Capacity of Volte User per cell

Now days there is massive shift for voice call to VoLTE calls from conventional CS calls. Here i am discussing about Max theoretical VoLTE User per cells.

For this first we have to calculate VoLTE call Packet size and Radio resource required for VoLTE packets . 

VoLTE call packet size mainly depends on below factors:
     > Codec used by UE
     >  UE Radio conditions
     > EnodeB Scheduling Algorithm
     > Protocol used.
Lets try to find out the VolTE call packet size with below assumption.

Assumptions:-
LTE System Bandwidth: 5MHZ(25 PRB)
Duplex Mode: FDD
MIMO: 2*2
Codec used: AMR-Wide band codec(12.65)
RoHC: Enabled.

Calculation: AMR-WB(12.65) coder generates about 253 bits of speech every 20ms( Voice data is genearted in every 20ms for VoLTE). In order to deliver each voice samples to UE needs to add protocol headers such as RTP header(12 bytes), a UDP header(8 bytes) and an IP header(40 bytes).

        So VolTE packet length with all headers are:
 =Codec bits + RTP Header + UDP Header + IP Header
 = 253bits + 12*8(=96bits) + 8*8(=64 bits) +40*8(=320bits) = 733bits/20ms.

Note: When RoHC is enabled it will replaced the RTP, UDP and IP header with a much smaller RoHC header(24 bits).

Further RLC and MAC layers will add their own headers hence approx. 300 bits are needed for every VoLTE voice call.

Radio resource calculation for VoLTE packets: In LTE one PRB has 12 subcarrier and 14 symbols(Normal CP) over 1ms duration. 
 Total number of REs over 1ms = 12*14=168 but some of the REs are used by control symbols(PDCCH and RS). So final count is around 120 REs.

LTE DL modulation supports QPSK, 16QAM, and 64 QAM for PDSCH which means each resources can carry 2 bits, 4 bits and 6 bits. But some of these bits used for error control also.

Consideration: Lets consider CQI 15= Good ,provides 64 QAM, CQI 7= Average ,provides 16 QAM and CQI 1= Poor, provides QPSK.

When CQI =15:-
 Modulation: 64 QAM(6 bits)
 Effective coding rate = 0.926
 Total data bits in 1 RE = 6*0.926 = 5.55
 Total data bits in 1 PRB = 120*5.55 = 666 data bits or equivalent to 2 VoLTE calls.
But LTE schedular can not allocates < 1PRB so 1 PRB is needed for VolTE calls with CQI=15.

When CQI = 7:-
Modulation: 16 QAM(4 bits)
 Effective coding rate = 0.369
 Total data bits in 1 RE = 4*0.369 = 1.476
 Total data bits in 1 PRB = 120*1.476 = 177 data bits. So 300 VolTE bits required 2 PRB.

When CQI =1:-
Modulation: QPSK(2 bits)
 Effective coding rate = 0.076
 Total data bits in 1 RE = 2*0.076 = 0.152
 Total data bits in 1 PRB = 120*0.152 = 18 data bits. So 300 VolTE bits required 16 PRB.

Now we are ready to calculate max theoritacal VoLTE user per cell:- In VoLTE voice data is generated every 20ms so if everything is good then about 20 VoLTE calls can share the same set of PRB one after another.

The max VolTE call that can be carried = (No of avg PRB)/ No of PRB required per VoLTE calls *20.
Hence VolTE calls per CQI and Bandwidth is as below:

Bandwidth             1.4MHZ         3 MHZ         5MHZ             10MHZ             15MHZ           20MHZ
No of total PRB         6               15               25                     50                   75                100
CQI15(1 PRB)         120             300              500                 1000                 1500            2000
CQI7(2 PRB)            60              150              250                  500                  750             1000
CQI1(16 PRB)           8                18               31                    63                    94               125

The above is the theoretical max value but in practical there are some issues. We will discuss it in next..