How is an OFDM symbol built from subcarriers?

You map your modulated data symbols (QPSK, 16QAM, etc.) onto the active subcarriers in the frequency domain, then take an IFFT of size N to produce the time-domain samples. The orthogonal subcarriers are spaced 1/T apart so they do not interfere, and a cyclic prefix is prepended before transmission. The generator does exactly this and plots the resulting waveform.

Why is a cyclic prefix needed?

The CP copies the tail of the symbol to its front, creating a guard interval that absorbs multipath delay spread. As long as the channel delay stays shorter than the CP, inter-symbol interference is avoided and each subcarrier stays orthogonal at the receiver. Longer CP gives more delay-spread protection but costs throughput, which is why NR offers normal and extended CP.

How does FFT size relate to subcarriers and bandwidth?

The FFT size N sets how many subcarrier bins exist; only a subset carries data while the rest are guard/null subcarriers at the band edges and DC. Occupied subcarriers × subcarrier spacing gives the occupied bandwidth, and N × spacing gives the sample rate. Bigger N supports more subcarriers and wider bandwidth at the cost of more computation.

OFDM Signal Generator

Pick an FFT size, cyclic-prefix type, subcarrier spacing and modulation, then see the OFDM waveform in three views: the constellation, a time-domain trace and the frequency spectrum. All math runs locally in your browser.

FFT size

Subcarrier spacing

CP type

Modulation

Used subcarriers (≤ FFT)

e.g. 600 for 10 MHz LTE @ 15 kHz.

Symbols to render (1–4)

2 symbol(s)

Useful symbol Tu

66.67 μs

Sample rate fs

30.72 MHz

CP (sym 1)

5.21 μs

CP (sym 2–7)

4.69 μs

Ts total (typical)

71.35 μs

Ts first symbol

71.88 μs

Subcarrier BW

15 kHz

Null subcarriers

1448

At 15 kHz SCS with FFT=2048, one OFDM symbol carries 600 active subcarriers (29.3% occupancy) and occupies 71.35 μs including the cyclic prefix.

Constellation — 16QAM

Time-domain waveform (2 symbols)

Frequency-domain (FFT=2048, used=600)

About OFDM

Orthogonal Frequency Division Multiplexing splits a wide channel into many narrow, mutually orthogonal subcarriers. Each subcarrier carries a modulation symbol (QPSK, 16QAM, 64QAM, 256QAM) taken from a complex-plane constellation. An inverse FFT of size N turns those N frequency-domain complex samples into N time-domain samples which are transmitted one after the other as one OFDM symbol. The sample rate is fs = N × Δf, and the useful symbol duration is Tu = 1 / Δf.

A cyclic prefix (CP) — a copy of the tail of the symbol appended to the front — is added before transmission to absorb inter-symbol interference from multipath. In LTE and 5G NR the normal CP uses 160 samples (≈5.2 μs at 15 kHz) on the first symbol of a slot and 144 samples (≈4.7 μs) on the others, so that the seven-symbol block aligns exactly with a 0.5 ms half-subframe.

What this tool shows

The constellation view draws the ideal QPSK / 16QAM / 64QAM / 256QAM decision points. The time-domain plot simulates a real OFDM symbol by summing twenty randomly-phased sinusoids at evenly-spaced subcarrier frequencies — the resulting Gaussian-like envelope is the hallmark of OFDM and the reason for its high PAPR. The frequency-domain plot shows how used subcarriers are filled inside the FFT bin, with the DC bin notched as is standard in 3GPP and LTE air-interface designs.

Related tools

How to use the OFDM Signal Generator

Set the FFT size. Choose N (e.g. 128, 256, 1024), which fixes the number of subcarrier bins.
Choose active subcarriers. Decide how many subcarriers carry data versus null guard bins.
Pick modulation. Select QPSK, 16QAM or 64QAM to map bits onto each subcarrier.
Set the CP length. Choose the cyclic-prefix length to model the guard interval.
Generate and inspect. Run the IFFT and view the time-domain waveform and spectrum.

Frequently asked questions

How is an OFDM symbol built from subcarriers?: You map your modulated data symbols (QPSK, 16QAM, etc.) onto the active subcarriers in the frequency domain, then take an IFFT of size N to produce the time-domain samples. The orthogonal subcarriers are spaced 1/T apart so they do not interfere, and a cyclic prefix is prepended before transmission. The generator does exactly this and plots the resulting waveform.
Why is a cyclic prefix needed?: The CP copies the tail of the symbol to its front, creating a guard interval that absorbs multipath delay spread. As long as the channel delay stays shorter than the CP, inter-symbol interference is avoided and each subcarrier stays orthogonal at the receiver. Longer CP gives more delay-spread protection but costs throughput, which is why NR offers normal and extended CP.
How does FFT size relate to subcarriers and bandwidth?: The FFT size N sets how many subcarrier bins exist; only a subset carries data while the rest are guard/null subcarriers at the band edges and DC. Occupied subcarriers × subcarrier spacing gives the occupied bandwidth, and N × spacing gives the sample rate. Bigger N supports more subcarriers and wider bandwidth at the cost of more computation.

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