DFT-s-OFDM(DFT spread OFDM)

You would know of SC-OFDM because this is the waveform that we use in current LTE. If you are familiar with SC-FDMA, you can easily understand DFT-s-OFDM(Discrete Fourier Transform spread Orthogonal Frequency Division Multiplexing) . High level view of DFT-s-OFDM waveform generation is illustrated as follows. You would notice that this is almost same as high level SC-OFDM process.

• Key Characteristics of DFT-s-OFDM
• Why does the DFT step lower the PAPR?
• What does DFT-s-OFDM cost, and why is CP-OFDM still the default?
• Where is DFT-s-OFDM used in 5G NR?
• Reference

The chain below has five blocks, and only one of them is new. Serial to parallel conversion takes the modulated symbol stream and groups it into blocks of K symbols. The K-point DFT then spreads each block across K frequency-domain values, and that is the block drawn in green. Subcarrier allocation places those K values on the K subcarriers the scheduler granted. It leaves the remaining subcarriers of the M-point grid at zero. The M-point IFFT converts the whole grid back to the time domain, and parallel to serial conversion produces the sample stream that is transmitted. Remove the green block and what remains is CP-OFDM.

Figure 1. The DFT-s-OFDM transmitter. Only the K-point DFT separates it from CP-OFDM, and every property discussed below follows from that one block.

Below is the breakdown and brief description of each of the blocks

• Serial to Parallel Conversion:
• The input data stream (usually modulated symbols such as QPSK, 16-QAM, or 64-QAM) is split into multiple parallel streams.
• This step organizes the data to be processed simultaneously.
• DFT (K-point):
• A K-point Discrete Fourier Transform is applied to the input symbols.
• This step spreads the input symbols across the frequency domain.
• This operation is what gives DFT-s-OFDM its "single-carrier-like" properties because it creates a frequency-domain representation of the signal while retaining low PAPR characteristics.
• Subcarrier Allocation:
• The DFT output is mapped onto a subset of the available subcarriers in the frequency domain.
• The unused subcarriers remain empty (zero-padding) to fit the desired bandwidth and avoid interference.
• This ensures efficient spectral usage and helps in uplink resource allocation.
• IFFT (M-point):
• An Inverse Fast Fourier Transform (IFFT) is applied to the mapped subcarriers, converting the signal back to the time domain.
• This creates the OFDM waveform that is transmitted over the air.
• Here, M is typically larger than K, as only a subset of the subcarriers are occupied.
• Parallel to Serial Conversion:
• The parallel time-domain samples are converted back into a single serial data stream for transmission.

Key Characteristics of DFT-s-OFDM:

DFT-s-OFDM combines the benefits of both single-carrier and multi-carrier techniques. This hybrid approach leverages the efficiency and flexibility of OFDM while addressing its limitations, such as high Peak-to-Average Power Ratio (PAPR), through the integration of a Discrete Fourier Transform (DFT) step. By preserving single-carrier-like characteristics and enabling efficient resource allocation, DFT-s-OFDM ensures optimal performance in power-constrained mobile devices. Additionally, its inherent robustness to multipath fading makes it well-suited for maintaining reliable communication in diverse and dynamic wireless environments.

• Low PAPR:
• Compared to standard OFDM, DFT-s-OFDM has a lower Peak-to-Average Power Ratio, which is crucial for efficient power amplifier operation in the uplink.
• Single-Carrier-like Behavior:
• The DFT step introduces frequency-domain spreading, making the transmitted signal behave similarly to single-carrier transmission, which is beneficial for uplink transmission where mobile devices have limited power.
• Efficient Resource Utilization:
• The subcarrier allocation step allows flexible and efficient assignment of frequency resources, making DFT-s-OFDM ideal for LTE’s uplink scheduling.
• Robustness to Multipath:
• Like standard OFDM, DFT-s-OFDM provides robustness against multipath fading, as the IFFT converts the signal to the time domain while maintaining orthogonality between subcarriers.

Why does the DFT step lower the PAPR?

The section above states the low PAPR several times and never says why. I found that harder than the mathematics, because it makes low PAPR sound like a property the DFT simply has. It is a consequence, and the reason is short enough to state here.

Start with CP-OFDM. Each modulation symbol drives one subcarrier, and the transmitted signal is the sum of M independently modulated carriers. A sum of many independent terms tends towards a complex Gaussian. Its envelope therefore shows occasional large peaks, and the peak grows with M. That is the PAPR problem, and it belongs to the summation rather than to the modulation.

Now add the DFT. The K-point DFT is applied to the K modulation symbols before they are mapped to subcarriers. Each symbol is therefore spread across all K allocated subcarriers, instead of sitting on one. The M-point IFFT that follows then largely undoes that spreading. What leaves the transmitter is close to the original serial symbol stream, interpolated onto the wider bandwidth and filtered.

Figure 2. The DFT and the IFFT nearly cancel each other. That is the whole mechanism, and the low PAPR is its consequence.

The consequence follows directly. The envelope statistics are those of the modulation constellation, and not those of a Gaussian sum. Therefore the PAPR depends on the modulation order rather than on the number of subcarriers. QPSK gives a lower PAPR than 16-QAM, and pi/2-BPSK gives a lower PAPR than QPSK. That is why pi/2-BPSK exists in NR only when transform precoding is enabled.

• The peaks are produced by summation, not by OFDM as such : Adding many independently modulated carriers produces a near-Gaussian envelope. The number of carriers sets the peak, and the constellation barely matters.
• The DFT and the IFFT nearly cancel : The DFT spreads each symbol over the allocation and the IFFT gathers it back. The transmitted waveform is therefore close to the serial symbol stream it started as.
• PAPR then follows the constellation : This is the reason pi/2-BPSK is only defined with transform precoding. Rotating every second symbol by 90 degrees keeps the trajectory away from the origin, which lowers the envelope variation further.
• Coverage is what the dB buys : A power amplifier has to back off by roughly the PAPR to stay linear. A lower PAPR lets a power-limited UE transmit at a higher mean power, and that converts directly into uplink range.
• The cancellation is not exact : M is larger than K, so the signal is interpolated and pulse shaped. That residual is what keeps the PAPR above the value an ideal single-carrier signal would have.

What does DFT-s-OFDM cost, and why is CP-OFDM still the default?

If DFT-s-OFDM only lowered the PAPR, NR would use it everywhere on the uplink. It does not. CP-OFDM is the default, and DFT-s-OFDM is the exception that has to be configured. The spreading that produces the low PAPR is also what creates every restriction below.

< DFT-s-OFDM against CP-OFDM in the NR uplink >

Each row below is a direct consequence of the DFT. Spreading a symbol over the whole allocation only works if the allocation is one contiguous block. It also has to be a size for which the DFT is cheap to compute. Finally, it works for one layer only, because two spread layers would not separate at the receiver.

The restriction that matters most is not in the table. It is what the spreading does at the receiver. Every modulation symbol is carried on every subcarrier of the allocation, so the receiver has to equalise the channel and then de-spread. A deep fade on part of the allocation therefore raises the noise on every symbol in the block. CP-OFDM has no such coupling. There a faded subcarrier damages only the bits carried on it, and the channel code recovers them from the rest.

That difference decides where each waveform wins. DFT-s-OFDM wins when the UE is power limited, which is at the cell edge. CP-OFDM wins when the UE has power to spare and the channel is frequency selective, which is most of the cell. Neither is better in general, and that is why NR specifies both.

• One layer only : Transform precoding supports a single layer, so uplink spatial multiplexing is unavailable while it is enabled.
• The scheduler loses freedom : The allocation has to be contiguous, and the PRB count is restricted to products of 2, 3 and 5. Frequency-selective scheduling inside the allocation is not possible either.
• Noise enhancement is the real cost : The spreading couples every symbol to every subcarrier, so one deep fade degrades the whole block. This is the part the multipath bullet above does not cover.
• It is an uplink waveform : NR never applies transform precoding in the downlink. A gNB is not power limited, so it has nothing to gain from the trade.
• The two waveforms are not ranked : The network chooses per channel and per configuration, and the right choice depends on where the UE is.

Where is DFT-s-OFDM used in 5G NR?

DFT-s-OFDM is not a mode the UE selects. The network configures it, and it configures it separately for each uplink channel. You will see it described as the NR uplink waveform, and that overstates it. CP-OFDM is the default, and DFT-s-OFDM is enabled where the link budget needs it.

For PUSCH the switch is the RRC parameter transformPrecoder. It appears in PUSCH-Config for a dynamic grant, and in ConfiguredGrantConfig for a configured grant. Both are per bandwidth part. When it is enabled, every restriction in the table above applies to that PUSCH.

Msg3 is configured separately, because the UE has no dedicated configuration at that point. RACH-ConfigCommon carries msg3-transformPrecoder, and the UE reads it from SIB1. That placement is deliberate. Msg3 is transmitted by a UE that has only just reached the cell, so it is exactly the case where the link budget is worst.

PUCCH is not configurable in the same way. Formats 3 and 4 always use DFT-s-OFDM, and format 2 always uses CP-OFDM. The choice is fixed in the format definition rather than in RRC.

• transformPrecoder is the switch for PUSCH : It is configured per bandwidth part, in PUSCH-Config or in ConfiguredGrantConfig.
• Msg3 has its own switch in SIB1 : msg3-transformPrecoder sits in RACH-ConfigCommon, because a UE performing random access has no dedicated configuration to read.
• PUCCH formats 3 and 4 are always DFT-s-OFDM : Those two carry the larger uplink control payloads, and they are the formats a cell-edge UE depends on.
• pi/2-BPSK depends on it : tp-pi2BPSK only has meaning when transform precoding is enabled, and it lowers the PAPR further on the smallest allocations.
• The MCS table changes as well : PUSCH with transform precoding uses its own MCS index table, shown here. The modulation order for the lowest indices depends on whether pi/2-BPSK is configured.

Reference

[1]  Frequency-Domain Equalization and Single-Carrier Transmission in OFDM Framework by Markku Renfors

[2] 3GPP TS 38.211 : NR; Physical channels and modulation

[3] 3GPP TS 38.214 : NR; Physical layer procedures for data