Rayleigh Fading Channel Signal Generator Using the Dent Model

% % % Rayleigh Fading Channel Signal Generator % 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] = % 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] = XCORR(...) % should be multiplied by the omega_mTau scaling factor to properly display % axis. Tk is a two dimensional vector [M, N] = SIZE(Tk) with % M=numWaverorms and N=Length 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 = 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 % % 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 % % 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. % 100 km/hr = 65 mi/hr. Normal values are 20-130 km/hr % % Usage Examples: % [omega_mTau, Tk] = ai_RayCh(2^7, 2^18, 64, 2, 900, 100) % % where % % NumAngles=2^7, Length=2^18, symbolRate=64, NumWaveforms=2, carrierFreq=900, Velocity=100 % [omega_mTau, Tk] = RayCh(NumAngles, Length, symbolRate, NumWaveforms, % carrierFreq, Velocity); % % function [omega_mTau, Tk] = ai_RayCh(NumAngles, Length, symbolRate, NumWaveforms, carrierFreq, Velocity) % Number of oscillators N0 = NumAngles/4; % Maximum Doppler shift of carrier at some wavelength omega_m = (2*pi) * fm(Velocity, carrierFreq); % specify variance of the Rayleigh channel % use this for *constant* variange - requires changing other params in prog sigma2 = 10; % make sigma2 a gaussian RV around u = sigma2 and var = sigma2/5 % use for *non constant* variaance - requires changing other params in prog sigma2 = sigma2 + sqrt(sigma2/5) .* randn(1,NumWaveforms); % Initialize phases alpha_n = []; beta_n = []; theta_nk = []; % make a hadamard matrix Ak = hadamard(N0); % determine phase values 'alpha' and 'beta' n=[1:N0]; alpha_n = 2*pi*n/NumAngles - pi/NumAngles; beta_n = pi*n/N0; % convert to time scale using 'fs' sampling frequency t=[1/(symbolRate*1000):1/(symbolRate*1000):1/(symbolRate*1000) * Length]; Tk = []; for q = 1 : NumWaveforms rand('state',sum(100*clock)) % reset randomizer theta_nk = rand(1,length(n)) * 2 *pi; % create uniform random phase in range [0,2pi] sumRes = 0; for i = 1 : N0 term1 = Ak(NumWaveforms,i); term2 = cos(beta_n(i)) + j*sin(beta_n(i)); term3 = cos(omega_m .* t .* cos(alpha_n(i)) + theta_nk(i)); sumRes = sumRes + (term1 .* term2 .* term3); end Tk(q,:) = sqrt(2/N0) .* sumRes; % use line below to apply *non-constant* variance Tk(q,:) = repmat(10.^(sigma2(q)/20),1, Length) .* Tk(q,:); %apply variable in dB end % apply *constant* variance unilaterly in dB % Tk = repmat(10^(sigma2/20), k, Length) .* Tk; % plot results figure(20); subplot(3,1,1); semilogy(t,abs(Tk(1,:))); xlabel('Time (sec)'); ylabel('Signal Strength (dB)'); title(['Received Envelope, Symbol Rate = ', num2str(symbolRate), ',Carrier = ', num2str(carrierFreq), ', Velocity = ', num2str(Velocity)]); % compute auto and cross correlations and plot them omega_mTau = (1/(symbolRate*1000)) * (omega_m/(2*pi)); % compute omega_m * tau scaling [C1, Lags] = crosscorr(Tk(1,:), Tk(2,:), 20000); [C2, Lags2] = autocorr(Tk(1,:), 20000); figure(20); subplot(3,1,3); plot(Lags * omega_mTau, C1); xlabel('Normalized Time Delay'); ylabel('Normalized Crosscorrelation'); title('Crosscorrelation between waveforms k=1 and k=2'); figure(20); subplot(3,1,2); plot(Lags2 * omega_mTau, C2); xlabel('Normalized Time Delay'); ylabel('Normalized Autocorrelation'); title('Autocorrelation of the first waveform k=1');