Adjacent Channel Power Ratio (ACPR)

Adjacent channel power ratio (ACPR) calculations (also known as adjacent channel leakage ratio (ACLR)), characterize spectral regrowth in a communications system component, such as a modulator or an analog front end. Amplifier nonlinearity causes spectral regrowth. ACPR calculations determine the likelihood that a given system causes interference with an adjacent channel.

Many transmission standards, such as IS-95, CDMA, WCDMA, 802.11, and Bluetooth, contain a definition for ACPR measurements. Most standards define ACPR measurements as the ratio of the average power in the main channel and any adjacent channels. The offset frequencies and measurement bandwidths (BWs) you use when obtaining measurements depends on which specific industry standard you are using. For instance, measurements for CDMA amplifiers involve two offsets (from the carrier frequency) of 885 kHz and 1.98 MHz, and a measurement BW of 30 KHz.

For more information, see the comm.ACPR help page.

Obtain ACPR Measurements

Communications Toolbox™ contains the comm.ACPR System object™. In this tutorial, you obtain ACPR measurements using a WCDMA communications signal, according to the 3GPP™ TS 125.104 standard.

This example uses baseband WCDMA sample signals at the input and output of a nonlinear amplifier. The WCDMASignal.mat file contains sample data for use with the tutorial. This file divides the data into 25 signal snapshots of 7e3 samples each and stores them in the columns of data matrices, dataBeforeAmplifier and dataAfterAmplifier.

The WCDMA specification requires that you obtain all measurements using a 3.84 MHz sampling frequency.

Create comm.ACPR System Object and Set Up Measurements

Define the sample rate, load the WCDMA file, and get the data by entering the following at the MATLAB^® command line:

% System sampling frequency, 3.84 MHz chip rate, 8 samples per chip
SampleRate = 3.84e6*8;
load WCDMASignal.mat
% Use the first signal snapshot
txSignalBeforeAmplifier = dataBeforeAmplifier(:,1);
txSignalAfterAmplifier = dataAfterAmplifier(:,1);

Create the comm.ACPR System object and specify the sampling frequency.

hACPR = comm.ACPR('SampleRate',SampleRate)

The System object presents the following information:

               NormalizedFrequency: false            
                        SampleRate: 30720000         
              MainChannelFrequency: 0                
          MainMeasurementBandwidth: 50000            
             AdjacentChannelOffset: [-100000 100000] 
      AdjacentMeasurementBandwidth: 50000            
           MeasurementFilterSource: 'None'           
                SpectralEstimation: 'Auto'           
                         FFTLength: 'Next power of 2'
                           MaxHold: false            
                        PowerUnits: 'dBm'            
        MainChannelPowerOutputPort: false            
    AdjacentChannelPowerOutputPort: false

Specify the main channel center frequency and measurement bandwidth.
Specify the main channel center frequency using the MainChannelFrequency property. Then, specify the main channel measurement bandwidth using the MainMeasurementBandwidth property.
For the baseband data you are using, the main channel center frequency is at 0 Hz. The WCDMA standard specifies that you obtain main channel power using a 3.84-MHz measurement bandwidth. Specify these by typing the following.
```
hACPR.MainChannelFrequency = 0;
hACPR.MainMeasurementBandwidth = 3.84e6;
```
Specify adjacent channel offsets and measurement bandwidths.
The WCDMA standard specifies ACPR limits for four adjacent channels, located at 5, -5, 10, -10 MHz away from the main channel center frequency. In all cases, you obtain adjacent channel power using a 3.84-MHz bandwidth. Specify the adjacent channel offsets and measurement bandwidths using the AdjacentChannelOffset and AdjacentMeasurementBandwidth properties.
```
hACPR.AdjacentChannelOffset = [-10 -5 5 10]*1e6;
hACPR.AdjacentMeasurementBandwidth = 3.84e6;
```
Notice that if the measurement bandwidths for all the adjacent channels are equal, you specify a scalar value. If measurement bandwidths are different, you specify a vector of measurement bandwidths with a length equal to the length of the offset vector.
Set the MainChannelPowerOutputPort and AdjacentChannelPowerOutputPort properties to true by entering the following at the MATLAB command line:
```
hACPR.MainChannelPowerOutputPort = true
hACPR.AdjacentChannelPowerOutputPort = true
```
Create a comm.ACPR System object to measure the amplifier output.
```
hACPRoutput = clone(hACPR);
```

Obtain the ACPR Measurements

The object returns the ACPR measurements, and can return power measurements for the main and adjacent channels. The PowerUnits property specifies the unit of measure. The property value defaults to dBm (power ratio referenced to one milliwatt (mW)).

Obtain the ACPR measurements at the amplifier input:

[ACPR mainChannelPower adjChannelPower] = hACPR(txSignalBeforeAmplifier);

The comm.ACPR System object produces the following output measurement data:

ACPR =

  -68.6668  -54.9002  -55.0653  -68.4604


mainChannelPower =

   29.5190


adjChannelPower =

  -39.1477  -25.3812  -25.5463  -38.9414

Obtain the ACPR measurements at the amplifier output:
```
[ACPR mainChannelPower adjChannelPower] = hACPRoutput(txSignalAfterAmplifier)
```
The comm.ACPR System object produces the following input measurement data:
```
ACPR =

  -42.1625  -27.0912  -26.8785  -42.4915

mainChannelPower =

   40.6725

adjChannelPower =

   -1.4899   13.5813   13.7941   -1.8190
```
Notice the increase in ACPR values at the output of the amplifier. This increase reflects distortion due to amplifier nonlinearity. The WCDMA standard specifies that ACPR values be below -45 dB at +/- 5 MHz offsets, and below -50 dB at +/- 10 MHz offsets. In this example, the signal at the amplifier input meets the specifications while the signal at the amplifier output does not.

Specifying a Measurement Filter

The WCDMA standard specifies that you obtain ACPR measurements using a root-raised-cosine filter. It also states that you measure both the main channel power and adjacent channel powers using a matched root-raised-cosine (RRC) filter with rolloff factor 0.22. You specify the measurement filter using the MeasurementFilter property. This property value defaults to an all-pass filter with unity gain.

The filter must be an FIR filter, and its response must center at 0 Hz. The ACPR object automatically shifts and applies the filter at each of the specified main and adjacent channel bands. (The power measurement still falls within the bands specified by the MainMeasurementBandwidth, and AdjacentMeasurementBandwidth properties.)

The WCDMASignal.mat file contains data that was obtained using a 96 tap filter with a rolloff factor of 0.22.

Create the filter (using rcosdesign, from the Signal Processing Toolbox™ software) and obtain measurements by entering the following at the MATLAB command line:
```
% Scale for 0 dB passband gain
measFilt = rcosdesign(0.22,16,8)/sqrt(8); 
```
Set the filter you created in the previous step as the measurement filter for the ACPR object.
```
release(hACPR);
hACPR.MeasurementFilterSource = 'Property';
hACPR.MeasurementFilter = measFilt;
```
Implement the same filter at the amplifier output by cloning the comm.ACPR System object.
```
hACPRoutput = clone(hACPR)
```
Obtain the ACPR power measurements at the amplifier input.
```
ACPR = hACPR(txSignalBeforeAmplifier)
```
The comm.ACPR System object produces the following measurement data:
```
ACPR =
  -71.4648  -55.5514  -55.9476  -71.3909
```
Obtain the ACPR power measurements at the amplifier output.
```
ACPRoutput = hACPRoutput(txSignalAfterAmplifier)
```
The comm.ACPR System object produces the following measurement data:
```
ACPR =
   -42.2364  -27.2242  -27.0748  -42.5810
```

Control the Power Spectral Estimator

By default, the ACPR object measures power uses a Welch power spectral estimator with a Hamming window and zero percent overlap. The object uses a rectangle approximation of the integral for the power spectral density estimates in the measurement bandwidth of interest. If you set SpectralEstimatorOption to 'User defined' several properties become available, providing you control of the resolution, variance, and dynamic range of the spectral estimates.

Enable the SegmentLength, OverlapPercentage, and WindowOption properties by entering the following at the MATLAB command line:
```
release(hACPRoutput)
hACPRoutput.SpectralEstimation = 'Specify window parameters'
```
This change allows you to customize the spectral estimates for obtaining power measurements. For example, you can set the spectral estimator segment length to 1024 and increase the overlap percentage to 50%, reducing the consequent variance increase. You can also choose a window with larger side lobe attenuation (compared to the default Hamming window).

Create a spectral estimator with a Chebyshev window and a side lobe attenuation of 200 dB.

hACPRoutput.SegmentLength = 1024;
hACPRoutput.OverlapPercentage = 50;
% Choosing a Chebyshev window enables a SidelobeAtten property
% you can use to set the side lobe attenuation of the window.
hACPRoutput.Window = 'Chebyshev';
hACPRoutput.SidelobeAttenuation = 200;

Run the object to obtain the ACPR power measurements at the amplifier output.
```
ACPRoutput = hACPRoutput(txSignalAfterAmplifier)
```
The ACPR object produces the following measurement data:
```
ACPR =
  -44.9399  -30.7136  -30.7670  -44.4450
```

Measure Power Using the Max-Hold Option.

Some communications standards specify using max-hold spectrum power measurements when computing ACPR values. Such calculations compare the current power spectral density vector estimation to the previous max-hold accumulated power spectral density vector estimation. When obtaining max-hold measurements, the object obtains the power spectral density vector estimation using the current input data. It obtains the previous max-hold accumulated power spectral density vector from the previous call to the object. The object uses the maximum values at each frequency bin for calculating average power measurements. A call to the reset method clears the max-hold spectrum.

Accumulate max-hold spectra for 25 amplifier output data snapshots and get ACPR measurements by typing the following at the MATLAB command line:
```
for idx = 1:24
    hACPRoutput(dataAfterAmplifier(:,idx));
end
ACPRoutput = hACPRoutput(dataAfterAmplifier(:,25))
```
The ACPR object produces the following output data:
```
ACPR =

  -43.1123  -26.6964  -27.0009  -42.4803
```

Plotting the Signal Spectrum

Use the MATLAB software to plot the power spectral density of the WCDMA signals at the input and output of the nonlinear amplifier. The plot allows you to visualize the spectral regrowth effects intrinsic to amplifier nonlinearity. Notice how the measurements reflect the spectral regrowth. (Note: the following code is just for visualizing signal spectra; it has nothing to do with obtaining the ACPR measurements).

win = hamming(1024);
[PSD1,F] = pwelch(txSignalBeforeAmplifier,win,50,1024,SampleRate,'centered');
[PSD2,F] = pwelch(txSignalAfterAmplifier,win,50,1024,SampleRate,'centered');
plot(F,10*log10(PSD1))
hold on
grid on
plot(F,10*log10(PSD2),'g')
legend('Amplifier input', 'Amplifier output')

Power spectral density plot showing amplifier input and output. Output shows spectral regrowth.