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.

In this letter, a simple parasitic structure consisting of a microstrip L-section array and a microstrip U-section array is proposed for mutual coupling reduction of dual-polarization (DP) patch antenna array. The additional coupling paths are introduced by the structure in the co-horizontal polarization (CHP) and co-vertical polarization (CVP) directions of the array respectively to offset the original coupling signals. A prototype array with the center to center distance of 0.42 $\lambda_0$ is fabricated and measured for verification. The isolation between DP array with decoupling structure reaches to 37.5dB and 33.6dB on CHP and CVP at 4.3GHz and envelope correlation coefficient is less than 0.004. The radiation gain of the antenna is almost not distorted while the total efficiency is increased from 84% to 91%. In comparison with other related works, our scheme has high isolation and high total efficiency with smaller space and lower profile.

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.

This paper investigates a machine learning-based power allocation design for secure transmission in a cognitive radio (CR) network. In particular, a neural network (NN)-based approach is proposed to maximize the secrecy rate of the secondary receiver under the constraints of total transmit power of secondary transmitter, and the interference leakage to the primary receiver, within which three different regularization schemes are developed. The key advantage of the proposed algorithm over conventional approaches is the capability to solve the power allocation problem with both perfect and imperfect channel state information. In a conventional setting, two completely different optimization frameworks have to be designed, namely the robust and non-robust designs. Furthermore, conventional algorithms are often based on iterative techniques, and hence, they require a considerable number of iterations, rendering them less suitable in future wireless networks where there are very stringent delay constraints. To meet the unprecedented requirements of future ultra-reliable low-latency networks, we propose an NN-based approach that can determine the power allocation in a CR network with significantly reduced computational time and complexity. As this trained NN only requires a small number of linear operations to yield the required power allocations, the approach can also be extended to different delay sensitive applications and services in future wireless networks. When evaluate the proposed method versus conventional approaches, using a suitable test set, the proposed approach can achieve more than 94% of the secrecy rate performance with less than 1% computation time and more than 93% satisfaction of interference leakage constraints. These results are obtained with significant reduction in computational time, which we believe that it is suitable for future real-time wireless applications.