In most cases rayleigh channel is a vector. can a rayleigh channel be a scalar quantity i.e., can we have only one element in rayleigh fading channel.
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Yes. A vector is the collection of scalar elements. – AlexTP May 24 '20 at 08:27
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Rayleigh channel is defined between transmit and receive antennas, if there is one transmit and one receive antennas then there is one Rayleigh fading coefficient.
If there is one transmit and multiple receive antennas then there is a vector or fading channel.
If there is one receive and multiple antennas then there is a vector or fading channel.
If there are multiple trasmit and receive antennas then you have a Rayleigh fading matrix represting the wireless channel
Dsp guy sam
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Ok understood. But I had query. Consider a case of single transmit and single receive antenna. Then in this also we write the following command to get Rayleigh coefficients. h = 1/sqrt(2)* randn(1,N)+I*randn(1,N); where N is greater than 1. Now here h will be row vector of N length. Then how to consider single coefficient in this case. – charu May 24 '20 at 14:50
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Don't ask new questions in the comments, @charu. You're citiing some code that probably does something you don't understand - maybe it's calculating a lot of different channel realizations, not just one. Your question can't be answered. – Marcus Müller May 24 '20 at 14:58
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When we talk about fading coefficients they are complex numbers, so it is not a vector it is 1 complex value. It is the magnitude of this complex number that is Rayleigh faded if the real and imaginary parts of the complex number is derived from IID gaussian distribution. In the code you paste you are preparing N fading coefficients looks like – Dsp guy sam May 24 '20 at 14:58
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@Dspguysam Your answer is imprecise. You are assuming a narrowband channel with slow fading. – MBaz May 24 '20 at 15:13
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@MBaz, I assume that is what the user is looking for, the OP seems to be confused in the definition of Rayleigh fading coefficient, so i thought to clarify that first before dwelving into frequency selectivity and slow/fast fading. I think OP was looking for this info. Please feel free to add a more precise and detailed answer – Dsp guy sam May 24 '20 at 15:17
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@Dspguysam You may very well be right. In my very personal and probably wrong perspective, an imprecise answer will not help the OP in the long term. But that's just me (and your answer was marked by OP as correct, so you probably guessed correctly at what was needed here). – MBaz May 24 '20 at 17:31