Towards Standardizing Affine Frequency Division Multiplexing (AFDM) for Future Wireless Networks

Affine frequency division multiplexing~(AFDM) has emerged as a compelling waveform candidate for future wireless networks, owing to its strong resilience to doubly selective channels and its ability to enable the seamless integration of communication and sensing functionalities. Against this context, this article provides a systematic study of AFDM from a standardization perspective. We first introduce the principles of AFDM and discuss the major considerations involved in waveform standardization. We then examine the backwards compatibility of AFDM with 4G/5G multi-numerology frameworks and their anticipated evolution, frequency-modulated continuous-wave (FMCW) radar waveforms, and long-range (LoRa) modulation, demonstrating that AFDM can be incorporated into legacy processing chains with limited modification. Key standardization-critical capabilities are further discussed, including multiple-antenna and multi-user support, and peak-to-average power ratio (PAPR). Finally, we investigate the potential of AFDM in several emerging scenarios, including non-terrestrial networks~(NTN), integrated sensing and communications (ISAC), vehicle-to-everything (V2X), and underwater acoustic (UWA) communications, whereby severe delay-Doppler dispersion places stringent demands on waveform robustness. Through these explorations, it is shown that that AFDM represents a timely and compelling technology for future wireless networks.

Adaptive $c_2$-Perturbed AFDM Waveform Design for Integrated Sensing and Communication

Affine frequency division multiplexing (AFDM) is a promising waveform for integrated sensing and communication (ISAC) systems owing to its superior performance in time--frequency doubly dispersive channels. However, AFDM still faces a pair of challenges: high PAPR and random data symbols produce imperfect autocorrelation sidelobes. To address these challenges, this paper proposes a real-time data-driven framework that optimizes the pre-chirp parameter $c_2$ to enhance the AFDM-ISAC performance. Specifically, a side-information-free optimization problem is formulated to reduce PAPR and the weighted integrated sidelobe levels of both aperiodic and periodic autocorrelation functions, with complexity comparable to that of the conventional AFDM receiver. Furthermore, an efficient non-monotone line-search spectral projected-gradient algorithm is developed by exploiting closed-form gradients. Simulation results demonstrate that the proposed method achieves a superior sensing vs. communications trade-off and is capable of striking a promoted bit error rate performance in the presence of severe power amplifier nonlinearity.

From Denoising to Decision Making: A Survey on Diffusion Model-Enabled Deep Reinforcement Learning for Wireless Networks

Deep reinforcement learning (DRL) has long been a promising solution for sequential resource management in wireless networks. However, conventional DRL methods are fundamentally limited by their reliance on unimodal policy distributions, inefficient exploration in high-dimensional action spaces, and poor adaptability to dynamic and heterogeneous environments. Meanwhile, diffusion models (DMs) as one of the most powerful families of generative AI have demonstrted remarkable capabilities in modeling complex, multi-modal data distributions across diverse domains. The integration of DMs and DRL has opened a new and rapidly growing research direction, in which DM-enabled policies substantially enhance decision quality by capturing the complex, discontinuous, and multimodal action structures inherent in wireless resource management. In this paper, we present a comprehensive survey of DM-enabled DRL algorithms and their applications for various issues in wireless networks. Particularly, we first provide the theoretical background of DM and present different DM-enabled DRL algorithms. We then systematically review applications of DM-enabled DRL for across computation offloading in mobile edge computing, UAV-assisted, vehicular, and AIGC-driven systems, as well as wireless resource allocation, physical-layer security, and robotics and UAV planning. We conclude the paper by higlight future research directions.

DAFT-s-AFDM Enabled ISAC Systems: Ambiguity Function Analysis and Waveform Design

Discrete affine Fourier transform spread affine frequency division multiplexing (DAFT-s-AFDM) is a promising waveform for integrated sensing and communication (ISAC) due to its low peak-to-average power ratio, robustness to Doppler shifts, and reduced multiuser interference in the uplink transmission. This paper presents a comprehensive ambiguity function (AF) analysis of DAFT-s-AFDM and derives the closed-form expression for the AF magnitude expectation. Several key insights into the impact of DAFT-s-AFDM parameters on ISAC performance are revealed, thus providing concrete guidance for the subsequent waveform design. Building on these insights, a novel probabilistic constellation shaping (PCS) framework is proposed for ISAC waveform enhancement, where the communication throughput and the sensing AF characteristics are jointly optimized by addressing a multi-objective problem. An efficient algorithm based on a closed-form bit error rate expression is developed to obtain the Pareto-optimal solutions. Extensive simulations validate the theoretical results and that the proposed PCS-enhanced DAFT-s-AFDM can significantly outperform the classical counterparts, achieving a superior and highly controllable tradeoff between the dual-functional performances.

A Novel Low-Complexity Dual-Domain Expectation Propagation Detection Aided AFDM for Future Communications

This paper presents a dual-domain low-complexity expectation propagation (EP) detection framework for affine frequency division multiplexing (AFDM) systems. By analyzing the structural properties of the effective channel matrices in both the time and affine frequency (AF) domains, our key observation is the domain-specific quasi-banded sparsity patterns, including AF-domain sparsity under frequency-selective channels and time-domain sparsity under doubly-selective channels. Based on these observations, we develop an AF-domain EP (EP-AF) detector for frequency-selective channels and a time-domain EP (EP-T) detector for doubly-selective channels, respectively. By performing iterative inference in the time domain using the Gaussian approximation, the proposed EP-T detector avoids inverting the dense channel matrix in the AF domain. Furthermore, the proposed EP-AF and EP-T detectors leverage the aforementioned quasi-banded sparsity of the AF domain and time domain channel matrices, respectively, to reduce the complexity of matrix inversion from cubic to linear order. Simulation results demonstrate that the proposed low-complexity EP-AF detector achieves nearly identical error rate performance to its conventional counterpart, while the proposed low-complexity EP-T detector offers an attractive trade-off between detection performance and complexity.

Low-Altitude Agentic Networks for Optical Wireless Communication and Sensing: An Oceanic Scenario

The cross-domain oceanic connectivity ranging from underwater to the sky has become increasingly indispensable for a plethora of data-consuming maritime applications, such as maritime meteorological monitoring and offshore exploration. However, broadband implementations can be severely hindered by the isolation from terrestrial networks, limited satellite resources, and the fundamental inability of radio waves to bridge the water-air interface at high rates. To this end, this paper introduces an optical network bridging underwater, air and near space, which features a number of cooperative low-altitude platforms (LAPs), serving as compute-capable, sensing-aware, and mission-adaptive agents. The network architecture consists of three scenario-specific segments, i.e., water-air direct link, low-altitude mesh network, and the near-space access network. With coordinate sensing and intelligent control, the system tightly couples beam tracking and resource optimization, enabling resilient networking under high mobility and harsh maritime dynamics. Furthermore, we review enabling technologies spanning from water-air channel modeling, adaptive beam alignment under sea-surface perturbations, to swarm-intelligence networking for decentralized control, integrated pose-topology planning, and optical Integrated sensing and communication (ISAC) for near-space target detection and beam alignment. Finally, open issues are also highlighted, constituting a clear roadmap toward scalable, secure, and ultra-broadband oceanic optical networks.

AFDM: Evolving OFDM Towards 6G+

As the standardization of sixth generation (6G) wireless systems accelerates, there is a growing consensus in favor of evolutionary waveforms that offer new features while maximizing compatibility with orthogonal frequency division multiplexing (OFDM), which underpins the 4G and 5G systems. This article presents affine frequency division multiplexing (AFDM) as a premier candidate for 6G, offering intrinsic robustness for both high-mobility communications and integrated sensing and communication (ISAC) in doubly dispersive channels, while maintaining a high degree of synergy with the legacy OFDM. To this end, we provide a comprehensive analysis of AFDM, starting with a generalized fractional-delay-fractional-Doppler (FDFD) channel model that accounts for practical pulse shaping filters and inter-sample coupling. We then detail the AFDM transceiver architecture, demonstrating that it reuses nearly the entire OFDM pipeline and requires only lightweight digital pre- and post-processing. We also analyze the impact of hardware impairments, such as phase noise and carrier frequency offset, and explore advanced functionalities enabled by the chirp-parameter domain, including index modulation and physical-layer security. By evaluating the reusability across the radio-frequency, physical, and higher layers, the article demonstrates that AFDM provides a low-risk, feature-rich, and efficient path toward achieving high-fidelity communications in the later versions of 6G and beyond (6G+).

MIMO-AFDM Outperforms MIMO-OFDM in the Face of Hardware Impairments

The impact of both multiplicative and additive hardware impairments (HWIs) on multiple-input multiple-output affine frequency division multiplexing (MIMO-AFDM) systems is investigated. For small-scale MIMO-AFDM systems, a tight bit error rate (BER) upper bound associated with the maximum likelihood (ML) detector is derived. By contrast, for large-scale systems, a closed-form BER approximation associated with the linear minimum mean squared error (LMMSE) detector is presented, including realistic imperfect channel estimation scenarios. Our first key observation is that the full diversity order of a hardware-impaired AFDM system remains unaffected, which is a unique advantage. Furthermore, our analysis shows that 1) the BER results derived accurately predict the simulated ML performance in moderate-to-high signal-to-noise ratios (SNRs), while the theoretical BER curve of the LMMSE detector closely matches that of the Monte-Carlo based one. 2) MIMO-AFDM is more resilient to multiplicative distortions, such as phase noise and carrier frequency offset, compared to its orthogonal frequency division multiplexing (OFDM) counterparts. This is attributed to its inherent chirp signal characteristics; 3) MIMO-AFDM consistently achieves superior BER performance compared to conventional MIMO-OFDM systems under the same additive HWI conditions, as well as different velocity values. The latter is because MIMO-AFDM is also resilient to the additional inter-carrier interference (ICI) imposed by the nonlinear distortions of additive HWIs. In a nutshell, compared to OFDM, AFDM demonstrates stronger ICI resilience and achieves the maximum full diversity attainable gain even under HWIs, thanks to its intrinsic chirp signalling structure as well as to the beneficial spreading effect of the discrete affine Fourier transform.

Error Rate Analysis and Low-Complexity Receiver Design for Zero-Padded AFDM

This paper studies the error rate performance and low-complexity receiver design for zero-padded affine frequency division multiplexing (ZP-AFDM) systems. By exploiting the unique ZP-aided lower triangular structure of the time domain (TD) channel matrix, we propose {a novel low-complexity} minimum mean square error (MMSE) detector and {a} maximum ratio combining-based TD (MRC-TD) detector. Furthermore, the theoretical bit error rate (BER) {performance} of both MMSE and maximum likelihood detectors {is} analyzed. Simulation results demonstrate {that} the proposed detectors can achieve identical BER performance to that of {the conventional MMSE detector based on matrix inversion} while {enjoying significantly reduced complexity.}

Optimal Real-time Communication in 6G Ultra-Massive V2X Mobile Networks

This paper introduces a novel cooperative vehicular communication algorithm tailored for future 6G ultra-massive vehicle-to-everything (V2X) networks leveraging integrated space-air-ground communication systems. Specifically, we address the challenge of real-time information exchange among rapidly moving vehicles. We demonstrate the existence of an upper bound on channel capacity given a fixed number of relays, and propose a low-complexity relay selection heuristic algorithm. Simulation results verify that our proposed algorithm achieves superior channel capacities compared to existing cooperative vehicular communication approaches.