Communications Toolbox 4.4

EVM Measurements for a 802.15.4 (ZigBee®) System

This demonstration shows how to use COMMMEASURE.EVM to measure the error vector magnitude (EVM) of a simulated IEEE® 802.15.4 [ 1 ] transmitter. IEEE 802.15.4 is the basis for the Zigbee specifications.

Contents

Error Vector Magnitude (EVM)

The error vector magnitude (EVM) is a measure of the difference between a reference waveform, which is the error-free modulated signal, and the actual transmitted waveform. EVM is used to quantify the modulation accuracy of a transmitter. [ 1 ] requires that a 802.15.4 transmitter shall not have an RMS EVM value worse than 35%.

System Parameters

An 802.15.4 system for 868 MHz band employs direct sequence spread spectrum (DSSS) with binary phase-shift keying (BPSK) used for chip modulation and differential encoding used for data symbol encoding.

dataRate = 20e3;   % Bit rate in Hz
M = 2;             % Modulation order (BPSK)
chipValues = [1;1;1;1;0;1;0;1;1;0;0;1;0;0;0];
                   % Chip values for bit 0.  Chip values for 1 is the opposi
te.

Section 6.7.3 of [ 1 ] specifies that the measurements are performed over 1000 samples of I and Q baseband outputs. To account for filter delays, we include 1 more bit in the simulation of the transmitted symbols. We chose to oversample the transmitted signal by four. We assume an SNR of 60 dB to account for transmitter and test hardware imperfections.

numSymbols = 1000;               % Number of symbols required for one EVM va
lue
numFrames = 100;                 % Number of frames
nSamps = 4;                      % Number of samples that represents a symbo
l
gain = length(chipValues);       % Spreading gain (number of chips per symbo
l)
chipRate = gain*dataRate;        % Chip rate
sampleRate = nSamps*chipRate;    % Final sampling rate
numBits = ceil((numSymbols)/gain)+1;
                                 % Number of bits required for one EVM value
SNR = 60;                        % Simulated signal-to-noise ratio in dB

Initialization

We can obtain BPSK modulated symbols with a simple mapping of 0 to +1 and 1 to -1. If we also map the chip values, then we can modulate before bit-to-chip conversion and use matrix math to write efficient MATLAB® code. ZigBee specifications also define the pulse shaping filter as having a raised cosine pulse shape with rolloff factor of 1.

% Map chip values
chipValues = 2*chipValues - 1;

% Specify the pulse shaping filter
rolloffFactor = 1;
filterSpecs = fdesign.pulseshaping(nSamps, 'Raised Cosine', ...
    'Nsym,Beta', nSamps, rolloffFactor, sampleRate);

% Design the filter and normalize
hFilter = design(filterSpecs);
normalize(hFilter)

EVM Measurements

The Communications Toolbox™ provides COMMMEASURE.EVM to calculate RMS EVM, Maximum EVM, and Xth percentile EVM values. Section 6.7.3 of [ 1 ] defines the EVM calculation method, where the average error of measured I and Q samples are normalized by the power of a symbol. For a BPSK system, the power of both constellation symbols is the same. Therefore, we can use the 'Peak constellation power' normalization option. Other available normalization options, which can be used with other communications system standards, are average constellation power and average reference signal power.

hEVM = commmeasure.EVM('NormalizationOption', 'Peak constellation power')

hEVM =

                   Type: 'EVM Measurements'
    NormalizationOption: 'Peak constellation power'
              PeakPower: 1
                 RMSEVM: NaN
             MaximumEVM: 0
             Percentile: 95
          PercentileEVM: NaN
        NumberOfSymbols: 0

Simulation

We first generate random data bits, differentially encode these bits, and modulate using BPSK. We spread the modulated symbols by employing a matrix multiplication with the mapped chip values. The spread symbols are then passed through a pulse shaping filter. The EVM object assumes that received symbols, rd, and reference symbols, c, are synchronized, and sampled at the same rate. We downsample the received signal, r, and synchronize with the reference signal, c.

[ 2 ] requires that 1000 symbols to are used in one RMS EVM calculation. To ensure we have enough averaging, we simulate 100 frames of 1000 symbols and use the maximum of these 100 RMS EVM measurements as the measurement result. We see that the simulated transmitter meets the criteria mentioned in Error Vector Magnitude section above.

% Calculate delays
refSigDelay = (length(hFilter.Numerator) - 1) / 2;

% Simulated number of symbols in a frame
simNumSymbols = numBits*gain;

% Initialize peak RMS EVM
peakRMSEVM = -inf;

% Loop over bursts
for p=1:numFrames
    % Generate random data
    b = randi([0 M-1], numBits, 1);
    % Differentially encode
    d = mod(cumsum(b), 2);
    % Modulate
    x = 2*d-1;
    % Convert symbols to chips (spread)
    c = reshape(chipValues*x', simNumSymbols, 1);
    % Pulse shape
    cUp = filter(hFilter, upsample(c, nSamps));
    % Add noise
    r = awgn(cUp, SNR, 'measured');
    % Downsample received signal.  Account for the filter delay.
    rd = downsample(r(refSigDelay+1:end), nSamps);
    % Update the EVM object
    update(hEVM, rd(1:numSymbols), c(1:numSymbols))
    % Update peak RMS EVM calcualtion
    rmsEVM = hEVM.RMSEVM;
    if (peakRMSEVM < rmsEVM)
        peakRMSEVM = rmsEVM;
    end
end

% Display results
hEVM
fprintf(' Worst case RMS EVM (%%): %1.2f\n', peakRMSEVM)

hEVM =

                   Type: 'EVM Measurements'
    NormalizationOption: 'Peak constellation power'
              PeakPower: 1
                 RMSEVM: 0.0866
             MaximumEVM: 0.4071
             Percentile: 95
          PercentileEVM: 0.1705
        NumberOfSymbols: 100000

 Worst case RMS EVM (%): 0.09

Comments

We demonstrated how to utilize COMMMEASURE.EVM to test if a ZigBee transmitter complies with the standard specified EVM values. We used a crude model that only introduces additive white Gaussian noise and showed that the measured EVM is less than the standard specified 35%.

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