One of the key problems in 802.11 standard networks are interferences. It is not possible to avoid the influence of other wireless systems. One can only minimize the power level of unwanted signals. Typically the designer should find the best localization of access points (AP), but there is no planning and coordination between different private networks. To reduce the level of interferences, the transmitting power reduction is applied. The mathematical model was built to analyze the relationship between the coverage and the level of interferences. The results of these simulations are presented in this article.
The 802.11 standard networks are the most popular solution of wireless
communication today, besides the mobile telephony networks. One of the key problems
in such networks is the issue of interferences (see [
Another method of interference reduction is the diminish of the transmitted
power (see [
The structure of the Physical Layer has a great influence on the internal system
interference level. For 2.4 GHz transmission frequency range, only three channels
(numbered 1, 6 and 11) are the so called not overlapping channels (see [
The channel masks overlap partly, even for non overlapping channels. Some
interchannel interferences are always present in the system, when more than one
network is operating on the same area. The final level of the interference signal
power depends strongly on many parameters. The distance plays an important
role, because the level of the received power decreases while increasing the
distance between Wi-Fi stations. Two disadvantages are produced by interferences
(see [
Pnoise = Pint + Pwhite noise :
The noise power diminishes the channel throughput. The throughput is the most
important parameter determining the QoS of the transmission. The channel
throughput could be described by the following formula (see [
(1) where B represents the bandwidth of the transmission channel. The second disadvantage of interferences especially, when their signal power is relatively high, is the effect of the spurious carrier detection. The high level of interference power blocks the transmission channel. Some methods of interference level reduction are discussed in the next section. 3
A high level of interference power could be reduced by a proper arrangement of
access points (see [
Many devices use the same channel (5 devices - channel nr 11), some devices
use channels other then 1, 6, 11, so the choice of a channel is random. Network
planning let us achieve capacity, range and QoS (see [
Q = p3N; (3) where the N is the number of available channels.
The second solution suggests [
The smaller is the coverage of one cell, the more cells we have to produce to obtain the full coverage. This means more APs and in the end, more transmissions at the same time, but it does not mean that we reduce the interference power level. The authors present some proof in Sec. 5 and Sec. 6. 4
The basic equation, which describes the radio wave distribution in a free space
is the Friis formula (see[
Prx (r) =
(4 r)2 =
(4 r)2 f 2 : This formula allows us to calculate the received power (Prx) depending on the transmitted power (Ptx), the gains of receiving and transmitting antennas (Gtx, Grx), the channel frequency f and the distance between the transmitter and receiver (in so called free space, the r power is equal 2): k Prx(r) = f 2r2 : Using the formula (4) we can calculate the attenuation of radio signal in a free space:
Podb (r) = PtxGrxGtxLfspl; Lfspl =
c2
(4 r)2 f 2
and finally we obtain the following formula [
Lfspl[dB] = 32; 44 + 20 log r[km] + 20 log f [M Hz];
(9)
where r is in [km] and f in [MHz]. The more general formula takes the following
form (see [
The coverage in the 802.11n standard is determined by the minimal received power (received signal sensitivity), which is necessary for obtaining required level of throughput. The set of minimal received power in the case of a single spatial transmission in 802.11n standard is presented in Table 1.
The minimal sensitivity is respectively -82 dBm for throughput of 6.5 Mbit/s and -64 dBm for 65 Mbit/s. It is difficult to correlate these values with a specific distance, because in practice this distance could vary in a broad range due to a lot of factors. 5
The authors tried to verify the assumption that the decreasing of transmission
power and reduction of coverage help to diminish the internal interferences in
802.11n networks (see [
The Table 2 includes the channel allocation, which is used in simulation.
We assume that all stations are the transmitters. The localization of a station within the cell (coverage area) could vary from the center of the area to its edge. We analyze the 802.11n standard with 20 MHz channel bandwidth. The center frequencies for channels 1, 6, 11 are shown in Table 3.
The interference power level was calculated as the sum of interferences from stations S1 and S2 and white noise and the noise figure representing the noise of electronic circuits (mainly electronic amplifiers).
Pint =
2
∑ Pintx + (Pwhite noise + PNF ) :
x=1
White noise or thermal noise [
Pwhite noise(f ) = kT [W=Hz] ; T denotes the environment temperature in K degree, while k is a Boltzman constant. Threshold of white noise in 1 Hz bandwidth at 0 Kelvin degree is -228.6 dBW. White noise in B bandwidth can be calculated as:
Pwhite noise[dBm] = 10 log(kT B) : The white noise in 20 MHz channel at 17 C degree could reach the following level: Pwhite noise(T = 17◦C; B = 20M Hz) = 174 + 10logB = 131dBm . The following formula was developed by the authors to calculate the received power:
Preceived(r) = M (f 2412 5(K
( 27; 56 + 10 log r[m] + 20 log f [M Hz]) + Gsum: (16) We will denote Preceived and Ptransmitted by Prx and Ptx respectively. The M (f ) function represents the mask (filter) of the relevant channel. The signal outside the mask is eliminated while the one below the mask characteristics passes. The authors assume that the mask characteristic determines the maximal internal level of interferences. Gsum is equivalent to the additional gain of the system including the influence of the antennas of the receiver and the transmitter and respectively the gain connected with modulation, coding and different types of signal dispersions. Ptx, and Gsum are the parameters of the simulation and their values are presented in Table 4.
The parameters of m(f ) function correspond to the mask of 802.11n standard. We assume that the function (for f in MHz) is continuous, piecewise linear and
The stations are placed on Cartesian plane. The S transmitter has the (x; y) coordinates and S1 respectively (x1; y1). The distance d1 between the above stations is equal: d1 = √(x x1)2 + (y y1)2 : The practical formula for interference power level, which influences the S station (operating on channel 6) in d1 distance from the station S1, producing interferences while operating on channel 11, will be as follows: Prx(d1) = M (f 2462) + Ptx ( 27:56 + 10 log d1[m] + 20 log 2462) + Gsum: (19) The average interference power within the whole channel is the integral from Prx over f within the proper channel (6th in our case):
Prx(d1)average = ∫ 2:447 2:427
Prxdf : The authors correlate the distance d1 with the minimal received signal sensitivity (see Table 3). 6
In the first simulation the station S, operating on channel 6, was disturbed by S1 station, operating on channel 11. The transmitting power distribution was firstly simulated. The figure 5 shows the distribution of points correlated with (17) (18) (20) and Gsum. Source: own preparespectively -64 dBm and -82 dBm of received power (upper and lower lines). This analysis concerns the transmission in channel 6. We assume that the power transmitted by the S station is equal to receiver sensitivity.
The points corresponding to the -64dBm received signal are within the range from single meters to about 25 meters, while these corresponding with -82 dBm are within the range from a few meters to more than 200 meters. The coverage diminishes especially for the higher value of . Figure 6 presents the characteristics of the diminish of transmitted power with distance for different values of Prx, and Gsum. The critical parameter is the . The highest slope is for = 8.
The characteristics of the interference power for the fixed distance beetwen S and S1 are presented in Fig. 7. The Pint characteristics are versus the level of the disturbances source power. The following assumptions are made: the S is transmiiting in the channel nr 6, Ptx is 10 dBm, Gsum is 0 [dBm] and = 3; while the S1 station (disturbing) is transmitting in the channel nr 11, Gsum is 0 [dBm], is 3 and the Ptx change in the range from -10 to 20 dBm. The point of the interference level calculation coresponds with the maximum coverage of the S station, where the Prx is -82dBm. This distance is 53,38 m while the distance between stations is 106.76m. The results are shown in Fig. 7.
The interference power level diminishes, when the Ptx of S1 diminish, but at the same time the coverage area is reduced, so the dead zone arises with no possibility of transmission. The white noise could have higher level than interference power for low Ptx of disturbing station and for non convenient transmission conditions (high value of the coefficient- eg. rooms, halls etc.).
The characteristics of interference level with another assumption is presented in fig. 8. In this case together with the change of the Ptx we change the point of S1 localization (x1,y1) to reduce the dead zone. The point of the interference level calculation (distance from S) is constant and its value is 53.38 m, but the distance between S and S1 stations (d1) diminishes relatively to Ptx (S1) reduction. The dead zone is minimized. The level of interference power is constant versus Ptx and values (Fig. 8). The next simulation concern the situation when the Ptx power is increased for both S and S1 and the interference power level is calculated for maximum coverage points corresponds with received power equal -82 dBm (Fig. 9). The results of the simulation are the same as previously. The inteference power level is higher than the thermal noise, but if we take into account the the electronic circuits noise figure, then the total noise could be above interference power level. The model for interference power level simulations from one or two disturbing sources (S1 /S2) was developed. The model includes the efects of the mask and several other parameters such as antennas gain, modulation coding and dispersion gain (Gsum coefficient). The following simulations based on this model were carried out : 1. the characteristic of interference power level, when the Ptx of source of disturbances is reduced, but the localisation remains the same (see Fig. 7) ,
Taking into account the mentioned above simulations, we can conclude: 1. for the 1st simulation: the power level of interferences decrease, but the coverage diminishes at the same time, 2. for the 2nd simulation: the interference level is constatnt, 3. for the 3rd simulation: the interference level is constatnt.
The achieved results let us make a conclusion, that reduction of Ptx could reduce the interference power level, but at the same time cause the dead zone to arise. This solution may be applied, if the station is close to AP, so we can temporary (for one or more sessions) reduce transmission power, keeping reasonable throughput. This solution requires communication between different APs to establish the most efficient transmission power level. Such solutions are not available nowadays.