A communication system uses QPSK modulation. The bit error rate requirement for

Question

A communication system uses QPSK modulation. The bit error rate requirement for this system is P_ = 10^-6. The transmission frequency is f_0 = 2.4 GHz. The transmitter power is 1 Watt. The feedline loss between the transmitter and the transmit antenna is 2 dB. The transmit antenna is omnidirectional and has a gain of 0 dBi. The transmit antenna height is 20 meters For the receiver, the low noise amplifier has a noise figure of 7 dB, the feedline loss is 1.5 dB. the antenna temperature is 290 K. and the receive antenna gain is 3 dBi Hie demodulator implementation loss is I dB The receive antenna height is 1.5 meters. A. Assuming free space loss in the channel, plot the data rate that the link supports for distances between 100 meters and 20 km Use a log-log graph to plot the data rate in bits/s as a function of distance, d, in meters B. Assuming a two-ray propagation loss model, plot the data rate that the link supports from d_c to 20 km, where d, = 4h_th_s/lambda = 4h_th_c f_o/c. On the same graph as part A, plot the data rate in bits/s as a function of distance, d, in meters.

Explanation / Answer

clc;

clear all;

bits=1000000;

data=randint(1,bits)>0.5;

ebno=0:10;

BER=zeros(1,length(ebno));

for i=1:length(ebno)

   

    %---Transmitter---------

    %mapping of bits into symbols

    symb=2.*data-1;

            %----Filter

    psf=ones(1,1);

    M=length(psf);

            % inserting zeros between the bits

            % w.r.t number of coefficients of

            % PSF to pass the bit stream from the PSF

    z=zeros(M-1,bits);

    upsamp=[symb;z];

    upsamp2=reshape(upsamp,1,(M)*bits);

    %Passing the symbols from PSF

    tx_symb=conv(upsamp2,psf);

    %--------CHANNEL-----------

    %Random noise generation and addition to the signal

    ebnos=10.^(ebno(i)/10);

    n_var=1/sqrt(2.*ebnos);

    rx_symb=tx_symb+n_var*randn(1,length(tx_symb));

    %xxxxxxxxxxxxxxxxxxxxxxxxxx

   

    %-------RECEIVER-----------

    rx_match=conv(rx_symb,psf);   

    rx=rx_match(M:M:length(rx_match));

    rx=rx(1:1:bits);

    recv_bits=(sign(rx)+1)./2;

   %xxxxxxxxxxxxxxxxxxxxxxxxxxx

   

   %---SIMULATED BIT ERROR RATE----

    errors=find(xor(recv_bits,data));   

    errors=size(errors,2);

    BER(i)=errors/bits;

    %xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal with Rectangular Pulse Shaping for BPSK');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

semilogy(ebno,BER,'b.-');

hold on

thr=0.5*erfc(sqrt(10.^(ebno/10)));

semilogy(ebno,thr,'rx-');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate for BPSK')

legend('simulation','theory')

grid on

QPSK MATLAB code

clc

clear all

bits=1000000;

data=randint(1,bits)>0.5;

%---debugging---

%data=[1 1 1]

%xxxxxxxxxx

ebno=0:10;

BER=zeros(1,length(ebno));

  

    %---Transmitter---------

    %Gray mapping of bits into symbols

    col=length(data)/2;

    I=zeros(1,col);

    Q=I;

   

    I=data(1:2:bits-1);

    Q=data(2:2:bits);

   

    I= -2.*I+1;

    Q= -2.*Q+1;

   

    symb=I+j.*Q;

   

           

            %----Filter

    psf=ones(1,1);

            %----

    M=length(psf);

for i=1:length(ebno)

            % inserting zeros between the bits

            % w.r.t number of coefficients of

            % PSF to pass the bit stream from the PSF

z=zeros(M-1,bits/2);

    upsamp=[symb;z];

    upsamp2=reshape(upsamp,1,(M)*bits/2);

    %Passing the symbols from PSF

    %tx_symb=conv(real(upsamp2),psf)+j*conv(imag(upsamp2),psf);

   

    tx_symb=conv(upsamp2,psf);

    %--------CHANNEL-----------

    %Random noise generation and addition to the signal

    npsd=10.^(ebno(i)/10);

    n_var=1/sqrt(2.*npsd);

    rx_symb=tx_symb+(n_var*randn(1,length(tx_symb)) +j*n_var*randn(1,length(tx_symb)) );

    %xxxxxxxxxxxxxxxxxxxxxxxxxx

   

    %-------RECEIVER-----------

    rx_match=conv(rx_symb,psf);   

    rx=rx_match(M:M:length(rx_match));

    rx=rx(1:1:bits/2);

    recv_bits=zeros(1,bits);

    %demapping

    k=1;

    for ii=1:bits/2

        recv_bits(k)= -( sign( real( rx(ii) ) ) -1)/2;

        recv_bits(k+1)=-( sign( imag( rx(ii) ) ) -1)/2;

        k=k+2;

    end

       

       %sign(   real( rx )   )

       %sign( imag( rx )   )

        %data

        %tx_symb

        %rx_symb

       

        %recv_bits

   %xxxxxxxxxxxxxxxxxxxxxxxxxxx

   

   %---SIMULATED BIT ERROR RATE----

    errors=find(xor(recv_bits,data));   

    errors=size(errors,2);

    BER(i)=errors/bits;

    %xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal with Rectangular Pulse Shaping for QPSK');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

semilogy(ebno,BER,'b.-');

hold on

thr=0.5*erfc(sqrt(10.^(ebno/10)));

semilogy(ebno,thr,'rx-');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate for QPSK')

legend('Simulation','Theory')

grid on

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