Joint Chirp Parameter Selection and Low-Complexity MMSE Receiver Design for AFDM Systems

Affine frequency division multiplexing (AFDM) has emerged as a promising waveform against doubly selective channels under high-mobility communication scenarios. Optimal chirp parameter selection and reduced-complexity receiver design in AFDM are essential for achieving satisfactory bit error rate (BER) performance with low computational complexity. In this paper, we investigate the joint optimization of chirp-parameter selection and low-complexity minimum mean square error (MMSE)-based receiver design by exploiting the structural characteristics of the AFDM effective channel matrix (ECM). First, a simplified BER performance metric is derived by leveraging the diagonal and circulant structure of the discrete affine Fourier transformation (DAFT), based on which a fast circulant-diagonal aggregation (FCDA) algorithm is developed for efficient $c_1$ selection. Then, a low-complexity banded MMSE (LC-BMMSE) receiver is developed by constructing a cyclic-banded ECM through path-wise structured sparsification, where banded Cholesky factorization is employed to avoid direct matrix inversion. Building upon the proposed BER metric and the LC-BMMSE receiver, a hierarchical-search-based joint chirp parameter and structured sparsification (HS-JCPS) algorithm is further proposed to jointly optimize the chirp parameter and sparsification pattern under a given complexity constraint. Simulation results demonstrate that the proposed FCDA reduces the search time for the optimal $c_1$ by an order of magnitude compared with using a BER-based criterion. Moreover, the proposed HS-JCPS algorithm with the LC-BMMSE receiver can identify a near-optimal $c_1$, while attaining a superior performance-complexity tradeoff.

AFDM-FTN: A Spectrally Efficient Waveform for High-Mobility Communications

This paper proposes an affine frequency division multiplexing (AFDM)-aided faster-than-Nyquist (FTN) waveform, termed AFDM-FTN, to enhance spectral efficiency (SE) in high-mobility communication scenarios. We first derive the AFDM-FTN input-output relationship and analyze the FTN-induced interference pattern in AFDM-FTN. To address the channel estimation challenges, a low-complexity channel estimator based on the basis expansion model (BEM) is developed. By exploiting the intrinsic characteristics of the AFDM channel matrix and the FTN coefficient matrix, a multi-layer message passing (MLMP) algorithm is proposed that leverages the sparsity of the time-domain (TD) channel and the FTN coefficient matrix, where belief messages are iteratively propagated across the TD channel, FTN, and transform layers. Building upon the BEM-assisted channel estimation and MLMP, a low-complexity joint channel estimation and data detection scheme (BEM-MLMP-JCED) is further developed to iteratively refine channel estimation with the aid of transmitted data. Finally, the channel estimation lower bound, the mean square error (MSE) performance of the BEM-MLMP-JCED, and the computational complexity are analyzed. Simulation results demonstrate that the proposed AFDM-FTN system with BEM-MLMP-JCED achieves comparable BER to conventional AFDM while providing enhanced SE and reduced complexity compared to benchmark receivers.

Rydberg Atomic Quantum Radio: A Comprehensive Survey From Wireless Communication Perspective

Next-generation space-air-ground-sea integrated networks (SAGSIN) impose unprecedented demands on advanced radio frequency (RF) receivers for full-spectrum agility, ultra-high sensitivity, and anti-jamming resilience, pushing conventional electronic receivers to their physical limits. To address these challenges, the Rydberg atomic quantum (RAQ) radio has emerged as a promising quantum-enabled receiver paradigm that directly maps electromagnetic fields onto atomic quantum states, offering an alternative to alleviate bottlenecks of conventional RF front ends. To provide a clear research roadmap, this survey presents a comprehensive review of RAQ radios by bridging atomic physics and wireless communications. Specifically, we first introduce the underlying quantum mechanisms, representative architectures, and atomic response models of RAQ radio. On this basis, state-of-the-art techniques for enhancing sensitivity, instantaneous bandwidth, and operating frequency are systematically reviewed, with particular emphasis on the inherent trade-offs among these key metrics. To connect quantum response with communication theory, we further analyze equivalent channel modeling frameworks for characterizing systematic performance limits. From the wireless communication perspective, some RAQ-enabled advanced technologies including cognitive, interference-resilient, low-frequency and multiple-input multiple-output (MIMO) communications are reviewed, alongside emerging deployment scenarios such as satellite networks, integrated sensing and communications, and reconfigurable intelligent surface-assisted systems. Finally, we identify open challenges and provide potential future directions of RAQ radio to inspire the further exploration.

Cell-Level Channel Shaping for Rydberg Atomic Quantum Receivers in Satellite Uplinks With Doppler-Enabled Superheterodyne Reception

In this paper, we propose a self-superheterodyne Rydberg uniform array receiver for satellite uplink communications, in which the Doppler shift naturally induced by satellite motion is exploited to generate the intermediate-frequency signal. We first develop a near-field local oscillator (LO) synthesis model and characterize the spatially varying LO electric field across the Rydberg vapor cells. Based on a vapor-cell-center approximation, a closed-form radio frequency (RF)-to-optical conversion is derived, establishing an explicit bridge between the incident satellite signal and the LO-induced cell-level response. The derived model reveals that the programmable LO serves as an analog-domain channel-shaping mechanism by controlling the cell-level transduction gain, phase response, and phase-matching behavior. Building upon this equivalent channel model, we formulate an LO design problem that maximizes the Shannon capacity of the effective channel, and develop an efficient optimization algorithm for the LO amplitudes and phases. Simulation results demonstrate that the vapor-cell transduction can reshape the effective channel, adjust the beam-pattern alignment, and moderately reduce the inter-user correlation under suitable LO configurations. Furthermore, the proposed LO design significantly improves the achievable capacity over benchmark schemes, offering a promising self-superheterodyne Rydberg architecture for future satellite communication systems.

Frame-Based AFDM-ISAC Waveform Design With Chirp-Enabled Pulse Compression

This paper proposes an Affine frequency division multiplexing (AFDM)-empowered integrated sensing and communications (ISAC) design, referred to as AFDM-ISAC. We first design a novel AFDM-ISAC frame structure that consists of both ISAC and pure data symbols. Each ISAC symbol consists of a single chirp subcarrier for both sensing and channel estimation, while the remaining subcarriers are allocated for communication. Building upon this structure, we present an analog-domain sensing receiver that down-mixes the received echo with a local chirp to fully exploit \textit{chirp compression} gains avoiding the need for full-duplex hardware. In addition, a sensing fusion algorithm, guided by AFDM modulation parameters, is further proposed in the digital domain. Leveraging the distinct features of the proposed AFDM-ISAC frame, we present a low-complexity channel estimation scheme for high mobility channels based on a generalized complex exponential basis expansion model (GCE-BEM), along with an optimal power allocation strategy between pilot and data symbols. Moreover, to support frame-based AFDM communications, a GCE-BEM-based Kalman filter is also employed for robust intra-frame channel estimation.

Spatially Coupled Sparse Code Multiple Access (SC-SCMA): A Spectral Graph Approach

This paper presents a spatially coupled sparse code multiple access (SC-SCMA) framework to overcome the performance and scalability limitations of conventional SCMA systems. By analyzing the pairwise error probability associated to multi-user error patterns, we show that spatial coupling projects the superimposed SCMA codewords into a higher-dimensional effective signal space, leading to a strictly improved minimum Euclidean distance (MED) compared with conventional SCMA, while simultaneously enhancing the coding gain through global message propagation and the diversity gain through inter-block resource spreading. Such a distance gain is shown to be governed by the effective access dimensionality (EAD) induced by the coupled factor graph. With the aid of spectral graph theory, we establish a direct relationship between the spectral gap of the factor graph and a lower bound on the EAD, providing a computable structural metric that guarantees MED improvement under various error patterns. Building upon these theoretical insights, we introduce a low-complexity structure-aware codebook design approach, including a spectral-gap-oriented construction of spatially coupled factor matrices and a localized codebook optimization strategy that exploits the dominant error-inducing local user group. Simulation results validate the analysis and demonstrate that the proposed SC-SCMA consistently outperforms conventional SCMA in overloaded massive access channels.

MCRB and MSE Analysis for Parameter Estimation in AFDM-ISAC Systems

Affine frequency division multiplexing (AFDM) is a promising waveform for integrated sensing and communication (ISAC). In AFDM systems, the complex gains, delays, and Doppler shifts are commonly estimated from the AFDM symbols carrying pilots and data simultaneously. In practice, however, the unknown data symbols and data-pilot coupling interference may render the estimator mismatched to the true signal model. In this paper, we systematically characterize the parameter-estimation performance of AFDM-ISAC systems under practical model misspecification. The main contributions are threefold. First, we extend the Cramér-Rao bound (CRB) for a general observation model that treats the data symbols as unknown, which generalizes existing AFDM CRB analyses and serves as the matched benchmark for the subsequent analysis. Second, we identify two practical sources of misspecification, namely a covariance mismatch caused by insufficient pilot-data isolation and a combined covariance-and-mean mismatch caused by sequential single-target estimation, and derive the corresponding misspecified CRB (MCRB). Third, we characterize the pseudotrue parameters under different levels of prior knowledge, analyze the resulting estimation bias, and establish a lower bound (LB) on the mean square error (MSE). Simulation results validate the derived bounds and show that, under model misspecification, the CRB is overly optimistic while the MCRB and LB faithfully characterize the achievable accuracy. The comparison further reveals how these bounds vary with the pilot length and pilot power, providing useful guidance for pilot configuration.

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.

Beyond the RF Paradigm: Rydberg Atomic Receivers for Next-Generation IoT

Next-generation Internet-of-Things (IoT) is evolving toward a ubiquitous, ultra-low-power, and multi-band heterogeneous networking paradigm that seamlessly integrates terrestrial, non-terrestrial, and ambient devices. This vision places unprecedented demands on conventional radio frequency (RF) receivers, whose fundamental bottlenecks in sensitivity, power consumption, coverage, and multi-band operation are rooted in the RF antenna. To tackle these issues, we show that the quantum properties of Rydberg atomic quantum receivers (RAQRs), including ultra-high sensitivity, broad frequency agility, and diverse reception modalities, provide a physically distinct receiver-side path that replaces the conventional antenna-and-low-noise-amplifier chain. Using LoRa, narrowband IoT, and ambient IoT as case studies, this article shows that RAQRs deliver significant gains in weak-uplink, low-power, and battery-free regimes. A stochastic-geometry analysis in cellular and cell-free architectures then maps these device-level gains onto network coverage, where the RAQR retains roughly a 4 dB half-coverage advantage over the RF receiver in sparse deployments at \(λ\sim 10^{-5}~{\mathrm m}^{-2}\), with the gain eroded as device density grows. The open challenges are presented to stand between current RAQR prototypes and deployable IoT infrastructure.

Signal-Dependent Shot Noise Modeling of Rydberg Atomic Quantum Receivers: A Design Perspective

In this paper, we develop a communication-oriented complex baseband equivalent model for superheterodyne Rydberg atomic quantum receivers (RAQRs). The model explicitly captures photodetection-induced signal-dependent shot noise and its coupling with the optical operating point. By leveraging an atomic superheterodyne architecture and a strong local oscillator, we construct a complex baseband representation for both the received signal and the signal-dependent shot noise under both direct incoherent optical detection and balanced coherent optical detection. The derived model reveals that the optical operating point jointly determines the normalized effective receive gain and the equivalent noise background, thereby establishing a traceable gain-noise tradeoff governed by system design. More importantly, the proposed model shows that neglecting signal-dependent shot noise may lead to inaccurate operating-point design. Finally, by extending to the multiple-input-multiple-output (MIMO) case, we derive a lower bound on the achievable rate while considering the signal-dependent shot noise. Our analysis \textcolor{black}{reveals} that the non-zero asymptotic rate of RAQ-MIMO and its superiority over conventional RF-MIMO hinge on the normalized noise floor of the RAQ receive chain falling below that of RF MIMO. Simulation results validate our analysis and yield practical, closed-form design guidelines for RAQR front ends, revealing parameter regimes in which RAQ-MIMO outperforms conventional MIMO systems.