We are pleased to share with you all an interesting article contributed by Mahmoud Ali who has 10 years of experience as Network, RF Planning and Optimization Team leader / Solutions Architect / Expert in GSM/UMTS/LTE.
Mahmoud Ali LTE Team Leader/SME at AdvaComm


Physical layer data throughput can be calculated accurately for different scenarios. In order to determine physical layer performance, we need to calculate the total physical resources available for different bandwidths of downlink transmission. On the other hand, we need to determine how many physical resources are associated with overhead.
Based on the parameters of physical layer proposed in 3GPP standard Releases, various scenarios are considered for physical layer throughput. Based on system bandwidth (1.4 to 20 MHz), number of antenna ports (1, 2, or 4, 8), number of OFDM symbols assigned for PDCCH (1, 2, or 3 symbols per subframe), code rate (0.33 to 0.92) and modulation scheme (QPSK, 16QAM, 64QAM, 256QAM) different throughput values can be addressed.
LTE Rel.8 supported up to four layers of MIMO multiplexing for downlink and no MIMO for uplink. LTEAdvanced supports single user MIMO (SUMIMO) scheme up to eight layers (8x8 MIMO) for downlink and four layers (4x4 MIMO) for uplink. With this technology, it achieves peak spectral efficiency of 30 bit/s/Hz for downlink and 15 bit/sec/Hz for uplink. In other words, single 20MHz bandwidth to achieve up to 600Mbps downlink speed.
note: All calculations below is for 20MHz, for less bandwidth you just divide. :)
FDD Downlink Throughput:
We need to calculate the total physical resources.
Resource Block (RB): 12 Subcarriers x 7 OFDM Symbols in Normal CP (0.5 ms = 1 Time Slot).
Q: Why 3GPP used 0.5 ms as Time Slot not more or less, where is the mathematical behind that? The answer is at the end of this article.
Physical Resource Block (PRB) = 2*Resource Block = 12 Subcarriers x 14 OFDM in 1ms.
One Physical Resource Block (PRB) = 12*7*2 = 168 Resource Element (RE)
RE can deliver 2, 4, 6, 8 bits in QPSK, 16QAM, 64QAM, 256QAM respectively.
If we calculate for 64QAM as 6bits since 256QAM not widely spread (check Samsung S7 in TMobile).
20MHz ==> 100 PRB ==> 100*168*1000 = 16,800,000 RE in 1 s.
Maximum Physical Throughput in LTE is (16800 RE) * (6bits) * (1000ms) = 100.8 Mbps. really???
As we mention above, Actual User Throughput we should exclude signaling.
PSS,SSS, BCH, PDCCH, Reference Signals.
PBCH: 72 middle subcarriers x 4 OFDM Symbols (Excl. whereRS) = 288  48 = 240 => 24,000RE in 1s.
PDCCH: Assuming CFI=1 ==> one OFDM symbol ==> (8 subcarriers) * (100 PRB) = 800 RE ==> 800,000 RE in 1s
PSS + SSS = middle 72 * 2 OFDM * 2 (Occurance in a frame) * 100 frame = 28,800 RE
Reference signal (8 + 2(Reserved), 16, 24 RE for 1x1, 2x2, 4x4 MIMO) for 1x1 => 10*100*1000 = 1,000,000 RE in 1s.
Now calculate how many PDSCH RE (Data):
Total REs  Signaling REs = 16,800,000  24,000 800,000  28,800  1,000,000 = 14,947,200 RE * (6bits) = 89,683,200 * (~0.85 Coding Rate for CFI 1) = 75,376 kbps
Check below 3GPP table for ITBS versus PRB ==> maximum transport block size for SISO.
now Simply:
considering the same overhead ~25% which is matching somehow.
2x2 = 1x1(75) *2 = ~150 Mbps, 4x4 = ~300Mbps, 8x8 (Beamforming) = ~600Mbps.
Q: 2x2 and 4x4 has more overhead in reference signals, why the throughput still ~75*2 or ~75*4, it should be less?
Well, Coding rate in 2x2 and 4x4 is higher than SISO, i.e 4x4 is 0.92 Coding rate which give actual throughput ~299 Mbps.
Q: Why 3GPP used 0.5 ms as Time Slot not more or less, where is the mathematical behind that? The answer is at the end of this article. Q Answer: In time domain the required spacing can be calculated considering the minimum sampling rate based on Nyquist‘s sampling criteria to support high speed mobility like 500 Km/h, we should calculate Tc = 1/ (2*fd). fd is known as Doppler shift and can be calculated by fd = (fc * v) / c, where fc is the carrier frequency that equals i.e 2 GHz for LTE, v is the highest speed for LTE supporting mobility (500 km/h), and c is the speed of light (3*10^8). By calculating fd = 950 Hz, Tc will be 0.5 ms, which leads to two reference symbols in one slot for accurate channel estimation. The modulation for all types of reference signals is based on QPSK.
Q: Similar, why Mod 3 is used in LTE ? think about it and answer in the comment please.
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Thanks for sharing details about why the 0.5ms difference in time domain is required between two successive RS on same subcarrier.
Now, few more queries comes:
1. Why difference between two staggered RS subcarriers is 3RE (equivalent to 45KHz) over different OFDM symbols?
2. What is the logic behind 6 RE difference (90KHz) between two successive RS over same OFDM symbol?
Could you please throw some light in this regard?