4G/LTE - PHY Measurement

 

 

 

RSRP, EPRE, Total Power

 

We often use different concept of power definition depending on situations and we often get confused by these different power concept. So it is important to have clear understanding on those different definition.

When you use various test equipment, there are cases where different equipment use different power concept. For example, some equipment would request you to specify the power in EPRE (power/15 Khz) and some equipment would request you to specify the total power (total power across all the allocated RBs).

How do RSRP, EPRE and Total Power differ inside one RB ?

Some of the most confusing power concepts are RSRP, EPRE and total power. Definition and Differences among these powers can be illustrated as follows. For the simplicity, I use the structure of only one RB and TM1 (Single Antenna)

The illustration below draws one RB over one slot. That is 12 subcarriers of 15 kHz by 7 symbols, with the REs numbered 1 to 84 column by column. The red REs 6, 12, 51 and 57 carry the Reference Signal, in symbol 0 and symbol 4. The green RE 62 marks a single RE, and the power of one RE is the EPRE. The formulas under the grid work out RSRP and total power for symbol 4 and for symbol 2.

One RB of one slot with the Reference Signal REs, EPRE, RSRP and the total power formulas for symbol 4 and symbol 2

Figure 1. RSRP, EPRE and total power in one RB of one slot with TM1. RSRP is the average EPRE of the Reference Signal REs, while total power adds up every RE of a symbol, so only total power grows with the number of RBs.

Directly or indirectly from this illustrations, you can infer some additional facts as follows :

  • EPRE indicate power for one resource element (RE). This can be used for any channel (e.g, Reference Signal, PDSCH etc). This value does not vary with system bandwidth or number of RBs.
  • RSRP is an averaged value for all the Resource Elements for Reference Signal within a symbol. Since this is the averaged value, the value would be similar to EPRE value you set for the Reference Signal. If there is no noise at all, RSRP would be same as EPRE you set for Reference Signal.
  • Total Channel Power is summed value of all EPREs within a symbol. This value may vary with different symbols since each symbol may have different channel combination (e.g, Symbol 0 in first slot is made up of multiple component - PCFICH, PHICH, RS. Symbol 4 is made up of PDSCH and Reference signal).
  • In symbol 4, two REs carry the Reference Signal and ten REs carry PDSCH. So the total power for the symbol is (RSRP x 2) + Total Power for PDSCH, where the PDSCH part is EPRE for PDSCH x 10.
  • In symbol 2, all twelve REs carry PDSCH. RSRP is N/A there, and the total power for the symbol is EPRE for PDSCH x 12.

36.214 clause 5.1.1 states the RSRP part precisely. RSRP is the linear average over the power contributions of the REs that carry cell-specific reference signals within the measurement bandwidth. The UE uses CRS port 0, and it may add port 1 if it can detect port 1 reliably. The number of REs and the averaging time are left to the UE implementation, as long as the accuracy requirements are met. The power per RE is taken from the useful part of the symbol, so the CP is excluded.

  • EPRE is a per RE power : it is the same whether the cell has 6 RBs or 100 RBs.
  • RSRP is the EPRE of the Reference Signal as the UE receives it : with no noise, it equals the Reference Signal EPRE.
  • Total power is a sum over all REs of a symbol : it changes from symbol to symbol, because each symbol carries a different mix of channels.

How is the Total Power calculated from EPRE ?

For simplicity, if we take the symbol which is made up of only PDSCH (e.g, Symbol 3,5,6) we may come out with the following formula. For different symbols, you may have a little bit different values depending on P-a, P-b configurations. But you can apply this formula for other symbols if you can tolerate around +/- 1dB differences.

    Total Power of PDSCH (in linear scale )

        = EPRE for PDSCH x Number of PDSCH RE

        = EPRE for PDSCH x Number of RB x 12 (assuming for the symbol with no Reference Signal)

 

    Total Power of PDSCH (in dB/dBm scale )

        = EPRE for PDSCH (in dBm) + 10 Log(Number of PDSCH RE)

        = EPRE for PDSCH + 10 Log(Number of RB x 12)

 

Total Power is not affected by the system bandwidth, it is affected by number of RBs being used at the specific moment of the calculation.

For example, if you allocated -90 dBm/EPRE for PDSCH and allocated 100 RBs for the PDSCH, the Total Power of PDSCH become as follows.

    Total Power of PDSCH (in dB/dBm scale )

      = EPRE for PDSCH + 10 Log(Number of RB x 12)

      = -90 + 10 Log(100 x 12)

      = -90 + 30.8

      = - 59.2 dBm

 

The same arithmetic runs in the other direction, and test equipment often needs that direction. If you know the total power over N RBs, then EPRE = Total Power - 10log10(N x 12). So -59.2 dBm over 100 RBs is -90 dBm per RE again. For 6 RBs, 10log10(72) is about 18.6 dB. So the same -90 dBm EPRE then gives only about -71.4 dBm of total power.

The symbols that carry the Reference Signal need one more term, as the illustration above shows for symbol 4. With one antenna port, each RB of such a symbol has 2 Reference Signal REs and 10 PDSCH REs. So the symbol power per RB is 2 x RS EPRE + 10 x PDSCH EPRE, in linear scale. When the two EPREs are equal, this is again EPRE x 12, and the formula above holds for every symbol. When they differ, the +/- 1dB tolerance above is the price of using one formula for all symbols.

  • Total power in dBm is EPRE plus 10log10(number of RB x 12) : this holds for a symbol that carries only PDSCH.
  • The allocated RBs set the total power, not the system bandwidth : an empty RB adds no power.
  • 100 RBs add 30.8 dB to the EPRE : 6 RBs add only about 18.6 dB.
  • Reference Signal symbols follow the same formula only when RS EPRE and PDSCH EPRE are equal : otherwise each RE group has to be added separately.

How do referenceSignalPower, P-a and P-b set each EPRE ?

The illustration above uses one EPRE for every RE. A real eNB does not have to do that. It sets the Reference Signal EPRE first, and then it sets the PDSCH EPRE relative to it with two parameters. So before you apply the total power formula, you need the right EPRE for each symbol.

The starting point is referenceSignalPower in PDSCH-ConfigCommon, which the UE reads in SIB2. It is an INTEGER from -60 to 50, and the value is the Reference Signal EPRE in dBm. 36.213 clause 5.2 defines it as the linear average over the power contributions of all REs that carry cell-specific reference signals within the operating system bandwidth. For RSRP and RSRQ measurements, the UE may assume that this EPRE is constant across the downlink system bandwidth and across all subframes, until it receives different cell-specific RS power information.

The PDSCH EPRE is then given as a ratio to the Reference Signal EPRE. 36.213 uses two ratios, and the OFDM symbol decides which one applies. ρA applies in the symbols without CRS, and ρB applies in the symbols with CRS. For one or two antenna ports with normal CP, the ρB symbols are 0 and 4 of each slot, and the ρA symbols are 1, 2, 3, 5 and 6. So the PDSCH only symbols 3, 5 and 6 in the formula above are ρA symbols.

ρA comes from p-a in PDSCH-ConfigDedicated, which is UE specific. Its values are -6, -4.77, -3, -1.77, 0, 1, 2 and 3 dB. In the usual case, ρA equals PA, because the power offset term is 0 dB for every transmission scheme except multi-user MIMO. For transmit diversity with 4 antenna ports, 36.213 adds 10log10(2) to it. ρB comes from p-b in PDSCH-ConfigCommon, which is cell specific. p-b is an INTEGER from 0 to 3, and it selects the ratio ρB/ρA from 36.213 Table 5.2-1 below.

 

PB

ρB/ρA, one antenna port

ρB/ρA, two and four antenna ports

0

1

5/4

1

4/5

1

2

3/5

3/4

3

2/5

1/2

 

Let's put numbers on it with a common two port setting, PA = -3 dB and PB = 1. Then ρA is 1/2, and ρB/ρA is 1, so ρB is also 1/2. Now look at one RB on one antenna port, in units of the Reference Signal EPRE. A symbol without CRS carries 12 PDSCH REs at 1/2, so its power is 6. A symbol with CRS carries 2 Reference Signal REs at 1, 2 REs left empty for the CRS of the other port, and 8 PDSCH REs at 1/2. Its power is 2 + 4 = 6 as well. So this setting keeps the power of every symbol the same, and the PDSCH EPRE sits 3 dB below the Reference Signal EPRE.

With that setting, the formula from the section above needs the PDSCH EPRE, not the Reference Signal EPRE. Take referenceSignalPower = 15 dBm and 100 RBs. The PDSCH EPRE is 15 - 3 = 12 dBm. So the total power per antenna port in a PDSCH only symbol is 12 + 30.8 = 42.8 dBm. If you had used the Reference Signal EPRE instead, the result would be 3 dB too high.

  • referenceSignalPower is the Reference Signal EPRE in dBm : the UE reads it from PDSCH-ConfigCommon in SIB2.
  • ρA applies to symbols without CRS and ρB to symbols with CRS : both are ratios of PDSCH EPRE to Reference Signal EPRE.
  • p-a is UE specific and p-b is cell specific : p-a gives ρA directly, and p-b gives ρB/ρA through Table 5.2-1.
  • PA = -3 dB with PB = 1 balances a two port cell : every symbol then carries the same power.
  • Use the PDSCH EPRE in the total power formula : it can differ from the Reference Signal EPRE by several dB.

Reference

  • 36.213 v19.4.0 : E-UTRA Physical layer procedures. Clause 5.2 Downlink power allocation, Table 5.2-1 and Table 5.2-2.
  • 36.214 v19.0.0 : E-UTRA Physical layer - Measurements. Clause 5.1.1 Reference signal received power.
  • 36.331 v19.3.0 : E-UTRA Radio Resource Control - RRC; Protocol specification. PDSCH-Config information element.