Overview
How is wireless transmission distance calculated?
Wireless transmission refers to data transmission using radio or other wireless technologies. With the ongoing development of wireless techniques, wireless transmission is increasingly applied across industries. Wireless image transmission is one specific application that has seen growing interest.
Basic Link Budget Formula
Wireless transmission distance calculation formula
Pr = Pt - Ct + Gt - FL + Gr - Cr
- Pr: receiver sensitivity, in dBm
- Pt: transmitter power, in dBm
- Ct: transmitter connector and cable loss, in dB
- Cr: receiver connector and cable loss, in dB
- Gt: transmitter antenna gain, in dB
- Gr: receiver antenna gain, in dB
- FL: free-space loss, in dB
Free-space loss:
FL = 20 lg R + 20 lg f + 92.44
- R: distance between two points, in km
- f: frequency, in GHz
Free-space Communication Range Equation
Assume transmit power PT, transmit antenna gain GT, operating frequency f, received power PR, receive antenna gain GR, and separation R. Under ideal conditions with no environmental interference, the propagation loss L0 is:
L0(dB) = 10 lg(PT/PR)
or
L0(dB) = 32.45 + 20 lg f(MHz) + 20 lg R(km) - GT(dB) - GR(dB)
Example
Given PT = 10 W = 40 dBm, GR = GT = 7 dBi, f = 1910 MHz. What is PR at R = 500 m?
Solution:
- L0 = 32.45 + 20 lg 1910 + 20 lg 0.5 - GR - GT = 32.45 + 65.62 - 6 - 7 - 7 = 78.07 dB
- From L0(dB) = 10 lg(PT/PR) compute PR = 0.156 μW
Note: A 1.9 GHz signal typically loses about 10–15 dB when penetrating a single brick wall.
Estimating Wireless Coverage
Coverage or transmission range is affected by many factors: transmit power, antenna gain, receiver sensitivity, frequency, free-space loss, noise and interference, and environmental factors such as buildings, trees, walls, human bodies, and weather. Pure free-space propagation rarely exists in practice.
For practical deployment, designers must estimate the expected coverage and scale of the network. A simple method to estimate a base station's coverage is as follows.
- Compute the total link gain for the uplink and downlink of the wireless system.
- Compute the maximum line-of-sight transmission distance using:
Maximum line-of-sight distance (m) = 10^((system total gain - 40)/30)
- Estimate the actual coverage distance on site.
Example Coverage Table
| Total gain (dBm) | Max distance (m) | Actual distance (m) |
|---|---|---|
| 91 | 50 | 43 |
| 100 | 100 | 80 |
| 109 | 200 | 149 |
| 121 | 500 | 342 |
| 125 | 700 | 463 |
| 130 | 1000 | 639 |
| 139 | 2000 | 1194 |
| 148 | 4000 | 2233 |
| 153 | 6000 | 3220 |
| 160 | 10000 | 5106 |
| 169 | 20000 | 9548 |
| 181 | 50000 | 21838 |
Using the three steps above provides an initial estimate of each base station's coverage and helps estimate the number of base stations and overall network scale required to cover a target area.
Free-space Propagation and Distance Calculation
Free-space propagation assumes the antenna is surrounded by an infinite vacuum and represents ideal conditions. In free space, radio energy is neither absorbed by obstacles nor subject to reflection or scattering.
Communication distance depends on transmit power, receive sensitivity, and operating frequency.
The free-space path loss formula shows that loss depends only on frequency f and distance D. Doubling either f or D increases loss by 6 dB.
Los is propagation loss in dB. D is distance in km. F is frequency in MHz. Lfs denotes transmission loss, with frequency in MHz.
Example: 433.92 MHz System
Consider a system operating at 433.92 MHz with transmit power +10 dBm (10 mW) and receiver sensitivity -105 dBm in free space.
- Required loss Los = 115 dB (from transmit power and receive sensitivity)
- Solving for D from Los and F yields D ≈ 31 km
This is the ideal free-space range. In practice, range will be lower due to atmospheric effects, obstructions, and multipath. Including a representative environmental loss of 25 dB reduces the estimated distance to about D ≈ 1.7 km.
Additional Example and Notes
Repeating the free-space example: under ideal free-space conditions, propagation loss depends only on frequency and distance, and doubling either increases Lfs by 6 dB.
Los is propagation loss in dB. Typical in-vehicle loss is 8–10 dB and feedline loss around 8 dB. If path loss is 50 dB and transmitter power is 10 dB, the received signal level would be -40 dB.
This ideal calculation is an upper bound. Environmental losses such as atmosphere, obstacles, and multipath should be included to estimate practical communication distance. Assuming an additional 25 dB loss yields an estimated distance of approximately 1.7 km.
Conclusion: Every 6 dB increase in propagation loss reduces the transmissible distance by about half.
