Snapdragon just announced the X16 LTE Modem that can achieve 1 Gbps throughput thanks to higher order modulation (256 QAM), 4×4 MIMO and 4x Carrier Aggregation of 20 MHz. But how can we calculate the maximum theorical peak LTE throughput depending on those parameters?

### Waveform and Modulation

LTE is using OFDM multiplexing method for the air interface. The OFDM symbols are grouped into resource blocks. The resource blocks have a total size of **180kHz** in the frequency domain and **0.5ms** in the time domain. Each resource block is composed of **12 subcarriers** which transmit **7 OFDM symbols** each in each slot.

Based on this, we can calculate that 84 symbols (7×12) can be transmitted in each resource block of 0.5ms, so an equivalent of 168,000 symbols per second per resource block (84/0.0005).

To convert symbols per second to bits per second we add the modulation factor (from 2 bits per symbol in QPSK to 8 bits per symbol for 256 QAM) and come up with something between 336 Kbps and 1,344 Mbps throughput per resource block.

### Carrier bandwidth size

The actual throughput per antenna will then depend on the bandwidth allocated for the downlink carrier. It can range from 1.4 MHz to 20 MHz. This bandwidth includes a guard band which needs to be removed to calculate the number of resource blocks that can be combined within 1 carrier. It is 10% except for 1.4 MHz where it is around 23%.

### Additional techniques to improve throughput

**MIMO.** can double or quadruple the maximum peak throughput achievable by having 2 or 4 antennas on both the transmitter and the receiver (2T2R or 4T4R respectively).

**Carrier Aggregation.** can also multiply the total peak throughput by summing the throughput of several carriers used together to make a single link between the network and a device.

Combinations of both MIMO and CA can be used but **not all combinations seem possible**. For instance the Snapdragon modem can go up to 4×4 MIMO and 4x 20 MHz CA with QAM 256, which in theory would allow a throughput above 2 Gbps (~1.6 Gbps user throughput).

### Conclusion

These are theorical numbers and far from what will be observed in the field. The calculations described here have been summarized in this Excel file you can download: 4g-lte-throughput-calculator

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