In a previous post I presented how to calculate the maximum throughput of LTE, and this was focusing on LTE FDD (Frequency Division Duplex), where an equal bandwidth of spectrum is allocated for both the Downlink and the Uplink. As a reader asked, in this post we do the same for LTE TDD (Time Division Duplex) a.k.a TD-LTE.

## The Time Division Duplex in LTE

On LTE TDD, Downlink and Uplink share the same piece of spectrum and the transmission switches between each other at specific time interval. Below is the comparison of the 10ms LTE radio frame in FDD and TDD:

*Source: blog.3G4G.co.uk*

So the main thing to do for TD-LTE is to determine the portion of time (normal subframes and portion of special subframes) allocated to the uplink and downlink based on the selected Time Division Duplex configuration.

### 1. Frame structure

For each frame, there are 10 subframes that can be allocated between Uplink and Downlink, and one special subframe that will always be needed for the synchronization of the periodicity (5ms or 10ms). There are 7 possible configurations as follows:

Based on this, for each configuration, we can determine the proportion of time allocated for the Downlink and Uplink by counting the number of subframes allocated:

UL/DL Config. |
Downlink | Special | Uplink |
---|---|---|---|

0 | 2 (20%) |
2 (20%) |
6 (60%) |

1 | 4 (40%) |
2 (20%) |
4 (40%) |

2 | 6 (60%) |
2 (20%) |
2 (20%) |

3 | 6 (60%) |
1 (10%) |
3 (30%) |

4 | 7 (70%) |
1 (10%) |
2 (20%) |

5 | 8 (80%) |
1 (10%) |
1 (10%) |

6 | 3 (30%) |
2 (20%) |
5 (50%) |

### 2. Special subframe structure

The special subframe is required to switch from the Downlink to the Uplink (but not required for the other way around). It is not wasted as it is also used to transmit data on the Downlink (DwPTS) and then on the Uplink (UpPTS) after a Guard interval (GP):

Here as well there is a limited number of possible configuration of this special subframe, and we can also calculate the proportion of time allocated to the Downlink, the Uplink:

### 3. Number of symbols per 10ms frame and per second

By combining both calculation done at frame level and special subframe level, we determine the overall number of symbols allocated to the Downlink, the Uplink and the Gap separation during one 10ms frame.

Here is the example of calculation of Number of Downlink Symbols, assuming a Normal Cycle Prefix of 7 symbols per slot or 14 symbols per subframe:

Number of Downlink Symbols = Σ(D) × 14 + Σ(S) × Σ(DwPTS)

Multiplying this by 100 (frame is 10ms) gives us the number of symbols per second.

### 4. From symbols to Mbps

From there you can follow the same principles as for LTE FDD to convert symbols to Mbps, taking into account modulation (e.g. 64 QAM), total bandwidth (e.g. 20 MHz), diversity mode (e.g. 2×2 MIMO) and carrier aggregation mode (e.g. Single Carrier).

### 5. Examples

Below is an example showing the calculation steps.

**Normal Cycle Prefix**(7 OFDM symbols per slot) with**20 MHz**spectrum bandwith with TDD configuration mode**3**and Subframe configuration**7**:**Downlink**- Normal CP = 14 OFDM symbols per subframe
- TDD configuration 3 = 6 D subframes and 84 symbols
- Special Subframe configuration 7 = 10 DwPTS symbols
- Total of 84+10 = 94 downlink symbols per frame
- 64 QAM = 6 bits per symbol = 564 downlink bits per frame = 56.4 kbps
- 12 subcarriers per resource block = 677 kbps per Resource Block
- 20 MHz = 100 Resource Blocks =
**67.68 Mbps per Antenna**

**Uplink**- Normal CP = 14 OFDM symbols per subframe
- TDD configuration 3 = 3 U subframes and 42 symbols
- Special Subframe configuration 7 = 2 UpPTS symbols
- Total of 42+2 = 44 uplink symbols per frame
- 16 QAM = 4 bits per symbol = 176 uplink bits per frame = 17.6 kbps
- 12 subcarriers per resource block = 211 kbps per Resource Block
- 20 MHz = 100 Resource Blocks =
**21.12 Mbps per Antenna**

You can also download this Excel file: 4g-lte-tdd-throughput-calculator. It describes all the steps of the calculation and will help you verify the example. If you spot any error please share in the comments!

### More information:

Graphical view of TD-LTE Frame and Special Subframes: http://niviuk.free.fr/lte_tdd.php