NR Waveforms: CP-OFDM & DFT-s-OFDM
Why 5G uses CP-OFDM downlink and optional DFT-s-OFDM uplink, and what changed from LTE.
5G sends bits over the air as OFDM: instead of one fast stream on a wide channel, it splits the band into hundreds of thin, orthogonal subcarriers, each carrying a slow, easy-to-equalize stream. The downlink always uses plain CP-OFDM; the uplink uses CP-OFDM by default but can switch to DFT-s-OFDM when a phone needs to shout further with a cleaner power amplifier. That one choice — transform precoding on or off — is most of what separates the two 5G waveforms, and both are defined in TS 38.211.
Introduction
The waveform is the physical shape of the signal that leaves the antenna — the very bottom of the protocol stack, below channels, below modulation, below coding. Every PDSCH symbol, every PUSCH grant, every SSB is ultimately a sum of subcarriers carried by an OFDM waveform. Before a UE can decode anything, its receiver must assume the same waveform structure the transmitter used, so the waveform is the one thing both ends agree on before any higher-layer configuration exists.
NR standardises exactly two waveforms, both cyclic-prefix OFDM at heart: CP-OFDM (the baseline, used on all downlink physical channels and as the uplink default) and DFT-s-OFDM (a transform-precoded, single-carrier-like variant available only on the uplink). Which one the uplink uses is not fixed — it is chosen per UE by RRC and applies from the very first scheduled transmission (Msg3) onward, so the same handset can run CP-OFDM at the cell centre and DFT-s-OFDM at the edge in the same session.
This page builds up from why OFDM is used at all, through the cyclic prefix and its exact timing maths, to the transform-precoding block that turns CP-OFDM into DFT-s-OFDM, and finally to the peak-to-average-power argument that decides which waveform a UE should use and when. Everything here is anchored in TS 38.211 (physical channels and modulation), with the per-UE waveform selection signalled by the RRC IEs called out along the way.
On this page
Why OFDM is needed
In plain words: imagine trying to have one loud, fast conversation across a large echoey hall — the echoes of each word smear into the next and nobody can follow you. OFDM instead splits your message among a hundred people each speaking slowly and at a slightly different pitch (frequency). Each slow voice is easy to hear clearly even with echoes, and because the pitches are carefully spaced they never drown each other out. Many slow, narrow streams beat one fast, wide one when the room echoes.
A wideband radio channel is frequency-selective: reflections make some frequencies fade while others stay strong, so a single wide, fast signal smears across time as inter-symbol interference (ISI) and demands a brutally complex equalizer. The deeper the delay spread, the longer the smear. OFDM sidesteps this entirely by dividing the band into many narrow subcarriers, each so thin that the channel looks essentially flat across it.
OFDM (Orthogonal Frequency Division Multiplexing) transmits data in parallel over many orthogonal subcarriers. "Orthogonal" means the spacing is chosen so that at each subcarrier's spectral peak, every other subcarrier is exactly zero — they overlap yet do not interfere. Each subcarrier is a sinc in frequency, and the sinc nulls land precisely on the neighbouring subcarrier centres.
Because each subcarrier is narrow, the channel is flat across it, so a single complex multiply per subcarrier undoes the channel — a trivial one-tap equalizer instead of a long time-domain filter. The signal also maps naturally onto a two-dimensional time/frequency resource grid the scheduler can carve up per user, per beam, per slot.
Data symbols are placed on subcarriers in the frequency domain, then an IFFT builds the time-domain waveform. A cyclic prefix is prepended to each symbol. The receiver strips the CP, runs an FFT, and reads each subcarrier straight back — turning a hard convolutional channel into simple per-subcarrier division.
Orthogonality is exact only when the subcarrier spacing Δf is the reciprocal of the useful symbol duration Tu, i.e. Δf = 1/Tu. NR fixes the reference spacing at 15 kHz (so Tu ≈ 66.7 μs at μ = 0) and scales it in powers of two as Δf = 15 × 2μ kHz for numerology μ = 0…4 (15/30/60/120/240 kHz). Any frequency error or timing drift that breaks the Δf = 1/Tu relationship reappears as inter-carrier interference (ICI) — which is exactly why wider spacings are favoured at high carrier frequencies where oscillator phase noise is worse.
The alternative — a single wideband carrier — forces the receiver to resolve and combine dozens of multipath taps with an adaptive time-domain equalizer whose complexity grows with bandwidth. At 100 MHz of channel that is impractical. OFDM converts one impossibly hard equalization problem into thousands of trivial ones, which is precisely why every modern broadband air interface (LTE, Wi-Fi, DVB, 5G NR) is built on it.
The core intuition: narrow subcarriers → per-subcarrier flat fading → equalization becomes one complex division per subcarrier. That single idea is why OFDM beats single-carrier transmission at wide bandwidths.
CP-OFDM: subcarriers and orthogonality
CP-OFDM is the baseline NR waveform: modulation symbols (QPSK, 16-QAM, 64-QAM, up to 256-QAM) are mapped directly onto subcarriers, an IFFT synthesizes the time waveform, and a cyclic prefix is prepended. It is used on every downlink channel (PDSCH, PDCCH, PBCH) and is the default uplink waveform for PUSCH and PUCCH.
A multicarrier waveform where each active subcarrier independently carries one modulation symbol per OFDM symbol. Orthogonality is guaranteed by choosing the subcarrier spacing Δf equal to the reciprocal of the useful symbol duration, so the IFFT/FFT pair is a perfect, lossless transform.
Direct subcarrier mapping keeps the transmitter simple and, crucially, lets different subcarriers (or subcarrier groups) carry independent spatial layers. That is what enables MIMO spatial multiplexing, frequency-selective scheduling, and multi-user MIMO — the capacity engines of 5G.
The frequency-domain symbols fill an IFFT of size NFFT; unused subcarriers (guard band and DC handling) are set to zero. The output is the time-domain sample block, and a CP is copied from its tail. The receiver reverses this exactly: remove CP, FFT, per-subcarrier equalize, demap.
The modulation applied to each subcarrier is the QAM order chosen by the MCS: QPSK (2 bits/symbol), 16-QAM (4), 64-QAM (6) and 256-QAM (8), with Rel-17 adding 1024-QAM (10 bits/symbol) for FR1 downlink under very good SINR. The scheduler addresses the grid in resource blocks of 12 subcarriers each; a carrier holds up to 275 RBs per numerology, i.e. at most 3300 active subcarriers, and the IFFT size NFFT is chosen larger than that (a power of two — e.g. 4096) with the surplus subcarriers zeroed as guard band and DC handling.
Because subcarriers are addressed individually, CP-OFDM gives the scheduler its finest tool: it can hand different resource blocks to different users, place a layer only where the channel is strong, and pack many streams onto the same time-frequency tile via spatial precoding. The price is a high peak-to-average power ratio (PAPR) — because hundreds of subcarriers can add constructively at one instant, the time waveform has large, spiky peaks. On the downlink that hardly matters; a base station has ample power headroom. On the uplink, where the handset PA is the bottleneck, it is exactly the problem the second waveform solves.
Spec anchor: both waveforms, the numerologies, and the CP structure are specified in TS 38.211. The choice of uplink waveform per UE is signalled by RRC/DCI as described below.
The cyclic prefix and CP maths
The cyclic prefix is the unsung hero of OFDM. Multipath means a symbol arrives several times, slightly delayed, and those echoes bleed into the following symbol. The cyclic prefix (CP) is a copy of the tail of the OFDM symbol pasted onto its front, acting as a disposable guard interval.
A guard interval at the start of each OFDM symbol containing a copy of the symbol's last samples. NR defines a normal CP (used almost everywhere) and an extended CP (only for 60 kHz spacing, for very high delay-spread or MBMS-like scenarios).
Two jobs. First, it absorbs multipath delay spread so echoes land inside the guard and never corrupt the next symbol — killing ISI. Second, by making each symbol look periodic, it turns the channel's linear convolution into circular convolution, which is exactly what lets the FFT diagonalize the channel into one complex tap per subcarrier.
As long as the CP is longer than the channel's delay spread, the receiver discards the CP samples and the remaining window holds only clean, self-contained symbol energy. The cost is overhead — CP samples carry no new data, so a longer CP means lower spectral efficiency.
The CP length is not arbitrary; TS 38.211 fixes it in units of the basic sample time Tc, tied to the numerology index μ. The useful (IFFT) part is always 2048 samples scaled by the numerology, and the normal CP is 144 of those same units — with a small top-up on the first symbol of each half-subframe so the symbols tile neatly into the 0.5 ms boundary.
useful part Nu = 2048 × κ × 2−μ
normal CP NCP = 144 × κ × 2−μ (+ 16κ on the first symbol of each half-subframe)
extended CP NCP = 512 × κ × 2−μ (μ = 2 / 60 kHz only)
so in time TCP ≈ 4.69 μs / 2μ (normal CP, ignoring the first-symbol top-up)
A few consequences fall straight out of these numbers. The normal-CP overhead is NCP/(Nu + NCP) = 144/2192 ≈ 6.6% for the regular symbols, edging up slightly on the top-up symbols — the same fractional overhead at every numerology, because both parts scale by the same 2−μ. The ~4.69 μs normal CP at 15 kHz corresponds to roughly 1.4 km of excess path delay, which is why 15 kHz suits large, delay-spread-heavy cells; at 120 kHz the ~0.59 μs CP tolerates only very short delay spread, matching FR2's small mmWave cells. The extended CP (60 kHz only) is ~4.17 μs — far longer than the 1.17 μs normal CP at the same spacing — which is what buys delay-spread robustness at the cost of dropping from 14 to 12 symbols per slot.
Everything scales inversely with spacing: double Δf and both the symbol and its CP halve. A wider spacing gives a shorter symbol and a shorter CP — good for high frequencies and low latency, but with less delay-spread tolerance. The table shows how the normal-CP duration collapses as numerology rises.
μ | Subcarrier spacing Δf | Useful symbol (approx) | Normal CP (approx) | Typical use |
|---|---|---|---|---|
| 0 | 15 kHz | 66.7 μs | 4.69 μs | FR1, wide coverage |
| 1 | 30 kHz | 33.3 μs | 2.34 μs | FR1 default (mid-band) |
| 2 | 60 kHz | 16.7 μs | 1.17 μs | FR1/FR2, extended CP option |
| 3 | 120 kHz | 8.33 μs | 0.59 μs | FR2 (mmWave) data |
| 4 | 240 kHz | 4.17 μs | 0.29 μs | FR2 SSB only |
The CP trade-off: longer CP = more delay-spread protection but more overhead; wider subcarrier spacing = shorter symbol and CP, more phase-noise robustness and lower latency, but less multipath tolerance. Numerology is the knob that balances these for each band.
DFT-s-OFDM: transform precoding and low PAPR
Both waveforms end in an IFFT and a cyclic prefix. The difference is one extra block at the transmitter for DFT-s-OFDM: a DFT (transform precoding) applied to the modulation symbols before they are mapped to subcarriers. That DFT spreads each data symbol across the whole allocation, so the emitted signal behaves like a filtered single carrier — which is what lowers its peak-to-average power ratio.
DFT-s-OFDM (DFT-spread-OFDM, also called SC-FDMA) is a transform-precoded single-carrier waveform carried inside an OFDM framework. An M-point DFT precodes the M modulation symbols, the result is mapped to M contiguous subcarriers, then the usual N-point IFFT and CP follow. NR calls turning this on transform precoding.
High PAPR forces the handset power amplifier to back off, wasting battery and range. DFT-s-OFDM's much lower PAPR lets the phone drive its PA closer to saturation, so it reaches further with better coverage at the cell edge — exactly where the uplink is weakest and link budget matters most.
The gNB enables it per-UE. Because each output subcarrier is now a linear combination of all input symbols, the waveform is a single stream: it is restricted to a single layer and a contiguous allocation. That loss of flexibility is the price paid for the lower PAPR.
The DFT size M is not free: because the M-point DFT and the block interleaving are implemented efficiently, NR constrains M (the number of allocated subcarriers, = 12 × the number of allocated RBs) to the form M = 2α2 × 3α3 × 5α5 — only products of the primes 2, 3 and 5 are allowed. That is why a DFT-s-OFDM grant of, say, 7 or 11 RBs is illegal while 6, 8, 9, 10, 12, 15 or 16 RBs are fine: the scheduler must pick an RB count whose subcarrier total factors as 2/3/5 only. On the receiver the gNB inserts an inverse M-point DFT after its FFT to undo the spreading before demodulation.
Note how little differs: strip out the DFT and you are left with CP-OFDM. That shared back-end is why NR can flip an individual UE between the two waveforms without redesigning the physical layer. On the receiver, the gNB simply inserts an inverse M-point DFT after its FFT to recover the symbols. One further trick lives here: at the extreme cell edge NR allows pi/2-BPSK with DFT-s-OFDM, whose phase-continuous constellation pushes PAPR down even further for the most power-starved links. DMRS handling also differs: with transform precoding enabled the DMRS itself is generated from low-PAPR Zadoff–Chu-based sequences rather than the QPSK-like DMRS of CP-OFDM, so the pilots keep the same single-carrier envelope as the data.
PAPR, waveform choice, and spectral shaping
Everything about the two-waveform design comes back to PAPR and the related cubic metric, a measure of how much a signal drives PA non-linearity. A CP-OFDM signal sums many independent subcarriers, so by the central limit theorem its envelope is nearly Gaussian with large, rare peaks — high PAPR. To transmit those peaks linearly, the PA must back off from saturation, and every dB of back-off is a dB of lost transmit power and coverage. DFT-s-OFDM's single-carrier-like envelope has markedly lower PAPR, so the same PA delivers more usable power. On the uplink that translates directly into cell-edge range and battery life.
Which waveform a UE uses is signalled explicitly. During random access, the Msg3 PUSCH follows msg3-transformPrecoder (an enabled/disabled enumeration) broadcast in RACH-ConfigCommon inside SIB1. For scheduled PUSCH thereafter, the field transformPrecoder in PUSCH-Config (and the fallback in PUSCH-ConfigCommon) selects enabled (DFT-s-OFDM) or disabled (CP-OFDM); when the field is absent the UE inherits the value from msg3-transformPrecoder. A UE near the cell centre with good SINR keeps transform precoding off to enjoy MIMO and flexible scheduling; a power-limited UE at the edge turns it on for coverage. Note the choice is made by the network, not the UE — the phone reports capability and headroom, but the gNB decides.
Subcarrier spacing interacts with the waveform choice too. DFT-s-OFDM is typically paired with the lower numerologies (15/30 kHz) that suit the wide-area, coverage-limited scenarios where it earns its keep, while the higher spacings (120 kHz) used in FR2 are dominated by CP-OFDM data with occasional DFT-s-OFDM for coverage. The waveform itself is spacing-agnostic — both ride the same 15 × 2μ kHz grid — but the deployment context usually pins down a sensible pairing.
A separate question is spectral containment: OFDM's rectangular time window produces sinc-shaped out-of-band leakage that must be suppressed to respect the adjacent-channel emission mask. NR handles this with windowing and filtering at the transmitter — techniques marketed as f-OFDM (filtered-OFDM) and W-OFDM (windowed-OFDM). Critically, these are implementation choices left to the vendor: they smooth the symbol edges or filter sub-bands so a narrow guard band suffices, but they do not change the over-the-air waveform definition. That is why NR standardizes only two waveforms — CP-OFDM and DFT-s-OFDM — and leaves windowing/filtering unspecified: any receiver can decode the signal regardless of how the transmitter shaped its spectrum, so interoperability is preserved while vendors compete on filter design.
Why only two waveforms: standardizing the transmit filter would freeze implementation and constrain future improvement. By defining only CP-OFDM and DFT-s-OFDM at the receiver-observable level, 3GPP keeps spectral shaping (f-OFDM/W-OFDM) as a vendor differentiator that never breaks interoperability.
At high carrier frequencies (FR2 and above), the oscillator's phase noise becomes significant relative to the wider subcarrier spacing and rotates the whole constellation (common phase error) plus adds inter-carrier interference. NR counters this with PT-RS (Phase-Tracking Reference Signal), sparse pilots interspersed in time that let the receiver track and correct the drifting phase. PT-RS density adapts to the scheduled MCS and bandwidth, and its pattern differs slightly between CP-OFDM and DFT-s-OFDM — but in both cases it is the mechanism that makes high-order modulation viable at mmWave.
| Property | CP-OFDM | DFT-s-OFDM |
|---|---|---|
| Transform precoding | No (symbols → subcarriers directly) | Yes (M-point DFT before mapping) |
| PAPR / cubic metric | Higher | Lower (single-carrier-like) |
| MIMO layers | Multiple (spatial multiplexing) | Single layer only |
| Allocation | Contiguous or non-contiguous | Contiguous only (RB count = 2a3b5c) |
| Scheduling / MU-MIMO flexibility | High | Lower |
| Extra low-PAPR modulation | — | pi/2-BPSK option |
| Signalled by | Default / transformPrecoder=disabled | msg3-transformPrecoder / transformPrecoder=enabled |
| Used in | Downlink (always); uplink default | Uplink only (optional) |
| Best for | Capacity, throughput, good SINR | Coverage, cell edge, power-limited UEs |
Why downlink never uses DFT-s-OFDM: the base station is not power-limited and wants MIMO capacity and flexible scheduling, so CP-OFDM is always the right trade. Only the battery-and-PA-limited uplink benefits from trading flexibility for coverage.
LTE ↔ NR: LTE hard-wired the waveform by direction — downlink was always CP-OFDM, uplink was always SC-FDMA (the LTE name for DFT-s-OFDM), with no per-UE choice. NR keeps CP-OFDM on the downlink but makes the uplink waveform configurable per UE via transformPrecoder, so a phone can run high-capacity CP-OFDM uplink at the cell centre and switch to DFT-s-OFDM only when it is power-limited. NR also adds the pi/2-BPSK low-PAPR option and the family of numerologies (15–240 kHz), where LTE was fixed at 15 kHz.
⚠ Common pitfalls / gotchas
- Requesting a DFT-s-OFDM allocation whose RB count does not factor as 2a×3b×5c (e.g. 7 or 11 RBs) — the grant is invalid because the M-point DFT size is constrained.
- Assuming DFT-s-OFDM supports MIMO spatial multiplexing — it is single-layer only, so no rank-2+ transmission and no non-contiguous allocation.
- Forgetting that when
transformPrecoderis absent inPUSCH-Config, the UE inherits the value frommsg3-transformPrecoder— a broadcast default, not a hard-coded one. - Confusing spectral shaping (f-OFDM/W-OFDM) with a distinct waveform — it is a vendor transmit-side technique that leaves the standardised waveform unchanged.
Summary
NR carries every bit on cyclic-prefix OFDM. On the downlink that is always plain CP-OFDM: symbols map straight onto subcarriers, the scheduler carves the grid per user and per layer, and the base station's power headroom makes the high PAPR a non-issue. The cyclic prefix — 144 units of the useful-symbol length, ~6.6% overhead, scaling by 2−μ with numerology — is what turns a nasty multipath convolution into a one-tap-per-subcarrier equalizer and defines how much delay spread (hence cell size) each spacing tolerates.
The uplink adds a second option. Insert one DFT (transform precoding) before subcarrier mapping and CP-OFDM becomes DFT-s-OFDM: a single-carrier-like waveform with much lower PAPR that lets a power-limited handset reach the cell edge, at the cost of single-layer, contiguous-only allocations sized to 2/3/5-factor RB counts. The gNB picks between them per UE with transformPrecoder (and msg3-transformPrecoder for Msg3): CP-OFDM for capacity in good coverage, DFT-s-OFDM for coverage when link budget is tight. Everything above — numerology, PT-RS at mmWave, vendor spectral shaping — hangs off these two receiver-observable waveforms defined in TS 38.211.
Quick Q&A
Q. Why does the uplink have two waveforms but the downlink only one?
A. The UE is power- and PA-limited, so at the cell edge the lower PAPR of DFT-s-OFDM buys real coverage. The gNB is not power-limited and prefers CP-OFDM's MIMO and scheduling flexibility, so downlink is always CP-OFDM.
Q. What is the cyclic prefix actually doing?
A. Two things: it absorbs multipath delay spread to prevent inter-symbol interference, and it makes the channel's linear convolution look circular so an FFT converts it into a one-tap-per-subcarrier equalizer. It works as long as the CP is longer than the delay spread.
Q. How is CP-OFDM turned into DFT-s-OFDM, and what does that buy you?
A. Add an M-point DFT (transform precoding) before the subcarrier mapping. It spreads each symbol across the allocation so the envelope looks single-carrier, lowering PAPR/cubic metric and improving uplink power efficiency and coverage.
Q. What is the main limitation of DFT-s-OFDM?
A. It is restricted to a single layer (no spatial multiplexing) and a contiguous allocation, and the RB count must factor into 2/3/5. You trade throughput and scheduling flexibility for lower PAPR and better coverage.
Q. How does a UE know which uplink waveform to use?
A. For Msg3 during random access it follows msg3-transformPrecoder; for scheduled PUSCH it follows transformPrecoder in PUSCH-Config. enabled means DFT-s-OFDM, disabled means CP-OFDM.
Q. Why does NR standardize only two waveforms when f-OFDM and W-OFDM exist?
A. Windowing and filtering are transmitter-side implementation choices for spectral containment that do not change the receiver-observable waveform. Leaving them unspecified preserves interoperability while letting vendors compete on filter design, so only CP-OFDM and DFT-s-OFDM are defined.
Where this fits
You now know how the bits become a waveform. See where that waveform lives in time, which uplink channel carries transform-precoded data, and how the high-band phase-noise pilots are placed.