Tailored OFDM: Enhanced Modulation Techniques

• Tailored OFDM is a modulation strategy that enhances conventional OFDM by integrating adaptive mapping, channel-aware modulation, and pulse shaping to boost spectral efficiency and resilience.
• Techniques like subcarrier power and number modulation embed extra information dimensions, achieving metrics such as doubled spectral efficiency and 2–4 dB coding gains.
• Advanced methods—such as AFDM, CT-OFDM, and UW-OFDM—optimize performance by reducing PAPR, achieving full diversity in mobile channels, and improving noise resilience through efficient redundancy.

Tailored orthogonal frequency division multiplexing (OFDM) refers to a class of modulation and signal processing strategies designed to enhance the baseline properties of conventional OFDM by introducing dimensions of adaptation, optimization, or structural changes specifically geared towards the requirements of emerging wireless scenarios, networks, and application demands. The term encompasses novel mapping domains (power, index, time-frequency-space), pulse designs, transform techniques, or prefix/coding modifications, all with the goal of attaining improvements such as higher spectral efficiency, resilience to time-frequency selectivity and Doppler, reduced computational complexity, optimized out-of-band emissions, or scenario-specific performance.

1. Enhanced Information Mapping Strategies

One principal approach in tailored OFDM is the multiplexing of additional information dimensions within the OFDM framework, beyond conventional symbol modulation:

• Subcarrier Power Modulation (OFDM-SPM):

OFDM-SPM increases spectral efficiency by modulating each subcarrier’s transmit power as a third dimension. Per (Hamamreh et al., 2020), an input bitstream is split such that each subcarrier carries one conventional symbol-bit and one independent power-bit. The subcarrier output is constructed as $X_i = \sqrt{P(b_{p,i})} s_i$, with $P(b_{p,i}) \in \{L^2E_s,\,H^2E_s\}$ selected according to the power-bit. Receiver detects symbol and power-bits via parallel non-coherent (power) and coherent (symbol) detectors. OFDM-SPM doubles spectral efficiency compared to classical BPSK OFDM and supports flexible energy allocation (power-saving or power-reallocation) policies.

• Subcarrier Number Modulation (OFDM-SNM):

As developed in (Dang et al., 2019), OFDM-SNM encodes information both in the number and position of active subcarriers within each OFDM symbol, alongside their modulation symbols. The enhanced version selects activation patterns via instantaneous channel state information (CSI), prioritizing subcarriers with strong channel gains, yielding significant coding gain and reliability improvement with minor complexity overhead.

2. Advanced Modulation Domains and Channel Adaptation

Several tailored OFDM designs operate by generalizing the underlying transformation domain or by applying channel-adaptive modulation:

• Affine Frequency Division Multiplexing (AFDM):

AFDM extends OFDM to doubly-selective channels via adaptive subcarrier waveforms—specifically, orthogonal chirped tones parameterized by two tunable constants $(c_1,c_2)$ (Yin et al., 7 Feb 2025). The time-domain signal is

$$x[n] = \sum_{m} X[m] \exp\left( j2\pi \left( c_1 n^2 + \frac{mn}{N} + c_2 m^2 \right) \right),$$

where $c_1$ and $c_2$ are selected to match the scenario's delay and Doppler spread. AFDM achieves full diversity in arbitrarily dispersive channels, fully mitigates inter-carrier interference, and subsumes OFDM as a special case.

• Orthogonal Time-Frequency Division Multiplexing (OTFDM):

OTFDM generalizes classical OFDM by employing a 2D time-frequency lattice and a dot-product channel model, enabling grid-free delay/Doppler handling and efficient 2D equalization (Ma et al., 2023). Each symbol is processed through a sequence of 1D transforms along time and Doppler axes, and the architecture supports single-CP operation with low-complexity dot-division or MMSE equalization, outperforming OFDM under high-mobility, doubly-selective channels.

3. Transform-Domain Processing and Complexity Reduction

Transform optimization serves as a key avenue for tailoring OFDM architectures:

• Complex-Transition Transform OFDM (CT-OFDM):

This approach introduces the complex-transition transform (CTT), combining the fast complex Walsh-Hadamard transform and FFT into a single unitary transform, implemented via the fast-complex transition (FCT) algorithm (Boussakta et al., 2023). CT-OFDM achieves notable reductions in peak-to-average power ratio (PAPR) and improved BER in multipath channels, with arithmetic complexity reduced compared to conventional FFT- or cascade-based OFDM systems.

• Hermitian-Symmetric Pulse Design for Spectral Shaping:

Modification of the base OFDM pulse to a Hermitian-symmetric structure whose window is centered in time yields a real Fourier spectrum (Giménez et al., 5 Nov 2025). This enables all spectral-shaping weights and boundary transitions to be real, thus reducing the number of real variables and multiplications needed by up to 50%, with no loss in out-of-band emission performance or PAPR. The framework applies to precoding, active interference cancellation, and adaptive symbol transition schemes.

4. Prefix Innovations, Coding, and Redundancy Integration

Prefix and coding innovations present another form of tailoring:

• Unique Word Prefix (UW-OFDM):

The classic cyclic prefix is replaced by a deterministic unique word, embedded inside the DFT interval (Huemer et al., 2010). This tailors the structure such that the arrangement of data and redundant subcarriers generates a complex-field Reed-Solomon code. The UW serves joint roles in synchronization and channel estimation. At the receiver, zero-forcing equalization is followed by Wiener smoothing that exploits subcarrier correlation for improved performance—demonstrating BER gains relative to CP-OFDM without loss of spectral efficiency.

5. Performance Characteristics and Numerical Validation

Tailored OFDM methods exhibit distinct improvements in spectral efficiency, reliability, complexity, and adaptability:

Tailored OFDM Scheme	Key Feature	Performance/Finding
OFDM-SPM (Hamamreh et al., 2020)	Subcarrier power modulation	Doubles spectral efficiency, BER closed-form, negligible complexity
Enhanced OFDM-SNM (Dang et al., 2019)	CSI-driven subcarrier activation	SNR coding gain 2–4 dB in slow Rayleigh fading, suited for IoT-MTC
AFDM (Yin et al., 7 Feb 2025)	Chirp-based, scenario-flexible	Full diversity, BER competitive with OTFS/ODCM, high mobility resilience
OTFDM (Ma et al., 2023)	2D time-frequency dot-product channel	BLER $2 \times 10^{-2}$ at 500 km/h, single CP, efficient equalization
CT-OFDM (Boussakta et al., 2023)	Unitary FCT-based transform	2–3 dB PAPR reduction, SNR gain 2–4 dB (BER), low complexity
Hermitian pulse OFDM (Giménez et al., 5 Nov 2025)	Real-coefficient spectral shaping	50% reduction in complexity, no performance degradation
UW-OFDM (Huemer et al., 2010)	RS-coded unique word prefix	BER gain, improved noise resilience, no spectral efficiency penalty

6. Design Guidelines and Implementation Considerations

Deployment of tailored OFDM schemes is context-dependent, requiring scenario-driven parameter selection and architectural modifications:

• Transform size and oversampling: CT-OFDM and AFDM benefit from large $N$ and suitable oversampling to leverage PAPR and diversity gains.
• Energy and power policies: OFDM-SPM supports both energy savings and throughput maximization via power allocation strategies.
• Windowing and pulse shaping: Hermitian-symmetric windowing should be coordinated with spectral mask constraints to optimize OOBE.
• Subcarrier set adaptation: OFDM-SNM mandates instantaneous CSI tracking; complexity remains manageable for stationary/low-mobility cases.
• Prefix design and redundancy generation: UW-OFDM requires generator matrix computation; per-symbol redundancy embedding and LMMSE smoothing are required for optimal decoding.

7. Future Directions and Research Frontiers

Emerging tailored OFDM research is likely to address integrated sensing/communication, multi-numerology coexistence, full-duplex self-interference mitigation, advanced index modulation over chirp domains (AFDM), and further reductions in pulse/transform complexity through mathematical innovations. Several open issues remain, particularly in joint design for ultra-reliable low-latency communication (URLLC), massive machine-type connectivity, and cross-layer waveform adaptation.

Tailored OFDM frameworks stand at the forefront of 6G and beyond air interface design, offering flexible, robust solutions for diverse scenarios characterized by extreme channel variability, stringent latency/reliability specifications, and unprecedented density of devices.