“Back-of-the Envelope” Calculation of VoIP Capacity in LTE

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“Back-of-the Envelope” Calculation of VoIP Capacity in LTE

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LTE supports voice over IP (Internet Protocol) (VoIP) to provide voice services.  A simplified analysis is carried out next to approximately estimate the achievable VoIP capacity per cell in case of 10 MHz downlink channel bandwidth and 10 MHz uplink channel bandwidth.  Refer to [2] for a comprehensive simulation-based analysis of VoIP capacity.  We will carry out a simplified analysis below to estimate the VoIP capacity under a given set of assumptions.  Refinement of assumptions and suitable modifications to calculations would lead to a more accurate prediction of VoIP capacity. 

Assume that full-rate 12.2 kbps Adaptive Multi Rate (AMR) speech codec is used.  Every 20 ms, AMR speech codec generates (12.2 kbps * 20 ms= 244 bits) during the “speech on” interval (i.e., the user is indeed talking and not just listening during such interval).  These bits are placed in an RTP/UDP/IP packet with about 3 bytes (=24 bits) of overhead.  IP header compression is assumed to be active.  The VoIP packet entering the air interface protocol stack would contain about (244 speech bits + 24 IP-related header bits = 268) bits.  The VoIP packet passes through these layers of the air interface protocol stack- PDCP, RLC, MAC, and PHY.  Let’s add 4 bytes (=32 bits) to account for headers added by PDCP (1 byte for short sequence number), RLC (1 byte for Unacknowledged Mode operation with a 5-bit sequence number), and MAC (2 bytes) layers, leading to the “target” payload of (268+32=300) bits entering the PHY layer from the MAC layer. 

Now, let’s calculate how many Physical Resource Blocks (PRBs) are needed to carry the target payload of 300 bits.  According to Table A.3-1 of [36.104], 1 PRB can carry the payload of 104 bits when the modulation scheme is QPSK and the coding rate is (1/3).  This payload is from the MAC layer to the PHY layer.  Three PRBs would then be able to carry (104 bits per PRB *3 PRBs =312 bits), which would be adequate for the target payload of 300 bits.  If a user’s channel conditions allow the modulation scheme of 16-QAM and the coding rate of (3/4), 1 PRB can carry 408 bits, which would suffice for the target payload of 300 bits (see Table A.4-1 of [36.104]).  When users are distributed across the cell, some would have good channel conditions and can support (16-QAM, coding rate=¾); others may have bad channels conditions and would require more robust (QPSK, coding rate=1/3).  If 50% of users are able to use (16-QAM, coding rate=¾) and 50% of users need (QPSK, coding rate=1/3), the average number of PRBs consumed by a typical VoIP user in a cell would be (0.50*3 PRBs + 0.50*1 PRB = 2 PRBs).  In 1 ms subframe, there are 50 PRBs, allowing (50 PRBs/2 PRBs per user = 25 users).  Since the AMR speech codec generates a new speech frame every 20 ms, during a span of 20 ms, we can have 20 subframes carrying VoIP packets for (20 subframes * 25 users per subframe= 500) users.  These calculations assume that every single packet with a specific modulation scheme and certain amount of coding is received without any errors all the time.  However, in practice, some packets would be lost, requiring HARQ retransmission.  If we need one (additional) retransmission on average, PRBS would need to be allocated to a given VoIP user twice per 20 ms interval instead of just once per 20 ms interval.  Since a VoIP users is now consuming twice as many PRBs during the 20 ms interval, the number of VoIP users would be reduced by half (i.e., 500/2= 250).  In summary, for the assumptions made here, the VoIP capacity in LTE is 250 in case of 10 MHz channel bandwidth.  Comprehensive simulation-based analysis indicates that 123 VoIP users can be supported in 5 MHz bandwidth [2], implying (123*2= 246) users can be supported in 10 MHz channel bandwidth. 

The VoIP capacity estimate calculated above can be adjusted by modifying assumptions and making suitable adjustments to the calculations.  For example, instead of using just two combinations of modulation scheme and coding rate, multiple combinations can be used to estimate the number of PRBs required by an average user in a cell.  The overall approach outlined above can still be used for an approximate VoIP capacity estimate. 

Several factors would increase the VoIP capacity estimated above.  If many users can work with reduced degree of channel coding, capacity would be higher.  We did not use 64-QAM in the analysis above, because only UE Category 5 can support such scheme in the uplink, and we may not see such UEs for quite some time.  Use of antenna techniques would also increase the capacity.  Consideration of the voice activity factor would also increase capacity because we do not need to send hundreds of speech bits during the silence interval.  Some factors would decrease the VoIP capacity estimated above.  If many users in the cell need more redundancy than that provided by (1/3) coding, we would need more PRBs per user, reducing the capacity.  If semi-persistent scheduling is not used, higher control channel overhead would decrease the achievable VoIP capacity. 

In summary, a 10 MHz channel bandwidth could support about 250 VoIP users in LTE.




[1] 3GPP, 36.104 V8.7.0.

[2] 3GPP, R1-072570, “Performance Evaluation Checkpoint: VoIP Summary.”

  • Is this 250 per sector or cell site. Thanks

  • 250 users per cell.  When 120 degree sectorization is used, the cell-site has three cells (= 3 sectors), and, the number of users supported by the cell-site would be 3*250=750.

  • Just a small question Nishith, i presume you mean Table A.3.2-1 of 36.101?

    If it's no problem for you, could you explain how you calculated the 104 bit payload from the table?

    Very good post by the way.