get cancelled and must be

picked up by a subsequent iteration of the algorithm.

There are times when the input signal exhibits a high density of over-threshold peaks in clusters

(for example, two non-adjacent carriers). This can lead to less than optimal allocation of CPGs

and contribute to high peak regrowth. To mitigate the degradation, an allocator spacing

parameter is used to prevent cancellation of peaks that are closer than some specified distance

from an already allocated peak.

Cancellation Pulse Generator

Each cancellation pulse generator, or CPG, produces an unscaled copy of the stored

cancellation pulse. The cancellation pulse is designed to occupy the same frequency bands as

the input signal. The cancellation pulse coefficients can be obtained using any preferred filter

design methodology and are computed off-line before being written to the PC-CFR design.

Memory that is external to the design may be used to store multiple sets of cancellation pulse

X-Ref Target - Figure 4

Figure 4:

Illustration of Peak Detection Method

0 5 10 15

Signal Magnitude

Time (Samples)

Example Signal Peaks

Selected

Not

Selected

γ–()

×=

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