Communications Toolbox 4.4

IEEE® 802.11b DBPSK PHY

This M code simulates DBPSK modulation and Barker code spreading on a perfectly synchronized 802.11b link. It calculates the BER rate at each Es/No and plots the result.

Contents

Simulation Parameters

For each BER loop, we specify the number of packets to transmit, the packet size and the range of channel Es/No values to test.

EsNoRange       = 0:2:10; % Range of noice levels to calculate BER
NumPackets      = 2;
PacketSizeBytes = 1024;
PacketSizeBits  = PacketSizeBytes*8; % Ignore preamble and sync bits
clear BERResults;
clear ErrorResults;

System Parameters and Constants

Specify a number of system constants.

% Spreading parameters
Barker        = [1 -1  1  1 -1  1  1  1 -1 -1 -1]'; % Barker sequence
SpreadingRate = length(Barker);                     % Spreading rate

% Upsampling rate
SamplesPerChip=8;

% Filter order and coefficients - root raised cosine
FilterOrder = 40; % Set to multiple of SamplesPerChip to make delay calculat
ion easy
h = firrcos(FilterOrder,7e6,.7,88e6,'rolloff','sqrt',FilterOrder/2,kaiser(Fi
lterOrder+1,1));

Delay Calculation

Calculate (i.e. specify) the net number of bits delay in the link due to the filtering.

We must delay the signal 6 more chips to align it with the 11 chip boundary. This results in an 11 chip delay or one symbol/bit delay. You must recalculate total and additional delay if you change any of these parameters.

BitDelay     = 1;
ChipDelayAdd = 6;

Main BER Loop

Calculates the BER for each Es/No level.

NumEsNos = length(EsNoRange);
ErrorResults = zeros(1,NumEsNos);

% Set state of random number generator
randn('state',2006);

disp(' ');disp('Start Simulation');
for EsNoIndex = 1:NumEsNos

    EsNo = EsNoRange(EsNoIndex);
    disp(['Simulating: Es/No=' num2str(EsNo) 'dB']);
    SNR = EsNo+10*log10(1/SpreadingRate)+10*log10(1/SamplesPerChip);

    % Initialize system and simulation measurements state

    % Bits
    TotalBits    = false;   % Bit count for BER calculation
    ErrorBits    = false;   % Error count for BER calculation
    LastTxSymbol = 1;       % Set DBPSK Modulator state
    LastRxSymbol = 1;       % Set DBPSK Demodulator state

    % Filters
    Rx_chips_delayed_store = zeros(ChipDelayAdd,1);
    Tx_bits_delayed_store  = false(BitDelay,1);

    Tx_Filter_State = h(1:end-1); % Fill filter with a +1 symbol
    Rx_Filter_State = h(1:end-1); % Fill filter with a +1 symbol

    % Main simulation loop
    % Each packet is transmitted, and the received bits compared with the
    % transmitted bits to calculate the BER.
    for Packet = 1:NumPackets

        % Construct frame of bits
        rand('twister', 0);
        Tx_bits = rand(PacketSizeBits,1)>.5;           % Random bits

        % Modulate
        Tx_bits_bp   = (1-2*Tx_bits);                    % Convert to bipola
r 0,1 --> 1, -1
        Tx_symbols   = LastTxSymbol*cumprod(Tx_bits_bp); % New DBPSK symbol 
= previous  * 1 or -1
        LastTxSymbol = Tx_symbols(end);                  % Store modulator s
tate (last symbol)

        % Spread symbols with Barker code, upsampling by spreading rate
        Tx_chips = reshape(Barker*Tx_symbols',[],1); % Multiply by barker an
d reshape to a columm
        Tx_chips = complex(Tx_chips); % Make complex to ensure correct baseb
and transmission

        % Upsample chips by SamplesPerChip factor
        Tx_samples = zeros(length(Tx_chips)*SamplesPerChip,1); % Create empt
y Tx_samples
        Tx_samples(1:SamplesPerChip:end,1) = sqrt(SamplesPerChip)*Tx_chips; 
% Normalize power due to upsampling
        % Tx Filter
        [Tx_samples_filtered,Tx_Filter_State] = filter(h,1,Tx_samples,Tx_Fil
ter_State); % Filter
        Tx_samples_filtered = Tx_samples_filtered*2.495; % Set output power 
to 1W
        var(Tx_samples_filtered); % Calculate Tx signal power, view by remov
ing ';'

        % Transmit though AWGN Channel assuming 0dBW input power (check
        % with line above)
        Rx_samples_unfiltered = awgn(Tx_samples_filtered,SNR,0);

        % Rx Filter
        [Rx_samples_filtered,Rx_Filter_State] = filter(h,1,Rx_samples_unfilt
ered,Rx_Filter_State);

        % Downsample - sample chips
        Rx_chips = Rx_samples_filtered(1:SamplesPerChip:end);

        % Add 1 chip delay to move signal to 11 chip boundary
        Rx_chips_delayed       = [Rx_chips_delayed_store; Rx_chips(1:end-Chi
pDelayAdd)];
        Rx_chips_delayed_store = Rx_chips((end-ChipDelayAdd+1):end); % Store
 delayed chips

        % Despread - sample symbol
        Rx_symbols = Barker'*reshape(Rx_chips_delayed,SpreadingRate,PacketSi
zeBits); % Multiply by Barker
        Rx_symbols = Rx_symbols(:)/SpreadingRate;   % Make a column and norm
alize

        % Demodulate
        Rx_symbols_plus_last      = [LastRxSymbol; Rx_symbols];
        Rx_symbols_plus_last_mult = Rx_symbols_plus_last(1:end-1).*conj(Rx_s
ymbols_plus_last(2:end));
        Rx_bits                   = Rx_symbols_plus_last_mult < 0;
        LastRxSymbol              = Rx_symbols(end);         % Demodulator s
tate

        % Calculate BER

        % Add BitDelay to Tx signal to align with Rx signal
        Tx_bits_delayed       = [Tx_bits_delayed_store; Tx_bits(1:end-BitDel
ay)];
        Tx_bits_delayed_store = Tx_bits(end-BitDelay+1:end); % Store delayed
 symbol

        if Packet==1 % Ignore delayed bits on first packet
            TotalBits = TotalBits+length(Rx_bits)-BitDelay;
            ErrorBits = ErrorBits+sum(Tx_bits_delayed(BitDelay+1:end)~=Rx_bi
ts(BitDelay+1:end));
        else
            TotalBits = TotalBits+length(Rx_bits);               % Calculate
 total bits
            ErrorBits = ErrorBits+sum(Tx_bits_delayed~=Rx_bits); % Compare T
x and Rx bits
        end
    end

ErrorResults(EsNoIndex) = ErrorBits; %error bits
end
BERResults = ErrorResults/TotalBits; % Calculate BER

Start Simulation
Simulating: Es/No=0dB
Simulating: Es/No=2dB
Simulating: Es/No=4dB
Simulating: Es/No=6dB
Simulating: Es/No=8dB
Simulating: Es/No=10dB

Plot BER Results

Plot the BER results Vs Es/No.

semilogy(EsNoRange,BERResults,'*-');
grid;
title('802.11b 1Mbps DBPSK BER');
ylabel('BER')
xlabel('Es/No (dB)');