LTE Physical Layer Measurements of RSRP and RSRQ (2024)

"Assume that only reference signals are transmitted in a resource block, and that data and noise and interference are not considered. In this case RSRQ is equal to -3 dB. If reference signals and subcarriers carrying data are equally powered, the ratio corresponds to 1/12 or -10.79 dB. At this point it is now important to prove that the UE is capable of detecting and decoding the downlink signal under bad channel conditions, including a high noise floor and different propagation conditions that can be simulated by using different fading profiles."

Can somebody explains in details about this . i did not understand .

Hi,

I'm wondering why the max is 1/12, or -3dB? 36.214 says the following:

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.

So if the RSRP measures only the reference symbol resource elements, and also the RSSI only considers the reference symbol resource elements, then why is the maximum RSRQ not zero dB?

Maybe there's an error in 36.214 because the RSRP definition looks the same as the RSSI definition, which would make RSRQ always zero (as it says "measurements in the numerator and denominator shall be made over the same set of resource
blocks.") and it says RSSI only considers ref symbols.

That doesn't look right. So assuming RSSI measures something sensible in LTE, and since 36.211 shows 4 ref symbols (all cell-specific) on antenna port zero, the max RSRQ when only ref signals are transmitted across the considered meas bandwidth, would be zero (4 ref symbols & remaining 80 OFDM symbols empty). i.e. 4/4=1.

For cases where the remaining 80 resource elements in each RB have energy, we would have 4/84 = -13.22dB RSRQ.

A reasonable average of 50% RE population would then give an approx. RSRQ average of 4/40 = -10dB

An absolute minimum almost guaranteed to cause a radio link failure would be where 3 of the ref symbol resource elements have interference and the UE can only detect energy in 1 ref symbol, giving a ratio and RSRQ of 1/84 = -19dB.

Only 2 detectable demodulation ref symbols in each RB of 84 REs would give RSRQ -16dB, matching places where I would start seeing radio link failures in logs.

Please let me know if these calculations appear logical? Or have I got this wrong? At least, these calculations above match what I see in UE logs....

It's true: 3gpp are not clear concerning RSRP and RSSI definition.
A simple and reasonable explanation I got is:
RSRP is calculated on avarage of the single RE where reference symbol is mapped.
RSSI is the wideband power measured on ALL RE and all RB.
IF cell in empty only 2RE\RB (those two are the RE where pattern of PSS and SSS are transported - no DATA)
Assuming no noise(other RE "off")
Then: RSSI=N*2(RE)*(pwrof1RE)
If power of REs is flat: pwrof1RE==RSRP
Now RSRQ=N*RSRP/N*2*RSRP=-3dB!

If cell is transporting data and cell is full(12RE\RB), then:
RSSI=N*12(RE)*pwrof1RE
Then RSRQ=-10.8dB
this condition is going worste if noise, interference etc...are considered; this is why RSRQ is by definition CELL LOAD dependent

This is an explanation of the fact that when no data is being transmitted and no noise is being considered the RSSQ is -3dB.

For simplicity we will consider an LTE signal comprised of one resource block (RB), which has 12 subcarriers. A resource block has 7 symbols, but we will look at only one symbol, namely the sybol during which reference signals are being broadcast.

We will first establish the power measured as RSSI, then we will establish the power measured as RSRP, and finally we will find from these two the ratio measured as RSRQ.

1) Remember that in any resource block (RB) when reference signals (RS) are transmitted they occupy two resource elements (RE) in parallel. So when we measure the received signal strength indicator (RSSI) at the time when RS are broadcast we will measure the power from two RE. Let us denote the power of one RE with RS in it as U watt, then the power of two RE with RS will be 2U watt, of course. So our RSSI will be 2U watt.

2) Now remember that the RSRP is the power of all received RE with RS in them averaged. So if in one resource block we receive two such RE, each with power U watt, the average power over the two RE will be (U + U)/2 = U watt. Thus, our RSRP will be U watt. This is a trick worth remembering: in LTE the power of the RSRP is NOT the power of RS in the resource block, it is the power of a single RE with RS in the resource block.

3) Now let us compile the ratio RSRQ = N * RSRP / RSSI, where by definition N is the number of resource blocks in the LTE signals. In our case we are looking at a single RB, so N = 1, RSRP = U (from point 2 above) and RSSI = 2U (from point 1 above). Therefore RSRQ = RSRP / RSSI = U / 2U = 1/2. When we convert this to decibels we get 10*log(1/2)=-3dB.

Finally, if we have more than one resource block, say N of them, we will get:

* RSRP for N resource blocks will remain the same as for a single resource block -- it is the average per RE, so even when we have thousands or millions of RE with RS in them the average power per one such RE will still be the same, in our example U watt (e.g. if we have one thousand resource blocks, then each of them will have two RE with RS, and the total power of all RE with RS will be 1000*2*U watt = 2000U watt, but the average power per one such element will be still 2000*U/2000 = U watt, which is the same result as for a single resource block).

* RSSI for N resource blocks will be N-times greater than the the RSSI of a single resource block. In our example we will get RSSI = N * 2U = 2N*U watt.

So let us calculate the formula for RSRQ, by definition it is:

RSRQ = N * RSRP / RSSI, in our case RSRP = U, RSSI = 2N*U, so we will get RSRQ = N * RSRP / RSSI = N * U / 2N * U = N / 2N = 1/2, which is equal to -3dB and is exactly the same as in point 3 above. This proves the case that when no data is transmitted and no noise is considered the RSRQ will be -3dB regardless of the number of resource blocks.

This is an explanation of the fact that when all resource elements are occupied with data (up to the channel capacity limit) and no noise is considered the RSRQ is 1/12 or -10.8dB.

Please read first the previous comment, which explains that with no data and no noise the RSRQ is -3dB.

Now consider that RSRP will remain the same in both cases (whether data is being transmitted or not, RSRP will be average power per resource element with a reference signal in it and will not be affected by the power of any other resource elements containing data). In the previous example we assumed that the power of one RE with RS in it was U watt. This will remain the same in this here case too, when all other RE are occupied with data.

The RSSI measured for a single resource block of 12 subcarriers will be 12U if the data RE have the same power as the reference signals RE (this is a hypothetical case, just used for illustration only). Therefore for N resource blocks the measured RSSI with no noise present will be N * 12U = 12N*U

Calculating the RSRQ from its definition we find:

RSRQ = N * RSRP/RSSI, where from the above two paragraphs we know that RSRP = U watt and RSSI = 12N*U watt, therefore RSRQ = N * RSRP/RSSI = N * U / 12N*U = N/12N = 1/12, in decibels 10*log(1/12) = -10.8dB.