📄 ai_raych.mht
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<BODY><PRE>%=20
%
% Rayleigh Fading Channel Signal Generator=20
% Using the Dent Model (a modification to the Jakes Model)
%
% Last Modified 10/18/05
%
% Author: Avetis Ioannisyan (avetis@60ateight.com)
%
%
% Usage:
% [omega_mTau, Tk] =3D=20
% ai_RayCh(NumAngles, Length, SymbolRate, NumWaveforms, CarrierFreq, =
Velocity)
%
% Where the output omega_mTau is a time scaling factor for plotting
% normalized correlations. The LAGS value output by [C,LAGS] =3D =
XCORR(...)
% should be multiplied by the omega_mTau scaling factor to properly =
display
% axis. Tk is a two dimensional vector [M, N] =3D SIZE(Tk) with
% M=3DnumWaverorms and N=3DLength specified in the RayCh(...) function =
call
%
% And the input variables are:
%
% NumAngles - scalar power of 2, NumAngles > 2^7 is used to specify =
the
% number of equally strong rays arriving at the receiver. It used to
% compute the number of oscillators in the Dent model with N0 =3D =
numAngles/4
%
% Length - scalar preferably power of 2 for faster computation, Length =
> 2^17
% is used to specify the length of the generated sequence. Lengths near =
1E6
% are close to realistic signals
%=20
% SymbolRate - scalar power of 2 and is in kilo-symbols-per-sec is used =
to
% specify what should be the transmission data rate. Slower rates will
% provide slowly fading channels. Normal voice and soem data rates are
% 64-256 ksps
%
% NumWaveforms - scalar used to specify how many 'k' waveforms to =
generate
% in the model. NumWaveforms > 2 to properly display plots
%=20
% CarrierFreq - scalar expressed in MHz is the carrier frequency of the
% tranmitter. Normally 800 or 1900 MHz for mobile comms
%
% Velocity - scalar expressed in km/hr is the speed of the receiver.=20
% 100 km/hr =3D 65 mi/hr. Normal values are 20-130 km/hr
%=20
% Usage Examples:
% [omega_mTau, Tk] =3D ai_RayCh(2^7, 2^18, 64, 2, 900, 100)
%=20
% where
%
% NumAngles=3D2^7, Length=3D2^18, symbolRate=3D64, NumWaveforms=3D2, =
carrierFreq=3D900, Velocity=3D100
% [omega_mTau, Tk] =3D RayCh(NumAngles, Length, symbolRate, =
NumWaveforms,
% carrierFreq, Velocity);
%
%
function [omega_mTau, Tk] =3D ai_RayCh(NumAngles, Length, symbolRate, =
NumWaveforms, carrierFreq, Velocity)
% Number of oscillators
N0 =3D NumAngles/4;
% Maximum Doppler shift of carrier at some wavelength
omega_m =3D (2*pi) * fm(Velocity, carrierFreq);
% specify variance of the Rayleigh channel
% use this for *constant* variange - requires changing other params in =
prog
sigma2 =3D 10;
% make sigma2 a gaussian RV around u =3D sigma2 and var =3D sigma2/5
% use for *non constant* variaance - requires changing other params in =
prog
sigma2 =3D sigma2 + sqrt(sigma2/5) .* randn(1,NumWaveforms);
% Initialize phases
alpha_n =3D []; beta_n =3D []; theta_nk =3D [];=20
% make a hadamard matrix
Ak =3D hadamard(N0);
% determine phase values 'alpha' and 'beta'
n=3D[1:N0];
alpha_n =3D 2*pi*n/NumAngles - pi/NumAngles;
beta_n =3D pi*n/N0;
% convert to time scale using 'fs' sampling frequency
t=3D[1/(symbolRate*1000):1/(symbolRate*1000):1/(symbolRate*1000) * =
Length];
Tk =3D [];
for q =3D 1 : NumWaveforms
rand('state',sum(100*clock)) % reset randomizer
theta_nk =3D rand(1,length(n)) * 2 *pi; % create uniform =
random phase in range [0,2pi]
sumRes =3D 0;
for i =3D 1 : N0
term1 =3D Ak(NumWaveforms,i);
term2 =3D cos(beta_n(i)) + j*sin(beta_n(i));
term3 =3D cos(omega_m .* t .* cos(alpha_n(i)) + theta_nk(i));
sumRes =3D sumRes + (term1 .* term2 .* term3);
end
=20
Tk(q,:) =3D sqrt(2/N0) .* sumRes;
% use line below to apply *non-constant* variance=20
Tk(q,:) =3D repmat(10.^(sigma2(q)/20),1, Length) .* Tk(q,:); %apply =
variable in dB=20
end
% apply *constant* variance unilaterly in dB=20
% Tk =3D repmat(10^(sigma2/20), k, Length) .* Tk;=20
% plot results
figure(20); subplot(3,1,1); semilogy(t,abs(Tk(1,:)));
xlabel('Time (sec)'); ylabel('Signal Strength (dB)');=20
title(['Received Envelope, Symbol Rate =3D ', num2str(symbolRate), =
',Carrier =3D ', num2str(carrierFreq), ', Velocity =3D ', =
num2str(Velocity)]);
% compute auto and cross correlations and plot them
omega_mTau =3D (1/(symbolRate*1000)) * (omega_m/(2*pi)); % compute =
omega_m * tau scaling
[C1, Lags] =3D crosscorr(Tk(1,:), Tk(2,:), 20000);
[C2, Lags2] =3D autocorr(Tk(1,:), 20000);
figure(20); subplot(3,1,3); plot(Lags * omega_mTau, C1);
xlabel('Normalized Time Delay'); ylabel('Normalized Crosscorrelation');=20
title('Crosscorrelation between waveforms k=3D1 and k=3D2');
figure(20); subplot(3,1,2); plot(Lags2 * omega_mTau, C2);
xlabel('Normalized Time Delay'); ylabel('Normalized Autocorrelation');=20
title('Autocorrelation of the first waveform k=3D1');
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