When a wireless signal travels from a transmitter to a receiver it follows multiple paths. The signal may travel directly following the line of sight between the transmitter and receiver, it may bounce off the ground and reach the receiver or it may be reflected by multiple buildings on the way to the receiver. When these copies of the same signal arrive at the receiver they are delayed and attenuated based upon the path length that they have followed and various other factors.

A well known technique to model such a wireless channel is to model it as an FIR (Finite Impulse Response) filter. The wireless channel thus performs the convolution operation on the transmitted signal. The multipath profile of three well known LTE channel models is shown below.

The channel profile quantifies the delays and relative powers of the multipath components. It can be observed that the EPA model has 7 multipath components whereas the EVA and ETU models have 9 multipath components each. However there is a small caveat here. The multipath components described in the above table are not uniformly spaced in the time domain. So if an FIR filter has to perform convolution operation on a signal uniformly sampled at 100 MHz (Ts=10 nsec) the number of filter taps would be much larger. To be exact the FIR filters corresponding to the above channel models would have 42, 252 and 501 filter taps respectively. Most of these taps would have no power so the FIR filter can be efficiently implemented in hardware.

Also, if the channel is time-varying as most wireless channels are, each filter tap can be modeled to have a Rayleigh or Ricean distribution with a mean value described in the table above. Lastly, the variation in the value of a channel tap from one sample to the next depends upon the Doppler frequency which in turn depends upon the speed of the mobile unit. Higher the velocity of a mobile unit higher would be the Doppler frequency and greater would be the variations in the channel. The Doppler frequency is defined as:

fd=v*cos(theta)/lambda

where

‘fd’ is the Doppler Frequency

‘v’ is the receiver velocity

‘lambda’ is the wavelength

and ‘theta’ is the angle between the direction of arrival of the signal and the direction of motion

The exact method of generating Rayleigh distributed channel co-efficients with the desired temporal correlation requires some more explanation and would be the subject of a future post.

Note:

1. The above multipath channel models have a maximum delay of 410 nsec, 2510 nsec and 5000 nsec which is well within the range of a long cyclic prefix of length 16.67 usec (16670 nsec). So the Intersymbol Interference (ISI) would not adversely effect the system performance.

2. If you are doing simulation of a system that operates on individual symbols then temporal correlation between channel co-efficients is not that important. But if the system operates on blocks of symbols or bits (as an interleaver or convolutional encoder does) then temporal correlation plays an important part in determining the system performance.

#### Author: Yasir Ahmed (aka John)

More than 20 years of experience in various organizations in Pakistan, the USA, and Europe. Worked as a Research Assistant within the Mobile and Portable Radio Group (MPRG) of Virginia Tech and was one of the first researchers to propose Space Time Block Codes for eight transmit antennas. The collaboration with MPRG continued even after graduating with an MSEE degree and has resulted in 12 research publications and a book on Wireless Communications. Worked for Qualcomm USA as an Engineer with the key role of performance and conformance testing of UMTS modems. Qualcomm is the inventor of CDMA technology and owns patents critical to the 4G and 5G standards.

Hi Sir,

Kindly share the matlab code for LTE multipath channel model.

Thanks

Have you looked at this post?

http://www.raymaps.com/index.php/lte-fading-simulator/

Particularly important statement in the end:

“This is the process for generating one Rayleigh distributed channel tap. This step would have to be repeated for the number of taps in the channel model which could be 7 or 9 for the LTE channel models. A Ricean distributed channel tap can be generated in a similar fashion. MIMO channel taps can also be generated using the above described method, however, we would need to understand the concept of antenna correlation before we do that.”

Hi Sir,

Do you explain signal modeling of Uniform Linear Array in the presence of multipath fading channel.

Regards

Hi Khurram,

So far I have only considered deterministic channels for Uniform Linear Array (ULA) but multipath fading channel is a simple extension. You can give it a try and I will share your contribution if you want?

Cheers

Sir,

Please refer me some video or literature so that I can perform mathematical modeling of ULA receives signal in the presence of multipath fading.

Regards

Here you go Khurram, if you make it through this book you will certainly know more than I do.

https://www.amazon.com/Optimum-Array-Processing-Estimation-Modulation/dp/0471093904

Hello

Can you tell me what are LTE-A channel models.

Are they the same for LTE?

Thank you very much

I think channel models remain the same.

Very good

In tat I am not accounting the delay, and I have only 7 taps instead of 42 you have told in ur article, so it is a bit confusing.

7 taps are fine. I suggested 42 taps for the case where sampling rates are mismatched. In that case you would have to do some zeros stuffing.

Can I use something like this to simulate LTE epa. How will I account the delays?

x is my input signal

tap_weights_db = [0 -1 -2 -3 -8 -17.2 -20.8];

tap_weights_ln = 10.^(tap_weights_db/10);

norm_fact = sqrt(sum(tap_weights_ln.^2));

epa= tap_weights_ln/norm_fact; % normalization

s=filter(epa,1,x);

Yes sure that is a way. Let me know if it works!

How are the above tables and discussions extended to MIMO LTE systems?

In the uncorrelated case, it is quite simple e.g. for a 2×2 case there would be 4 independently generated Rayleigh fading channels h11, h12, h21 and h22 (usually a one tap channel is used in MIMO simulations). However if the MIMO channels are correlated the process becomes a bit more complicated.

Look here for details.

http://www.raymaps.com/index.php/rayleigh-fading-simulator/

I want to to thank you for this very good read!! I absolutely loved every bit of it.

I have you book marked to check out new things you post…

my web site … 古着 検査合格

Hi John,

Can you give equations/examples explaining how filter taps are modeled to have a Rayleigh or Ricean distribution with a mean value described in the tables above and doppler frequency shift in time-varing channels?

Best regards,

Cindy

Cindy,

Please look at the following post.

http://www.raymaps.com/index.php/lte-fading-simulator/

John

Could you please include the source of the model provided here. I will be needing to cite reference for using these models formally.

Ron,

I usually use multiple references when writing an article but you can get the information from 3GPP.org.

John

A three tap filter which models time varying, flat fading Rayleigh channel.

h=(1/sqrt(2))*randn(1,3)+j*(1/sqrt(2))*randn(1,3)

In phase and quadrature components have Gaussian distribution with zero mean, and variance 0.5.

Dear John,

Can you tell me how can I obtain path gains [complexNum complexNum complexNum] (3 paths) for a set of 3 channel coefficients.

Best Thanx

Talha

good !