It is common sense that the performance of any wireless system has a direct relationship with the RF conditions at the time. To aid with performance analysis then, it is typical to define some ranges of RF measurements that correspond to some typical RF conditions one might find themselves in.

The following table represents a good classification of RF conditions Vs LTE KPIs

The source of this table is a EUTRAN vendor and has been complied during the RF tuning process for a major US operator. Of course there are no rules as to how various RF conditions are classified, so different tables will exist but to a great extent you can expect them to align.

In this particular example, three measurement quantities are used

**RSRP**(Reference Signal Received Power)**RSRQ**(Reference Signal Received Quality)**SINR**(Signal to Interference & Noise Ratio)

You can find more info about RSRP and RSRQ in our HOT article: RSRP and RSRQ Measurement in LTE

Instead, in this article we would like to highlight some of question about SINR & RSRQ relations.**SINR** is defined as:

where:

**S**: indicates the power of measured usable signals. Reference signals (RS) and physical downlink shared channels (PDSCHs) are mainly involved**I**: indicates the average interference power – the power of measured signals or channel interference signals from other cells in the current system**N**: indicates background noise, which is related to measurement bandwidths and receiver noise coefficients

All quantities are measured over the same bandwidth and normalized to one sub-carrier bandwidth.

*SINR is a measure of signal quality as well but it is not defined in the 3GPP specs but defined by the UE vendor. It is not reported to the network. SINR is used a lot by operators, and the LTE industry in general, as it better quantifies the relationship between RF conditions and Throughput. UEs typically use SINR to calculate the CQI (Channel Quality Indicator) they report to the network.*

It is a common practice to use Signal-to-Interference Ratio (SINR) as an indicator for network quality. It should be however noted that 3GPP specifications do not define SINR; therefore UE does not report SINR to the network. SINR is still internally measured by most UEs and recorded by drive test tools.

Unfortunately, UE chipset and RF scanner manufacturers have implemented SINR measurement in various different ways which in the field experience is not always easily comparable. While at first it may seem that defining SINR should be unambiguous, in case of LTE downlink this is not the case. This is because different REs within a radio frame carry different physical signals and channels each of which, in turn, see different interference power depending on inter-cell radio frame synchronization.

For example, in a frame-synchronized network, **SINR estimation based on synchronization signals** (PSS/SSS) results in different SINR than SINR estimation based on Reference Signals, since in the latter case the frequency shift of the RS depends on the PCI plan.

**RSRQ is defined as**

In what follows we show one way of converting RSRQ to SINR.

In OFDM own cell interference is often assumed to be negligible and consequently **I** is due to other cell interference only.

**RSSI **is defined as

where the subscript ** tot** indicates that the power is measured over the 12NRE sub-carriers of the measurement bandwidth.

The total serving cell received power depends on the number of transmitted sub-carriers in the OFDM symbol carrying R0, and on the number of transmit antennas.

We can model this impact using the per-antenna sub-carrier activity factor x and set

*The value of x = 1 indicates full load such that all sub-carriers of one transmit antenna are transmitted for the OFDM symbol carrying R0. If only RS is transmitted (i.e., unloaded cell) the resulting sub-carrier activity factors would be x = 1/6 and x = 1/3 for one and two transmit antennas, respectively.*

*When calculating x for two transmit antennas, one should take into account that REs overlapping with adjacent antenna RS transmission are muted, and therefore, for example, in a fully loaded 2Tx cell the scaling factor is x = 5/3, instead of two.*

It is assumed that all sub-carriers have the same power, i.e., there is no power boosting for any channel. Since sub-carrier interference plus noise power is:

Combining above equations, we have the following relation of average sub-carrier SINR and RSRQ:

## Sub-Carrier Activity Factor

An uncomfortable property of the RSRQ to SINR mapping is that it depends on the instantaneous serving cell sub-carrier activity factor **x**, which is typically not known in live network measurements…

As before, the value of x = 1 indicates full load such that all sub-carriers of one transmit antenna are transmitted for the OFDM symbol carrying R0.

*If only RS is transmitted (i.e., unloaded cell) the resulting sub-carrier activity factors would be x = 1/6 and x = 1/3 for one and two transmit antennas, respectively.*

**When calculating x for two transmit antennas, one should take into account that REs overlapping with adjacent antenna RS transmission are muted, and therefore, for example, in a fully loaded 2Tx cell the scaling factor is x = 5/3, instead of two**

Another problem is the sensitivity of the mapping on RSRQ values. A small change in RSRQ can result in a very large change in SINR which makes such mapping difficult to use in fading radio conditions.

Indeed, plotting a RSRQ versus SINR scatter graph from a drive test measurement one rarely obtains such a nice-looking curve as shown in the Figure above.

Currently available measurement UEs and scanners report SINR directly.

## 43 Responses

I love the article,it is very interesting.

But I want to ask why “If only RS is transmitted (i.e., unloaded cell) the resulting sub-carrier activity factors would be x = 1/6 and x = 1/3 for one and two transmit antennas, respectively” is there any formula about it?

Hi Vella, you can find our explanation in our ANSWER Section: https://arimas.com/dev/question-and-answer/

Your answer is at the specific link https://arimas.com/dev/answers-to-your-questions/answer/

Thank you! I could understand that.

Actually I am doing a research in LTE networks with my professor.Your articles helps me a lot and I am really appreciated .

what is RE and RB in the formula?

RE is a Resource Element and RB a Resource Block

Hello Sir @Maurizio La Rocca

I am facing difficulties in calculating SINR . I have taken the following parameters in calculation :

1. Distance 100 m to 2000 m at an interval of 100 m.

2. I have calculated the path loss by using this model : 128.1 + 37.6 log(distance in km)

I have used this link “https://www.dropbox.com/s/qvjrfnwc0bvqjki/RSRQ.xlsx ” for the calculation of “RSRP and RSSI” . Then i have calculated RSRQ and then “SINR”. But i am getting SINR in the range of ” -1.0378″ in an around which is offcourse not expected.

Any help will be highly appreciated .

Thanking you.!!

Can anyone help me to “Fix” my problem.

Hello Mukesh,

could you kindly explain more about your flow? I mean, I have a look at the file on Dropbox but I didn’t understand how you are doing this calculation…

SINR, as you can see above, is a function of RSRQ and it is a function of RSRP & UTRA Carrier RSSI. Please, see https://arimas.com/dev/78-rsrp-and-rsrq-measurement-in-lte/)

Could you explain more what you need to do? I need to read step by step you calculation algorithm and look into it before to answer you.

Let me know.

Thx!

In a LTE network I want to calculate the CQI for downlink channel. While exploring multiple blogs and research papers i came to the conclusion that CQI is a function of SINR. In turn SINR is a function of transmitting power. So ultimately I am looking for an expression which will be able to correlate the transmitting power and CQI. In addition to this, SINR is most likely to be in between 0 to 30 dB.

Kindly suggest me the way to find out CQI for downlink channel in LTE.

The value of x should be unified in the equation of SINR.

SINR=X/[(1/12*RSRQ)-X]

and the max. value of x should be 1.How can it equal to 2,4…12 in the legend of plot?

Hi Qing, you are right! I’ve just updated the picture and inserted on it the right value.

So you will see now SINR for 2x, SINR for 4x, and so on.

Please note that this graph is with the assumption of unloaded Cell. This means that only 2 RE are used in the RB!

Hi Maurizio

Very interesting article. There as small error in the plot of SINR vs RSRQ. In the legend “x” should be the ratio between used REs and total RBs so it should be less than 1. Furhtermore the two plots of x=1/4 and x=1/2 are exchanged

Best regards

Marco

Hi Marco, as explained before to Qing, there was an error in the Legend of the Graph and we uploaded a new version just now.

I’m not understanding what you mean about 1/4 and 1/2 are exchanged…

Please let me understand

Hi Marco,

I am doing a capacity simulation with load metric as PRB Utilization impacting RSRQ which inturns impacts SINR. When i try to apply this formula of RSRQ to SINR mapping i am not getting a smooth trendline as shown in the section. More over with increasing load SINR seems to improve which shouldnt be the case. Not sure if i am missing anything here.

Regards,

Badri

Hi Badri,

I am Maurizio, not Marco… 🙂

BTW, It is not totally clear what you write. Could you kindly provide us more info?

e.g. Could you share your formula and how you build it up?

Thx,

Maurizio

Hi Maurizio,

Extremely sorry for the mix up of names..,

To be precise i am estimating the SINR from RSRQ values for Dynamic Load Simulation. The expectation is RSRQ value varies with DL PRB load in the cell which will be used for calculating the value X (from Network Performance counters). So the flow of algorithm is

Load Changes -> RSRQ Changes–> SINR Changes –> Throughput changes

Pls find in below link the sheet i used to calculate SINR from different RSRQ values. Appreciate your comments.

https://www.mediafire.com/?njc1pcqjhbbhtix

Thanks,

S.Badri Narayanan

Hi Maurizio,

Good day to you. Did you have a chance to look into the data shared. Appreciate your comments and update if any..,

Thanks,

S.Badri Narayanan

Hello Badri, yes I saw it…

Let’s think about a

SISOanalysis first.From my understanding you assumed x=1,16666667. This mean that you are calculating SINR for 10x of our graph. Is this right?

Just in case, you use the formula with 12 at numerator but you done a mistake into the file excel. You forgot to change x to (12*x).

Please have a look at: EstimatedSINR_fromRSRQ_1-Rev.LRS.xlsx

I have just write some comments into your Excel file and I add some calculation in the same sheet.

About

MIMOplease read above:“

If only RS is transmitted (i.e., unloaded cell) the resulting sub-carrier activity factors would be x = 1/6 and x = 1/3 for one and two transmit antennas, respectively

”When calculating x for two transmit antennas, one should take into account that REs overlapping with adjacent antenna RS transmission are muted, and therefore, for example, in a fully loaded 2Tx cell the scaling factor is x = 5/3, instead of twoFurthermore, we are going to publish as soon as possible another article about “Throughput analysis on LTE”. Keep in touch and subscribe to our newsletters!!!

Last but not least, please vote this article and Share!!!

Thx,

Maurizio

Thanks Maurizio. I downloaded the sheet but the formulas are referenced to your local machine data so i am getting #Ref. Can you pls copy paste the values and if possible seperate calculations for SISO and MIMO would be of assistance.

Thanks,

S.Badri Narayanan

Hello Badri, I have just upload a new file with better quality. You can find it at:

http://www.mediafire.com/download/ob3nudtvxbw4bek/EstimatedSINR_fromRSRQ_1-Rev._2.0_LRS.xlsx

Maurizio,

You are giving detailed and clear answers for everyone. Thank you for that.

My question is, How we can know if there Up-link interference from filed ( Physical Layer) for Lte network ?

Or lets say is there any way to check the Up-link interference from normal drive test data ?

Thanks

Hani

Hello Hani! First of all thanks for your comment. At laroccasolutions we are happy to answer all your questions!

About your point, I would like to understand more: are you talking about interference that network could receive when mobile send data or…?

Please give me more details as you can to be able to concentrate on the right point!.

Thx!

So, from your table at the top, excellent has an RSRQ of -10 or better, and a SINR of 20 or better… but in the calculator excel sheets linked, an RSRQ of -10 corresponds to a SINR of 1.27 for SISO. Even an RSRQ of -3 comes out to a SINR of ~8.5.

What am I missing here?

Hi Ben,

maybe it is just our mistake. The table at top of the page is just an example about a classification of RSRP, RSRQ & SINR levels. In fact, you can define such threshold base on your analysis. A good level, could be a bad one. All depend from the approach that you desire. Naturally TOP & BOTTOM threshold are fixed by technology.

Hi Maurizio

For 2 Tx case, which is correct?

SINR= 1/(1/(10*RSRQ) – x) or 1/(1/(20*RSRQ) – x)

Thx,

Soon Young

Hi! The correct formula is the same I indicated before and not the one you wrote. I think you done a mistake about 12 to 10… 🙂

BTW, the only thing will change is x. When calculating x for two transmit antennas, you have ot remember that REs overlapping with adjacent antenna RS transmission are muted, and therefore, for example, in a fully loaded 2Tx cell the scaling factor is x = 5/3 (20/12), instead of two.

Dear Maurizio,

It seems, that your formula (SINR = SINR(RSRQ)) and the figure contradict the table that you give in the beginning:

according to your formula SINR(dB) = RSRQ(dB) + a, 10 < a < 15, and according to the table SINR(dB) = RSRQ(dB) + b, 20 < b < 30.

So where is the truth?

Stepan K.

Dear Stepan K,

that Table, as I’ve already explained, is just a simple reference table where you can classification of RF conditions Vs LTE KPIs. Furthermore, in the table there’s no any formula!

Maybe I will have to cut out the table… Is creating confusion… ?

The right formula is the one at the end of the page!

Thx,

Maurizio

Hello,

what is relation of “x” and PRB utilization?

I have noticed from drive test results that cell will “low PRB util” will have lot better SINR compare to “high PRB util”

Thanks

Stev

Hello Stev,

Drive Tests results from a simulation with some parameters locked or real Drive Tests on field?

Could you kindly share a .csv of data you are talking about? We would like to look at it. Of course, please put a short comment into it.

Thx!

Maurizio, thanks so much for the detailed analysis. Do you have a source for the table at the top?

This table is just an example about how RF Conditions could be classified to define different satisfaction levels. It is something that any RF Engineer can build by himself.

In case of needs we could help to build up such table.

Hello Maurizio,

In reference to the question by Hani, is there a possibility of finding the UPLINK (UL) SINR at the eNB using an equivalent (appropriate) formula. This of course should take into consideration that the LTE UPLINK (UL) is using SC-FDMA.

I would presume your above formula is applicable for only the DOWNLINK (DL) since the measurements are done in the UE.

Thanks,

Abubaker

Abubaker, roughly I could say that you can use this formula both for DOWNLINK & UPLINK. In fact, during the exposure we was talking about SINR, RSRQ & RSSI definition.

Of course, if you would like to analyze in details the SINR in this case, you will have to adapt the formula.

Let us know if would like to do it; we could do it together and write another article about it. We are looking for new Authors.

Hello Maurizio,

Thanks for your feedback.

However, I really did not understand the way the formula can be adapted in the the UPLINK case. I believe in the UPLINK we don’t have the reference signal but rather the sounding reference signal that is coming from a given UE.

I wonder whether you know any common practice followed by any vendors in the SINR measurements either in the UEs (i.e. DOWNLINK) or in the eNB (i.e. UPLINK).

Thanks,

Abubaker

We don’t know the common practise followed by vendors, but if I can find it I will share immediately.

Thank you and stay tuned!

When you deriving SINR = 12/((1/RSRQ)-12x), you assume that x = 1 in the beginning. However, x is a variable, why do you make this assumption? If you do not make this assumption, the final result is SINR = (12x)/((1/RSRQ)-12x)!

Hello Maurizio,

I found your article to be the best out there on this subject, so thank you!

However, I ran across the very error that hacper above pointed out. The activity factor in the numerator needs to be accounted for. S should equal:

S = Stot / (12 · Nprb) = x · 12 · Nprb · RSRP / (12 · Nprb) = x · RSRP

and the correct formula should be:

SINR = S / (1 + N) = x / (1 / (12 · RSRQ) – x )

which equals what hacper has above.

PLEASE could you comment on this and how it affects your explanation?

THANK YOU!

Hi Dylan,

I’m happy to know that this article was useful to you!

Regarding the formula, what you and Hacper say is correct!

In this article, anyway, an approximation has been made (x=1 on numerator, that is full load) in order to make the SINR estimation a bit less sensitive to cell load.

Hi Maurizio,

This is a very well explained and helpful article.

Could you please clear out my one query.

What are the conditions of getting poor RSRQ even if the RSRP & SINR both are good…??

I have seen this in many drive tests but couldn’t get the exact reason for it..

Thanks,

Shubhangi

Hi Maurizio,

This article is helpful to understand the relations of SINR, RSRP and RSRQ.

I have two questions about the table “x value as a function of Tx”:

1. For unload cell, x=1/6, 2/6, 4/6 for 1Tx, 2Tx and 4Tx are based on the number of CRS. But the maximum number of CRS for LTE is four, how did the x value be x=1, x=4/3 for 6Tx and 8Tx cases?

2. For load cell, in my understanding, the data RE transmitted power would not increase for mult-antenna ports since its precoder will normalized the power. For example, the 2Tx precoder is [1 -1]/sqrt(2) normalized the power for each antenna. How did the x value larger than 1?

Thanks,

Jao

Hi Jao,

The maximum number of CRS must be ≤ the Total number of Antennas, so if you have more than 4 Tx antennas the CRS can be greater and so does the activity factor “x”.

Regarding the transmitted power, in this case an assumption has been made of not using a normalization.

Thank you for reading our articles!!

Thanks a lot …it was very helpful article