Ferkans — Interactive Telecom Tutor

LTE as the Foundation of Modern Cellular

Long Term Evolution (LTE), standardised in 3GPP Release 8 (2008), was the first cellular system built entirely on OFDM and MIMO — the two pillars developed in Chapters 14 and 7. LTE's physical layer design made concrete choices that translate the theoretical principles into a deployable system: 15 kHz subcarrier spacing (balancing delay spread tolerance and Doppler robustness), a 1 ms TTI (balancing latency and overhead), OFDMA downlink with SC-FDMA uplink (balancing spectral efficiency and PAPR), and up to 4-layer MIMO. Understanding LTE is essential both historically — it remains the world's dominant cellular technology — and technically, as 5G NR deliberately evolved from LTE, inheriting much of its structure while generalising the parameters.

Definition:
LTE Frame Structure and Resource Grid

The LTE physical layer organises time and frequency into a resource grid:

Subcarrier spacing: $\Delta f = 15$ kHz (fixed).
OFDM symbol duration: $T_u = 1/\Delta f \approx 66.7$ $\mu$ s.
Cyclic prefix: Normal CP $\approx 5.2$ $\mu$ s (first symbol) and $4.7$ $\mu$ s (remaining); extended CP $\approx 16.7$ $\mu$ s.
Slot: 0.5 ms = 7 OFDM symbols (normal CP) or 6 (extended CP).
Subframe (TTI): 1 ms = 2 slots.
Frame: 10 ms = 10 subframes.
Resource Block (RB): 12 subcarriers $\times$ 1 slot = 84 REs (normal CP). The minimum scheduling unit.
Channel bandwidths: 1.4, 3, 5, 10, 15, 20 MHz (6 to 100 RBs).

The downlink uses OFDMA (each RB assigned to one user); the uplink uses SC-FDMA (DFT-precoded OFDM) to reduce PAPR at the UE transmitter.

The choice of 15 kHz SCS was a careful trade-off: wide enough to tolerate Doppler shifts up to $\sim$ 500 Hz (corresponding to $\sim$ 300 km/h at 2 GHz) while narrow enough that the CP of $\sim$ 4.7 $\mu$ s handles delay spreads up to $\sim$ 1.4 km (sufficient for all but the largest macro cells).

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Definition:
LTE Physical Channels and Reference Signals

LTE defines the following key physical channels:

Downlink:

PDSCH (Physical Downlink Shared Channel): carries user data, scheduled dynamically per TTI via DCI on PDCCH.
PDCCH (Physical Downlink Control Channel): carries DCI (scheduling grants, MCS, HARQ feedback). Occupies the first 1--3 OFDM symbols of each subframe.
PBCH (Physical Broadcast Channel): carries MIB (master information block) for initial cell access.

Uplink:

PUSCH (Physical Uplink Shared Channel): user data, SC-FDMA.
PUCCH (Physical Uplink Control Channel): HARQ ACK/NACK, CQI, PMI, RI feedback.

Reference signals:

CRS (Cell-specific Reference Signals): known pilot symbols on a fixed grid (every 6th subcarrier, every other symbol), used for channel estimation, CQI measurement, and demodulation.
DM-RS (Demodulation Reference Signals): UE-specific pilots for MIMO demodulation (introduced in Release 10).
SRS (Sounding Reference Signals): uplink pilots for channel estimation at the eNB, enabling frequency-selective scheduling.

The CRS design in LTE — always on, cell-wide — creates a fixed overhead of approximately 5--15% depending on antenna configuration. This "always-on" reference signal was identified as a limitation and removed in 5G NR, which uses configurable DM-RS and CSI-RS instead.

Theorem: LTE Peak Data Rate

The theoretical peak data rate of LTE (Release 10, Category 8) with 20 MHz bandwidth, 4 $\times$ 4 MIMO, 64-QAM, and code rate $948/1024$ is:

$R_{\text{peak}} = N_{\text{RB}} \times N_{\text{sc}}^{\text{RB}} \times N_{\text{sym}} \times N_{\text{layers}} \times Q_m \times R \times \frac{1}{T_{\text{TTI}}}$

$= 100 \times 12 \times 14 \times 4 \times 6 \times \frac{948}{1024} \times \frac{1}{10^{-3}}$

$\approx 299.6 \;\text{Mbps}$

Accounting for reference signal overhead ( $\sim$ 25% for 4-port CRS and control channels), the practical peak is approximately $\sim$ 225 Mbps per 20 MHz carrier.

Each resource element carries $Q_m \times R = 6 \times 0.926 = 5.56$ coded bits. With $100 \times 12 \times 14 = 16{,}800$ REs per TTI and 4 layers, the total is $\sim$ 373{,}000 coded bits per ms. Reference signals and control consume roughly 25% of REs.

Proof

Resource counting

20 MHz bandwidth: 100 RBs $\times$ 12 subcarriers = 1200 subcarriers. Per subframe (1 ms): 14 OFDM symbols (normal CP). Total REs per subframe: $1200 \times 14 = 16{,}800$ .

Data capacity per RE

With 4-layer MIMO, 64-QAM ( $Q_m = 6$ ), code rate $R = 948/1024$ : Bits per RE per layer: $6 \times 0.926 = 5.56$ . Bits per RE (4 layers): $5.56 \times 4 = 22.22$ .

Peak rate

Gross: $16{,}800 \times 22.22 / 10^{-3} = 373$ Mbps. After overhead ( $\sim$ 20% for CRS, PDCCH, PBCH): $373 \times 0.80 \approx 299$ Mbps. $\blacksquare$

Example: LTE Throughput Calculation

An LTE cell operates with 10 MHz bandwidth (50 RBs), 2 $\times$ 2 MIMO, and a UE reporting CQI 9 (16-QAM, code rate $\approx 0.6$ ).

(a) How many data REs are available per subframe after accounting for 3 OFDM symbols of PDCCH and 2-port CRS overhead? (b) Compute the expected per-UE throughput if the UE is allocated all 50 RBs. (c) With 10 active UEs and PF scheduling, estimate the average per-UE throughput (assuming equal channel statistics).

Solution

Available data REs

(a) Total REs: $50 \times 12 \times 14 = 8{,}400$ . PDCCH (3 symbols): $50 \times 12 \times 3 = 1{,}800$ . CRS (2-port, $\sim$ 4 REs per RB per slot $\times$ 2 slots): $50 \times 8 = 400$ . Data REs: $8{,}400 - 1{,}800 - 400 = 6{,}200$ .

Per-UE throughput

(b) Bits per RE: $\log_2(16) \times 0.6 = 2.4$ bits. With 2 layers: $2.4 \times 2 = 4.8$ bits/RE. Throughput: $6{,}200 \times 4.8 / 10^{-3} = 29.8$ Mbps.

Multi-UE estimate

(c) With PF and symmetric users, each UE gets $\sim 1/10$ of the time, but with multiuser diversity gain ( $\sim 1.3\times$ for 10 users from Chapter 20): Per-UE: $29.8 / 10 \times 1.3 \approx 3.9$ Mbps. $\blacksquare$

Quick Check

Why does LTE use SC-FDMA (DFT-precoded OFDM) on the uplink instead of OFDMA?

SC-FDMA achieves higher spectral efficiency than OFDMA

SC-FDMA has lower PAPR, allowing more efficient PA operation at the UE

SC-FDMA is simpler to implement than OFDMA in the UE

SC-FDMA provides better frequency diversity than OFDMA

Correction:

SC-FDMA has lower PAPR, allowing more efficient PA operation at the UE

The DFT precoding in SC-FDMA gives the transmitted signal a single-carrier-like envelope with lower PAPR ( $\sim$ 2--4 dB less than OFDMA). Since UEs are power-limited and battery- constrained, the lower PAPR allows the PA to operate closer to saturation, improving power efficiency — which directly extends battery life and cell-edge coverage.

Historical Note: The Road to LTE

2004--2011

LTE was the outcome of a 3GPP study item launched in 2004 and completed as Release 8 in 2008. The first commercial deployments followed in late 2009 (TeliaSonera in Scandinavia, MetroPCS in the US). The design was driven by the success of OFDM in Wi-Fi and the desire to close the gap with WiMAX, which had already adopted OFDMA. Key contributors included Ericsson (who championed SC-FDMA for the uplink), Qualcomm (MIMO and scheduling), and Nokia (turbo code optimisation). LTE-Advanced (Release 10, 2011) added carrier aggregation, 8-layer MIMO, and relay nodes, achieving ITU IMT-Advanced certification as a true 4G technology.

Common Mistake: CRS Overhead Scales with Antenna Ports

Mistake:

Assuming that adding more antenna ports in LTE is free because the capacity gain from MIMO always exceeds the reference signal cost.

Correction:

LTE CRS overhead scales with the number of antenna ports: 2-port CRS uses $\sim$ 9.5% of REs, 4-port CRS uses $\sim$ 14.3%. For 8-port CSI-RS (Release 10+), the overhead grows further. At moderate SNR, the capacity gain from 4-port MIMO may not compensate for the 14.3% RE loss, especially in low-mobility scenarios where the spatial multiplexing gain is limited. This "always-on" CRS limitation motivated NR's shift to configurable DM-RS and CSI-RS.

OFDMA

Orthogonal Frequency-Division Multiple Access: a multi-user extension of OFDM where different subsets of subcarriers (resource blocks) are assigned to different users. Used on the LTE downlink and both NR downlink and uplink.

Related: SC-FDMA, Resource Block (RB)

SC-FDMA

Single-Carrier Frequency-Division Multiple Access: DFT-precoded OFDM that preserves the single-carrier envelope, reducing PAPR by 2--4 dB compared to OFDMA. Used on the LTE uplink for power efficiency. Optional in NR uplink (transform precoding).

Related: OFDMA, Resource Block (RB)

Resource Block (RB)

The minimum scheduling unit in LTE and NR: 12 consecutive subcarriers in frequency by 1 slot in time. One RB contains 84 resource elements (normal CP, 7 symbols) in LTE.

Related: OFDMA, SC-FDMA

LTE Physical Layer