Fading Multiple Access Channel Research Articles

Linear feedback coding scheme for multiple-access fading channels with degraded message sets.

Channel coding technology plays an important role in wireless communication systems, and it serves as a crucial mechanism to reduce interference during the transmission process. As the fifth-generation (5G) and sixth-generation (6G) wireless communication systems rapidly advance, requirements of the users on the quality and security of wireless service are increasing. To solve these problems, it calls for us to explore the new channel coding technologies. In this paper, a linear feedback coding scheme for fading multiple-access channels with degraded message sets (FMAC-DMS) is proposed. In this scheme, the transmitting beamforming and channel splitting are used to transform the channel with complex signals into scalar equivalent sub-channels. Then, the extended Schalkwijk-Kailath coding scheme (SK) is further applied to each sub-channel. The channel capacity, finite blocklength (FBL) sum-rate and FBL secrecy achievable sum-rate of the FMAC-DMS in single-input single-output (SISO) and multi-input single-output (MISO) cases are derived. Finally, we show that the proposed scheme not only provides a FBL coding solution but also guarantees physical layer security(PLS). The numerical and simulation results show the effectiveness of the proposed scheme as a channel coding solution. The study of this paper provides a new method to construct a practical FBL scheme for the FMAC-DMS.

Federated Learning With Over-the-Air Aggregation Over Time-Varying Channels

We study federated learning (FL) with over-the-air aggregation over time-varying wireless channels. Independent workers compute local gradients based on their local datasets and send them to a parameter server (PS) through a time-varying multipath fading multiple access channel via orthogonal frequency-division multiplexing (OFDM). We assume that the workers do not have channel state information, hence the PS employs multiple antennas to alleviate the fading effects. Wireless channel variations result in inter-carrier interference, which has a detrimental effect on the performance of OFDM systems, especially when the channel is rapidly varying. We examine the effects of the channel time variations on the convergence of the FL with over-the-air aggregation, and show that the resulting undesired interference terms have only limited destructive effects, which do not prevent the convergence of the learning algorithm. We also validate our results via extensive simulations, which corroborate the theoretical expectations.

Lossy State Communication over Fading Multiple Access Channels.

Joint communications and sensing functionalities integrated into the same communication network have become increasingly relevant due to the large bandwidth requirements of next-generation wireless communication systems and the impending spectral shortage. While there exist system-level guidelines and waveform design specifications for such systems, an information-theoretic analysis of the absolute performance capabilities of joint sensing and communication systems that take into account practical limitations such as fading has not been addressed in the literature. Motivated by this, we undertake a network information-theoretic analysis of a typical joint communications and sensing system in this paper. Towards this end, we consider a state-dependent fading Gaussian multiple access channel (GMAC) setup with an additive state. The state process is assumed to be independent and identically distributed (i.i.d.) Gaussian, and non-causally available to all the transmitting nodes. The fading gains on the respective links are assumed to be stationary and ergodic and available only at the receiver. In this setting, with no knowledge of fading gains at the transmitters, we are interested in joint message communication and estimation of the state at the receiver to meet a target distortion in the mean-squared error sense. Our main contribution here is a complete characterization of the distortion-rate trade-off region between the communication rates and the state estimation distortion for a two-sender GMAC. Our results show that the optimal strategy is based on static power allocation and involves uncoded transmissions to amplify the state, along with the superposition of the digital message streams using appropriate Gaussian codebooks and dirty paper coding (DPC). This acts as a design directive for realistic systems using joint sensing and transmission in next-generation wireless standards and points to the relative benefits of uncoded communications and joint source-channel coding in such systems.

Federated Learning via Over-the-Air Computation With Statistical Channel State Information

Federated learning (FL) is a popular distributed learning paradigm, in which a global model at a server learns private data of clients without data shared among clients or the server. In this paper, we consider FL over a noisy fading multiple access channel (MAC) via over-the-air computation (AirComp). Benefiting from waveform-superposition propriety of wireless signals, AirComp is able to achieve fast aggregations in FL and improve spectral efficiency. However, most of the schemes exploiting AirComp require intensive channel estimations as the demands from precoders, which results in considerable communication overheads. For this reason, we propose two novel FL schemes with statistical channel state information (FL-SCSI-A and FL-SCSI-B) to reduce the efforts required by channel estimations. In FL-SCSI-A, precoders adjust phases of transmitted signals with phases of instant channel state information (CSI), and scale transmitted signal powers based on statistical CSI. The precoder design has the following two advantages. First, phases of instant CSI can be easier to estimate than complete instant CSI. Second, since clients only need to estimate phases of their own instant CSI (instead of CSI of all clients), with channel reciprocity, this can be easily achieved by letting the server broadcast pilots to all clients. The server in FL-SCSI-A is also efficient. It only needs to estimate the sum of channel gains of all clients, which can be easily achieved by letting clients transmit pilots simultaneously. To further reduce the communication overhead, FL-SCSI-B is proposed. The precoders in FL-SCSI-B are similar to FL-SCSI-A, while the server does not require any knowledge of instant CSI, which reduces the demands of channel estimations. For both schemes, we prove that the distortion caused by the noisy fading MAC is bounded, and the convergences of the learning processes are guaranteed for strongly smooth losses with heterogeneous data assumptions. Experimental results show that the proposed schemes perform better than benchmark schemes while reducing efforts required by channel estimation.

Secrecy Rate Region Enhancement in Multiple Access Wiretap Channel

It is commonly known that physical layer security is achieved with a trade-off in terms of the achievable rate. Hence, security constraints generate rate losses in wiretap channels. To mitigate such rate losses in multi-user channels, we propose a coding/decoding scheme for multi-user multiple access wiretap channel (MAC-WT), where previously transmitted messages are used as a secret key to enhance the secrecy rates of the transmitting users, until the usual Shannon capacity region of a multiple access channel (MAC) is achieved without the secrecy constraint. With this coding scheme, all messages transmitted in the recent past are secure with respect to all the information of the eavesdropper till now. To achieve this goal, we introduce secret key buffers at both the users and the legitimate receiver. Finally, we consider a fading MAC-WT and show that with this coding/decoding scheme, we can achieve the capacity region of a fading MAC channel (in the ergodic sense).

Performance analysis of one‐source‐with‐one‐helper transmission over shadowed κ$\kappa$‐μ$\mu$ fading multiple access channels

The performance of correlated sources transmission over multiple access shadowed κ $\kappa$ - μ $\mu$ fading channels is investigated, in which one of the correlated sources needs to be recovered at the destination, whereas the other serves as a helper. The sufficient condition for lossless coding is determined by the intersection of the modified Slepian–Wolf region and the multiple access channel region. The outage probability upper bounds are derived based on the sufficient condition, with the Gaussian codebook capacity and the constellation constrained capacity, respectively. The difference between the outage probabilities derived with the two kinds of capacities is found to be very minor, when the spectrum efficiency or source rate is low; however, with high spectrum efficiency or high source rate, such difference becomes significant. A closed-form outage approximation is also obtained at the high signal-to-noise ratio region. The accuracy of the analytical results is verified by the Monte-Carlo simulations. It is found that shadowing significantly affects the outage performance, however, it has no effect on the diversity gain. Furthermore, the power allocation between the source and the helper is studied to minimize the outage probability and it is found that generally more power should be allocated to the helper in the case with higher source-helper correlation.

User Identification and Channel Estimation by Iterative DNN-Based Decoder on Multiple-Access Fading Channel

User Identification and Channel Estimation by Iterative DNN-Based Decoder on Multiple-Access Fading Channel

Accelerated Gradient Descent Learning Over Multiple Access Fading Channels

We consider a distributed learning problem in a wireless network, consisting of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> distributed edge devices and a parameter server (PS). The objective function is a sum of the edge devices&#x2019; local loss functions, who aim to train a shared model by communicating with the PS over multiple access channels (MAC). This problem has attracted a growing interest in distributed sensing systems, and more recently in federated learning, known as over-the-air computation. In this paper, we develop a novel Accelerated Gradient-descent Multiple Access (AGMA) algorithm that uses momentum-based gradient signals over noisy fading MAC to improve the convergence rate as compared to existing methods. Furthermore, AGMA does not require power control or beamforming to cancel the fading effect, which simplifies the implementation complexity. We analyze AGMA theoretically, and establish a finite-sample bound of the error for both convex and strongly convex loss functions with Lipschitz gradient. For the strongly convex case, we show that AGMA approaches the best-known linear convergence rate as the network increases. For the convex case, we show that AGMA significantly improves the sub-linear convergence rate as compared to existing methods. Finally, we present simulation results using real datasets that demonstrate better performance by AGMA.

Distributed Detection Fusion in Clustered Sensor Networks Over Multiple Access Fading Channels

In this paper, we tackle decision fusion for distributed detection in a randomly-deployed clustered Wireless Sensor Networks (WSNs) operating over a non-ideal multiple access channels (MACs), i.e. considering Rayleigh fading, path loss and additive noise. To mitigate fading, we propose the distributed equal gain transmit combining (dEGTC) and distributed maximum ratio transit combining (dMRTC). The first and second order statistics of the received signals were analytically computed via stochastic geometry tools. Then the distribution of the received signal over the MAC are approximated by Gaussian and log-normal distributions via moment matching. This enabled the derivation of moment matching optimal fusion rules (MOR) for both distributions. Moreover, suboptimal simpler fusion rules were also proposed, in which all the CHs data are equally weighed, which is termed moment matching equal gain fusion rule (MER). It is shown by simulations that increasing the number of clusters improve the performance. Moreover, MOR-Gaussian based algorithms are better under free-space propagation whereas their lognormal counterparts are more suited in the ground-reflection case. Also, the latter algorithms show better results in low SNR and SN numbers conditions. We have proved that the received power at the CH in MAC is proportional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(\lambda ^{2} R^{2})$</tex-math></inline-formula> and to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(\lambda ^{2} \ln ^{2} R)$</tex-math></inline-formula> in the free-space propagation and the ground-reflection cases respectively, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> is SN deployment intensity and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R$</tex-math></inline-formula> is the cluster radius. This implies that having more clusters decreases the required transmission power for a given SNR at the receiver.

Distributed Constrained Online Convex Optimization Over Multiple Access Fading Channels

In this paper, we study distributed constrained online convex optimization for a wireless system consisting of a parameter server and multiple agents. Each agent has a local constraint function and a time-varying local loss function, and needs to choose sequential actions based on causal information. The goal of the overall system is to minimize the accumulated total loss of all agents over a time horizon subject to total constraints of the agents. To this end, the agents communicate with the server over multiple access noisy fading channels, where the information is exchanged imperfectly. We first consider the full information scenario, where the local loss function of each agent is fully revealed to the corresponding agent in each time slot. We propose a modified saddle-point algorithm, where each agent sends an analog signal pertaining to the current value of the local constraint function and the server receives a superposition of these signals distorted by the noisy fading channels. We analyze the performance of the proposed algorithm, and establish <inline-formula><tex-math notation="LaTeX">$\mathcal {O}(\sqrt{T})$</tex-math></inline-formula> regret bound and <inline-formula><tex-math notation="LaTeX">$\mathcal {O}(T^\frac{3}{4})$</tex-math></inline-formula> constraint violation bound for the algorithm, where <inline-formula><tex-math notation="LaTeX">$T$</tex-math></inline-formula> is the time horizon. Further, we extend the algorithm and performance analyses to the scenario of bandit feedback, where only the values of the local loss functions at two random points are disclosed to the agents in every time slot. In such a case, performance bounds similar to the full information scenario are established. Finally, numerical examples are presented to corroborate the efficacy of the proposed algorithms.

Blind Federated Learning at the Wireless Edge With Low-Resolution ADC and DAC

We study collaborative machine learning systems where a massive dataset is distributed across independent workers which compute their local gradient estimates based on their own datasets. Workers send their estimates through a multipath fading multiple access channel with orthogonal frequency division multiplexing to mitigate the frequency selectivity of the channel. We assume that there is no channel state information (CSI) at the workers, and the parameter server (PS) employs multiple antennas to align the received signals. To reduce the power consumption and the hardware costs, we employ complex-valued low-resolution digital-to-analog converters (DACs) and analog-to-digital converters (ADCs), at the transmitter and the receiver sides, respectively, and study the effects of practical low-cost DACs and ADCs on the learning performance. Our theoretical analysis shows that the impairments caused by low-resolution DACs and ADCs, including those of one-bit DACs and ADCs, do not prevent the convergence of the federated learning algorithms, and the multipath channel effects vanish when a sufficient number of antennas are used at the PS. We also validate our theoretical results via simulations, and demonstrate that using low-resolution, even one-bit, DACs and ADCs causes only a slight decrease in the learning accuracy.

The Role of Correlation in the Doubly Dirty Fading MAC With Side Information at the Transmitters

We investigate the impact of fading correlation on the performance of the doubly dirty fading multiple access channel (MAC) with non-causally known side information at transmitters. Using Copula theory, we derive closed-form expressions for the outage probability (OP) and the coverage region under positive/negative dependence conditions. We show that a positive dependence structure between the fading channel coefficients is beneficial for the system performance, as it improves the OP and extends the coverage region compared to the case of independent fading. Conversely, a negative dependence structure has a detrimental effect on both performance metrics.

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.

Outage Probability of One-Source-With-One- Helper Sensor Systems in Block Rayleigh Fading Multiple Access Channels

Two correlated sources are transmitted over a block Rayleigh fading multiple access channel (MAC), where information recovery from only one of the sources is aimed at, and the other is used as a helper which helps recover the source sequences at the destination. In this article, the successful transmission is defined as in the case the transmission rates satisfy the intersection of both the MAC region and the Slepian-Wolf (SW) region with a helper, referred to as h-SW region, even though it is a sufficient condition. Then, the outage is defined as the average probability that the two regions do not have an intersection. The explicit expressions of the outage probability of the system are derived, in the form of multiple integrals with respect to the probability density function of instantaneous signal-to-noise ratios of each link. To have an in-depth insight regarding the contributions of some special cases to the successful transmission probability, the occurrence probabilities of these cases are also evaluated. The results indicate that outage probabilities decrease as the correlation between the source and helper information increases. The impacts of geometric gains of each link and the correlation of each link's fading variation are also considered. The most significant finding of this article is that h-SW over a MAC improves the throughput efficiency compared to the orthogonal transmission both in independent and correlated block Rayleigh fading channels without sacrificing the outage probability.

On the secrecy rate region and outage probability of secondary wiretap multiple access channel over dissimilar Rayleigh/Nakagami fading

A secondary fading multiple access channel (S-FMAC) with two transmitters, having random available bandwidth taking values 0 or 1 and one coherent receiver knowing random and independent channel coefficients, has been studied before. In this paper, we investigate the wiretap version of S-FMAC as a secondary multiple access wiretap channel (S-MAC-WT) over similar Rayleigh/ Rayleigh and dissimilar Rayleigh/Nakagami fading, and having briefly reviewed the point to point version, we obtain closed-form expressions for the secrecy rate region and the corresponding outage probability. To validate the theoretical results, secrecy outage probability for sum-rate of S-FMAC-WT is numerically computed.

Simple Bounds for the Symmetric Capacity of the Rayleigh Fading Multiple Access Channel

Communication over the i.i.d. Rayleigh slow-fading MAC is considered, where all terminals are equipped with a single antenna. Further, a communication protocol is considered where all users transmit at (just below) the symmetric capacity (per user) of the channel, a rate which is fed back (dictated) to the users by the base station. Tight bounds are established on the distribution of the rate attained by the protocol. In particular, these bounds characterize the probability that the dominant face of the MAC capacity region contains a symmetric rate point, i.e., that the considered protocol strictly attains the sum capacity of the channel. The analysis provides a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel. We then extend this analysis to general multiple-input multiple-output MAC and finally, a practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario.

On Analog Gradient Descent Learning Over Multiple Access Fading Channels

We consider a distributed learning problem over multiple access channel (MAC) using a large wireless network. The computation is made by the network edge and is based on received data from a large number of distributed nodes which transmit over a noisy fading MAC. The objective function is a sum of the nodes' local loss functions. This problem has attracted a growing interest in distributed sensing systems, and more recently in federated learning. We develop a novel Gradient-Based Multiple Access (GBMA) algorithm to solve the distributed learning problem over MAC. Specifically, the nodes transmit an analog function of the local gradient using common shaping waveforms and the network edge receives a superposition of the analog transmitted signals used for updating the estimate. GBMA does not require power control or beamforming to cancel the fading effect as in other algorithms, and operates directly with noisy distorted gradients. We analyze the performance of GBMA theoretically, and prove that it can approach the convergence rate of the centralized gradient descent (GD) algorithm in large networks. Specifically, we establish a finite-sample bound of the error for both convex and strongly convex loss functions with Lipschitz gradient. Furthermore, we provide energy scaling laws for approaching the centralized convergence rate as the number of nodes increases. Finally, experimental results support the theoretical findings, and demonstrate strong performance of GBMA using synthetic and real data.

Achievable Throughput of Energy Harvesting Fading Multiple-Access Channels Under Statistical QoS Constraints

This paper studies the achievable throughput of fading multiple-access channels (MACs) with energy harvesting transmitters subject to statistical quality of service (QoS) constraints in the form of limitations on the buffer overflow probability. Effective capacity, which characterizes the maximum constant arrival rate that a given process can support while satisfying the QoS constraints, is employed as the performance metric. Perfect channel state information (CSI) and energy arrivals are assumed to be available at both the transmitters and the receiver. With the assumption of naive power control scheme, in which the transmission power level is irrespective of the CSI and decided by the instantaneous harvested energy, the effective throughput regions of time division multiple access and superposition coding (SC) with fixed decoding are characterized. In the special case of the same QoS constraints, the optimal decoding order strategy for SC with variable decoding order is obtained. With the assumption that the channel states and harvested energy in all time slots are known at the transmitters, the point-to-point link is first revisited. Then, for a given decoding order strategy in two-user MACs, a suboptimal power control policy based on the average energy arrivals and causal energy and channel information is proposed and shown to achieve performance close to the optimal one.

Resource allocation in a MAC with and without security via game theoretic learning

In this paper, we study a K-user fading multiple access channel (F-MAC), with and without an eavesdropper (Eve). In the system without Eve, we assume that each user knows only its own channel gain and is completely ignorant about the other users’ channel state. The legitimate receiver sends a short acknowledgement message Acknowledge (ACK) if the message is correctly decoded and a No Acknowledge (NACK) if the message is not correctly decoded. Under these assumptions, we use game theoretic learning setup to make transmitters learn about the power allocation under each state. We use multiplicative weight no-regret algorithm to achieve an ε-coarse correlated equilibrium. We also consider the case where a user can receive other users’ ACK/NACK messages. Now, we can maximize a weighted sum utility and achieve Pareto optimal points. We also obtain Nash bargaining solutions, which are Pareto points that are fairer to the transmitting users. Fairness among users is quantified using Jain’s index.With Eve, we first assume each user knows only its own channel gain to the receiver as well as to Eve. The receiver decides whether to send an ACK or a NACK to the transmitting user based on the secrecy-rate condition. We use the above developed algorithms to get the equilibrium points. Next, we study the case where each user knows only the distribution of the channel state of Eve. Finally, we also consider the system where the users do not know even the distribution of the Eve’s channel.

Modeling the lossy transmission of correlated sources in multiple access fading channels

In this paper, we develop accurate distortion models for the lossy transmission of two correlated sources in a multiple access Rayleigh fading channel. We focus on a class of real-life communication systems, where the source and channel coders have already been designed separately and can only be configured during the system operation. We investigate three different source coding schemes: distributed source coding (DSC), layered source coding, and independent compression through quantization. With the later scheme the sources are jointly decoded with minimum mean square error (MMSE) estimation at the receiver. We also consider two different transmission schemes: Orthogonal transmissions and interfering transmissions decoded with a successive interference cancellation (SIC) decoder. Our final closed-form analytical models are used to determine the optimal combination of source coding and transmission schemes, as well as their optimal configuration. Hence, we exercise joint source and channel coding (JSCC) by optimizing the system configuration. Through simulations, we first validate the analytical model and illustrate the performance of different schemes. Finally, we demonstrate the JSCC gains achieved by our system.