Factors critical in implementing the threshold algorithm

There are two major factors that affect the implementation of the algorithm. These are the effects of multipath on RSS and the relationship between RSS, room size and the client location..

4.3.1 Multipath environment

The nature of the environment inside a building is such that RF propagation is severely affected by multipath distortion. This will affect the received signal strength readings reported by sensors. It is important that deviation in received signal strengths recorded at same point be minimised. This is determined by averaging across the channel as described in section 6.3.2. By applying this technique, the received signal strengths are accurate and with a residual spread of readings within a 3dB range. Any error in the RSS leads to an error in range calculations and thus an error in locating the client.

4.3.2 Selecting room for placing access points

The second factor that influenced the design of the algorithm is the dimensions (shape) of the room. It is assumed that the rooms where access points (sensor) are placed are square or rectangular in shape. The relationship between room dimensions, RSS and client location is investigated firstly for a square room.

4.4

Design threshold for a square room

The following assumptions are made for the threshold design to work for a square room.

• Each sensors is placed in the centre of the room • The wall loss is considered to be 5 dB.

• The room dimensions are known • The room is square

• The received signal strength follows free space path loss. • AP (sensors) and client antennas are omni-directional

Requirement To determine that the client is beyond the wall.

Solution: Consider the conditions where the client is assumed to be at the shortest distance from the AP that is just beyond the wall as shown in figure 4-2. Using equation 3-13 (free space loss equation), the received signal strength of a client (RSS) can be calculated. Client placed just beyond the wall will have a loss (RSS), given by

( )

[

]

RSS=− + + (dBm) (4-2)

Where

RSS = received signal strength of client just beyond the wall in dBm Xs= small side half length

Consider figure 4-2, where client’s position, Xs (half side length) and diagonal length (Xd) are shown. From the figure it can be explicitly deduced that the signal strength

(RSS) of a client must be less than the signal strength of Xd (diagonal length) which is represented by LXd, in order to guarantee that the client is beyond the wall. So, the

condition becomes:

If RSS<−L_Xd then client is outside the room (4-3)

If this condition is true then the probability of having client inside the room is zero, which means that client is outside the room. The 5 dB wall loss added in equation 4-2 ensures that the clients (RSS) circle will be greater than the threshold circle LXd as

shown in figure 4-2. This condition allows algorithm to detect wall between client and the access point with certainty.

RSS

-L

Xd

Xs

From free space loss equation 3-13, now we can calculate LXdwhich is

(

)

Assuming infinitely thin wall with a wall loss of 5 dB and a client just on the other side of a wall at Xs. Using the two equations 4-2 and 4-4 we can plot a graph to analyse the condition of equation 4-3. From figure (4-3), it is clear that for any side length of a square room the RSS (loss reported by a client) is always less than the loss of diagonal length LXd. The difference between RSS just beyond the wall, at the nearest point Xs,

and Lxd is a constant 2 dB, as plotted in figure 4-4.This shows confidence about

selecting square rooms. The threshold algorithm will pick a wall between a client and an access point with certainty.

Figure 4-3 Illustration for RSS always less than LXdfor a square room provided wall loss is

assumed as 5 dB RSS < -LXdat

any length for a square room

This proves that for a square room, a minimum of 3dB wall loss is sufficient to fulfil the condition of equation 4-3 i.e.

RSS < -LXd

Or -(LXs+ 3) < -LXd

Therefore, the client is always definitely outside the room. Only if the wall loss is < 3 dB there is an ambiguity as to whether a client is inside or outside the room. There is still a 2 dB margin to ensure that this threshold works for rectangular rooms as well.

Figure 4-4 Differences between graphs in figure 4-3

From figure 4-4, it can be deduced that the absorption by walls play a very vital role. The research (Li et al, 2005) gives a wall absorption figure as 5.5 dB.

for square room, thus meeting the condition set in 4-3. However, not all the rooms are square. In a rectangular room the shorter side needs to qualify a minimum length for this condition to be true.

If the wall loss is greater than 3dB then certain rectangular rooms will also meet the criteria identified above. The loss exhibited by the shorter side length (-LXs) of the

rectangular room and 5dB loss added to it together should always be less than the (-LXd),

when client is placed just beyond the shortest possible distance beyond the wall of a rectangular room. Again, the condition in equation 4-3 is required to be satisfied.