Phn 2: Bi tp matlab thng tin v tuyn.Bi 1.1% exercise1.1% claulation of the probability density function (PDF) of a Gaussian% distributed random variableclear;t_a=0.05; %sampling intervalx= -4:t_a:4;% Clauculation of the PDF of a Gaussian distributed random variablep=(1/sqrt(2*pi))*exp(-x.^2/2);check=trapz(x,p); %integration of pplot(x,p);title('\fontsize{12}PDF of a Gaussian distributed random variable');xlabel('x','FontSize',12);ylabel('P(x)', 'FontSize',12);

Bi 1.2% E1.2% Comparison of Gaussian distribute PDF with simulation resultclear;m_mu=0; %mean valuesigma_mu=1; %variancen=1000000; %length of the noise vectorx=-4:0.05:4;%length of the noise vectorp=(1/sqrt(2*pi)*sigma_mu)*exp(-(x-m_mu).^2/2*sigma_mu^2); %calculate the Gaussian distributed PDFcheck=trapz(x,p); %the integration of P(x)for -4G+1)&(i>1) previous_symbol=rs_frame(i-1,:); %previous OFDM symbol ISI_term=previous_symbol(NFFT+2*G+1:NFFT+G+N_P-1); ISI=[ISI_term,zeros(1,length(previous_symbol)-length(ISI_term))]; rs_i=rs_frame(i,:)+ISI; %the ISI term is added to the current OFDM symbol else rs_i=rs_frame(i,:); end; %OFDM demodulator Demodulated_signal_i=OFDM_Demodulator(rs_i,NFFT,NFFT,G); %OFDM Equalization d=Demodulated_signal_i./H; demodulated_symbol_i= ddemodce(d,1,1,'QAM',M_ary); data_symbol=[data_symbol, demodulated_symbol_i]; end; data_symbol= data_symbol'; %calculation of error symbols [number, ratio]=symerr(symbols, data_symbol); ser=[ser, ratio];end; snr=snr_min:step:snr_max;semilogy(snr,ser,'*--');hold off;ylabel('SER');xlabel('SNR in dB');

Bi 8.3%Main function: OFDM system over a time-variant channelclear all;NFFT=64;G=9;M_ary=16;t_a=50*10^(-9);%load rho.am-ascii;rho=[1, 0.6095, 0.4945, 0.3940, 0.2371, 0.19, 0.1159, 0.0699];N_P=length(rho); %Parameters for Monte Carlo channelsymbol_duration=NFFT*t_a;number_of_summations=40; %Number of summations for Monte-Carlo methodf_dmax=50; NofOFDMSymbol=100;length_data=(NofOFDMSymbol)*NFFT; %Source bitessource_data=randint(length_data,sqrt(M_ary)); %bit to symbol codersymbols=bi2de(source_data); %QAM modulation in base bandQAM_Symbol=dmodce(symbols,1,1,'qam',M_ary); %Preparing data patternData_Pattern=[];for i=0:NofOFDMSymbol-1; QAM_tem=[]; for n=1:NFFT; QAM_tem=[QAM_tem,QAM_Symbol(i*NFFT+n)]; end; Data_Pattern=[Data_Pattern;QAM_tem]; clear QAM_tem;end; Number_Relz=50;ser_relz=[];for number_of_relialization=1:Number_Relz; u=rand(N_P,number_of_summations); %A random variable for Monte-Carlo method ser=[]; snr_min=0; snr_max=25; step=1; for snr=snr_min:step:snr_max; snr=snr-10*log10((NFFT+G)/NFFT); %Miss matching effect caused by using guard interval rs_frame=[]; h_frame=[]; initial_time=0; for i=0:NofOFDMSymbol-1; %OFDM modulation OFDM_signal_tem=OFDM_Modulator(Data_Pattern(i+1,:),NFFT,G); [h, t]=MCM_channel_model(u, initial_time, number_of_summations, symbol_duration, f_dmax, rho); h_frame=[h_frame; h]; %The received signal over multipath channel is created by a %convolutional operation rs=conv(OFDM_signal_tem,h); %Additive noise is added rs=awgn(rs,snr,'measured','dB'); rs_frame=[rs_frame;rs]; initial_time=t; clear OFDM_signal_tem; end; %Receiver Receiver_Data=[]; d=[]; data_symbol=[]; for i=1:NofOFDMSymbol; if (N_P>G+1)&(i>1) previous_symbol=rs_frame(i-1,:); ISI_term=previous_symbol(NFFT+2*G+1:NFFT+G+N_P-1); ISI=[ISI_term,zeros(1,length(previous_symbol)-length(ISI_term))]; rs_i=rs_frame(i,:)+ISI; else rs_i=rs_frame(i,:); end; %OFDM demodulator Demodulated_signal_i=OFDM_Demodulator(rs_i,NFFT,NFFT,G); %OFDM Equalization h=h_frame(i,:); H=fft([h,zeros(1,NFFT-N_P)]); d=Demodulated_signal_i./H; demodulated_symbol_i=ddemodce(d,1,1,'QAM',M_ary); data_symbol=[data_symbol, demodulated_symbol_i]; end; data_symbol=data_symbol'; %Calculation of error symbols [number, ratio]=symerr(symbols, data_symbol); ser=[ser, ratio]; end; ser_relz=[ser_relz;ser]; end; ser=sum(ser_relz)/Number_Relz; snr=snr_min:step:snr_max; semilogy(snr,ser,'bo'); hold on %Parameters for Monte Carlo channelsymbol_duration=NFFT*t_a;number_of_summations=40; %Number of summations for Monte-Carlo methodf_dmax=0;NofOFDMSymbol=100;length_data=(NofOFDMSymbol)*NFFT; %Source bitessource_data=randint(length_data,sqrt(M_ary)); %bit to symbol codersymbols=bi2de(source_data); %QAM modulation in base bandQAM_Symbol=dmodce(symbols,1,1,'qam',M_ary); %Preparing data patternData_Pattern=[];for i=0:NofOFDMSymbol-1; QAM_tem=[]; for n=1:NFFT; QAM_tem=[QAM_tem,QAM_Symbol(i*NFFT+n)]; end; Data_Pattern=[Data_Pattern;QAM_tem]; clear QAM_tem;end; Number_Relz=50;ser_relz=[];for number_of_relialization=1:Number_Relz; u=rand(N_P,number_of_summations); %A random variable for Monte-Carlo method ser=[]; snr_min=0; snr_max=25; step=1; for snr=snr_min:step:snr_max; snr=snr-10*log10((NFFT+G)/NFFT); %Miss matching effect caused by using guard interval rs_frame=[]; h_frame=[]; initial_time=0; for i=0:NofOFDMSymbol-1; %OFDM modulation OFDM_signal_tem=OFDM_Modulator(Data_Pattern(i+1,:),NFFT,G); [h, t]=MCM_channel_model(u, initial_time, number_of_summations, symbol_duration, f_dmax, rho); h_frame=[h_frame; h]; %The received signal over multipath channel is created by a %convolutional operation rs=conv(OFDM_signal_tem,h); %Additive noise is added rs=awgn(rs,snr,'measured','dB'); rs_frame=[rs_frame;rs]; initial_time=t; clear OFDM_signal_tem; end; %Receiver Receiver_Data=[]; d=[]; data_symbol=[]; for i=1:NofOFDMSymbol; if (N_P>G+1)&(i>1) previous_symbol=rs_frame(i-1,:); ISI_term=previous_symbol(NFFT+2*G+1:NFFT+G+N_P-1); ISI=[ISI_term,zeros(1,length(previous_symbol)-length(ISI_term))]; rs_i=rs_frame(i,:)+ISI; else rs_i=rs_frame(i,:); end; %OFDM demodulator Demodulated_signal_i=OFDM_Demodulator(rs_i,NFFT,NFFT,G); %OFDM Equalization h=h_frame(i,:); H=fft([h,zeros(1,NFFT-N_P)]); d=Demodulated_signal_i./H; demodulated_symbol_i=ddemodce(d,1,1,'QAM',M_ary); data_symbol=[data_symbol, demodulated_symbol_i]; end; data_symbol=data_symbol'; %Calculation of error symbols [number, ratio]=symerr(symbols, data_symbol); ser=[ser, ratio]; end; ser_relz=[ser_relz;ser]; end; ser=sum(ser_relz)/Number_Relz; snr=snr_min:step:snr_max; semilogy(snr, ser, '*--'); hold off ylabel('SER'); xlabel('SNR in dB'); legend('time-variant', 'time-invariant');