Different sketches in Matlab

Step 1 : Implementation of the scatterers in our environment

The first step is to design our indoor environment as we have described it previously. We

assume that we have a model with scatterers which are uniformly distributed. We will

assume for simplicity that all the scatterers are fixed and that only the terminal will move.

Hence we avoid having Monte-Carlo phenomenon. This model tends to be realistic, since in

an indoor environment most of the scatterers are walls, chairs or table, which are fixed.

Scatterers can also be other terminals or even people in the office. But we will consider that

in a first time all those particular scatterrers are fixed in order to simplify the model. It is pretty

accurate because the only terminals that move a lot in Wlan environments are PDAs and

actually only few people have got this kind of devices. For simplicity we will assume in a first

time that people don’t often move in this office in order to fix all the scatterers in our model.

We will also assume that the scatterrers are randomly distributed in all the environment.

We experience single bounce multipath and thus ought to have Rayleigh fading. Indeed

we assume that we are in the narrowband situation. So we have a flat fading channel which

can be described by a Rayleigh distribution. Moreover we are in a non line-of-sight situation.

This figure represents the model that we are using in Matlab to describe our environment.

We typically described a rectangle room that is represented by the X and Y axis. We placed

the mobile station on the left side of the room and the base station on the right side of the

room. All the circles in the “room” represent a scatterrer. We also add on this figure the

phenomenon of single bounce multipath. The mobile station sends a signal and this signal is

reflected by all the scatterers to the base station. Because we are in a non line of sight

situation there are no direct communication between the mobile station and the base station.

Step 2 : Motion of the mobile station

The next step in our environment design is to illustrate the fading that we can encounter

in Rayleigh environment. One of the principal aspects of Rayleigh channels is that we have

the well known phenomenon of multipath. The different multipaths create fading when a

device is moving in the environment because the multipaths change. In fact we now look at

the sum over all the multipath to have the response of the whole environment with this

motion. So the impulse response that we calculate at the base station is also changing while

the multipaths are changing.

In our test case, we took a number of 20 scatterrers and we made the mobile station

moving on the Y axis. The mobile station starts at the position (0,2.5) and goes to the

position (0,4.5). The first figure is the environment’s modelisation and we can clearly see that

the multipaths in blue are changing while the mobile station is moving. The second figure

shows us the variation of the impulse response h while the mobile station. We clearly see

that this impulse response is not constant and that we have some fading. We obtain the

representation of the Rayleigh fade effect on the signal. The amplitude is indeed varying

according to the Rayleigh distribution.

Representation of the indoor environment

Response of the environment

Step 3 : angle of arrival, angle of departure

This simulation refers to the “Lee” model, where the scatterers are uniformly distributed on a

ring of radius R. The mobile station is placed on the centre of the ring, while the base station

is at a distance D from the mobile station.

It can be chosen an arbitrary number of scatterers on the ring, and of course it is possible to

change the spatial orientation of both base station and mobile station in the region of

interest. Then the angle of departure distribution at the mobile station is calculated, and it

seems to be uniformly distributed like expected .

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Now the angle of arrival distribution at the base station is calculated and it seems to follow

an U-shaped model. In fact the base station see only a limited angle spread of multipath

components, and in those angles that are near to the tangent line to the ring that passes for

the base station, we find a large density of scatterers. Though this model was originally

referred to macrocell environment, if we include several rings,

we can define a more complex model that better fits an indoor environment. This study will

be performed later.

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In this simulation we have an uniform distribution of scatterers (100) in a room 10m x 10m

and we make the mobile station moving towards the base station in 500 steps.

The size of each step is 0.01m .

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the received signal amplitude we can conclude that it follows a Rayleigh fading model, as

expected for our model.

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In this simulation we can see as the direction of departure profile changes as the mobile

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The previous image shows us that exists a correlation between the angle of departure of the

multipath components.

In the next simulation, performed with more scatterers and more mobile trip, we can see as

the direction of departure changes suddenly sometime. The explanation of this is because of

the passing of the mobile first before and then after a certain scatterer.

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In this simulation we move the mobile towards the base station and we look at the

instantaneous power angular spectrum at the BS and at the time delay profile.

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We can see that as we approach to the base station, the delay spread is higher (error?).

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Step 4 :

In this simulation we assume that we have a uniform distribution of 2000 scatterers, and

at each iteration we change the position of the mobile with a lambda/4 step over 250 total

steps. At each step we calculate the amplitude of the impulsive response and the

instantaneous angle power spectrum at the base station placed in the middle of the right

wall.

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In this experiment we can see how the instantaneous angle power spectrum changes

over spatial iterations. Each angle of arrival represents a single multipath component

reaching the base station, and we can see that there is little modification from one step to

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In fact the signal received will suffer only a slightly different fading, because of the

similar position environment of the mobile station.

Step 5

In this experiment we introduce an algorithm to find the optimum window, whose size will

correspond to our half-power bandwidth, to collect the highest amount of power coming from

each multipath component.

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optimum window to get the highest instantantaneous power angular spectrum at BS

Now we introduce a scanning linear array of 4 elements equally spaced of lambda/2.

This array can change its maximum direction only changing phases, and in the next figure

we can see an example of radiation pattern when the maximum is towards 45 degrees.

It is also displayed the -3dB bandwidth.

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polar Antenna pattern in dB

We can see the received power angular spectrum at the base station in both omni

directional and directive antenna pattern. We can see how the components near 45 degrees

are amplified depending on the antenna gain.

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instantantaneous power angular spectrum at BS (directive pattern)

Step 6

The next figure shows as the optimum window changes when the mobile moves. In

250 iterations the mobile trip is about 62.5 wavelengths and the window changes 8 times. So

we observe the modification of the optimum window over 7.8125 wavelengths on the

average. This suggests us how perform an algorithm of jittering. In fact, thus we may know

theoretically the optimum window; a real antenna has first to search the direction of

maximum. So the first step will be the initialization part, in which we use three beams to find

a first target area. When we find the correct 60 degrees sector we can perform two narrow

scan of 30 degrees. Then we can start our jittering towards the direction of maximum, and

we can also compare our target choice with the optimum window. Because we know that the

optimum window will change, we will perform an adaptive updating back to the post-

initialization part. We have to consider that it we could find some spatial scatterer

distributions that are not very suited to perform a jittering algorithm; in fact if the

instantaneous power angular profile at the base station does not change very much, after we

find the optimum direction, a jittering will be not so useful. This can suggest several new

model of spatial scatterer distribution that can include a clustering in the multipath

components. These models will be more realistic, because real scattering obey to models

that can better describe the effect of different size objects.

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In this picture we can see how the instantaneous angle power spectrum changes over

spatial iterations in a 3-d plot. Each angle of arrival represents a single multipath component

reaching the base station, and we can see that there is little modification from one step to

another.

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