Wireless Multiple Access Channel Research Articles

Over-the-Air Computation with Quantized CSI and Discrete Power Control Levels

In this paper, an Over-the-Air Computation (AirComp) scheme for fast data aggregation is considered. Multisource data are simultaneously transmitted by single-antenna mobile devices to a single-antenna fusion center (FC) through a wireless multiple-access channel. The optimal power levels at the devices and a postprocessing scaling function at the FC are jointly derived such that mean square error of the computation is minimized. Different than the existing approaches that rely on perfect channel state information (CSI) at the FC and assume that the devices’ optimal power levels can be selected from an infinite solution set, in the present paper, it is assumed that only quantized CSI is available at the FC and that the aforementioned optimal power levels lie in a finite discrete set of solutions. To derive the optimal power levels and FC’s scaling factor, a difficult nonconvex constrained optimization problem is formulated. An efficient and robust solution to quantization errors is developed via the deep reinforcement learning framework. Numerical results verify the good performance of the proposed approach while it exhibits a significant reduction in the required feedback.

Accelerating Distributed Optimization via Over-the-Air Computing

Distributed optimization is ubiquitous in emerging applications, such as robust sensor network control, smart grid management, machine learning, resource slicing, and localization. However, the extensive data exchange among local and central nodes may cause a severe communication bottleneck. To overcome this challenge, over-the-air computing (AirComp) is a promising medium access technology, which exploits the superposition property of the wireless multiple access channel (MAC) and offers significant bandwidth savings. In this work, we propose an AirComp framework for general distributed convex optimization problems. Specifically, a distributed primal-dual (DPD) subgradient method is utilized for the optimization procedure. Under general assumptions, we prove that DPD-AirComp can asymptotically achieve zero expected constraint violation. Therefore, DPD-AirComp ensures the feasibility of the original problem, despite the presence of channel fading and additive noise. Moreover, with proper power control of the users’ signals, the expected non-zero optimality gap can also be mitigated. Two practical applications of the proposed framework are presented, namely, smart grid management and wireless resource allocation. Finally, numerical results confirm DPD-AirComp’s excellent performance, while it is also shown that DPD-AirComp converges an order of magnitude faster compared to two digital orthogonal multiple access schemes, specifically, time-division multiple access (TDMA), and orthogonal frequency-division multiple access (OFDMA).

Effects of relay (source) side information on the coverage region in wireless Rayleigh and Rician fading multiple access relay channel

In this paper, we analyze the side information (SI) effect on the coverage region of the wireless multiple-access relay channel (MARC) in two different communications scenarios: SI only at one source and SI only at the relay. Aiming at this work, (I) a general achievable rate region is proved for wireless MARC with SI at one source and SI at the relay in two fading models (Rayleigh model, which has been widely studied in the literature; and Rician model the rate region of which for MARC has not been obtained before); (II) This obtained region, while including previous regions as its special cases, (a) shows the advantage of the SI known at the relay compared to the SI known at one encoder in removing the SI interference at the receiver (as seen in Theorem 2.2, Remark 2.1), and on the related coverage regions, too; and (b) can be exploited to prove corresponding coverage regions; (III) Then, the SI effect on the coverage region is scrutinized in different situations (SI only at one source and SI only at the relay), and also the differences between two fading models (Rayleigh and Rician) are investigated. (IV) Finally, theoretical findings are evaluated numerically.

Performance Analysis Over Correlated/Independent Fisher-Snedecor $\mathcal {F}$ Fading Multiple Access Channels

In this article, we investigate the impact of correlated fading on the performance of wireless multiple access channels (MAC) in the presence and absence of side information (SI) at transmitters, where the fading coefficients are modeled according to the Fisher-Snedecor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {F}$</tex-math></inline-formula> distribution. Specifically, we represent two scenarios: ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$i$</tex-math></inline-formula> ) clean MAC (i.e, without SI at transmitters), ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ii$</tex-math></inline-formula> ) doubly dirty MAC (i.e., with the non-causally known SI at transmitters). For both system models, we derive the closed-form expressions of the outage probability (OP) as well as the average capacity (AC) under independent fading conditions. Besides, exploiting copula theory, we obtain the exact analytical expressions for the OP and the AC under positive dependence fading conditions in both considered models. Finally, the validity of the analytical results is illustrated numerically.

Copula-Based Analysis of Power Allocation for Two-Sensor Composite Fading MAC With Dependent Channel Coefficients

In this article, the problem of power allocation in a wireless multiple access channel with two sensors is addressed, where squared channel coefficients, and, hence, signal-to-noise ratios are assumed to have Gaussian mixture distributions and the dependence between channel coefficients is described by using copula theory. For this model, outage probability is analyzed as the objective function for formulating the power allocation, and for the product copula function or in the independent channels case, a closed form of outage probability is obtained. Considering that the corresponding optimizations do not lead to convex optimization problems, MATLAB simulation is employed to solve the power allocation problem. Various Gaussian mixture distribution parameters are exploited for the links between the sensors and the fusion center with different dependencies and the results are compared.

Blind Federated Edge Learning

We study federated edge learning (FEEL), where wireless edge devices, each with its own dataset, learn a global model collaboratively with the help of a wireless access point acting as the parameter server (PS). At each iteration, wireless devices perform local updates using their local data and the most recent global model received from the PS, and send their local updates to the PS over a wireless fading multiple access channel (MAC). The PS then updates the global model according to the signal received over the wireless MAC, and shares it with the devices. Motivated by the additive nature of the wireless MAC, we propose an analog `over-the-air' aggregation scheme, in which the devices transmit their local updates in an uncoded fashion. However, unlike recent literature on over-the-air FEEL, here we assume that the devices do not have channel state information (CSI), while the PS has imperfect CSI. On the other hand, the PS is equipped with multiple antennas to alleviate the destructive effect of the channel, exacerbated due to the lack of perfect CSI. We design a receive beamforming scheme at the PS, and show that it can compensate for the lack of perfect CSI when the PS has a sufficient number of antennas. We also derive the convergence rate of the proposed algorithm highlighting the impact of the lack of perfect CSI, as well as the number of PS antennas. Both the experimental results and the convergence analysis illustrate the performance improvement of the proposed algorithm with the number of PS antennas, where the wireless fading MAC becomes deterministic despite the lack of perfect CSI when the PS has a sufficiently large number of antennas.

Over-the-Air Computation With Spatial-and-Temporal Correlated Signals

Over-the-air computation (AirComp) leveraging the superposition property of wireless multiple-access channel (MAC), is a promising technique for effective data collection and computation of large-scale wireless sensor measurements in Internet of Things applications. Most existing work on AirComp only considered computation of spatial-and-temporal independent sensor signals, though in practice different sensor measurement signals are usually correlated. In this letter, we propose an AirComp system with spatial-and-temporal correlated sensor signals, and formulate the optimal AirComp policy design problem for achieving the minimum computation mean-squared error (MSE). We develop the optimal AirComp policy with the minimum computation MSE in each time step by utilizing the current and the previously received signals. We also propose and optimize a low-complexity AirComp policy in closed form with the performance approaching to the optimal policy.

Integrated Sensing, Computation and Communication in B5G Cellular Internet of Things

In this article, we investigate the issue of integrated sensing, computation and communication (SCC) in beyond fifth-generation (B5G) cellular internet of things (IoT) networks. According to the characteristics of B5G cellular IoT, a comprehensive design framework integrating SCC is put forward for massive IoT. For sensing, highly accurate sensed information at IoT devices are sent to the base station (BS) by using non-orthogonal communication over wireless multiple access channels. Meanwhile, for computation, a novel technique, namely over-the-air computation (AirComp), is adopted to substantially reduce the latency of massive data aggregation via exploiting the superposition property of wireless multiple access channels. To coordinate the co-channel interference for enhancing the overall performance of B5G cellular IoT integrating SCC, two joint beamforming design algorithms are proposed from the perspectives of the computation error minimization and the weighted sum-rate maximization, respectively. Finally, extensive simulation results validate the effectiveness of the proposed algorithms for B5G cellular IoT over the baseline ones.

Over-the-Air Computation Systems: Optimal Design With Sum-Power Constraint

Over-the-air computation (AirComp), which leverages the superposition property of wireless multiple-access channel (MAC) and the mathematical tool of function representation, has been considered as a promising technique for effective collection and computation of massive sensor data in wireless Big Data applications. In most of the existing work on AirComp, optimal system-parameter design is commonly considered under the peak-power constraint of each sensor. In this paper, we propose an optimal transmitter-receiver (Tx-Rx) parameter design problem to minimize the computation mean-squared error (MSE) of an AirComp system under the sum-power constraint of the sensors. We solve the non-convex problem and obtain a closed-form solution. Also, we investigate another problem that minimizes the sum power of the sensors under the constraint of computation MSE. Our results show that in both of the problems, the sensors with poor and good channel conditions should use less power than the ones with moderate channel conditions.

Copula function‐based analysis of outage probability and coverage region for wireless multiple access communications with correlated fading channels

From practical and theoretical viewpoints, performance analysis of communications with correlated fading channels is important. In this study, the authors exploit a novel approach based on Copula function concept to investigate the impact of correlation of Rayleigh fading channels on communication performances. One of the most convenient ways to describe the dependence between several variables is using Copula functions. For this purpose, by applying the Farlie–Gumbel–Morgenstern Copula function, they derive closed-form expressions for outage probability as well as coverage region in a wireless multiple access channel. It is shown that the fading correlation improves the outage probability and coverage region for negative dependence structure. Specifically, whenever the dependence structure tends to negative values, the outage and coverage region performance improvement is increased. Finally, the efficiency of the analytical results is illustrated numerically.

Federated Learning Over Wireless Fading Channels

We study federated machine learning at the wireless network edge, where limited power wireless devices, each with its own dataset, build a joint model with the help of a remote parameter server (PS). We consider a bandwidth-limited fading multiple access channel (MAC) from the wireless devices to the PS, and propose various techniques to implement distributed stochastic gradient descent (DSGD) over this shared noisy wireless channel. We first propose a digital DSGD (D-DSGD) scheme, in which one device is selected opportunistically for transmission at each iteration based on the channel conditions; the scheduled device quantizes its gradient estimate to a finite number of bits imposed by the channel condition, and transmits these bits to the PS in a reliable manner. Next, motivated by the additive nature of the wireless MAC, we propose a novel analog communication scheme, referred to as the compressed analog DSGD (CA-DSGD), where the devices first sparsify their gradient estimates while accumulating error from previous iterations, and project the resultant sparse vector into a low-dimensional vector for bandwidth reduction. We also design a power allocation scheme to align the received gradient vectors at the PS in an efficient manner. Numerical results show that D-DSGD outperforms other digital approaches in the literature; however, in general the proposed CA-DSGD algorithm converges faster than the D-DSGD scheme, and reaches a higher level of accuracy. We have observed that the gap between the analog and digital schemes increases when the datasets of devices are not independent and identically distributed (i.i.d.). Furthermore, the performance of the CA-DSGD scheme is shown to be robust against imperfect channel state information (CSI) at the devices. Overall these results show clear advantages for the proposed analog over-the-air DSGD scheme, which suggests that learning and communication algorithms should be designed jointly to achieve the best end-to-end performance in machine learning applications at the wireless edge.

Federated Learning via Over-the-Air Computation

The stringent requirements for low-latency and privacy of the emerging high-stake applications with intelligent devices such as drones and smart vehicles make the cloud computing inapplicable in these scenarios. Instead, edge machine learning becomes increasingly attractive for performing training and inference directly at network edges without sending data to a centralized data center. This stimulates a nascent field termed as federated learning for training a machine learning model on computation, storage, energy and bandwidth limited mobile devices in a distributed manner. To preserve data privacy and address the issues of unbalanced and non-IID data points across different devices, the federated averaging algorithm has been proposed for global model aggregation by computing the weighted average of locally updated model at each selected device. However, the limited communication bandwidth becomes the main bottleneck for aggregating the locally computed updates. We thus propose a novel over-the-air computation based approach for fast global model aggregation via exploring the superposition property of a wireless multiple-access channel. This is achieved by joint device selection and beamforming design, which is modeled as a sparse and low-rank optimization problem to support efficient algorithms design. To achieve this goal, we provide a difference-of-convex-functions (DC) representation for the sparse and low-rank function to enhance sparsity and accurately detect the fixed-rank constraint in the procedure of device selection. A DC algorithm is further developed to solve the resulting DC program with global convergence guarantees. The algorithmic advantages and admirable performance of the proposed methodologies are demonstrated through extensive numerical results.

Machine Learning at the Wireless Edge: Distributed Stochastic Gradient Descent Over-the-Air

We study federated machine learning (ML) at the wireless edge, where power- and bandwidth-limited wireless devices with local datasets carry out distributed stochastic gradient descent (DSGD) with the help of a remote parameter server (PS). Standard approaches assume separate computation and communication, where local gradient estimates are compressed and transmitted to the PS over orthogonal links. Following this digital approach, we introduce D-DSGD, in which the wireless devices employ gradient quantization and error accumulation, and transmit their gradient estimates to the PS over a multiple access channel (MAC). We then introduce a novel analog scheme, called A-DSGD, which exploits the additive nature of the wireless MAC for over-the-air gradient computation, and provide convergence analysis for this approach. In A-DSGD, the devices first sparsify their gradient estimates, and then project them to a lower dimensional space imposed by the available channel bandwidth. These projections are sent directly over the MAC without employing any digital code. Numerical results show that A-DSGD converges faster than D-DSGD thanks to its more efficient use of the limited bandwidth and the natural alignment of the gradient estimates over the channel. The improvement is particularly compelling at low power and low bandwidth regimes. We also illustrate for a classification problem that, A-DSGD is more robust to bias in data distribution across devices, while D-DSGD significantly outperforms other digital schemes in the literature. We also observe that both D-DSGD and A-DSGD perform better by increasing the number of devices (while keeping the total dataset size constant), showing their ability in harnessing the computation power of edge devices.

Optimization of Resource Allocation Model With Energy-Efficient Cooperative Sensing in Green Cognitive Radio Networks

Green cognitive radios show promise for high energy efficiency (EE) in the future of wireless communications. Spectrum sensing refers to an energy-consuming procedure that allows cognitive users to independently identify unused radio spectrum segments and prevent interference to primary users, and it should be minimized due to resource limitations. In this paper, we present a wireless multiple-access channel function to establish the primary users’ presence and the mean EE optimization problem of the cognitive radio systems with mathematical structure computation purposes. EE, as the average throughput to the average energy consumption ratio, is used to measure the network’s performance subject to detection constraint. More specifically, since secondary users are generally battery-powered devices, saving on energy is crucial. We aim to decrease the energy consumption of secondary users while maximizing the total EE and preserving the accurate sensing by maximizing the sensing time detection subject to secondary user power constraints and minimum data rate. To address the non-convexity optimization problem, one can consider energy-efficient power allocation based on an iterative method. Simulation results show the optimum of our framework when combined by the multiple-access channel computation-based scheme. Green cognitive radio should consider the tradeoff against its complexity and maximum available EE metric. However, one can observe from the simulation results that the improved EE presented in this work yields much higher when compared with others with the same detection performance.

Structure Learning of Sparse GGMs Over Multiple Access Networks

A central machine is interested in estimating the underlying structure of a sparse Gaussian Graphical Model (GGM) from a dataset distributed across multiple local machines. The local machines can communicate with the central machine through a wireless multiple access channel. In this paper, we are interested in designing effective strategies where reliable learning is feasible under power and bandwidth limitations. Two approaches are proposed: Signs and Uncoded methods. In the Signs method, the local machines quantize their data into binary vectors and an optimal channel coding scheme is used to reliably send the vectors to the central machine where the structure is learned from the received data. In the Uncoded method, data symbols are scaled and transmitted through the channel. The central machine uses the received noisy symbols to recover the structure. Theoretical results show that both methods can recover the structure with high probability for a large enough sample size. Experimental results indicate the superiority of the Signs method over the Uncoded method under several circumstances.

The Wiretapped Diamond-Relay Channel

In this paper, we study a diamond-relay channel where the source is connected to $M$ relays through orthogonal links and the relays transmit to the destination over a wireless multiple-access channel in the presence of an eavesdropper. The eavesdropper not only observes the relay transmissions through another multiple-access channel but also observes a certain number of source-relay links. The legitimate terminals know neither the eavesdropper’s channel state information nor the location of source-relay links revealed to the eavesdropper except the total number of such links. For this wiretapped diamond-relay channel, we establish the optimal secure d.o.f. In the achievability part, our proposed scheme uses the source-relay links to transmit a judiciously constructed combination of message symbols, artificial noise symbols, and fictitious message symbols associated with secure network coding. The relays use a combination of beamforming and interference alignment in their transmission scheme. For the converse part, we take a genie-aided approach assuming that the location of wiretapped links is known.

On Quantizer Design for Distributed Bayesian Estimation in Sensor Networks

We consider the problem of distributed estimation under the Bayesian criterion and explore the design of optimal quantizers in such a system. We show that, for a conditionally unbiased and efficient estimator at the fusion center and when local observations have identical distributions, it is optimal to partition the local sensors into groups, with all sensors within a group using the same quantization rule. When all the sensors use identical number of decision regions, use of identical quantizers at the sensors is optimal. When the network is constrained by the capacity of the wireless multiple access channel over which the sensors transmit their quantized observations, we show that binary quantizers at the local sensors are optimal under certain conditions. Based on these observations, we address the location parameter estimation problem and present our optimal quantizer design approach. We also derive the performance limit for distributed location parameter estimation under the Bayesian criterion and find the conditions when the widely used threshold quantizer achieves this limit. We corroborate this result using simulations. We then relax the assumption of conditionally independent observations and derive the optimality conditions of quantizers for conditionally dependent observations. Using counter-examples, we also show that the previous results do not hold in this setting of dependent observations and, therefore, identical quantizers are not optimal.

Universal Non-Linear Cheat-Proof Pricing Framework for Wireless Multiple Access Channels

The success of future wireless networks depends on the correct and robust operation with selfish or even malicious nodes. Game theory provides methods to design such wireless systems. In this paper, we study a general multiple access system (with linear and nonlinear receiver) with three types of agents: the regulator, the system optimizer and the mobile users. The users formulate the signal to interference-plus-noise ratio (SINR) based quality-of-service (QoS) requirements and pay a corresponding virtual fee to the regulator depending on their transmit power. The regulator ensures the QoS requirements of all users by clever non-linear pricing and prevents cheating. The simple system optimizer solves the system utility maximization problem to allocate the power. The feasible utility region, power allocation, weights, the universal pricing, which is linear in the pricing parameters and logarithmic in power, and the resulting cost terms are derived in closed form. The user misbehavior is analyzed. Finally a repeated game is formulated with the worst case strategy for all the honest users and trigger strategy for the cheater. Analysis and simulation results show that the proposed framework is strategy-proof.

Robust Analog Function Computation via Wireless Multiple-Access Channels

Wireless sensor network applications often involve the computation of pre-defined functions of the measurements such as for example the arithmetic mean or maximum value. Standard approaches to this problem separate communication from computation: digitized sensor readings are transmitted interference-free to a fusion center that reconstructs each sensor reading and subsequently computes the sought function value. Such separation-based computation schemes are generally highly inefficient as a complete reconstruction of individual sensor readings at the fusion center is not necessary to compute a function of them. In particular, if the mathematical structure of the channel is suitably matched (in some sense) to the function of interest, then channel collisions induced by concurrent transmissions of different nodes can be beneficially exploited for computation purposes. This paper proposes an analog computation scheme that allows for an efficient estimate of linear and nonlinear functions over the wireless multiple-access channel. A match between the channel and the function being evaluated is thereby achieved via some pre-processing on the sensor readings and post-processing on the superimposed signals observed by the fusion center. After analyzing the estimation error for two function examples, simulations are presented to show the potential for huge performance gains over time- and code-division multiple-access based computation schemes.

On the study of network coded AF transmission protocol for wireless multiple access channels

On the study of network coded AF transmission protocol for wireless multiple access channels