**Received Signal Strength Indicator** (RSSI) is a key metric in wireless communication that quantifies the power level of a received signal. It is commonly used to assess the quality of wireless links in technologies such as Wi-Fi, Bluetooth, and cellular networks.

**An important aspect of RSSI is its relationship with distance: as the distance between the transmitter and receiver increases, the RSSI typically decreases.**

This article explores how RSSI varies with distance and the factors influencing this relationship. It also provides a calculator to find the RSSI as a function of distance from the transmitter.

**Understanding RSSI**

RSSI is a relative measurement of signal strength perceived by a receiver. It is often represented as a negative value in dBm, with values closer to zero indicating stronger signals. For instance, an RSSI of -30 dBm is stronger than an RSSI of -80 dBm.

**The Inverse Square Law**

The fundamental principle governing the relationship between **RSSI** and **distance** is the inverse square law. According to this law, the power density of a signal decreases proportionally to the square of the distance from the source. Mathematically, this can be expressed as:

**P _{Rx} ∝ 1/d^{2}**

where **P _{Rx}** is the received power and

**d**is the distance from the transmitter.

**Calculator**

This tool calculates the RSSI based on the following user inputs.

Enter

- Transmit Power
**P**(select the appropriate units of Watt or dBm)_{t} - Frequency of operation
**f** - Distance
**d** - Transmit Antenna Gain
**G**_{Tx} - Receive Antenna Gain
**G**_{Rx}

**Example Calculation**

Consider a **30 dBm** transmitter operating at 915 MHz. At a distance of 100 meters, the received signal power is 6.79*10^{-8} Watt. This is equivalent to **-42 dBm**.

When the distance increases to 1000 meters, the received signal strength is further reduced to 6.79*10^{-10} Watt or **-62 dBm**.

The received power of an RF signal drops exponentially with increasing distance.

**RSSI vs Distance Formula**

In free space, the Friis Transmission Equation provides a model for **RSSI**. The equation is:

**RSSI = (Pt*Gt*Gr*λ ^{2})*(1/(4π*d^{2}))**

Where:

**Pt**is the power transmitted,**Gt** is the gain of the transmitting antenna,**Gr** is the gain of the receiving antenna,**λ**is the wavelength of the RF signal,**d**is the distance between the antennas.

The equation above shows that the **RSSI** decreases with the square of the distance (d^{2}) between the transmitter and receiver. This means that doubling the distance between the transmitter and receiver results in only one-fourth of the received power, under ideal free space conditions.

Note that this equation only applies in the far field of the antenna. In other words, **d >> λ**. It is sufficient if the distance between the two antennas is at least 10 times larger than the wavelength.

**Factors Affecting RSSI with Distance**

**Free-Space Path Loss**:- In an ideal free-space environment with no obstacles, RSSI decreases predictably with distance according to the inverse square law.

**Obstacles and Interference**:- Real-world environments introduce various obstacles such as walls, furniture, and other structures that attenuate the signal. Materials like concrete, metal, and water can significantly reduce signal strength.
- Interference from other electronic devices and overlapping networks can also affect RSSI.

**Multipath Propagation**:- Signals can reflect off surfaces, causing multiple paths to the receiver. This can lead to constructive or destructive interference, affecting the received signal strength.

**Antenna Characteristics**:- The gain and orientation of the transmitting and receiving antennas influence RSSI. Higher gain antennas can focus the signal more effectively, improving RSSI over longer distances.

**Frequency**:- Higher frequencies typically experience greater attenuation over distance compared to lower frequencies. This is why 2.4 GHz Wi-Fi signals have a longer range than 5 GHz signals under similar conditions.

**Practical Considerations**

**Wi-Fi Networks**:- In a typical indoor Wi-Fi network, RSSI might start at around -30 dBm near the router and drop to -70 dBm or lower as you move further away, especially with walls and other obstructions in the way.

**Bluetooth Devices**:- Bluetooth devices, operating over shorter ranges, experience a rapid decline in RSSI with distance. Bluetooth Low Energy (BLE) typically shows significant drops in RSSI beyond a few meters.

**Cellular Networks**:- In cellular networks, base stations are strategically placed to ensure overlapping coverage areas. However, RSSI can still vary significantly with distance and environmental factors.

**Conclusion**

Understanding the relationship between RSSI and distance is crucial for designing and optimizing wireless communication systems. By considering factors such as obstacles, interference, multipath propagation, antenna characteristics, and frequency, engineers can better predict and improve signal strength over varying distances. This knowledge is essential for ensuring reliable connectivity in Wi-Fi, Bluetooth, cellular networks, and other wireless technologies.