In LTE, the time axis is divided into entities that play an important role in the transmission of different channels. These time entities have the following hierarchy:

• The fundamental time unit of LTE transmission is a radio frame, which has a duration of 10 ms.
• Each radio frame is divided into 10 subframes (each being 1ms long). Subframes are the fundamental time unit for most LTE processing, like scheduling.
• Each subframe consists of two slots, which are each 0.5 ms long.
• Each slot consists of 7 (or 6) symbols. Duration of the different units is often given in terms of the sampling time Ts = 1/30,720,000 s.
• Note that this “sampling time” is a bookkeeping unit; RXs are not obligated to actually sample at the corresponding rate. In particular, for bandwidths $\lt$ 15 MHz ,a larger sampling rate (lower sampling frequency ) is feasible.

Let us now turn to the details of a symbol. Since the modulation format is OFDM (regular OFDM for the downlink, and DFT-precoded OFDM in the uplink), multiple subcarriers are present.

The regular spacing between the subcarriers is = 15 kHz. The 15-kHz spacing of the subcarriers leads to an OFDM symbol duration (without cyclic prefix) of 67 μs = 2048 Ts. One subcarrier, for the duration of 1 OFDM symbol, is called a resource element.

We can fit 6 or 7 OFDM symbols into one slot, depending on the duration of the cyclic prefix. In the “regular” case, the duration of the cyclic prefix is 160 Ts in the first OFDM symbol and 144 Ts for the subsequent symbols.

A long cyclic prefix is 512 Ts, so that only a total of 6 OFDM symbols fit into one slot. Such a long cyclic prefix is used in environments with large delay spread and/or for MB-SFN.

To simplify the notation, the description in the remainder of this chapter assumes “normal-length” cyclic prefix unless otherwise stated.

Time/frequency resources are assigned to different users as integer multiples of a Resource Block (RB). More precisely, an RB is 12 subcarriers (180 kHz) over the duration of one slot.3. For the uplink, only contiguous RBs can be assigned to one MS.

Furthermore, the number of RBs has to be decomposable into factors of 2, 3, and 5; this is done to ensure an efficient implementation: with that prescription, any of the necessary DFTs can be composed of radix-2, radix-3, and radix-5 butterfly structures.

In the TDD case, subframes can be assigned flexibly to uplink and downlink, with the exception of subframes 0 and 5, which are always used for the downlink, and subframe 2, which is always used for the uplink.

For every transition from downlink to uplink, there is a guard interval, to avoid collisions between the packets “on the air” .

Consequently, there are subframes that contain three distinct parts: a Downlink Pilot Time Slot (DwPTS), Uplink Pilot Time Slot (UpPTS), and a guard interval between them.

Note that a guard interval is not necessary for a transition from uplink to downlink.