Your approach looks correct.

In Rician fading, the channel response consists of both a deterministic line-of-sight (LOS) component and a random non-line-of-sight (NLOS) component. The Rician factor K represents the power ratio between the LOS and NLOS components.

In your code, you generate random complex gaussian variables for the LOS and NLOS components using randn. The scaling factor sqrt(1/2) is used to normalize the variance of the gaussian random variables.

To combine the LOS and NLOS components with the appropriate scaling, you correctly use the formula sqrt(K/(K + 1))*hLOS + sqrt(1/(K + 1))*hNLOS. This formula ensures that the power of the LOS component is weighted by sqrt(K/(K + 1)), while the power of the NLOS component is weighted by sqrt(1/(K + 1)). The sum of the two components gives you the rician fading channel response h.

To compute rician fading in MATLAB, you can use the ricianchan function from the Communications Toolbox. This function generates a random realization of a Rician fading channel.

For example:

% Set the parameters

K = 10; % rician factor (ratio of power in LOS component to power in NLOS component)

fd = 100; % maximum doppler shift (in Hz)

Ts = 1/1000; % Sampling time (in seconds)

T = 1; % Duration of the simulation (in seconds)

% Create a Rician fading channel object

channel = ricianchan(Ts, fd, K);

% Set the number of paths for the channel

channel.NRays = 1;

% Generate a random realization of the Rician fading channel

channelOutput = channel(T);

% Access the complex channel coefficients

h = channelOutput(1).PathGains;

% Print the channel coefficients

disp(h);

In this example, the ricianchan function is used to create a Rician fading channel object with the specified parameters: Rician factor K, maximum Doppler shift fd, sampling time Ts, and duration of the simulation T. The NRays property is set to 1 to indicate a single-ray channel.

By calling the channel object with the simulation duration T, a random realization of the Rician fading channel is generated. The complex channel coefficients h can be accessed from the PathGains property of the channel output.

I don’t think the code is correct since hLOS should only have a random phase, not a random amplitude.

You can write like this:

hLOS = exp(1i*2*pi*rand(1,1));

Rician fading is a statistical model used to describe the effect of multipath propagation in wireless communication systems. In Matlab, you can generate Rician fading using the `ricianchan` function in the Communications Toolbox. Here's an example code to generate a Rician fading channel:

```matlab

% Define the simulation parameters

fc = 2.4e9; % Carrier frequency in Hz

fs = 20e6; % Sample rate in Hz

fd = 100; % Maximum Doppler shift in Hz

v = 100/3.6; % Velocity of the mobile in m/s

dly = [0 10 20]*1e-9; % Path delays in seconds

pwr = [0 -5 -10]; % Path powers in dB

% Create a Rician fading channel object

chan = ricianchan(fs, fd, dly, pwr, v);

% Generate a random bit stream

tx = randi([0 1], 1000, 1);

% Apply the channel to the signal

rx = filter(chan, tx);

% Plot the channel impulse response

stem(chan.PathDelays, chan.ChannelGains);

xlabel('Delay (s)')

ylabel('Gain')

title('Rician Fading Channel Impulse Response')

```

In the above code, `fc` is the carrier frequency, `fs` is the sample rate, `fd` is the maximumDoppler shift, `v` is the velocity of the mobile in meters per second, `dly` is a vector of path delays in seconds, and `pwr` is a vector of path powers in decibels.

The `ricianchan` function creates a Rician fading channel object with the specified parameters. The `filter` function applies the channel to a random bit stream `tx` to simulate the effect of the channel on the transmitted signal. Finally, the code plots the channel impulse response using the `stem` function.

Note that the `ricianchan` function can also be used to generate multiple independent Rician fading channels with different parameters for simulation purposes.

Yashil Morar As you said, you already did the work on Rayleigh fading, so you already know what is Rayleigh fading. In short, when a signal passes through a Rayleigh fading channel, the signal is multiplied by a complex channel attenuation whose magnitude fluctuates randomly following the well-known Rayleigh distribution, while its phase changes randomly following uniform distribution. This part represents the NLOS propagation.

Now when you are trying to extend your work to Rician fading, you need to review what is the difference between Rician distribution and Rayleigh distribution. In Rician fading, similar as in Rayleigh fading, the complex channel attenuation is constituted as the sum of two orthogonal iid zero-mean normal distributed RVs, but also contains an additional constant term (which may be complex in general). This additional (complex) constant term represents the LOS propagation.

Hope this helps. Good luck.

The LoS component may need to be modelled by a normalized complex number, whose phase is determined by the transmission distance between the source and the destination.

hLOS = exp(j*2*pi*d/\lambda); % d represents the propagation distance.

In the case of the antenna array, the hLOS can be expanded to form a steering vector. The LoS component of the MIMO link can be regarded as the multiplication of two steering vectors, each associated with the TX array and RX array, respectively. Hope it helps!

To generatericianchan functionCommunications Toolbox.Rician fading channel object thatwireless communication system.

Herericianchan functionRician fading channel:

ini

Copy

% Set Rician factor and other simulation parameters

K = 10; % Rician factor

Fs = 1e6; % Sampling frequency (in Hz)

T = 1/Fs; % Sampling period (in seconds)

t = 0:T:1-T; % Time vector (in seconds)

fc = 2e9; % Carrier frequency (in Hz)

% Generate Rician fading channel object

chan = ricianchan(T, fc, K);

% Apply the channel to a signal

x = randn(size(t)) + 1i*randn(size(t)); % Generate random complex signal

y = filter(chan, x); % Apply Rician fading channel

% Plot the results

figure;

subplot(2,1,1); plot(t, real(x), t, imag(x)); title('Input Signal');

subplot(2,1,2); plot(t, real(y), t, imag(y)); title('Output Signal');

In this code,Rician factor K, thesampling frequency Fs, thecarrier frequency fc,simulation time vector t. We then use thericianchan functionRician fading channel objectchan, which we canx using thefilter function.

Notericianchan function providesDoppler spectrum, and the path gains andMATLAB documentation for more information on how to use this function.