Hanoi University of Science and Technology

School of Electronics and Telecommunications

EXERCISE

Radio Communication Course

Instructor: Dr. Nguyễn Văn Đức

Class: Telecommunication K53- Advance Program

Group 2

Member:

(1) Lê Cao Hoàng

(2) Nguyễn Xuân Hiếu

Question:

a) Simulate channel with Monte Carlo method and the delay power spectrum for large interval (showing in table below):

Channel(k)

Delay timeτ k=μs

Delay power coefficientρ [k ]

1 0 1.02 80 0.84873 160 0.76634 240 0.78805 320 0.66586 400 0.66687 480 0.51748 560 0.05439 640 0.0465

Bandwidth of system B=1.25MHz. Compare the transfer function of channel for several cases Doppler frequency f_dmax= 5Hz and 500Hz.

b) Analysis and compare Time Autocorrelation Function of channel for 2 cases: f_dmax= 9Hz and 90Hz

Solution:

a)

We have two function: Sub-function “MCM_channel_model” for supporting the main function

*****************MCM_channel_model function********************

%***************Monter Carlo Method channel******************%************************************************************function [ h,t_next ] = MCM_channel_model(u,initial_time,..., number_of_summations,symbol_duration,f_dmax,channel_coefficients); %Parameter:%- u is random variable which is used to transform to discrete Dopler%frequencies.discrete phases %- number_of_summations is the number of discrete frequencies or phased%used by MCM %- symbol_duration is the duration of a symbol (~the spampling interval%in single carrier system) %- f_dmax: the maximum Dopler frequency : We need to compare many value %- channel_coefficients are the coefficients of the discrete channel delay%profile %**********************************Setup*********************%************************************************************* t= initial_time;Channel_Length=length(channel_coefficients);h_vector=[]; for k=1:Channel_Length; u_k=u(k,:); phi=2*pi*u_k; f_d=f_dmax*sin(2*pi*u_k); h_tem=channel_coefficients(k)*1/(sqrt(number_of_summations))... *sum(exp(j*phi).*exp(j*2*pi*f_d*t)); h_vector=[h_vector, h_tem];end; h=h_vector;t_nect= initial_time+ symbol_duration; end;

**************************MAIN FUNCTION***************************************************Main function for question a**************%**********************Parameters***********************

%*********************************************************** %FFT lengthNFFT=64; %Sampling intervalt_a=8.0000e-007 %Duration of observed windowT_S= NFFT*t_a; %Number of summationsnumber_of_summations=40; %Maximum Dopler frequencyf_dmax=500.0; %Channel profilechannel_profile=[1.0000, 0.8487, 0.7663, 0.7880, 0.6658, 0.5644,..., 0.5174, 0.0543, 0.0465]; %channel impulse response lengthrho=channel_profile;N_P=length(rho); %Random variables for N_P pathsu=rand(N_P, number_of_summations); %***********************Setup*************************%**************************************************** initial_time=1.1; h=[];H=[];for i=1:100; h_i=MCM_channel_model(u, initial_time,..., number_of_summations, T_S, f_dmax, rho); h_i_tem=[h_i,zeros(1,NFFT-N_P)]; H_i_tem=fft(h_i_tem); H_i=[H_i_tem(NFFT/2+1:NFFT), H_i_tem(1:NFFT/2)]; initial_time=initial_time+ T_S; h=[h;h_i]; H=[H;H_i];end; %*******************Plot the graph************************%********************************************************* %plot the CIRfigure(1);mesh(abs(h))xlabel('\ tau in 8.0e-7s')ylabel('t in 1.024e-04s')zlabel('h(\tau,t)')title('Doppler frequency 500.0 Hz') %plot the CTFfigure(2);mesh(abs(h))

xlabel('f in 9.7 KHz')ylabel('t in 1.024e-04s')zlabel('H(f,t)')title('f_{D,max}=500.0 Hz')

***********************Result on graph********************

Case 1 : f_dmax =0 Hz

Time-invariant channel

Case 2: f_dmax=5.0 Hz

Slowly Time-Invariant Channel

Case 3: f_dmax=500.0 Hz

Fast Time-Invariant Channel

b) Code:

%******************************Set parameter******************%************************************************************* %Length of FFTNFFT =64;%Set the sampling interval:t_a then the bandwidth of the channel is 1/t_at_a=8.0000e-007;%Set the duration of a observerd window : T_ST_S= NFFT*t_a; %Number of summationsnumber_of_summations=40; %Maximum Dopler frequencyf_dmax=90.0; %Channel profilechannel_profile=[1.0000, 0.8487, 0.7663, 0.7880, 0.6658, 0.5644,..., 0.5174, 0.0543, 0.0465]; %channel impulse response length

rho=channel_profile;N_P=length(rho); %Random variables for N_P pathsu=rand(N_P, number_of_summations); %Duration symbol%T_S=NFFT*t_a; %************************Setup***********************************%****************************************************************% h is the channel impulse response vector at the time t,which should% be transfer into frequency domain inorder to compute the time and% frequency correlation function% H is the channel transfer vector (has length of NFFT) , denoted as H(f,t) %Initial timeNofSymbol=1000;t=0.1; %Sequence of channel coefficients at a fixed frequencyH_sequence=[]; for i=0:NofSymbol-1; [h]=MCM_channel_model(u,t,number_of_summations,T_S,f_dmax,rho); %MCM: Monte Carlo method h_extended= [h,zeros(1,NFFT-length(h))]; H=fft(h_extended); H_f1=H(3); H_sequence=[H_sequence,H_f1]; %*******************Computing******************* %*********************************************** %observe the channel for the next time window t=t+T_S; end; time_autocorrelation=xcorr(H_sequence,'coeff'); tau= -(NofSymbol-1)*T_S:T_S:(NofSymbol-1)*T_S; %***********************Plot the result****************%****************************************************** %plot for f_dmax =9 HZ plot(tau,real(time_autocorrelation),'k.');xlabel('\Deltat in seconds');ylabel('Time correlation function R(\Deltat)');grid on;hold on;

Result