In LTE, the time axis is divided into entities. These time entities have the following hierarchy, as illustrated in Figure 10.

• 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 (illustrated in Figure 11), 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 $T_s = 1/30,720,000 s$ which is the reference time for defining any slot in LTE and also called as book keeping time.

Now consider 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 $f = 15 KHz $. Therefore an OFDM symbol duration (without cyclic prefix) is $1/15K = 67 \mu s = 2048 T_s$.
• One subcarrier, for the duration of 1 OFDM symbol, is called a resource element.
• Number of OFDM symbols into one slot = $15630/ 2048 = 7.6 $. That is 6 or 7 OFDM symbols can fit in to one time slot, depending on the duration of the cyclic prefix. LB represents the load block or OFDM symbol.
• In the “regular” case, the duration of the cyclic prefix is 160 $T_s$ in the first OFDM symbol and 144 $T_s$ for the subsequent symbols. Therefore, $\text {one time slot} = 160T_s +(6 \times 144T_s)+(7 \times 2048)= 15360 T_s = 0.5ms$
• A long or extended cyclic prefix is $512 T_s$, 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 Multicast/Broadcast over Single Frequency Network (MB-SFN).

In this chapter “normal-length” cyclic prefix is considered unless otherwise stated. Time/frequency resources are assigned to different users as integer multiples of a Resource Block (RB).

• Specifically, an RB is 12 subcarriers ($12 \times15kHz=180 kHz$) over the duration of one slot.
• 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.

Allocation of resource blocks to a MS for downlink is illustrated in Figure 12.

• 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, a guard interval is kept to avoid collisions between the packets on the air. Therefore 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.
• A guard interval is not necessary for a transition from uplink to downlink.