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  1. For a dense urban environment with rich scattering and no Line of sight (LoS) path, the Rayleigh distribution can be used to model the fading.
  2. Rician fading is a stochastic model for radio propagation anomaly caused by partial cancellation of a radio signal by itself.

How can the knowledge of the statistical distribution of the noise impact the way the channel estimation is done ?

I need to model a type of channel with the knowledge of its statiscal distribution: for that i use a Discrete FIR Filter block, and then impaired with the AWGN block.

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    $\begingroup$ I suggest you thoroughly read chapter 2 of the book 'Introduction to Wireless Communication' by David Tse . It is freely available pdf. They described the rayleigh and rician fading models and how the AWGN noise is modeled as per the signal path followed by these models. $\endgroup$ – jithin Mar 24 at 10:11
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My personal point of view: what matters much more than the distribution is the second-order statistics of the channel. In particular things like delay spread / coherence bandwidth and Doppler spread / coherence time. These parameters tell you a thing or two that you must take into account when estimating your channels:

  • The coherence bandwidth (roughly equal to the inverse of the delay spread) tells you for what bandwidth you can consider the channel approximately flat. If the bandwidth you want to transmit is below that, you can consider the channel a scalar quantity, which is simple to estimate. If your bandwidth is higher, you either need to go to frequency-domain techniques like OFDM and then estimate the channel on several frequencies (spaced no more than the coherence bandwidth) or estimate channel taps in time domain, e.g., when using a Rake receiver.

  • The coherence time (roughly equal to the inverse Doppler spread) tells you how quickly the channel changes in time, i.e., for how long you can consider it approximately constant. After the coherence time has passed, your channel estimate is no longer valid and you need to train again (or employ tracking if you can).

That said, the channel conditions (like LOS/NLOS) do influence these quantities as well. If you have a strong LOS, chances are your coherence time is higher since the LOS will not change rapidly in time.

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  • $\begingroup$ the channel impulse response is estimated periodcially in the coherence time: it is a time based channel estimation. So I only need those two information from the channel model, i.e., the coherence time and coherence bandwidth , $\endgroup$ – Abby_DSP Mar 24 at 12:53
  • $\begingroup$ At least for the channel estimator, I would claim these are the two most relevant parameters. You do need the distributions too to design your whole communication system, in particular the modulation and coding schemes. Maybe not so much for the channel estimator itself. $\endgroup$ – Florian Mar 24 at 17:16
  • $\begingroup$ yes @Florian, For example, a 30 Hz doppler spread means that the coherence time is of the order of 80 symbols at 2400 baud. This thus indicates the duration of validity of a channel estimate, since beyond that, the response of the channel is no longer correlated. Right ? $\endgroup$ – Abby_DSP Mar 26 at 11:16
  • $\begingroup$ Yep, that's what it means. $\endgroup$ – Florian Mar 26 at 14:07

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