# RSRQ calculation when assuming ONLY Reference signal transmitted

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#### RSRQ calculation when assuming ONLY Reference signal transmitted

Assuming I have 10 Mhz band for LTE (Upper C Block) and I want to calculate RSRQ with only the reference signal transmitting in the resource blocks - No noise and interference.... based on the formula: N* RSRP / RSSI i would come up with .5 or -3 dB - Based on definition of RSSI, the power seen by the UE would be over the full bandwidth (10 Mhz) which for the reference signal would imply over the 100 Resource elements.  However the numerator only multiplies the RSRP by the number of resource blocks which is 50.  Why would I get RSRQ of -3 dB when i am only tx the reference signal - it should be 0 dB - the N in terms of resource blocks but not in terms of resource elements does not make sense to me.

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• Hello rmahant,

I looked up the 3GPP spec 36.214 for the definitions of RSRP, RSSI and RSRQ.

Find below the same:

RSRP:

Reference signal received power (RSRP), is defined as the linear average over the power contributions (in [W]) of the resource elements that carry cell-specific reference signals within the considered measurement frequency bandwidth.

Note1: The number of resource elements within the considered measurement frequency bandwidth and within the measurement period that are used by the UE to determine RSRP is left up to the UE implementation with the limitation that corresponding measurement accuracy requirements have to be fulfilled.

E-UTRA Carrier Received Signal Strength Indicator (RSSI), comprises the linear average of the total received power (in [W]) observed only in OFDM symbols containing reference symbols for antenna port 0, in the measurement bandwidth, over N number of resource blocks by the UE from all sources, including co-channel serving and non-serving cells, adjacent channel interference, thermal noise etc.

RSRQ:

Reference Signal Received Quality (RSRQ) is defined as the ratio N×RSRP/(E-UTRA carrier RSSI), where N is the number of RB’s of the E-UTRA carrier RSSI measurement bandwidth. The measurements in the numerator and denominator shall be made over the same set of resource blocks.

From this it seems to me that the RSSI is calculated like this:

1. Measure power from all sources during a particular PRE when the reference signal is present.

2. Repeat above step for all the PREs in this PRB  during which reference signal is present.

3. Find the average of the above power values.

4. Find the total of all these averages over N PRBs.

So now RSSI is actually reflecting average power per PRE over N PRBs, that is why there is the factor N in denominator.

Note: N is not the entire 50 PRBs in 10 MHz but only those PRBs that are used in RSSI calculations.

Let me know if you have any comments.

Thanks.

Regds,

Raj.

• Thank you!

To make sure I understand this I'll use an example.

Assume I have a 10 Mhz BW

Looking only at RS (reference signal) assigned to Port 0 during Symbol 0

Thus, two PRE will be used for every PRB (Reference signal mapping is every 6th RE)

1.  UE measures power from all sources in 1st PRE

2.  UE measure power from all sources in 2nd PRE (this RE is shifted 6 RE above the 1st)

3.  Find average power

4. Repeat steps 1 to 3 for the other 49 PRB (there are a total of 50 PRB in a 10 Mhz BW)

5. There will be 50 average power values and these will be summed

I believe N is actually 50 since this is due to the fact that the RS is actually mapped to every PRB (2 RE per PRB) since according to TS 36.211 section 6.10.1.2 the RS sequence length is from 0,1,2,3.....2*(#RB in DL-1).  Using this length, the RS sequence length for a 10 Mhz Band would be 100.

Thus, based on the above, if I only tx the RS and nothing else, my RSRQ should be 0 dB.

Thanks

Raj

• Hello rmahant,

Are you making the assumption that RSSI = RSRP?

Note that RSSI includes also the thermal noise and interference from other cells etc. So RSSI might not be equal to RSRP.

Hope this helps.

Regds,

Raj.

• No, from my original question, I'm using the assumption that there is NO interference and noise.

The RSRQ calc. has been confusing me for some time....

• Looking at this more clearly now - for a 2x2 mimo system I understand the max RSRQ = -3 dB assuming NO interference and noise.  Since RSRQ = N(rb)*RSRP/RSSI  ---- Under a condition where ONLY THE REFERENCE SIGNALS EXISTS, the UE's RSSI will consist of both reference signals from each port (0,1) - The RSRP is measured from one port, thus the reason for RSRQ=-3 dB

• Shouldn't the RSSI be calculated as the sum of the power measured in all OFDM symbols carrying the reference signal for N RBs. If N+I = 0 this means that RSSI = N * 2 * RSRP -> RSRQ=-3dB.

• The standard, in fact, stipulates that RSSI is measured only at OFDM Symbols that carry RS at antenna port 0. That means RS in Symbol 0 and Symbol 4 are measured. However, port 1 also carry RS at OFDM Symbol 0 and 4, just not at the location (RE) that port 0 does.  For reference, take a look at Figure 9 at

The standard does not stipulate that RSRP must be measured at port 0 only; it specifically says that if the signal from port 1 is of a good quality, then R1 should be used to determine RSRP in addition to R0. This makes sense, because we expect that the reference signal coming from two transmit antennas should be of a better quality than the signal coming from one antenna.

• Still think this is hard to understand. Should the RSSI be calculated as the total received power in N resource blocks in the resource elements carrying reference signal (N * 4 resource elements in the 2 Tx antenna case)?

Assuming equal reception of R0 and R1 that would mean RSRQ = -6 dB

• it is -3 db because RSRPis based on liner averaged on received power while the dominator in RSRQ is based on summation of received power. For example for 10 MHz, we have 50 RBs each with two RE so the RSRQ=50*RSRP(avrg)/(50*2*RSRP(avrg))

the 2 in the dominator because we have two RE in each RB.