Hello Ahmed,

if you have the delays and the path losses of each path, the simulation of time-varying channel via a Monte Carlo method is easy and follows the same principle whatever the channel including the indoor channel model A.

Follows these steps, for each independent path (the l^th for instance):

- create a vector of WGN denoted w (the length is the duration of your signal)

- get W = FFT(w)

- filter W by the Doppler spectrum profile S (usually a Jakes, called U spectrum as well). We note K = W*S

- get h_l = IFFT(K)

Repeat that for each path.

For more information, I recommend my PhD report to you, which can be dowload here : http://hal.archives-ouvertes.fr/docs/00/98/82/83/PDF/SAVAUX_Vincent_these_VS_VFsup.pdf

It is written in english, see in particular the last section of Chapter 1.

Best regards,

Vincent

Hi Vincent;

Thank you very much for your help and reply , i really appreciate this :) ; i will read your thesis to understand more , however , what should i do after calculate it for each path ? just add them ? or how can merge them , also where the effect of the time delays? and sampling frequency ? . Those are all information i have :

Average Relative Power (dB) = [0 -0.9 -1.7 -2.6 -3.5 -4.3 -5.2 -6.1 -6.9 -7.8 -4.7 -7.3 -9.9 -12.5 -13.7 -18 -22.4 -26.7].

Delay [ns]=[0 10 20 30 40 50 60 70 80 90 110 140 170 200 240 290 340 390].

Ricean K=0 for all paths.

Doppler Spectrum= classical (Jake’s) corresponding to a terminal speed of 3 m/s is assumed for all taps.

average rms delay spread = 50ns.

sampling freq= 40 MHz

Thank You very Much :)

Ahmed,

physically, a received signal that has been transmitted over a transmission channel is the sum of different delayed echoes of the same transmitted signal, and the channel may vary during the transmission (e.g. the receiver is in motion). It is then a function of 1/ the delays \tau and 2/ the time t as

h(\tau,t) = sum_{l}^{L} h_{l}(t) d(\tau-\tau_{l}), 

where L is the number of path (18 in your case), \tau_{l} is the delay for the l^th path. the gains h_{l}(t) are random processes whose variances are the power (in linear) that you have. Those are built with the Monte Carlo method I described.

For the other parameters, note that:

- a Ricean channel with K=0 corresponds to a Non line-of-sight transmission, i.e. a Rayleigh channel

- The Jakes' spectrum: its equation is usual in the literature. In my thesis, it is given in eq. (1.12). The width of the Jakes' spectrum is defined by the Doppler frequency which is linked to the defined vehicular speed. Thus, in the 3rd step of the Monte Carlo method, you have to filter the W=FFT(w) by this spectrum. Note that, if your considered signal has a bandwidth B (and W as well) and your 'U' spectrum a width Bj, it is normal if B>>Bj (the outside of the Jakes' spectrum is only zero)

- The delay rms is not necessarily usefull for the channel simulation

- The sampling freq is very usefull to simulate the system. Indeed, it gives you the time gap between two consecutive samples.

Practically, you create all the different paths with the Monte Carlo method, and you store it in a matrix. One dimension of the matrix is the time t and the other is the delay \tau. Thus, the gaps (in terms of samples) between your delays is defined by your Delay [ns] and the sampling freq.

Regards,

Vincent

Thank you very much Vincent Savaux ; i tried to implement the different paths following your steps ,but it seems not working( when i plot the result for each path , got nothing ). Also when i get h_l = IFFT(K) for each path , this is a vector not single value , however i should take one value to add it to the channel right ? please, can you check the draft code ? Thanks in advance :)

I see what is the problem: it comes from the fact that you took the Doppler frequency as bounds of your signal.

In fact, note that you consider your signal in [-fs/2,fs/2], and since fd

Thanks again:); i think i did not get it ; i mean for each path should i get only one power value ? or vector  of values? i thought  that for each path i should get only one power value then i have to construct the channel using these values and the corresponding delays . the power value can change each run however the delay is fixed . here i am confused cause i got a vector of power values for each path .

I am trying to simulate IEEE802.11g indoor environment almost static TX _RX, It uses OFDM with IFFT length 64 ,but i am struggling with the channel , i found this model but i want the powers to be changed each run.

thank you very much

For each path, you get a vector. If you consider (as usual) a channel as being constant during one OFDM symbol duration, then each sample of these vectors corresponds to one OFDM symbol. More precisely, you will do the delayed sum of all the k^th samples of each path for the k^th OFDM symbol.

Concerning the variation of the channel, since you consider a very low speed, you have to consider a very large number of OFDM symbols to see the variations.