Channel Estimation for AFDM With Superimposed Pilots

The recent proposed affine frequency division multiplexing (AFDM) employing a multi-chirp waveform has shown its reliability and robustness in doubly selective fading channels. In the existing embedded pilot-aided channel estimation methods, the presence of guard symbols in the discrete affine Fourier transform (DAFT) domain causes inevitable degradation of the spectral efficiency (SE). To improve the SE, we propose a novel AFDM channel estimation scheme by introducing the superimposed pilots in the DAFT domain. An effective pilot placement method that minimizes the channel estimation error is also developed with a rigorous proof. To mitigate the pilot-data interference, we further propose an iterative channel estimator and signal detector. Simulation results demonstrate that both channel estimation and data detection performances can be improved by the proposed scheme as the number of superimposed pilots increases.

Knowledge and Data Dual-Driven Channel Estimation and Feedback for Ultra-Massive MIMO Systems under Hybrid Field Beam Squint Effect

Acquiring accurate channel state information (CSI) at an access point (AP) is challenging for wideband millimeter wave (mmWave) ultra-massive multiple-input and multiple-output (UMMIMO) systems, due to the high-dimensional channel matrices, hybrid near- and far- field channel feature, beam squint effects, and imperfect hardware constraints, such as low-resolution analog-to-digital converters, and in-phase and quadrature imbalance. To overcome these challenges, this paper proposes an efficient downlink channel estimation (CE) and CSI feedback approach based on knowledge and data dual-driven deep learning (DL) networks. Specifically, we first propose a data-driven residual neural network de-quantizer (ResNet-DQ) to pre-process the received pilot signals at user equipment (UEs), where the noise and distortion brought by imperfect hardware can be mitigated. A knowledge-driven generalized multiple measurement vector learned approximate message passing (GMMV-LAMP) network is then developed to jointly estimate the channels by exploiting the approximately same physical angle shared by different subcarriers. In particular, two wideband redundant dictionaries (WRDs) are proposed such that the measurement matrices of the GMMV-LAMP network can accommodate the far-field and near-field beam squint effect, respectively. Finally, we propose an encoder at the UEs and a decoder at the AP by a data-driven CSI residual network (CSI-ResNet) to compress the CSI matrix into a low-dimensional quantized bit vector for feedback, thereby reducing the feedback overhead substantially. Simulation results show that the proposed knowledge and data dual-driven approach outperforms conventional downlink CE and CSI feedback methods, especially in the case of low signal-to-noise ratios.

Near-Field Channel Estimation in Dual-Band XL-MIMO with Side Information-Assisted Compressed Sensing

Near-field communication comes to be an indispensable part of the future sixth generation (6G) communications at the arrival of the forth-coming deployment of extremely large-scale multiple-input-multiple-output (XL-MIMO) systems. Due to the substantial number of antennas, the electromagnetic radiation field is modeled by the spherical waves instead of the conventional planar waves, leading to severe weak sparsity to angular-domain near-field channel. Therefore, the channel estimation reminiscent of the conventional compression sensing (CS) approaches in the angular domain, judiciously utilized for low pilot overhead, may result in unprecedented challenges. To this end, this paper proposes a brand-new near-field channel estimation scheme by exploiting the naturally occurring useful side information. Specifically, we formulate the dual-band near-field communication model based on the fact that high-frequency systems are likely to be deployed with lower-frequency systems. Representative side information, i.e., the structural characteristic information derived by the sparsity ambiguity and the out-of-band spatial information stemming from the lower-frequency channel, is explored and tailored to materialize exceptional near-field channel estimation. Furthermore, in-depth theoretical analyses are developed to guarantee the minimum estimation error, based on which a suite of algorithms leveraging the elaborating side information are proposed. Numerical simulations demonstrate that the designed algorithms provide more assured results than the off-the-shelf approaches in the context of the dual-band near-field communications in both on- and off-grid scenarios, where the angle of departures/arrivals are discretely or continuously distributed, respectively.

Block-Dominant Compressed Sensing for Near-Field Communications: Fundamentals, Solutions and Future Directions

Near-field (NF) communications draw much attention in the context of extremely large-scale antenna arrays (ELAA). Owing to a large number of antennas and high carrier frequency, the NF coverage distance is quite substantial, where the electromagnetic radiation propagates by spherical waves, in contrast to the conventional planar waves of the far-field. Motivated by these facts, the block-dominant compressed sensing (BD-CS) assisted NF communications are proposed. Specifically, we elucidate why block sparsity exists in the distance-limited NF region. Then, block-dominant side-information (BD-SI) is introduced in support of the actual NF communication implementation. We validate that BD-CS is capable of providing exceptional channel estimation accuracy and high spectral efficiency, where the associated challenges, opportunities and its actual implementation in NF communications need to be carefully addressed.

Wavenumber Domain Sparse Channel Estimation in Holographic MIMO

In this paper, we investigate the sparse channel estimation in holographic multiple-input multiple-output (HMIMO) systems. The conventional angular-domain representation fails to capture the continuous angular power spectrum characterized by the spatially-stationary electromagnetic random field, thus leading to the ambiguous detection of the significant angular power, which is referred to as the power leakage. To tackle this challenge, the HMIMO channel is represented in the wavenumber domain for exploring its cluster-dominated sparsity. Specifically, a finite set of Fourier harmonics acts as a series of sampling probes to encapsulate the integral of the power spectrum over specific angular regions. This technique effectively eliminates power leakage resulting from power mismatches induced by the use of discrete angular-domain probes. Next, the channel estimation problem is recast as a sparse recovery of the significant angular power spectrum over the continuous integration region. We then propose an accompanying graph-cut-based swap expansion (GCSE) algorithm to extract beneficial sparsity inherent in HMIMO channels. Numerical results demonstrate that this wavenumber-domainbased GCSE approach achieves robust performance with rapid convergence.

Block-Sparse Tensor Recovery

This work explores the fundamental problem of the recoverability of a sparse tensor being reconstructed from its compressed embodiment. We present a generalized model of block-sparse tensor recovery as a theoretical foundation, where concepts measuring holistic mutual incoherence property (MIP) of the measurement matrix set are defined. A representative algorithm based on the orthogonal matching pursuit (OMP) framework, called tensor generalized block OMP (T-GBOMP), is applied to the theoretical framework elaborated for analyzing both noiseless and noisy recovery conditions. Specifically, we present the exact recovery condition (ERC) and sufficient conditions for establishing it with consideration of different degrees of restriction. Reliable reconstruction conditions, in terms of the residual convergence, the estimated error and the signal-to-noise ratio bound, are established to reveal the computable theoretical interpretability based on the newly defined MIP, which we introduce. The flexibility of tensor recovery is highlighted, i.e., the reliable recovery can be guaranteed by optimizing MIP of the measurement matrix set. Analytical comparisons demonstrate that the theoretical results developed are tighter and less restrictive than the existing ones (if any). Further discussions provide tensor extensions for several classic greedy algorithms, indicating that the sophisticated results derived are universal and applicable to all these tensorized variants.

Angular-Distance Based Channel Estimation for Holographic MIMO

This paper investigates the channel estimation for holographic MIMO systems by unmasking their distinctions from the conventional one. Specifically, we elucidate that the channel estimation, subject to holographic MIMO's electromagnetically large antenna arrays, has to discriminate not only the angles of a user/scatterer but also its distance information, namely the three-dimensional (3D) azimuth and elevation angles plus the distance (AED) parameters. As the angular-domain representation fails to characterize the sparsity inherent in holographic MIMO channels, the tightly coupled 3D AED parameters are firstly decomposed for independently constructing their own covariance matrices. Then, the recovery of each individual parameter can be structured as a compressive sensing (CS) problem by harnessing the covariance matrix constructed. This pair of techniques contribute to a parametric decomposition and compressed deconstruction (DeRe) framework, along with a formulation of the maximum likelihood estimation for each parameter. Then, an efficient algorithm, namely DeRe-based variational Bayesian inference and message passing (DeRe-VM), is proposed for the sharp detection of the 3D AED parameters and the robust recovery of sparse channels. Finally, the proposed channel estimation regime is confirmed to be of great robustness in accommodating different channel conditions, regardless of the near-field and far-field contexts of a holographic MIMO system, as well as an improved performance in comparison to the state-of-the-art benchmarks.

Cross-Domain Waveform Design for 6G Integrated Sensing and Communication

Orthogonal frequency division multiplexing (OFDM) is one of the representative integrated sensing and communication (ISAC) waveforms, where sensing and communications tend to be assigned with different resource elements (REs) due to their diverse design requirements. This motivates optimization of resource allocation/waveform design across time, frequency, power and delay-Doppler domains. Therefore, this article proposes two cross-domain waveform optimization strategies for OFDM-based ISAC systems, following communication-centric and sensing-centric criteria, respectively. For the communication-centric design, to maximize the achievable data rate, a fraction of REs are optimally allocated for communications according to prior knowledge of the communication channel. The remaining REs are then employed for sensing, where the sidelobe level and peak to average power ratio are suppressed by optimizing its power-frequency and phase-frequency characteristics. For the sensing-centric design, a `locally' perfect auto-correlation property is ensured by adjusting the unit cells of the ambiguity function within its region of interest (RoI). Afterwards, the irrelevant cells beyond RoI, which can readily determine the sensing power allocation, are optimized with the communication power allocation to enhance the achievable data rate. Numerical results demonstrate the superiority of the proposed communication-centric and sensing-centric waveform designs for ISAC applications.

Deep Learning Empowered Type-II Codebook: New Perspectives for Enhancing CSI Feedback

Deep learning based channel state information (CSI) feedback in frequency division duplex systems has drawn widespread attention in both academia and industry. In this paper, we focus on integrating the Type-II codebook in the wireless communication standards with deep learning to enhance the performance of CSI feedback. In contrast to the existing deep learning based studies on the Release 16 Type-II codebook, the Type-II codebook in Release 17 (R17) exploits the angular-delay-domain partial reciprocity between uplink and downlink channels to select part of angular-delay-domain ports for measuring and feeding back the downlink CSI, where the performance of deep learning based conventional methods is limited due to the deficiency of sparse structures. To address this issue, we propose two new perspectives of adopting deep learning to improve the R17 Type-II codebook. Firstly, considering the low signal-to-noise ratio of uplink channels, deep learning is utilized to accurately select the dominant angular-delay-domain ports, where the focal loss is harnessed to solve the class imbalance problem. Secondly, we propose to adopt deep learning to reconstruct the downlink CSI based on the feedback of the R17 Type-II codebook at the base station, where the information of sparse structures can be effectively leveraged. Furthermore, a weighted shortcut module is designed to facilitate the accurate reconstruction, and a two-stage loss function that combines the mean squared error and sum rate is proposed for adapting to practical multi-user scenarios. Simulation results demonstrate that our proposed deep learning based port selection and CSI reconstruction methods can improve the sum rate performance compared with the traditional R17 Type-II codebook and deep learning benchmarks.

Doppler-Resilient Design of CAZAC Sequences for mmWave/THz Sensing Applications

Ultra-high-resolution target sensing has emerged as a key enabler for various cutting-edge applications, which can be realized by utilizing the millimeter wave/terahertz frequencies. However, the extremely high operating frequency inevitably leads to significant Doppler shift effects, especially for high-mobility applications, causing the degradation of sensing performance with high false alarm rate. To this end, this paper proposes a parameter design methodology of the well-known constant amplitude zero auto correlation (CAZAC) sequences, which aims at enhancing their resilience to Doppler shifts. Specifically, we suppress the sidelobes incurred by Doppler shifts for the peak-to-sidelobe ratio (PSLR) improvement within the range of interest (RoI) of the radar range profile. The Zadoff-Chu (ZC) sequence, as a representative member in the CAZAC family, is firstly considered. The impacts of its root index on range sidelobes are investigated based on number theory. For an arbitrary-length ZC sequence, a feasible range of the root index is derived to satisfy the requirement of PSLR within the scope of RoI. Furthermore, these design guidelines are extended to a general form of CAZAC sequences, where a low-complexity heuristic algorithm is developed for PSLR improvement. Simulation results demonstrate that under severe Doppler shifts, our proposed methodology could enhance the sensing performance by lowering the false alarm rate while maintaining the same detection rate, compared with its classical counterpart.