Glossary term

Subcarrier Spacing

Engineering definition of OFDM subcarrier spacing covering FFT sample rate, useful symbol time, occupied bandwidth, CFO normalization and validation tradeoffs.

Branch: Telecommunications Engineering
Glossary type: quantity
Content: Glossary term
Updated: Jun 26, 2026
Revision: v1.0.0 · reviewed

Definition

quantity

Subcarrier spacing is the frequency separation between adjacent OFDM subcarriers.

Subcarrier spacing, often written as Delta f, sets the useful OFDM symbol time, occupied bandwidth for a given number of active subcarriers, and sensitivity to residual carrier frequency offset and Doppler shift. Smaller spacing gives longer useful symbols and can help delay-spread efficiency, but it is more sensitive to frequency offset and phase drift. Larger spacing shortens symbols and improves mobility tolerance, but can increase guard-interval pressure for the same channel delay spread.

Subcarrier spacing is the frequency separation between adjacent OFDM subcarriers. It is often written as Delta f. In an OFDM waveform, subcarrier spacing is not only a frequency-grid parameter; it also sets useful symbol time, bandwidth scaling and sensitivity to frequency offset.

Choosing subcarrier spacing is a tradeoff. Narrow spacing gives longer useful symbols and can make a cyclic prefix more efficient. Wide spacing gives shorter symbols and usually improves tolerance to residual carrier frequency offset, Doppler shift and phase drift.

FFT Relationship

For sample rate f_s and FFT size N_FFT:

\displaystyle \Delta f=\frac{f_s}{N_{FFT}}

where:

Delta f is subcarrier spacing;
f_s is sampling rate;
N_FFT is FFT length.

This relationship assumes the usual OFDM frequency grid. Implementation details such as oversampling, guard bands and inactive tones still need to be handled separately.

Useful Symbol Time

Useful OFDM symbol time is the reciprocal of subcarrier spacing:

\displaystyle T_u=\frac{1}{\Delta f}

The total symbol time also includes cyclic prefix:

T_s=T_u+T_{cp}

Wider subcarrier spacing shortens T_u. For the same absolute cyclic-prefix duration, that changes time efficiency and delay-spread margin.

Occupied Bandwidth

If N_occ subcarriers are occupied, a first-pass occupied-bandwidth screen is:

B_{occ}\approx N_{occ}\Delta f

Actual emission bandwidth also depends on guard subcarriers, windowing, filtering, spectral mask, measurement bandwidth and resource allocation.

Frequency-Offset Normalization

Residual carrier frequency offset is often normalized by subcarrier spacing:

\displaystyle \epsilon=\frac{\Delta f_{err}}{\Delta f_{sc}}

where epsilon is normalized frequency offset. A larger epsilon means stronger risk of inter-carrier interference and constellation rotation. For the same absolute offset, narrower subcarrier spacing produces a larger normalized error.

A simple margin is:

M_\epsilon=\epsilon_{limit}-|\epsilon|

The limit depends on waveform, pilot design, tracking loop, modulation order, EVM target and channel conditions.

Worked Example

An OFDM receiver uses:

f_s=30.72\ \text{MHz}

and:

N_{FFT}=2048

Subcarrier spacing is:

\displaystyle \Delta f=\frac{30.72\times10^6}{2048}=15.0\ \text{kHz}

Useful symbol time is:

\displaystyle T_u=\frac{1}{15000}=66.7\ \mu\text{s}

If:

N_{occ}=1200

then:

B_{occ}\approx1200(15.0\ \text{kHz})=18.0\ \text{MHz}

Suppose residual carrier frequency offset after tracking is:

\Delta f_{err}=180\ \text{Hz}

The normalized offset is:

\displaystyle \epsilon=\frac{180}{15000}=0.012

If the release limit is:

\epsilon_{limit}=0.020

then:

M_\epsilon=0.020-0.012=0.008

The mode passes this frequency-offset screen.

If the same residual offset were used with 7.5 kHz subcarrier spacing:

\displaystyle \epsilon=\frac{180}{7500}=0.024

and:

M_\epsilon=0.020-0.024=-0.004

The narrower spacing would fail the same normalized-offset screen, even though it would double useful symbol time.

Engineering Interpretation

Subcarrier spacing links frequency planning and time-domain behavior. A narrow grid can be attractive for long delay spread, but it is less forgiving of oscillator error, Doppler and phase tracking. A wide grid can help mobility and frequency-offset tolerance, but it shortens useful symbols and may require different cyclic-prefix choices.

This is why OFDM numerology should be validated with channel impulse response, residual frequency offset, phase-noise behavior, EVM, BER, packet errors and throughput evidence.

The value also affects how engineers discuss the resource grid. Two systems can occupy similar bandwidth while using different spacing, FFT size and active-subcarrier count. Those systems may have different latency, pilot density, tracking-loop burden, guard-band shape and scheduler granularity, so the spacing must be stated with the full waveform boundary.

Common Mistakes

Do not choose subcarrier spacing only from occupied bandwidth. The same bandwidth can be achieved with different FFT sizes and active-tone counts, but the receiver timing and frequency-offset behavior can be very different.

Do not compare CFO in hertz without normalizing it to subcarrier spacing. A residual 180 Hz offset is small for 30 kHz spacing but more serious for 7.5 kHz spacing.

Validation Evidence

A defensible subcarrier-spacing decision should state:

sample rate and FFT size;
active subcarrier count and occupied bandwidth;
useful symbol time and cyclic-prefix duration;
expected oscillator error and residual CFO;
Doppler range and mobility condition;
EVM, BER and packet-error behavior;
channel-estimation and tracking-loop assumptions;
measurement uncertainty and release limit.

With those details, subcarrier spacing becomes a controlled waveform parameter rather than a hidden numerology choice.

REF

Disciplines