RSRP, RSRQ & SINR Calculator
Work out LTE RSRP, RSSI, RSRQ and RS-SINR to the 3GPP TS 36.214 definitions, from a cell's power or a measured RSRP.
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Worked example: a 10 MHz cell at 120 dB path loss
RSRQ: −10.87 dB
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How it works
RSRQ formula and RSRP calculation
RSRP is the average power of one resource element carrying cell reference signals, 15 kHz wide (3GPP TS 36.214 clause 5.1.1), not the power of the cell. The cell's power is shared between its antenna ports and spread over the 12 subcarriers of every resource block, and the P_B setting of TS 36.213 Table 5.2-1a sets the reference signal level against the data. So RSRP is the cell power less 10 log₁₀(p × 12 × N_RB × ρ_A), less the path loss.
RSRQ is N × RSRP / RSSI (clause 5.1.3), where N is the number of resource blocks in the RSSI measurement bandwidth and RSSI is the total power received in the symbols carrying antenna port 0 reference signals: the serving cell, other cells and noise. RS-SINR (clause 5.1.23) is RSRP over the interference and noise in the same resource element. These definitions are exact. How RSSI grows with load is a model: the serving cell puts n reference signal elements' worth of power into each resource block, and interference and noise fill all 12 subcarriers.
RSRP = P − 10 log₁₀(p × 12 × N_RB × ρ_A) − L
RSRQ = N × RSRP / RSSI, or 10 log₁₀(N) + RSRP − RSSI in dB
RSSI = N × (n × RSRP + 12 × I + 12 × N₀), in mW
RS-SINR = RSRP / (I + N₀)
N₀ = −173.975 + 10 log₁₀(15000) + NF, in dBm
- RSRP
- reference signal received power, the power in one reference signal resource element, in dBm (mW in the linear lines)
- P, L
- the cell's power across all its antenna ports, in dBm, and the path loss to the terminal, in dB
- p, N_RB
- reference signal antenna ports (1, 2 or 4), and resource blocks in the channel (50 for 10 MHz, 100 for 20 MHz)
- ρ_A, ρ_B
- data to reference signal power per port, in symbols without and with reference signals, for each P_B (TS 36.213 Table 5.2-1a); ½ and ½ with two ports at P_B 1
- N, RSSI
- resource blocks in the RSSI measurement bandwidth, and the total power received over them
- n
- serving cell power in each resource block of the measured symbol, in reference signal elements: r + (12 − r) × p × ρ_B × load, where r is 2 for one port and 4 for two or four
- load
- cell load, the share of resource blocks scheduled with data, from 0 (reference signals only) to 1 (every resource block); a scheduled block carries data on all 12 − r of its other elements in the measured symbol
- I, N₀
- co-channel interference and thermal noise in one 15 kHz subcarrier; −173.975 dBm/Hz is kT₀ at T₀ = 290 K of ITU-R P.372-18, often rounded to −174
- NF
- receiver noise figure, in dB
Standards
- 3GPP TS 36.214 clause 5.1.1: RSRP
- 3GPP TS 36.214 clause 5.1.3: RSRQ and E-UTRA carrier RSSI
- 3GPP TS 36.214 clause 5.1.23: RS-SINR
- 3GPP TS 36.133: RSRP and RSRQ measurement report mapping
Worked example
Worked example: a 10 MHz cell at 120 dB path loss
A private LTE cell on a 10 MHz channel (50 resource blocks) with 40 dBm across two antenna ports at P_B 1, 120 dB of path loss to the terminal, every resource block scheduled, no co-channel interference, a 7 dB noise figure and RSSI measured over all 50 resource blocks.
| Step | Working | Result |
|---|---|---|
| RSRP at the antenna | 40 − 10 log₁₀(2 × 12 × 50 × ½) | 12.22 dBm |
| RSRP at the terminal | 12.22 − 120 | −107.78 dBm |
| RS-SINR | −107.78 − (−173.975 + 10 log₁₀(15000) + 7) | 17.43 dB |
| RSSI, full load | 50 × (12 × RSRP + 12 × N₀), in mW | −79.92 dBm |
| RSRQ | 10 log₁₀(50) − 107.78 + 79.92 | −10.87 dB |
With two ports at P_B 1, a full cell puts 12 reference signal elements' worth of power into each resource block. Empty, only the 4 reference signal elements carry power in the measured symbol, so RSSI falls to −84.54 dBm and RSRQ rises to −6.25 dB, while RSRP and RS-SINR do not move. The RSSI step is the calculator's model; the RSRQ that follows from it is the TS 36.214 definition exactly.
How do you calculate RSRQ?
RSRQ is N × RSRP / RSSI, from 3GPP TS 36.214 clause 5.1.3, where N is the number of resource blocks in the RSSI measurement bandwidth. In dB it is 10 log₁₀(N) + RSRP − RSSI, so an RSRP of −95 dBm and an RSSI of −65 dBm measured over 50 resource blocks give 16.99 − 95 + 65 = −13.01 dB. Because N is part of the formula, an RSRQ should be quoted with its measurement bandwidth.
How do I calculate RSRP from RSSI?
Not from RSSI alone, because RSSI also counts the cell's traffic, other cells and noise. With the RSRQ as well, RSRP = RSSI + RSRQ − 10 log₁₀(N), the TS 36.214 definition rearranged. The common shortcut RSRP = RSSI − 10 log₁₀(12 × N) holds only for a fully loaded cell with every resource element carrying as much power as a reference signal element and no interference or noise, which puts RSRP 30.79 dB below RSSI over 100 resource blocks. A lighter load makes the gap smaller, and interference and noise make it larger.
Why is RSRP so much lower than the cell transmit power?
RSRP is the average power of one reference signal resource element, not the whole carrier. A 20 MHz carrier spreads its power across 1200 subcarriers, which is about 31 dB, so RSRP is far below the total cell power even before path loss. Reading the carrier power as RSRP overstates coverage by roughly that amount.
Why does RS-SINR behave differently from RSRQ?
RS-SINR is measured on the reference signal resource elements, which are sent regardless of traffic, so loading a cell moves RSRQ but not RS-SINR. When RSRQ is poor and RS-SINR is good, the cell is busy rather than interfered with.
What is specified and what is modelled?
The definitions come from TS 36.214 and the reporting ranges from TS 36.133. How RSSI is predicted from cell load and interference is a model, because the specification defines what RSSI is but not how to predict it. The page labels the model wherever it is used.
Are the quality labels from 3GPP?
No. The labels excellent, good, fair to poor and poor are the bands Teltonika Networks publishes for its LTE routers. They do not appear in any 3GPP document, other vendors draw the lines elsewhere, and they are shown as a reading aid with their source.
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