# Calculation of SINR, having the RSRQ

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#### Calculation of SINR, having the RSRQ

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Hi,

Can anyone please tell me if there is a formula that allows the calculation of the SINR having the RSRQ?

Thanks a lot

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• There is no direct formula for it.

For more details about RSRQ and SINR you may refer this

• Short answer: My approximation in dB is SINR=RSRQ + 10*log10(rB*Nsc), where Nsc=12 is the number of subcarriers per Resource Block and rB is the ratio of RS EPRE to PDSCH EPRE as per section 5.2 in TS36.213.

Long answer: The RSRQ can only be measured during OFDM symbols carrying Reference Signals (i.e. symbols 0 and 4 within each slot for 2 transmit antennas), while the PDSCH SINR can be measured on any symbol carrying the PDSCH (i.e. symbols 1, 2, 3, 4, 5 and 6 within slot 0 and 0-6 within slot 1). My formulation is thus valid only for symbol 4 in slot 0 and for symbols 0 and 4 in slot 1. Hence, assuming that the UE is measuring the PDSCH SINR over the whole bandwidth, the SINR in linear units can be written as:

snr=pdsch_rp/pdsch_ni,

where pdsch_rp is the total power (in mW) received in PDSCH resource elements across the whole bandwidth. Similarly, pdsch_ni is the total noise plus interference (in mW) received in PDSCH resource elements across the whole bandwidth, which can be approximated from the RSSI as

where N_RS is the number of resource elements carrying Reference Signals in one resource block during a symbol carrying Reference Signals. In addition, the pdsch_rp can be written as

pdsch_rp=rsrp*rB*(Nsc-N_RS)*N,

where N is the number of resource blocks across the whole bandwidth. Then, since rsrq=rsrp*N/rssi, then

snr=rsrq*rB*Nsc

Opinions on this derivation are highly appreciated.

• Kubrick, your derivation (approximation) seems correct to me. However a colleague of mine insists that the RSSI contains the power received from any source, including your own signal power, which you don't want to account for in the interference term when calculating the SINR.

So, back to your notation, the interference+noise term would look something like pdsch_ni = rssi - psdch_rp.

Does it make any sense? or should we assume that when TS 36.214 says "RSSI definition: The received wide band power [...]" it only refers to received wide band interference power?

Best regards,