Measure EVM for 802.15.4 (ZigBee) System

Define System Parameters

Define system parameters for an 802.15.4 system for the 868 MHz band, direct sequence spread spectrum (DSSS) with binary phase-shift keying (BPSK) for chip modulation, and differential encoding for data symbol encoding.

The BPSK bit-to-chip mapping spreads each input bit with a 14 chip sequence. Input bits with value 0 are represented by the chipValues parameter and input bits with value 1 are represented by (1-chipValues). Use an oversampling rate of four for the transmitted signal and a filter span of eight symbols. To simulate transmitter and test hardware imperfections, use an SNR of 60 dB.

dataRate = 20e3;   % Bit rate in Hz
M = 2;             % Modulation order (BPSK)
chipValues = ...   % Chip values for 0-valued input bits
[1;1;1;1;0;1;0;1;1;0;0;1;0;0;0];

numSymbols = 1000; % Number of symbols required to measure EVM
numFrames = 100;   % Number of frames
nSamps = 4;        % Oversample rate
filtSpan = 8;      % Filter span in symbols
SNR = 60;          % Simulated signal-to-noise ratio in dB

Calculate the spreading gain, chip rate, final sampling rate, and the number of bits required to obtain one EVM measurement value. Include one extra bit in the simulation of the transmitted symbols to account for filter delays.

gain = length(chipValues);     % Spreading gain (chips per symbol)
chipRate = gain*dataRate;      % Chip rate
sampleRate = nSamps*chipRate;  % Final sampling rate
numBits = ...                  % Bits for one EVM measurement
    ceil((numSymbols)/gain)+1;

Initialization

Obtain BPSK modulated symbols by using a simple mapping of 0 to +1 and 1 to -1. To allow use of matrix math and to write efficient MATLAB® code, map the chip values so that modulation can be applied before bit-to-chip conversion. To apply the pulse shape filtering specified for ZigBee, define a pair of square-root-raised-cosine filters with a roll-off factor of 1.

chipValues = 1 - 2*chipValues; % Map chip values
rctFilt = comm.RaisedCosineTransmitFilter( ...
    RolloffFactor=1, ...
    OutputSamplesPerSymbol=nSamps, ...
    FilterSpanInSymbols=filtSpan);
rcrFilt = comm.RaisedCosineReceiveFilter( ...
    RolloffFactor=1, ...
    InputSamplesPerSymbol=nSamps, ...
    FilterSpanInSymbols=filtSpan, ...
    DecimationFactor=nSamps);

Configure EVM Measurements

As defined in section 6.7.3 of IEEE® 802.15.4, the EVM calculation method normalizes the average error of the measured I and Q samples by the power of a symbol. Since the power of both constellation symbols is the same for a BPSK system, configure the EVM measurement object to use peak constellation power normalization. For more information on EVM calculation methods and normalization options, see the comm.EVM System object reference page.

evm = comm.EVM(Normalization='Peak constellation power');

Simulate Transmission and Reception

Generate random data bits, differentially encode these bits by using a comm.DifferentialEncoder System object, and apply BPSK modulation. Spread the modulated symbols by using a matrix multiplication with the mapped chip values. Pass the spread symbols through a pulse shaping filter.

The EVM object assumes that the received and reference symbols are synchronized and sampled at the same rate. The received signal must be downsampled and synchronized with the reference signal.

To ensure sufficient averaging, simulate 100 frames with 1000 symbols in each frame. Save the maximum measured EVM check that satisfies the requirement of EVM $\le$ 35%.

Since the transmit and receive filters are identical and the delay from each equals half the filter span, the total delay equals the span of one filter.

refSigDelay = rctFilt.FilterSpanInSymbols;
diffenc = comm.DifferentialEncoder;

simNumSymbols = numBits*gain; % Number of symbols in a frame
peakRMSEVM = -inf;            % Initialize peak RMS EVM value

Use a for-loop to process transmission frames. On the transmit side, generate random data, apply differential encoding, apply BPSK modulation, spread the chip, apply pulse shaping and add noise to the transmitted signal. On the receive side, downsample and filter the signal, account for the signal delay, measure the EVM, update the peak EVM to save the maximum value measured. After processing all frames of data, display the maximum EVM value.

for p=1:numFrames
    % Transmit side
    b = randi([0 M-1],numBits,1);
    d = diffenc(b);
    x = 1-2*d;                                  % Modulate
    c = reshape(chipValues*x',simNumSymbols,1); % Spread data
    cUp = rctFilt(c); 
    r = awgn(cUp,SNR,"measured");
    % Receive side
    rd = rcrFilt(r);                            % Downsample and filter
    rmsEVM = evm( ...
        complex(rd(refSigDelay+(1:numSymbols))), ...
        complex(c(1:numSymbols)));
    % Update peak RMS EVM calculation
    if (peakRMSEVM < rmsEVM)
        peakRMSEVM = rmsEVM;
    end
end

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

 Worst case RMS EVM (%): 0.19

Further Exploration

You can add more impairments to the transmitted signal, such as IQ imbalance, by using the iqimbal2coef function. For more examples and information, see the Measure Modulation Accuracy and Visualize RF Impairments topics.

References

1. IEEE Standard 802.15.4, Wireless Medium Access Control (MAC) and Physical Layer (PHY) Specifications for Low-Rate Wireless Personal Area Networks, 2003.