6G Received Power via RIS Calculator & Formula

Use the 6G Received Power via RIS Calculator to estimate the received power in a 6G wireless communication system that utilizes Reconfigurable Intelligent Surfaces (RIS). This tool helps engineers and researchers optimize system performance by calculating received power based on various input parameters.

6G Received Power through RIS:

Scenario: A 140 GHz link where the direct path is blocked. A 1m x 1m RIS is placed to create a virtual line of sight path. d1 = 20m, d2 = 10m.

INPUTS:

• Frequency = 140 GHz
• Transmit power, Pt = 1 Watts
• Transmit antenna gain, Gt = 0 dBi
• Receive antenna gain, Gr = 0 dBi
• RIS size = 1 m x 1 m
• Distance from transmitter to RIS, d1 = 20 meters
• Distance from RIS to receiver, d2 = 10 meters

Assumption:

• Each RIS element is λ/2 x λ/2

OUTPUTS:

• Effective Area of RIS, A_eff = 3.65e-7 meter^2
• Total number of elements in RIS, N = 8,71,111
• Received power, Pr = 1.27e-9 Watts
• Received power, Pr = -58.93 dBm

6G Received Power via RIS Formula

The received power via RIS can be calculated using the following formula: Pr = (Pt × Gt × Gr × (Area0 × Area0) × Nelements^2) / ( (4π)^3 × d1^2 × d2^2 ) Where:

• Frequency (in GHz) = Operating frequency of the 6G system
• Pt (in Watts) = Transmit power
• Gt (in dBi) = Transmit antenna gain
• Gr (in dBi) = Receive antenna gain
• Area0 (in meter^2) = Effective area of an isotropic antenna at the given frequency
• Nelements = Number of elements in the RIS
• d1 (in meters) = Distance from transmitter to RIS
• d2 (in meters) = Distance from RIS to receiver
• Pr (in Watts) = Received power via RIS

How to Use the Calculator

1. Input the operating frequency (in GHz) of your 6G system.
2. Enter the transmit power (Pt) in Watts.
3. Provide the transmit (Gt) and receive (Gr) antenna gains in dBi.
4. Specify the size of the RIS in square meters.
5. Input the distances from the transmitter to the RIS (d1) and from the RIS to the receiver (d2) in meters.
6. The calculator will compute the effective area of the RIS, the total number of elements, and the received power via RIS in both Watts and dBm.
7. Use the results to optimize your 6G system design and improve communication performance.

Assumptions

To estimate the received power via RIS, we assume that each RIS element is λ/2 x λ/2 in size, where λ is the wavelength corresponding to the operating frequency. This assumption allows us to calculate the effective area of each RIS element and subsequently the total number of elements in the RIS.
This simplification is commonly used in RIS analysis to facilitate calculations and provide a reasonable estimate of system performance.

References

• This formula is a standard derivation found in many foundational RIS papers. A good starting point is the work by Marco Di Renzo, for example, “Reconfigurable Intelligent Surfaces vs. Relaying: Differences, Similarities, and Performance Comparison.” (IEEE Open Journal of the Communications Society, 2020).