# Average Cell Throughput Calculations for LTE

Average Cell Throughput requires the following simulation results

• Average SINR distribution table (system level result), which provides the SINR probability

• Average throughput or spectral efficiency versus average SINR table (link level result)

For urban channel model and a fixed inter-site distance of 1732m,downlink throughput for LTE for different values of SINR is shown below.

MCS vs SINR

Average Cell Throughput=Σ(Pi*Ri)

where

Pi=Probability of occurrence of a specific SINR value at cell edge obtained using simulations
Ri=Average throughput corresponding to SINR range

Let us consider the following distribution for the SINR at the cell edge:

P1=0.5 (SINR=1.50-3.50 dB)
P2=0.25 (SINR=3.50-7.00 dB)
P3=0.15 (SINR=7.00-9.50 dB)
P4=0.10 (SINR=9.50-11.50 dB)

Cell Throughput=(0.50*4)+(0.25*6)+(0.15*8)+(0.10*12)=5.9 Mbps

Note: This throughput is much less than the theoretical maximum which assumes that the full 20 MHz bandwidth is being utilized in a 4×4 MIMO configuration.

# LTE Data Rate Calculation

Peak LTE data rate can be calculated using the following parameters:

1 Time-slot=0.5 ms (i.e 1 Sub-frame = 1 ms)
1 Time-slot=7 Modulation Symbols (when normal CP length is used)
1 Modulation Symbol=6 bits; if 64 QAM is used as modulation scheme

Data rate for a single carrier=Number of symbols per time slot*Bits per symbol/Duration of a time slot=7*6/0.5e-3=84kbps

If 1200 carriers (100RBs) are used then the aggregated throughput would be=1200*84kbps=100.8Mbps

If 4×4 MIMO is used then the capacity would increase four fold to=403.2Mbps

With 3/4 channel coding the data rate would be reduced to=302.4Mbps

Note:

1. A Resource Block (RB)=12 Carriers

2. Actual data rate would depend upon the instantaneous channel conditions and number of users sharing the resources e.g. going down from 64QAM to QPSK in adverse channel conditions would reduce the data rate from 302.4Mbps to 100.8Mbps.  Changing the code rate from 3/4 to 1/3 would further reduce the data rate to 44.8Mbps.

# Shannon Capacity of LTE (Effective)

In the previous post we calculated the Shannon Capacity of LTE as a function of bandwidth. We now calculate the capacity as a function of SNR (bandwidth fixed at 20MHz and signal power varied). We also use the concept of effective bandwidth to get a more realistic estimate of the capacity. The modified Shannon Capacity formula is given as:

C=B_eff*log2(1+SNR)

where

B_eff=Bandwidth*eff1*eff2*eff3*eff4

eff1=0.9=due to adjacent channel leakage ratio and practical filter issues

eff2=0.93=due to cyclic prefix

eff3=0.94=due to pilot assisted channel estimation

eff4=0.715=due to signalling overhead

B_eff=0.57*B

Therefore

C=0.57*B*log2(1+SNR)

Note: This is the capacity in a SISO channel with no fading.