The information that I put down are from the site http://www.gaussianwaves.com/2011/05/ebn0-vs-ber-for-bpsk-over-rayleigh-channel-and-awgn-channel-2/ . My QUestions are due to some misconception and will really appreciate if some help is provided to clear the concepts.
If $y$ is the received data and $n$ is the input, then signal is received as $y = x + n$. This is an FIR model.
The received signal here is $y = hx +n$ where $h$ can be $h_1$ or $h_2$. This is also an FIR model.
- Case1: When $h = h_1$:
h_1 = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; % Rayleigh channel creates the coefficients $h$ of length $N$ representing the channel, where $N$ is the number of data samples. This is a flat fading Rayleigh channel because the number of taps = 1. Please correct me if I am wrong in saying that the number of taps =1, so it is a flat fading. In general, number of taps = number of delays.
- Case2: When $h=h_2$
If $h_2 = [1, 0, 0.5, -0.2]$ then also we call it Rayleigh but now it is also called multi-path. So, number of multipaths = length(h_2) = 4 ?
How is $h_2$ a Rayleigh random variable? What is the proper way to represent $h_2$ as rayleigh channel and the output $y$? Explanation with the help of code statement will be useful.
Theory says that there is Clarke's and Young's model for channel representation. Clarke's model uses FIR representation using sinusoids and cosines. Why do we need this model when we can simply apply the technique used to generate $h_1$ ?