Orthogonal Frequency Division Multiplexing in Long-Term Evolution
Upon completing this study guide, you will be able to:
Long-Term Evolution (LTE) adopted Orthogonal Frequency Division Multiplexing (OFDM) as its air interface technology due to its robustness against multipath fading, high spectral efficiency, and flexibility in bandwidth allocation. OFDM enables LTE to achieve peak data rates of 300 Mbps (downlink) and 75 Mbps (uplink) while maintaining efficient use of scarce spectrum resources.
Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation technique that divides the available bandwidth into multiple narrowband subcarriers that are orthogonal to each other. In LTE, this technology forms the foundation of both the downlink (OFDMA) and uplink (SC-FDMA) transmission schemes.
The 3rd Generation Partnership Project (3GPP) selected OFDM for LTE Release 8 (2008) after extensive evaluation of competing technologies including CDMA and single-carrier schemes. The decision was driven by OFDM's ability to efficiently handle wideband channels in high-mobility environments while supporting scalable bandwidths from 1.4 MHz to 20 MHz.
OFDM used in DSL and digital broadcasting (DAB, DVB-T)
IEEE 802.16e adopts OFDMA for broadband wireless access
3GPP Release 8 specifies OFDMA for LTE downlink
First commercial LTE networks launch in Scandinavia
OFDM remains fundamental to 4G LTE and 5G NR evolution
The core principle of OFDM is orthogonality between subcarriers. In LTE, subcarrier spacing is carefully chosen to ensure that the peak of one subcarrier's spectrum coincides with the nulls of all other subcarriers, eliminating inter-carrier interference (ICI).
Orthogonality Condition:
Δf = 1/Tu
Where:
An OFDM signal is the sum of N orthogonal subcarriers, each modulated by complex data symbols. The baseband representation for the LTE downlink is:
s(t) = Σk=0N-1 Xk · ej2πkΔft, 0 ≤ t ≤ Ts
Where:
LTE uses a Cyclic Prefix to maintain orthogonality in multipath channels. The CP is a copy of the end of the OFDM symbol appended to the beginning, converting linear convolution with the channel to circular convolution.
■ Cyclic Prefix (CP) ■ Useful Symbol (Tu = 66.67 μs)
One of LTE's key features is bandwidth scalability, achieved by varying the number of subcarriers while maintaining constant 15 kHz spacing and symbol duration.
| Bandwidth (MHz) | Resource Blocks (RB) | Subcarriers (N) | FFT Size | Sample Rate (MHz) |
|---|---|---|---|---|
| 1.4 | 6 | 72 | 128 | 1.92 |
| 3 | 15 | 180 | 256 | 3.84 |
| 5 | 25 | 300 | 512 | 7.68 |
| 10 | 50 | 600 | 1024 | 15.36 |
| 15 | 75 | 900 | 1536 | 23.04 |
| 20 | 100 | 1200 | 2048 | 30.72 |
While the downlink uses OFDMA, the LTE uplink uses Single-Carrier FDMA (SC-FDMA) to reduce Peak-to-Average Power Ratio (PAPR) and improve power amplifier efficiency in mobile devices.
Overlapping but orthogonal subcarriers maximize bandwidth utilization. LTE achieves up to 5 bps/Hz with 64-QAM and MIMO.
The cyclic prefix converts multipath channel into parallel flat-fading channels, eliminating complex time-domain equalization.
Scalable from 1.4 MHz to 20 MHz using same fundamental parameters, enabling deployment in various spectrum allocations.
Channel coding across subcarriers provides inherent frequency diversity. Frequency-selective scheduling exploits CSI.
OFDM facilitates straightforward implementation of spatial multiplexing (up to 4×4 in LTE) and beamforming.
IFFT/FFT implementation is computationally efficient. Channel equalization reduces to simple scalar division per subcarrier.
Spectral Efficiency Calculation:
η = (Nused/NFFT) × (Tu/Ts) × log2(M) × r × NMIMO
Where M = modulation order, r = code rate, NMIMO = spatial streams
Example: 20 MHz, 64-QAM (6 bps), r=0.93, 2×2 MIMO → ~15 bps/Hz peak
OFDM signals exhibit high PAPR due to the superposition of multiple subcarriers, causing occasional constructive interference.
Doppler shift and oscillator inaccuracies destroy subcarrier orthogonality, causing Inter-Carrier Interference (ICI).
Doppler Shift Requirement:
fd << Δf/10
For LTE (Δf = 15 kHz): Maximum Doppler ~1.5 kHz
At 2.6 GHz: Supports mobile speeds up to ~500 km/h
OFDM is sensitive to timing and frequency synchronization errors.
| Parameter | Requirement | LTE Mechanism |
|---|---|---|
| Frequency Offset | < 2% of subcarrier spacing | Auto-correlation (PSS) + tracking |
| Timing Offset | Within CP duration | Cross-correlation (PSS/SSS) |
| Sampling Clock | < 0.1 ppm error | Reference signals tracking |
OFDM has relatively high spectral sidelobes (-13 dB first sidelobe) that can interfere with adjacent channels.
Single-Carrier FDMA (SC-FDMA) was selected for the LTE uplink to address the high PAPR of conventional OFDM, which is critical for mobile device battery life.
SC-FDMA can be implemented using DFT-spread OFDM (DFT-s-OFDM), where a DFT precoding step is applied before the IFFT:
DFT-spread OFDM:
1. DFT: Transform time-domain symbols to frequency domain
2. Subcarrier Mapping: Map DFT outputs to OFDM subcarriers
3. IFFT: Convert to time-domain OFDM signal
4. CP Insertion: Add cyclic prefix
| Mode | Description | Advantages | Use Case |
|---|---|---|---|
| Localized FDMA (LFDMA) | DFT outputs mapped to contiguous subcarriers | Channel-dependent scheduling, frequency diversity | Default LTE mode |
| Distributed FDMA (DFDMA) | DFT outputs mapped to equally spaced subcarriers | Maximum frequency diversity | High mobility scenarios |
While SC-FDMA reduces PAPR by 3-4 dB compared to OFDMA, it introduces some trade-offs:
| Feature | LTE (OFDM) | WCDMA (3G) | 5G NR |
|---|---|---|---|
| Multiple Access | OFDMA/SC-FDMA | CDMA | OFDMA/SC-FDMA + DFT-s-OFDM |
| Subcarrier Spacing | 15 kHz (fixed) | N/A (1.25 MHz carriers) | 15, 30, 60, 120 kHz (scalable) |
| Frame Structure | 10 ms frame, 1 ms subframe | 10 ms frame, variable slots | 10 ms frame, flexible slots |
| CP Overhead | ~7% (normal) | Rake receiver (no CP) | ~7% (configurable) |