On the heels of orthogonal time frequency space (OTFS) modulation, the recently discovered affine frequency division multiplexing (AFDM) is a promising waveform for the sixth-generation wireless network. In this paper, we study the widely-used embedded pilot-aided (EPA) channel estimation in multiple-input multiple-output AFDM (MIMO-AFDM) system with fractional Doppler shifts. We first formulate the vectorized input-output relationship of MIMO-AFDM, and theoretically prove that MIMO-AFDM can achieve full diversity in doubly selective channels. Then we illustrate the implementation of EPA channel estimation in MIMO-AFDM and unveil that serious inter-Doppler interference (IDoI) occurs if we try to estimate the channel gain, delay shift, and Doppler shift of each propagation path. To address this issue, the diagonal reconstructability of AFDM subchannel matrix is studied and a low-complexity embedded pilot-aided diagonal reconstruction (EPA-DR) channel estimation scheme is proposed. The EPA-DR scheme calculates the AFDM effective channel matrix directly without estimating the three channel parameters, eliminating the severe IDoI inherently. Since the effective channel matrix is necessary for MIMO-AFDM receive processing, we believe this is an important step to bring AFDM towards practical communication systems. Simulation results validate the effectiveness of the proposed EPA-DR scheme.

In bistatic integrated sensing and communication (ISAC), the transmitter and receiver of communication and sensing are the same, so the transceiver directly shares the same channel. Considering the commonality of channel state information and sensing information of target scatterers, in this letter, we propose a bistatic sensing-aided channel estimation (SACE) scheme that exploits the superior sensing and communication performance of affine Fourier division multiplexing (AFDM). In addition, we provide a parameters selection criteria that makes AFDM a simplified orthogonal chirp division multiplexing (OCDM) and provides it with a relatively ideal ambiguity function. Simulation results show that, compared with other state-of-the-art waveforms, the AFDM with this parameters selection has not only the best sensing resolution but also the best communication performance under the proposed SACE scheme.

Next-generation wireless networks are designed to provide reliable, high-data-rate communication services for diverse scenarios such as vehicle-to-vehicle, unmanned-aerial-vehicle, and satellite networks. Large Doppler spreads in the underlying time-varying channels induce destructive inter-carrier interference (ICI) in the widely adopted orthogonal frequency-division multiplexing (OFDM) waveform, leading to severe performance degradation. This calls for a new air-interface design that can accommodate the severe delay–Doppler spreads of highly dynamic channels while offering sufficient flexibility to cater to various applications. This article provides a comprehensive overview of a promising chirp-based waveform, Affine Frequency Division Multiplexing (AFDM). Featuring two tunable parameters, AFDM achieves the optimal diversity order in doubly dispersive channels (DDC). We examine the fundamental principles of AFDM, illustrating its intrinsic suitability for DDC; on this basis, several potential applications are explored. Furthermore, the main challenges of AFDM and their corresponding solutions are presented, followed by key directions for future research. Finally, we draw instructive conclusions about AFDM to provide useful insights for its continued development.

Affine frequency division multiplexing (AFDM) is a promising chirp-based waveform with high flexibility and resilience, making it well-suited for next-generation wireless networks, particularly in high-mobility scenarios. In this paper, we investigate the ambiguity functions (AFs) of AFDM signals, which fundamentally characterize their range and velocity estimation capabilities in both monostatic and bistatic settings. Specifically, we first derive the auto-ambiguity function (AAF) of an AFDM chirp subcarrier, revealing its “spike-like” local property and “periodic-like” global property along the rotated delay and Doppler dimensions. This structure naturally forms a parallelogram for each localized pulse of the AAF of the AFDM chirp subcarrier, enabling unambiguous target sensing. Then, we study the cross-ambiguity function (CAF) between two different AFDM chirp subcarriers, which exhibits the same local and global properties as the AAF but with an additional shift along the Doppler dimension. We then extend our analysis to the AF of various typical AFDM frames, considering both deterministic pilot and random data symbols. In particular, we demonstrate that inserting guard symbols in AFDM facilitates interference-free sensing. Simulation results validate our theoretical findings, highlighting AFDM’s strong potential for ISAC applications.

Next-generation wireless networks require enhanced flexibility, efficiency, and reliability in physical layer waveform design to address the challenges posed by heterogeneous channel conditions and stringent quality-of-service demands. To this end, this paper proposes a unified multicarrier waveform framework that provides a systematic characterization and practical implementation guidelines to facilitate waveform selection for the sixth-generation (6G) mobile networks and beyond. We commence by examining the design principles of the state-of-the-art waveforms, which are categorized into one-dimensional modulation waveforms (e.g., orthogonal frequency division multiplexing (OFDM) and affine frequency division multiplexing (AFDM)) and two-dimensional modulation waveforms (e.g., orthogonal time frequency space (OTFS)). Their inherent resilience against various channel-induced interference is further studied, revealing their distinct suitability in diverse channel conditions. Furthermore, an in-depth performance analysis is presented by comparing their key performance indicators (KPIs), followed by an extensive exploration of these advanced waveforms in various applications. Consequently, this work aims to serve as a pivotal reference for waveform adoption in future 6G standardization and network deployment.

Channel models are crucial for theoretical analysis, performance evaluation, and deployment of wireless communication systems. Traditional channel sounding systems are insufficient for handling the dynamic changes of channels in the next-generation space–air–ground–sea integrated networks (SAGSIN), which often results in outdated channel models that fail to provide reliable prior information for communication systems. To address this challenge, this article proposes an integrated channel sounding and communication (ICSC) method as a practical solution. Unlike orthogonal frequency division multiplexing (OFDM), affine frequency division multiplexing (AFDM) provides a full delay-Doppler representation of the channel, achieving optimal diversity in time-frequency doubly dispersive channels and effectively addressing the aforementioned challenges. Thus, this article investigates the fundamental principles of AFDM, showing how it enables simultaneous communication and channel sounding, and explores key performance metrics for both functionalities. Additionally, the distinction and relationship between channel sounding, estimation, tracking, and scatterer sensing are clarified. Several potential application scenarios for AFDM-ICSC are also examined. Finally, the article highlights the key challenges in implementing AFDM-ICSC, outlines future research directions, and offers valuable insights for the continued development of this technology.