Block Fading Channels Research Articles

Manifold Optimization-Based Data Detection Algorithm for Multiple-Input–Multiple-Output Orthogonal Frequency-Division Multiplexing Systems under Time-Varying Channels

Recently, multiple-input–multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems have gained significant attention in the field of wireless communications. The utilization of the Riemannian manifold has become prevalent in MIMO-OFDM systems. However, the existing data detection algorithms for MIMO-OFDM systems are mostly designed for block fading channels. Additionally, these algorithms often suffer from high computational complexity. In this paper, we propose a data detection algorithm on the basis of Riemannian manifold optimization for MIMO-OFDM systems under time-varying channels. The core concept of this algorithm is to optimize the transmitted signals by solving the manifold optimization problem in the case of time-varying channels. In order to reduce the computational complexity of the algorithm, we improve the proposed algorithm by dividing the transmitted signals into multiple subframes for solving the optimization problem separately and using the pilots to maintain the performance of the algorithm. In the simulation, the performance of multiple proposed algorithms and the forced-zero detection algorithm under different parameter settings are compared. The simulation results show that the proposed algorithm demonstrates good bit error rate and computational complexity performances.

Index Modulation-Aided Unsourced Random Access in the Block-Fading Channel

Index Modulation-Aided Unsourced Random Access in the Block-Fading Channel

Improving Timeliness-Fidelity Tradeoff in Wireless Sensor Networks: Waiting for All and Waiting for Partial Sensor Nodes

Emerging Internet of Things applications pursue both data timeliness and fidelity at the fusion center (FC), raising challenges for network design. This work investigates the optimal node number achieving the best timeliness-fidelity tradeoff. Specifically, we consider a wireless network where homogeneous sensors observe one source simultaneously and deliver their observations to the FC over orthogonal block fading channels. Two scenarios are considered: The FC waits for observations from all nodes and the FC waits for observations from partial nodes. We evaluate the data timeliness and fidelity using the age of information (AoI) and the mean squared error (MSE), respectively. We first present a tight approximation of the average AoI in closed-form and derive a tight lower bound on the MSE of the sensing system. Then, sub-optimal numbers of sensor nodes minimizing a weighted-sum of the average AoI and the MSE are obtained in closed-forms for both scenarios based on high signal-to-noise ratio regime analysis. Iteration algorithms are further provided to approach the optimums. It is shown that the optimal partial number of nodes is proportional to the square root of total number of nodes asymptotically. Numerical results validate the accuracy and effectiveness of the solutions in improving the timeliness-fidelity tradeoff.

Constrained Riemannian Noncoherent Constellations for the MIMO Multiple Access Channel

We consider the design of multiuser constellations for a multiple access channel (MAC) with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> users, with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> antennas each, that transmit simultaneously to a receiver equipped with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> antennas through a Rayleigh block-fading channel when no channel state information (CSI) is available to either the transmitter or the receiver. In full-diversity scenarios where the coherence time is at least <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ≥ ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> + 1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> , the proposed constellation design criterion is based on the asymptotic expression of the multiuser pairwise error probability (PEP) derived by Brehler and Varanasi (2001). In non-full diversity scenarios, for which the previous PEP expression is no longer valid, the proposed design criteria are based on proxies of the PEP recently proposed by Ngo and Yang (2021). Although both the PEP expression and its bounds or proxies were previously considered intractable for optimization, in this work we derive their respective unconstrained gradients. These gradients are in turn used in the optimization of the proposed cost functions in different Riemannian manifolds representing different power constraints. In particular, in addition to the standard unitary space-time modulation (USTM) leading to optimization on the Grassmann manifold, we consider a more relaxed percodeword power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">oblique manifold</i> , and an average power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trace manifold</i> . Equipped with these theoretical tools, we design multiuser constellations for the MIMO MAC in full-diversity and non-full-diversity scenarios with state-of-the-art performance in terms of symbol error rate (SER).

Efficient Evaluation of the Error Probability for Pilot-Assisted URLLC With Massive MIMO

We propose a numerically efficient method for evaluating the random-coding union bound with parameter <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> on the error probability achievable in the finite-blocklength regime by a pilot-assisted transmission scheme employing Gaussian code-books and operating over a memoryless block-fading channel. Our method relies on the saddlepoint approximation, which, differently from previous results reported for similar scenarios, is performed with respect to the number of fading blocks (a.k.a. diversity branches) spanned by each codeword, instead of the number of channel uses per block. This different approach avoids a costly numerical averaging of the error probability over the realizations of the fading process and of its pilot-based estimate at the receiver and results in a significant reduction of the number of channel realizations required to estimate the error probability accurately. Our numerical experiments for both single-antenna communication links and massive multiple-input multiple-output (MIMO) networks show that, when two or more diversity branches are available, the error probability can be estimated accurately with the saddlepoint approximation with respect to the number of fading blocks using a numerical method that requires about two orders of magnitude fewer Monte-Carlo samples than with the saddlepoint approximation with respect to the number of channel uses per block.

Information Rates for Channels with Fading, Side Information and Adaptive Codewords.

Generalized mutual information (GMI) is used to compute achievable rates for fading channels with various types of channel state information at the transmitter (CSIT) and receiver (CSIR). The GMI is based on variations of auxiliary channel models with additive white Gaussian noise (AWGN) and circularly-symmetric complex Gaussian inputs. One variation uses reverse channel models with minimum mean square error (MMSE) estimates that give the largest rates but are challenging to optimize. A second variation uses forward channel models with linear MMSE estimates that are easier to optimize. Both model classes are applied to channels where the receiver is unaware of the CSIT and for which adaptive codewords achieve capacity. The forward model inputs are chosen as linear functions of the adaptive codeword's entries to simplify the analysis. For scalar channels, the maximum GMI is then achieved by a conventional codebook, where the amplitude and phase of each channel symbol are modified based on the CSIT. The GMI increases by partitioning the channel output alphabet and using a different auxiliary model for each partition subset. The partitioning also helps to determine the capacity scaling at high and low signal-to-noise ratios. A class of power control policies is described for partial CSIR, including a MMSE policy for full CSIT. Several examples of fading channels with AWGN illustrate the theory, focusing on on-off fading and Rayleigh fading. The capacity results generalize to block fading channels with in-block feedback, including capacity expressions in terms of mutual and directed information.

A new HARQ scheme for 5G systems via interleaved superposition retransmission

Within the framework of the 5G new radio (NR), we propose a new hybrid automatic repeat request (HARQ) scheme to improve the throughput performance. The difference between the proposed scheme and the conventional one lies in the first retransmission, where the erroneous coded block group is interleaved and superimposed (XORed) onto a fresh coded block group. At the receiver, an iterative message-passing decoding algorithm can be employed to recover the target erroneous code block group (CBG). Only when the superposed retransmission fails, the conventional incremental redundancy (IR) or repetition redundancy (RR) retransmission is initiated. In any case, since the first retransmission is along with but has negligible effect on the fresh CBG, it costs neither transmitted power nor bandwidth. Monte-Carlo simulation results reveal that the presented HARQ schemes can achieve throughput improvements up to 10% over block fading channels and up to 50% over fast fading channels in comparison with the original 5G CBG-level HARQ scheme but without excessively increasing the implementation complexity.

(Non)-Coherent MU-MIMO Block Fading Channels With Finite Blocklength and Linear Processing

Driven by the stringent demands of future ultra reliable and low latency communication (URLLC), we provide a comprehensive study for a coherent and non-coherent multiuser multiple-input multiple-output (MU-MIMO) uplink system in the finite blocklength regime. The independent and identically distributed (i.i.d.) Gaussian codebook is assumed for each user. To be more specific, the base station (BS) first uses two popular linear processing schemes to combine the signals transmitted from all users, namely maximum-ratio combining (MRC) and zero-forcing (ZF). Following it, the matched maximum-likelihood (ML) and mismatched nearest-neighbour (NN) decoding metric for the coherent and non-coherent cases are respectively employed at the BS. Under these conditions, the refined third-order achievable coding rate, expressed as a function of the blocklength, average error probability, and the third-order term of the information density (called as the channel perturbation), is derived. With this result in hand, a detailed performance analysis is then pursued, through which, we derive the asymptotic results of the channel perturbation, achievable coding rate, channel capacity, and the channel dispersion. These theoretical results enable us to obtain a number of interesting insights related to the impact of the finite blocklength: i) in our system setting, massive MIMO helps to reduce the channel perturbation of the achievable coding rate, which can even be discarded without affecting the performance with just a small-to-moderate number of BS antennas and number of blocks; ii) under the non-coherent case, even with massive MIMO, the channel estimation errors cannot be eliminated unless the transmit powers in both the channel estimation and data transmission phases for each user are made inversely proportional to the square root of the number of BS antennas; iii) in the non-coherent case and for fixed total blocklength, the scenarios with longer coherence intervals and smaller number of blocks will offer higher achievable coding rate.

Union Bound Minimization Approach for Designing Grassmannian Constellations

In this paper, we propose an algorithm for designing unstructured Grassmannian constellations for noncoherent multiple-input multiple-output (MIMO) communications over Rayleigh block-fading channels. Unlike the majority of existing unitary space-time or Grassmannian constellations, which are typically designed to maximize the minimum distance between codewords, in this work we employ the asymptotic pairwise error probability (PEP) union bound (UB) of the constellation as the design criterion. In addition, the proposed criterion allows the design of MIMO Grassmannian constellations specifically optimized for a given number of receiving antennas. A rigorous derivation of the gradient of the asymptotic UB on a Cartesian product of Grassmann manifolds, is the main technical ingredient of the proposed gradient descent algorithm. A simple modification of the proposed cost function, which weighs each pairwise error term in the UB according to the Hamming distance between the binary labels assigned to the respective codewords, allows us to jointly solve the constellation design and the bit labeling problem. Our simulation results show that the constellations designed with the proposed method outperform other structured and unstructured Grassmannian designs in terms of symbol error rate (SER) and bit error rate (BER), for a wide range of scenarios.

Covert Communication for Spatially Sparse mmWave Massive MIMO Channels

Covert communication, also known as communication with low probability of detection, aims to provide reliable communication for legal users and prevent any other user from detecting the occurrence of legal communication. Motivated by the strong need of security links of the next generation communication systems, we study covert communication with millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) hybrid beamforming. Consistent with existing studies on covert communication, we use the Kullback-Leibler (KL) divergence and the total variation (TV) distance as the covertness measure. Under both covertness measures, for block fading channels, we derive the covert transmission rate with and without artificial noise. These results are obtained by optimizing the transmit power and the jamming power to satisfy the covertness constraints and to maximize the transmission rate. Specifically, when artificial noise is allowed, we show that there exists an optimal jamming power to achieve the covert transmission rate given the transmit signal power. Furthermore, we propose a metric to measure the inherent sparsity of the mmWave massive MIMO channel in the spatial domain, and study its effect on the covertness measures and the corresponding covert transmission rates. Our results provide insights and benchmarks for the design of practical covert communication systems with mmWave massive MIMO.

Union bounds on the symbol error probability of LoRa modulation for flat Rician block fading channels

In this paper the symbol error performance of LoRa modulation is addressed for flat Rician block fading channels. First the exact symbol error probability of the LoRa modulation on Rician fading is derived. Then the upper and lower union bounds are employed on the derived symbol error probability. The proposed bounds are compared against the exact symbol error probability, the numerical evaluation of the symbol error probability and the state-of-art approximation of the LoRa symbol error probability. Numerical results show that while the proposed upper bound is very tight to the exact symbol error probability, there is approximately a 2.5 dB gap for the lower bound.

Symbol-Level GRAND for High-Order Modulation Over Block Fading Channels

Guessing random additive noise decoding (GRAND) is a noise-centric decoding method, which is suitable for low-latency communications, as it supports error correction codes that generate short codewords. GRAND estimates transmitted codewords by guessing the error patterns that altered them during transmission. The guessing process requires the testing of error patterns that are arranged in increasing order of Hamming weight. This approach is fitting for binary transmission over additive white Gaussian noise channels. This letter considers transmission of coded and modulated data over block fading channels and proposes a more computationally efficient variant of GRAND, which leverages information on the modulation scheme and the fading channel. In the core of the proposed variant, referred to as symbol-level GRAND, is an expression that approximately computes the probability of occurrence of an error pattern and determines the order with which error patterns are tested. Analysis and simulation results demonstrate that symbol-level GRAND produces estimates of the transmitted codewords faster than the original GRAND at the cost of a small increase in memory requirements.

Coded Asymmetric Modulation Design for Block-Fading Channels With Nonlinear Energy Harvesting

In this letter, the design of coded modulation for simultaneous wireless information and power transfer (SWIPT) block-fading channels is proposed, for both power-splitting (PS) and time-switching (TS) nonlinear energy harvesting (EH). With PS, although the diversity-rate tradeoff is not affected, nonlinear EH requires asymmetric modulations design which leads to an information transfer (IT) performance penalty. We thus design an asymmetric circular quadrature amplitude modulation (ACQAM) scheme that provides large performance gains compared to conventional modulations. On the other hand, we show that TS negatively impacts the diversity-rate tradeoff of the coded modulation, while an optimal QAM can be employed in the IT phase. We next derive an upper bound on the average word error rate (WER) based on a pairwise error probability analysis for both EH methods. Finally, WER simulation results are shown together with the derived bounds.

Channel Aging-Aware Precoding for RIS-Aided Multi-User Communications

Reconfigurable intelligent surfaces (RISs) have received intensive attention for their outstanding potential of reconstructing wireless propagation channels to significantly enhance the communication quality. In this article, we study the sum spectral efficiency (SE) of a multi-user communication system aided by an RIS. As opposed to previous works that assume independent and identically distributed block-fading channel models, we focus on a realistic scenario with the impact of channel aging due to user mobility and the spatial correlation among the reflecting elements of the RIS. Particularly, we first present a joint pragmatic model which encompasses the impact of channel estimation error and channel aging that facilitate the analytical derivations for the sum SE of the RIS-aided system. On this basis, we formulate the joint transmit beamforming and phase shift design as a nonconvex optimization problem to maximize the system sum SE. To address the design problem, we propose an efficient suboptimal channel aging-aware precoding (CAP) algorithm to obtain efficient suboptimal solutions for the considered problem capitalizing on the generalized fractional programming, the alternating direction method of multipliers method, and the alternating optimization method. Simulation results are provided to verify the effectiveness of the proposed algorithm and illustrate the impact of key system and channel parameters on the system performance. Our analysis unveils that a higher transmit power at the base station, a larger value of temporal correlation coefficients, a larger number and the size of RIS elements are beneficial to the system performance.

Irregular Repetition Slotted ALOHA Over Rayleigh Block Fading Channels: Bounds and Threshold Saturation via Spatial Coupling

Irregular Repetition Slotted ALOHA Over Rayleigh Block Fading Channels: Bounds and Threshold Saturation via Spatial Coupling

Secrecy Performance Evaluation of Scalable Cell-Free Massive MIMO Systems: A Stochastic Geometry Approach

This paper presents the first performance analysis of physical layer downlink secure transmissions in a scalable cell-free massive MIMO (SCF-mMIMO) system. A stochastic geometry approach is used to model the locations of the access points (APs), user equipments (UEs) and eavesdroppers (Eves) as independent homogeneous Poisson point processes (HPPPs). In addition to applying maximum ratio transmission (MRT) to send the confidential messages, null-space artificial noise is also injected for secrecy enhancement. We analytically characterize the secrecy performance in terms of both the outage-based secrecy transmission rate (STR) and the ergodic secrecy rate (ESR), appropriate for slow quasi-static fading channels and fast block-fading channels, respectively. By utilizing moment matching and Gil-Pelaez inversion theorem, we are able to obtain mathematically tractable approximations for the performance metrics. These approximations are shown to have high accuracy as compared to simulation results. Our numerical results reveal useful design insights that cannot be inferred from existing studies. These insights answer important questions such as whether it is best to deploy as many APs each with fewer antennas and to what extent the artificial noise insertion is beneficial.

Design of Protograph LDPC Codes Using Resolvable Block Designs for Block Fading Channel

In this letter, we propose new protograph low-density parity-check (LDPC) codes of high code rates using resolvable block designs (RBDs) for block fading (BF) channels. To analyze the performance of the proposed LDPC codes, we derive an upper bound on bit error rate (BER) using the novel method, called the gamma evolution. Finally, we numerically show that the frame error rate (FER) of the proposed LDPC codes has a slope approaching the channel outage probability.

Near optimal scheduling for opportunistic spectrum access over block fading channels in cognitive radio assisted vehicular network

With the increasing use of cognitive radio technology in vehicular communications, vehicles will be enabled with cognitive radio in the future. Cognitive radio assisted vehicular networks make cognitive radio enabled vehicles utilize licensed spectrum on highways opportunistically. This work tackles cognitive radio assisted vehicular networks including M primary users (transmitter), M primary receivers, a secondary user (transmitter) with K channels and K secondary receivers. A channel is assigned to each primary user for data transmission whenever they need to use. The secondary user has data backlog. It knows neither the states (good or bad) of M channels, or statistics of channel evolution processes. It selects K of M channels to send data at each time slot. If it senses that a selected channel is in good state, it uses that channel for data packet transmission in same time slot. If not, it chooses another channel at the next time slot. We tackle this problem under average reward criteria for finite and infinite time horizon. This work presents Uniforming Random Ordered Policy (UROP) and shows UROP achieves near-optimal throughput under block fading assumption for generic channel evolution process. Numerical results show that our policy achieves near-optimal throughput (more than 80% of optimal throughput for scarce number of available channels) under average reward criteria whereas MP may achieve less than even 25% of optimal throughput for scarce number of available channels.

A Network-Assisted Game-Theoretic Design to Power Control in Autoregressive Fading Channels

Several previous works have proposed game-theoretic approaches to controlling the pilot and data power levels in the uplink of both single and multi-cell multi-user multiple input multiple output (MU-MIMO) systems. Unfortunately, the vast majority of existing works design these power control schemes under the assumption that the wireless channels between the mobile terminals and the serving base station are block fading. Meanwhile, several letters have shown that modeling fast fading channels as autoregressive (AR) processes with known or estimated state transition matrices give much more accurate results than those suggested by block fading models. Thus, this letter proposes a game-theoretic approach to controlling the uplink pilot and data power levels in a MU-MIMO system, in which the wireless channels are AR processes with mobile terminal-specific state transition matrices. We find that the proposed approach outperforms a classical cellular path-loss compensating fractional power control scheme and a game-theoretic power control scheme designed for block fading channels.

Performance Analysis for Covert Communications Under Faster-Than-Nyquist Signaling

In this letter, we analyze the performance of covert communications under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">faster-than-Nyquist</i> (FTN) signaling in the Rayleigh block fading channel. Both maximum likelihood criterion- and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Kullback-Leibler</i> (KL) divergence-based covertness constraints are considered. Especially, for KL divergence-based one, we prove that both the maximum transmit power and covert rate under FTN signaling are higher than those under Nyquist signaling. Numerical results coincide with our analysis and validate the advantages of FTN signaling to realize covert data transmission.