This work studies the problems of channel estimation and beamforming for active reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) communication, incorporating the mutual coupling (MC) effect through an electromagnetically consistent model. We first demonstrate that MC can be incorporated into a compressed sensing (CS) formulation, albeit with an increase in the dimensionality of the sensing matrix. To overcome this increased complexity, we propose a two-stage strategy. Initially, a low-complexity MC-unaware CS estimation is performed to obtain a coarse channel estimate, which is then used to implement a dictionary reduction (DR) for the MC-aware estimation, effectively reducing the dimensionality of the sensing matrices. This method achieves estimation accuracy close to the direct MC-aware CS method with less overall computational complexity. Furthermore, we consider the joint optimization of RIS configuration, base station precoding, and user combining in a single-user MIMO system. We employ an alternating optimization strategy to optimize these three beamformers. The primary challenge lies in optimizing the RIS configuration, as the MC effect renders the problem non-convex and intractable. To address this, we propose a novel algorithm based on the successive convex approximation (SCA) and the Neumann series expansion. Within the SCA framework, we propose a surrogate function that rigorously satisfies both convexity and equal-gradient conditions to update the iteration direction. Numerical results validate our proposal, demonstrating that the proposed channel estimation and beamforming methods effectively manage the MC in RIS, achieving higher spectral efficiency compared to state-of-the-art approaches.

As advancements close the gap between current device capabilities and the requirements for terahertz (THz)-band communications, the demand for terabit-per-second (Tbps) circuits is on the rise. This paper addresses the challenge of achieving Tbps data rates in THz-band communications by focusing on the baseband computation bottleneck. We propose leveraging parallel processing and pseudo-soft information (PSI) across multicarrier THz channels for efficient channel code decoding. We map bits to transmission resources using shorter code-words to enhance parallelizability and reduce complexity. Additionally, we integrate channel state information into PSI to alleviate the processing overhead of soft decoding. Results demonstrate that PSI-aided decoding of 64-bit code-words halves the complexity of 128-bit hard decoding under comparable effective rates, while introducing a 4dB gain at a 10−3block error rate. The proposed scheme approximates soft decoding with significant complexity reduction at a graceful performance cost.

The recent breakthroughs in electronic and photonic technologies enabled the design and implementation of intelligent reflective surfaces (IRSs) to manipulate electromagnetic waves and control the wireless environment. A promising application of IRSs is their integration with Terahertz (THz) communications. IRSs can cope with the blockage sensitivity of THz propagation by providing alternative line-of-sight (LoS) links to user equipment (UEs) which are initially blocked. However, deploying more IRSs may degrade the network performance as it leads to non-negligible interference levels. In this paper, we use tools from stochastic geometry to investigate the coverage probability of a downlink (DL) indoor THz network assisted by IRSs, which are added to a subset of the existing blockages. The numerical results reveal that there is an optimal density of IRSs that should be deployed to maximize the coverage of UEs in THz networks.

Guessing random additive noise decoding (GRAND) has recently demonstrated maximum-likelihood (ML) decoding performance on efficient, universal silicon realizations. Leveraging input bit-reliability soft information extracted from the channel and noise statistics, GRAND rank-orders and queries noise sequences in non-decreasing likelihood to recover code-words of arbitrary code-book structures. We consider soft-input, soft-output (SISO) GRAND that generates bit-reliability log-likelihood ratios (LLRs) via successive Euclidean-distance computations over a list of noise-recovered words. Noise guessing and list construction follow an ordered reliability bits GRAND (ORBGRAND) mechanism, the guess budget of which controls the performance and complexity trade-offs. The generated LLRs form enhanced a priori information that adapts noise-sequence ordering in a subsequent soft-GRAND iteration. We derive bounds on the achievable rates under per-realization and marginal input soft information and empirically study the achievable rates of SISO-GRAND. We also examine the complexity of the joint data detection and GRAND core, highlighting its superiority to conventional list-based detection schemes. SISO-ORBGRAND can outperform conventional sphere decoding in data detection and LLR generation; the corresponding channel-mismatched rates approximate ML decoding.

Wireless communications over Terahertz (THz)-band frequencies are vital enablers of ultra-high rate applications and services in sixth-generation (6G) networks. However, THz communications suffer from poor coverage because of inherent THz features such as high penetration losses, significant molecular absorption, and severe path loss. To surmount these critical challenges and fully exploit the THz band, we explore a coexisting radio frequency (RF) and THz finite indoor network in which THz small cells are deployed to provide high data rates, and RF macrocells are deployed to satisfy coverage requirements. Using stochastic geometry tools, we assess the performance of coexisting RF and THz networks and derive tractable analytical expressions for the coverage probability and average achievable rate. The analytical results are validated with Monte-Carlo simulations. Several insights are devised for accurate tuning and optimization of THz system parameters, including the THz bias, and the fraction of THz access points (APs) to deploy. The obtained results recognize a clear coverage/rate trade-off where a high fraction of THz AP improves the rate significantly but may degrade the coverage performance. Furthermore, the location of a user in the finite area highly affects the fraction of THz APs that optimizes its quality of service.

Guessing random additive noise decoding (GRAND) is a universal maximum-likelihood decoder that recovers codewords by guessing rank-ordered putative noise sequences and inverting their effect until one or more valid code-words are obtained. This work explores how GRAND can leverage additive-noise statistics and channel-state information in fading channels. Instead of computing per-bit reliability information in detectors and passing this information to the decoder, we propose leveraging the colored noise statistics following channel equalization as pseudo-soft information for sorting noise sequences. We investigate the efficacy of pseudo-soft information extracted from linear zero-forcing and minimum mean square error equalization when fed to a hardware-friendly soft-GRAND (ORBGRAND). We demonstrate that the proposed pseudo-soft GRAND schemes approximate the performance of state-of-the-art decoders of CA-Polar and BCH codes that avail of complete soft information. Compared to hard-GRAND, pseudo-soft ORBGRAND introduces up to 10 dB SNR gains for a target 10–3block-error rate.

Guessing random additive noise decoding (GRAND) is a maximum likelihood (ML) decoding method that identifies the noise effects corrupting code-words of arbitrary code-books. In a joint detection and decoding framework, this work demonstrates how GRAND can leverage crude soft information in received symbols and channel state information to generate, through guesswork, soft bit reliability outputs in log-likelihood ratios (LLRs). The LLRs are generated via successive computations of Euclidean-distance metrics corresponding to candidate noise-recovered words. Noting that the entropy of noise is much smaller than that of information bits, a small number of noise effect guesses generally suffices to hit a code-word, which allows generating LLRs for critical bits; LLR saturation is applied to the remaining bits. In an iterative (turbo) mode, the generated LLRs at a given soft-input, soft-output GRAND iteration serve as enhanced a priori information that adapts noise-sequence guess ordering in a subsequent iteration. Simulations demonstrate that a few turbo-GRAND iterations match the performance of ML-detection-based soft-GRAND in both AWGN and Rayleigh fading channels at a complexity cost that, on average, grows linearly (instead of exponentially) with the number of symbols.

Terahertz (THz)-band communications are a key enabler for future-generation wireless communication systems that promise to integrate a wide range of data-demanding applications. Recent advances in photonic, electronic, and plasmonic technologies are closing the gap in THz transceiver design. Consequently, prospect THz signal generation, modulation, and radiation methods are converging, and corresponding channel model, noise, and hardware-impairment notions are emerging. Such progress establishes a foundation for well-grounded research into THz-specific signal processing techniques for wireless communications. This tutorial overviews these techniques, emphasizing ultramassive multiple-input–multiple-output (UM-MIMO) systems and reconfigurable intelligent surfaces, vital for overcoming the distance problem at very high frequencies. We focus on the classical problems of waveform design and modulation, beamforming and precoding, index modulation, channel estimation, channel coding, and data detection. We also motivate signal processing techniques for THz sensing and localization.

The prospect of ultra-massive multiple-input multiple-output (UM-MIMO) technology to combat the distance problem at the Terahertz (THz) band is considered. It is well-known that the very large available bandwidths at THz frequencies come at the cost of severe propagation losses and power limitations, which result in very short communication distances. Recently, graphene-based plasmonic nano-antenna arrays that can accommodate hundreds of antenna elements in a few millimeters have been proposed. While such arrays enable efficient beamforming that can increase the communication range, they fail to provide sufficient spatial degrees of freedom for spatial multiplexing. In this paper, we examine spatial modulation (SM) techniques that can leverage the properties of densely packed configurable arrays of subarrays of nano-antennas, to increase capacity and spectral efficiency, while maintaining acceptable beamforming performance. Depending on the communication distance and the frequency of operation, a specific SM configuration that ensures good channel conditions is recommended. We analyze the performance of the proposed schemes theoretically and numerically in terms of symbol and bit error rates, where significant gains are observed compared to conventional SM. We demonstrate that SM at very high frequencies is a feasible paradigm, and we motivate several extensions that can make THz-band SM a future research trend.

Low-complexity data detectors targeted for large multiple-input multiple-output (MIMO) systems are considered. By systematically puncturing the channel matrix to have a specific structure, the complexity of standard non-linear detectors can be significantly reduced. The performance of these detectors is characterized and analyzed mathematically, and bounds on the achievable diversity gain and probability of bit error are derived. It is shown that puncturing does not negatively impact the receive diversity gain in hard-output detectors. Moreover, in soft-output detection, significant performance gains are attainable by ordering the layer of interest to be at the root when puncturing the channel. The proposed schemes scale up efficiently both in the number of antennas and constellation size.

A family of low-complexity detection schemes based on channel matrix puncturing targeted for large multiple-input multiple-output (MIMO) systems is proposed. It is well known that the computational cost of MIMO detection based on QR decomposition is directly proportional to the number of nonzero entries involved in back-substitution and slicing operations in the triangularized channel matrix, which can be too high for low-latency applications involving large MIMO dimensions. By systematically puncturing the channel to have a specific structure, it is demonstrated that the detection process can be accelerated by employing standard schemes, such as chase detection, list detection, nulling-and-cancellation detection, and sub-space detection on the transformed matrix. The performance of these schemes is characterized and analyzed mathematically, and bounds on the achievable diversity gain and probability of bit error are derived. Surprisingly, it is shown that puncturing does not negatively impact the receive diversity gain in hard-output detectors. The analysis is extended to soft-output detection when computing per-layer bit log-likelihood ratios; it is shown that significant performance gains are attainable by ordering the layer of interest to be at the root when puncturing the channel. Simulations of coded and uncoded scenarios certify that the proposed schemes scale up efficiently both in the number of antennas and constellation size, as well as in the presence of correlated channels. In particular, soft-output per-layer sub-space detection is shown to achieve a 2.5 dB signal-to-noise ratio gain at 10-4bit error rate in 256-quadratic-amplitude modulation 16 × 16 MIMO, while saving 77% of nulling-and-cancellation computations.

In this paper, a family of cost-efficient hard-output detection algorithms for large multiple-input multiple-output (MIMO) systems is proposed. The schemes employ punctured QR decomposition (QRD) instead of regular QRD to reduce complexity. The bit error rate performance is studied analytically, where it is shown that channel matrix puncturing does not affect the diversity gain of the detectors. Through empirical simulations, the proposed schemes are shown to achieve significant reductions in computational complexity with graceful performance degradation. In particular, at an SNR cost of 4dB, 77% of complex multiplications in nulling and cancellation are saved in 16 × 16 MIMO, while 30% of multiplications are saved at a 2dB cost in 4×4 MIMO. The savings can reach 94% in 64×64 MIMO.

In this paper, low-complexity multiple-input multiple-output (MIMO) subspace detection schemes are studied, which decompose a channel into multiple decoupled streams to be detected disjointly. Existing schemes require a number of matrix decomposition operations equal to the number of detected streams, which is computationally complex, especially in high-order MIMO systems. We propose two computationally efficient detection algorithms, based on a preprocessing stage that consists of special layer ordering, followed by permutation-robust QR decomposition (QRD) and elementary matrix operations. The algorithms are illustrated in the context of a 4-layer MIMO system, and their complexity is studied. Simulations demonstrate that using the proposed scheme, the QRD overhead is reduced by almost 50% for very high order MIMO, without incurring any performance degradation.

Optimum data detection schemes for dual layer multi-user multiple-input multiple-output (MU-MIMO) systems are studied. A joint maximum likelihood (ML) modulation classification (MC) of the co-scheduled user and data detection receiver is developed. By expanding the max-log-maximum-a-posteriori MC approach to include distances of counter ML hypothesis symbols, the decision metric for MC is shown to be an accumulation over a set of tones of Euclidean distance computations also used by the ML detector for bit log-likelihood ratio soft decision generation. With a small complexity overhead, the proposed approach achieves near-optimal performance. An efficient hardware architecture is presented for the proposed approach.

In this paper, optimum soft-output (SO) multiple-input multiple-output (MIMO) sphere detectors (SDs) are studied. Noting that ordering the channel matrix columns plays an important role in reducing the tree-search complexity of a SD, we propose an optimized layer-ordering scheme based on the minimum cumulative residual criterion. The proposed scheme is studied in the context of a 4 × 4 MIMO system, and a low-complexity dataflow architecture is proposed. The implementation employs a permutation-robust QR decomposition (PR-QRD) scheme, based on the modified Gram-Schmidt orthogonalization procedure. Simulations demonstrate that using the proposed scheme, the node count of a SO MIMO SD is reduced by one order of magnitude, while the QRD overhead is reduced by more than 25% in computations and 36% in time, without incurring any performance degradation.

In this paper, a low-complexity near-optimal detector for 8-layer MIMO systems is proposed. The detector employs subspace detection schemes, which decompose a spacially multiplexed MIMO channel into multiple decoupled streams to be detected separately. Several existing subspace detection algorithms are studied, all of which require a significant overhead for channel matrix decomposition. We propose computationally efficient schemes based on special layer ordering, followed by permutation-robust QR Decomposition (PR-QRD) using the modified Gram-Schmidt orthogonalization procedure, and elementary matrix operations. A hardware architecture is proposed, which allows building an 8-layer detector from 4-layer and 2-layer constituent detector blocks. Simulations demonstrate that using the proposed scheme, the QRD overhead is reduced by 30%, without incurring any performance degradation.

In this paper, dual-layer multi-user multiple-input multiple-output systems are studied. Building on the low-complexity layered orthogonal lattice detector (LC-LORD), an efficient sub-optimal joint modulation classification (MC) of the co-scheduled user and data detection receiver is developed. By adjusting the Max-Log-Maximum-a-Posteriori MC approach to the limitations of LC-LORD, and expanding it to include distances of counter maximum likelihood hypothesis symbols, the decision metric for MC is shown to be an accumulation over a set of tones of Euclidean distance computations also used by the LC-LORD detector for bit log-likelihood ratio soft decision generation. Simulations demonstrate that with a small complexity overhead, the proposed approaches achieve near interference-aware performance. An efficient hardware implementation scheme is presented.