Modeling Signal Attenuation in IEEE 802.11 Wireless LANs ...

1 Modeling Signal Attenuation in ieee Wireless LANs - Vol. 1. Daniel B. Faria Computer Science Department Stanford University Abstract and around a standard office environment. This model Path loss models are used to approximate Signal atten- has been chosen for its simplicity and its effectiveness uation as a function of the distance between transmit- at Modeling Signal propagation over several frequen- ters and receivers, being an important building block cies [10, 9]. Our effort differs from previously published for both research and industry efforts. In this paper we ones in several ways: present experimental data that validates the use of the No spatial averaging. It is common practice to repre- log-distance model both inside and outside a standard of- sent a given location L by the average Signal strength fice building. Our measurements were performed using over an area around L, usually in the order of sev- off-the-shelf ieee hardware and with distances eral wavelengths [10, 7].

2 Such spatial averaging is per- varying from 1 to 50 meters. The values found for the formed to remove outliers, reducing the effects of small- path loss exponent agree with previously published re- scale fading and producing values more representative sults ( = , ). Moreover, linear regression pro- of large-scale path loss. Despite better Modeling results, duced models with acceptable standard deviations (< 8. such procedure has a couple of disadvantages. First, as dB) and suggest the occurrence of log-normal shadow- clients are usually stationary [6, 3], the values generated ing, as the deviations from the mean (in decibels) closely through spatial averaging may produce incorrect statis- follow a Gaussian distribution. tics. Second, it increases the costs associated with mod- 1 Introduction eling an environment. For instance, access points can autonomously create Signal strength samples in overpro- The ability to predict the Signal strength provided by ac- visioned networks, relieving operators from unnecessary cess points in a Wireless LAN (WLAN) is not only useful time-consuming experiments.

3 Such autonomous cali- to researchers but is also a convenient capability in prac- bration is viable only if spatial averaging is not neces- tice. For instance, it gives operators an idea of the cover- sary. age provided by a set of access points (APs) based only on their locations, possibly eliminating the need for site Off-the-shelf ieee hardware. Instead of using surveys when provisioning the network. Moreover, it al- pole-mounted antennas and spectrum analyzers, we em- lows the network to more accurately implement services ploy regular hardware to collect samples. We such as device localization, transmission power control, believe such setting to produce results more representa- and interference prediction. tive of real installations for a set of reasons. First, Signal The standard way of estimating Signal strength across strength estimates may be noisier, as they are generated an environment is by means of a path loss model, usu- by standard PCMCIA client devices during frame recep- ally found empirically [9].

4 Simple models estimate the tion. Second, standard cards do not produce exact omni- mean Signal strength between transmitters and receivers directional transmission patterns, which also affects sig- based solely on the distance between them, while more nal Attenuation in practice. Finally, the use of such accurate (and complicated) models use extra information hardware allows our measurements to benefit from tech- about the environment, such as building blueprints, wall niques implemented to improve reception quality. For materials, and location of obstacles. Due to scattering, instance, most devices today implement antenna reflection, and diffraction of waves, path loss models diversity, which reduces some effects attributed to small- are strongly environment-dependent. Moreover, while scale fading ( sudden drops in Signal strength) [9]. free space propagation dictates that Signal attenuates as a function of the square of the distance, measurements Standard setting.

5 We modeled Signal propagation have shown higher Attenuation in practice, both inside within and around the Gates Computer Science Building and outside office buildings [8, 5, 9]. at Stanford University. Indoors, 41 locations were sam- In this paper we demonstrate the applicability of pled within a 66m 24m area in the fourth floor, with the log-distance model to predict Signal strength within measurements taken in corridors and inside offices, with 24. meters 66 meters Figure 1: Measurement locations in the 4th floor of the Computer Science Building. transmitter-receiver separation ranging from 1 to 50 me- Measurements in the literature have reported empirical ters. Outside, we sampled 40 locations with distances values for in the range between (lightly obstructed varying between 1 and 31 meters from the building's environments with corridors) and 5 (multi-floored build- external wall. In both cases, the experiments were per- ings), while values for usually fall into the interval formed using the installed ieee Wireless infras- [4, 12] dB [9].

6 For example, Seidel et al. report the tructure. results of Modeling two office buildings at 914 MHz, Our results suggest that the log-distance model can be with best fits ( , ) = ( , ) and ( , ) for used successfully both indoors and outdoors. First, the single-floor measurements [10]. Other installations that values found for the path loss exponent ( ) agree with have also been shown to follow this model can be found previously published numbers: and for in- in [9, 8, 5]. door and outdoor Attenuation , respectively. Second, our measurements produced models with acceptable stan- 3 Modeling Attenuation Indoors dard deviation values: dB inside and dB outside We performed experiments using a subset of the de- the building. Finally, the deviations from the mean (in ployed Wireless infrastructure in the Computer Science decibels) could be closely approximated by Gaussians, building at Stanford University. We concentrated our what is usually referred to as log-normal shadowing.

7 Indoor measurements at one of the wings in the fourth 2 Log-distance Path Loss Model floor, as depicted in figure 1. As shown, 41 locations were sampled within a 66m 24m area. From these, 13. In order to predict received Signal strength between were located inside offices ( ), 15 inside con- clients and access points, in this paper we employ the ference rooms (at least 8m ), and 13 in corridors. log-distance path loss model [9]. In this model, received Such a mix allows for the resulting model to be repre- power (in dBm) at a distance d (in meters) from the trans- sentative of the whole floor. mitter (P r(d)) is given by: A total of four access points were employed, their lo- cations being represented by triangles in figure 1. All P r(d) = P r(d) + X access points are Cisco Aironet 1200, operating at GHz ( ), and mounted close to the ceiling. These P r(d) = P r0 10 log(d) + X (1). APs are provisioned with two antennas and were config- where P r0 is the Signal strength 1 meter from the trans- ured to transmit at 20 dBm [2].

8 Mitter, is known as the path loss exponent, and X rep- Our client device is a Cisco Aironet 340 PCMCIA. resents a Gaussian random variable with zero mean and card, which is used in our experiments as a receiver. The standard deviation of dB [9]. In the equation above, card has a receive sensitivity of -90 dBm when operating P r(d) represents the mean (expected) Signal strength d at 1 Mbps, is able to transmit at 15 dBm, and is provided meters from the transmitter, while P r(d) denotes a ran- with an integrated internal antenna with diversity sup- dom outcome. This model takes into account the dif- port [1]. In order to collect Signal strength statistics we ferent obstacles present in multiple transmitter-receiver employed a modified Linux driver, that recorded power paths with the same separation, this phenomenon re- in dBm for received frames. ferred to as log-normal shadowing. For each of the 41 locations shown in figure 1 we The parameters ( , ) define the statistical model and measured the quality of the Signal relative to each access are viewed as heavily dependent on the environment.

9 Point. In total, 146 AP-client associations were used, as -20. alpha= 35. -30 Free space (alpha= ). 30. -40. Signal strength (dBm). 25. -50. Samples 20. -60. 15. -70. -80 10. -90 5. -100 0. 10 20 30 40 50 -3 -2 -1 0 1 2 3 Distance (m) Std deviations from mean (a) Average Signal strength as a function of distance. (b) Deviation distribution as a function of . Figure 2: Modeling propagation inside the building. some locations were covered by only two or three of the rameter , thus yielding higher values. access points. In all locations, the laptop was positioned Our dataset also suggests that the deviations from in the same orientation, facing the left wall in figure 1. the mean (X ) closely follow a log-normal distribution In each location and for each AP, the following proce- (normal distribution in dBm), as other researchers have dure was executed: proposed [9]. Figure 2(b) shows the number of sam- ples as a function of the deviations from the mean (in 1.)

10 Force association between client and the desired terms of multiples of ). The deviations closely follow a access point. This was done to avoid hand-offs Gaussian distribution, with of the samples within during the experiments. Additionally, the card was 1 standard deviation from the mean, within 2 de- configured to transmit at 1 Mbps. viations, and within 3 standard deviations (the ex- 2. generate incoming traffic (AP to client). The pected values are respectively 68%, 95%, and ). client sends 30 ICMP ECHO request messages For clients in close range to access points (up to 10-15. (ping) to a computer in the local network and esti- meters), the path loss model found for a given environ- mates the Signal strength for each ECHO response ment can be used to provide an approximate lower bound received. A delay between 300 and 1000 ms was on Signal strength. From all 19 samples with distances used between ping messages. smaller or equal to 8 meters, 14 ( ) are located Figure 2(a) presents the 146 Signal strength samples above the fitted line.