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MBaz
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Your question is quite unclear, but it seems like you're trying to simulate the continuous-time radio channel. In this model, you do not multiply by complex coefficients; rather, you add delayed and attenuated copies of the transmitted signal.

Say you transmit $s(t)$. Then, the received signal is $$r(t)=\sum_k g_k s(t-\tau_k) + n(t),$$ where $g_k$ is the gain of each path and $\tau_k$ is the delay along that path. Your indoor channel model should provide a framework for generating the gains and delay for simulation. $n(t)$ is white noise.

In the discrete-time channel model, you don't care about how the signal looks in the air; all you care about is the samples at the output of the matched filter. It turns out that if the number if paths is large, and if the delays and gains meet certain statistical conditions, and furthermore assume that the receiver is synchronized, then the matched filter samples have the form $$r=hs+n,$$ where $s$ is one transmitted symbol, $n$ is a sample from a Gaussian random variable, and $h$ is the channel gain, a complex number with Gaussian real and imaginary parts. This is known as flat Rayleigh fading (AlexTP's answer covers the more general case of frequency-selective fading).

You're right in assuming that mobility speed (either of the transmitter, receiver, or reflectors) will affect the channel. In the discrete-time model, a slow fading channel is one where $h$ remains constant for several symbol durations. In the continuous channel, this means that the paths the signal takes between transmitter and receiver stay constant for several symbol times.

Edited to add: How to generate the channel gains $h$ is the subject of a lot of literature, and it can get quite complicated. The simplest approach is this: assume a channel coherence time, or equivalently, a number of symbols that will be subject to the same $h$. After that, generate a new $h$ independently from the previous one. Many researchers (me included) take this approach, which is valid as a first approximation to the real, physical problem.

Your question is quite unclear, but it seems like you're trying to simulate the continuous-time radio channel. In this model, you do not multiply by complex coefficients; rather, you add delayed and attenuated copies of the transmitted signal.

Say you transmit $s(t)$. Then, the received signal is $$r(t)=\sum_k g_k s(t-\tau_k) + n(t),$$ where $g_k$ is the gain of each path and $\tau_k$ is the delay along that path. Your indoor channel model should provide a framework for generating the gains and delay for simulation. $n(t)$ is white noise.

In the discrete-time channel model, you don't care about how the signal looks in the air; all you care about is the samples at the output of the matched filter. It turns out that if the number if paths is large, and if the delays and gains meet certain statistical conditions, and furthermore assume that the receiver is synchronized, then the matched filter samples have the form $$r=hs+n,$$ where $s$ is one transmitted symbol, $n$ is a sample from a Gaussian random variable, and $h$ is the channel gain, a complex number with Gaussian real and imaginary parts. This is known as flat Rayleigh fading (AlexTP's answer covers the more general case of frequency-selective fading).

You're right in assuming that mobility speed (either of the transmitter, receiver, or reflectors) will affect the channel. In the discrete-time model, a slow fading channel is one where $h$ remains constant for several symbol durations. In the continuous channel, this means that the paths the signal takes between transmitter and receiver stay constant for several symbol times.

Your question is quite unclear, but it seems like you're trying to simulate the continuous-time radio channel. In this model, you do not multiply by complex coefficients; rather, you add delayed and attenuated copies of the transmitted signal.

Say you transmit $s(t)$. Then, the received signal is $$r(t)=\sum_k g_k s(t-\tau_k) + n(t),$$ where $g_k$ is the gain of each path and $\tau_k$ is the delay along that path. Your indoor channel model should provide a framework for generating the gains and delay for simulation. $n(t)$ is white noise.

In the discrete-time channel model, you don't care about how the signal looks in the air; all you care about is the samples at the output of the matched filter. It turns out that if the number if paths is large, and if the delays and gains meet certain statistical conditions, and furthermore assume that the receiver is synchronized, then the matched filter samples have the form $$r=hs+n,$$ where $s$ is one transmitted symbol, $n$ is a sample from a Gaussian random variable, and $h$ is the channel gain, a complex number with Gaussian real and imaginary parts. This is known as flat Rayleigh fading (AlexTP's answer covers the more general case of frequency-selective fading).

You're right in assuming that mobility speed (either of the transmitter, receiver, or reflectors) will affect the channel. In the discrete-time model, a slow fading channel is one where $h$ remains constant for several symbol durations. In the continuous channel, this means that the paths the signal takes between transmitter and receiver stay constant for several symbol times.

Edited to add: How to generate the channel gains $h$ is the subject of a lot of literature, and it can get quite complicated. The simplest approach is this: assume a channel coherence time, or equivalently, a number of symbols that will be subject to the same $h$. After that, generate a new $h$ independently from the previous one. Many researchers (me included) take this approach, which is valid as a first approximation to the real, physical problem.

Source Link
MBaz
  • 15.4k
  • 9
  • 32
  • 46

Your question is quite unclear, but it seems like you're trying to simulate the continuous-time radio channel. In this model, you do not multiply by complex coefficients; rather, you add delayed and attenuated copies of the transmitted signal.

Say you transmit $s(t)$. Then, the received signal is $$r(t)=\sum_k g_k s(t-\tau_k) + n(t),$$ where $g_k$ is the gain of each path and $\tau_k$ is the delay along that path. Your indoor channel model should provide a framework for generating the gains and delay for simulation. $n(t)$ is white noise.

In the discrete-time channel model, you don't care about how the signal looks in the air; all you care about is the samples at the output of the matched filter. It turns out that if the number if paths is large, and if the delays and gains meet certain statistical conditions, and furthermore assume that the receiver is synchronized, then the matched filter samples have the form $$r=hs+n,$$ where $s$ is one transmitted symbol, $n$ is a sample from a Gaussian random variable, and $h$ is the channel gain, a complex number with Gaussian real and imaginary parts. This is known as flat Rayleigh fading (AlexTP's answer covers the more general case of frequency-selective fading).

You're right in assuming that mobility speed (either of the transmitter, receiver, or reflectors) will affect the channel. In the discrete-time model, a slow fading channel is one where $h$ remains constant for several symbol durations. In the continuous channel, this means that the paths the signal takes between transmitter and receiver stay constant for several symbol times.