Formula for LTE data rate

[tester]

Please explain how to calculate LTE data rate if we know
Bandwidth - 10 MHz
Modulation - 64QAM
Code rate - 3/4
MIMO - 2x2

[wolverine]

From the table below (taken from the specs) you can see that using 10MHz results in having 50 PRBs.

A PRB consists of 12 subcarriers and in each subcarrier we can transmit 7 symbols per slot (0.5ms).

Using 64QAM means that each symbol represents 6 bits.

So each PRB can deliver 12 x 7 x 6 x 2 x 1000 = 1008000 bits per second

Since we have 50 PRBs in 10MHz we can transmit 50.4Mbps

Since we are using 2x2 MIMO we can transmit two streams so 100.8Mbps

However we have to use coding to protect the data, so at 3/4 that means 0.75 x 100.8Mbps = 75.6Mbps

The above assumes no control channels etc, which of course is not possible so the "real" theoretical max throughput will be a bit lower.

[tester]

Thanks a lot!

In all documents I saw that theoretical rate for these conditions is 64.8 Mbps. So the difference between 75.6 Mbps and 64.8 Mbps is control channels etc.

Next question - How to calculate "real" theoretical max throughput?

[wolverine]

Ok, as we said you have 50 PRB.

Each PRB looks like the picture below. As we said the PRB consists of 12 subcarriers and the slot (0.5ms) carries 7 symbols. This is represented as a two-dimensional matrix.

Each subcarrier/symbol combination is referred to as a RB (Resource Element).

In total we have 12 x 7 = 84 RE per PRB.

Control channels will use 12 RE per PRB (6 for the PDCCH and 6 for the Reference Signals)

So now you are left with 72 RE per PRB.

72 x 50 (total PRB per 10MHz) x 2 (to give value in ms) = 7200 RE per ms

Each RE can carry 6 bits (64 QAM) so 43200 bits per ms or 43.2Mbps

Since we are using MIMO 43.2 x 2 = 86.4Mbps

But with coding 86.4 x 0.75 = 64.8MBps!

[kamy]

it is amazing, do you have some detail calculation for certain planes and interfaces?

[desi_larka]

Wolver great explanation

i was also going to ask you detailed explanation or reference material which could explain it for junior members like

Also can you specify which standard has the Mhz to PRB conversion

[wolverine]

The 3GPP spec is 36.101 for the MHz to PRB table.

The reference material is various LTE white papers and the 3GPP specs.

There is lots of stuff on the forum as well.

Wolver great explanation

i was also going to ask you detailed explanation or reference material which could explain it for junior members like

Also can you specify which standard has the Mhz to PRB conversion

[pablo123]

Dear All,

Let's assume there is no retransmissions on MAC layer. Does the code rate 3/4 is always used in LTE or it is part of link adaptation procedure?

How many coded user data bits are transmitted in case of code rate = 3/4?

[Bogus]

What is PRB? Could anyone explain what does it mean?

[redrooster]

Good explanation wolverine. Just wanted to add.

In addition, per 10ms frame additional Physical Channel Overheads are also present, i.e. the PSS, SSS and PBCH. This would bring the rate slightly down 64.5516Mbps (assuming a 3/4 rate coding).

Added: Note that this assumes a Normal Cyclic prefix. If the extended CP is used the rate for the same 3/4 mimo 2x2 would be 53.7516Mbps.

To answer pablo123 question - link adaption is used. However the system relies more on HARQ mechanisms with RRC configuring the number of HARQ retries (note that the uplink and downlink different HARQ methods).

If these fail RLC (in AM mode) includes re-segmentation of existing RLC AM PDUs - which can then be sent with link adapted Modumation and coding....with HARQ...VERY Flexible!

Note that the downlink and uplink are slightly different in terms of effective coding rates (based on TB(Transport Block Size)) the effective coding rate in the downlink in Release 8 is limited to 0.9 (Not 1).

Cheers

Redrooster