Preamble

In the wireless LAN, besides throughput, the main performance is coverage, and in order to calculate the coverage of Wi-Fi, we must first sort out its link model. In this paper, we analyze the link model in 802.11 based on the basic transmission loss model (Free-space path loss).

Note: After this article, we will continue to discuss how to calculate the wireless coverage based on the understanding of the link model, as well as the specific channel model in the 802.11 protocol. Since it is mainly for understanding, please forgive me if there are some mistakes in this article.

Factors Affecting Coverage (Wireless Link Quality)

The theoretical coverage of Wi-Fi is related to many factors, we simply list them as follows:

Transmit power : The greater the transmit power, the greater the coverage of the signal. The FCC recommends a standard value of 70mW.
Power amplification gain : including PA (Power Amplifier) when transmitting and LNA (Low Noise Amplifier) when receiving. If the local can provide an amplifying function for the signal, then the strength of the signal can be improved.
Antenna Gain : Include transmit antenna gain and receive antenna gain. The antenna can increase the signal, and the index to evaluate the gain performance is the gain value. Different antenna types, such as omnidirectional antennas or directional antennas, have different gain performance.
- The directional antenna has better focusing ability, and can effectively improve the receiving power (ie focusing) of the receiver under the condition of the same total power. Directional antennas can be used for smart antenna beam forming.
- The omnidirectional antenna has better coverage ability, and can cover all the surrounding nodes more evenly with energy.
- Transmit beamforming (TxBF) can be done by using multiple omnidirectional antennas for transmission. It is accomplished by using the precoding technology of the signal. TxBF adjusts the phase of the transmitted signal to make the signal present the effect of interference and superposition at the receiver. The use of multiple omnidirectional antennas for reception can also be used for receive diversity to increase signal quality.
Channel fading and interference : The influence of the channel includes two parts, fading and interference.
- Fading is caused by the characteristics of the channel. Fading is divided into three parts, large-scale fading, meso-scale fading (shadow fading) and small-scale fading (multipath).
  - Large-scale fading: The electromagnetic wave fading mainly affected by the transmission distance, the longer the distance, the stronger the signal fading.
  - Mesoscale fading: Also known as shadow fading, mainly caused by occluders. (In fact, this definition is not used much, but in the wireless LAN environment, it is more suitable, so I put it up)
  - Small-scale fading: Also known as multipath fading, it is mainly caused by mutual interference between signals arriving from different paths. According to whether the sender and receiver are within the Line-Of-Sight (LOS) range, it is divided into Rayleigh Fading (Rayleigh Fading, that is, within the LOS range) and Rice fading (Rice Fading, that is, within the NLOS range).
- The interference consists of two parts, one is the interference of other devices in the same frequency band, and the other is the background noise (generally, in theory, we think it is Gaussian white noise, which is mainly caused by thermal noise).

link model

In this section, we build a model to describe some of the factors that affect Wi-Fi coverage as described earlier, as shown in the following figure:

That is, the received power can be expressed as (expressed in dBm):

$P_{RX} = P_{TX} + G_{TX} - PL - N + G_{RX}$

where $P_{RX}$ is the received power, $P_{TX}$ is the transmit power, $G_{TX}$ is the transmit gain (including power amplification gain and antenna gain), $PL$ is the channel fading, $N$ is the noise power (assuming no interference), and $G_{RX}$ is the receive gain.

Note: The thermal noise represented by the noise here is partly on the channel and partly caused by the lossy coupling between the antenna and the receiver.

In the above formula, $P_{RX}$ , $P_{TX}$ , $G_{TX}$ , $G_{RX}$ are inherent settings of the transmitter and receiver, and can be regarded as constants.

$PL$ We assume Free-Space Path Loss (FSPL) and $N$ thermal noise. We will focus on these two parts below.

Free space loss model: This model is an ideal large-scale fading model. In general, the ideal channel we assume is this model (that is, there is only large-scale fading). The physical meaning of the model is as follows:

In the center of free space (that is, without obstructions), the sender transmits with $P_{T}$ a power of , and the distance between the receiver and the sender is $d$ . Further referring to the figure above, we can imagine that all the points that are at a distance from the sender $d$ (that is, where the receiver might appear) form a sphere with an area of $4\pi d^{2}$ . The total transmit power $P_{T}$ is evenly distributed on any point on the sphere, and the receive power $P_{R}$ is $P_{T} /4\pi d^{2}$ .

And we further assume that the receiver is receiving with an $\ lambda ^ {2} / 4 \ pi$ antenna with an effective area (generally, the area of the antenna is related to the wavelength), and finally we can obtain the received power as: $P_{R}= \left[ P_{T}\lambda^2 \right] / \left[ \left( 4\pi \right)^2d^2 \right]$ . After dividing by the transmit power $P_{T}$ (i.e. finding the attenuation of the link), we can obtain the free space loss (FSPL) as follows:

In general, it is also very common to express the free space loss in dB ( $f$ in MHz, $d$ in km):

$PL=32.44+20\times log_{10}\left( f \right) +20\times log_{10}\left( d \right)$

In fact, these two expressions are actually the same. Let's make a mathematical derivation (the initial $f$ unit is Hz, the $d$ unit is m, and the final result $f$ is MHz, and the $d$ unit is km):

Therefore, the above two expressions are essentially the same, and then we will estimate the wireless transmission range based on this model example. Since the shadow fading is not considered in the free space model, and the CWNA book gives some influences of the occlusion medium on the signal (when the signal is 2.4G), it is recorded here (refer to the CWNA textbook):

Wood door: –3 dB
Metal rack: –6 dB
Cubicle wall: –2 dB
Foundation wall: –15 dB
Nontinted glass windows: –3 dB
Drywall or sheetrock: –3 dB
Elevator or metal obstacle: –10 dB
Brick, concrete, concrete blocks: –12 dB

noise floor (thermal noise )

In the paper assumptions, we generally directly assume that the background noise is white Gaussian noise with 0 mean (in the book Digital Communications Fundamentals and Applications, Section 5.3.4: Since the thermal noise power spectral density $10^{12}$ is constant below frequency, so Generally, the thermal noise process of the receiver is treated as Gaussian white noise), and a noise power can be given. In fact, in general, we can refer to the formula of background noise based on thermal noise, as follows:

where the noise power $N$ is given in dBW, $BC$ is Boltzmann's constant ( $1.38\times 10^{-23} J/K$ or $-228.6 \ dBW/k/Hz$ ), $C^{\circ}$ is the temperature in Celsius (directly entered in parentheses $290K$ ), $B$ is the bandwidth (such as 802.11a/g $20MHz$ ), and $F$ is the noise figure ( noisefigure, generally $9dB$ ).

Note: The above parameter selection refers to the code of baseband simulation in MATLAB2016a.

Therefore, the final result of bringing in 802.11 is:

In fact, this value is even smaller than the reference value of the background noise (that is, the noise floor) given in the 07 version of the agreement. Sections 3.4 and 3.6 of the CWNA book point out that the local noise of a general 2.4G channel is $-110dBm \sim -100dBm$ , So in addition to thermal noise, there may also be some other white noise on the channel. However, you can also refer to the "RSSI range and actual power are independent" described in Table 19-10 of the 07 version of the protocol. In other words, the specific value of the local noise can also be set by yourself, mainly based on the actual usage scenario.

802.11 Protocol Intensive Reading 15: Link Model (Based on Free-Space Path Loss)

Preamble

link model

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