We study function computation over a Gaussian multiple-access channel (MAC), where multiple transmitters aim at computing a function of their values at a common receiver. To this end, we propose a novel coded-modulation framework for over-the-air computation (OAC) based on hierarchical constellation design, which supports reliable computation of multiple function outputs using a single channel use. Moreover, we characterize the achievable computation rate and show that the proposed hierarchical constellations can compute R output functions with decoding error probability epsilon while the gap to the optimal computation rate scales as O(\log_2(1/ε)/K) for independent source symbols, where K denotes the number of transmitters. Consequently, this gap vanishes as the network size grows, and the optimal rate is asymptotically attained. Furthermore, we introduce a shielding mechanism based on variable-length block coding that mitigates noise-induced error propagation across constellation levels while preserving the superposition structure of the MAC. We show that the shielding technique improves reliability, yielding a gap that scales optimally as O(\log_2\ln{(1/ε)}), regardless of the source distribution. Together, these results identify the regimes in which uncoded or lightly coded OAC is information-theoretically optimal, providing a unified framework for low-latency, channel-agnostic function computation.

We consider binary input deletion/substitution channels, which model certain types of synchronization errors encountered in practice. Specifically, we focus on the regime of small deletion and substitution probabilities, and by extending an approach developed for the deletion-only channel, we obtain an asymptotic characterization of the channel capacity for independent and identically distributed (i.i.d.) deletion/substitution channels. To do so, given a target probability of successful decoding, we first develop an upper bound on the codebook size for arbitrary but fixed numbers of deletions and substitutions, and then extend the result to the case of random deletions and substitutions to obtain a bound on the channel capacity. Our final result is: The i.i.d. deletion/substitution channel capacity is approximately 1 − H(pd) − H(ps), for pd, ps≈ 0, where pdand psare the deletion and substitution probabilities, respectively.

We present an alternative take on the recently popularized concept of ‘joint sensing and communications’, which focuses on using communication resources also for sensing. Here, we propose the opposite, where we utilize the receiver’s sensing capabilities for communication. Our goal is to characterize the fundamental limits of communication over such a channel, which we call ‘communication via sensing’. We assume that changes in the sensed attributes, such as location and speed, are limited due to practical constraints, which are captured by assuming a finite-state channel (FSC) with an input cost constraint. We first formulate an upper bound on the N-letter capacity as a cost-constrained optimization problem over the input sequence distribution, and then convert it to an equivalent problem over the state sequence distribution. Moreover, by breaking a walk on the underlying Markov chain into a weighted sum of traversed graph cycles in the long walk limit, we obtain a compact single-letter formulation of the capacity upper bound. Finally, for a specific case of a two-state FSC with noisy sensing characterized by a binary symmetric channel (BSC), we obtain a closed-form expression for the capacity upper bound. Comparison with an existing numerical lower bound shows that our proposed upper bound is very tight for all crossover probabilities.

We consider the unsourced random access problem with multiple receivers and propose a cell-free type solution. In our proposed scheme, active users transmit their signals to the access points (APs) distributed in a geographical area and connected to a central processing unit (CPU). The transmitted signals are composed of a pilot and a polar codeword, where the latter occupies only a small fraction of the data part of the transmission frame. The receiver operations of pilot detection and channel and symbol estimation take place at the APs, while the actual message bits are detected at the CPU by combining the symbol estimates from different APs. The effect of successfully decoded messages is then subtracted at the APs by successive interference cancellation, and the decoding iterations continue with the residual signal. Numerical examples illustrate that the proposed scheme can support up to 1400 users with high energy efficiency, and the distributed structure decreases the error probability by more than two orders of magnitude.

This paper considers an unsourced random access (URA) set-up equipped with a passive reconfigurable intelligent surface (RIS), where a massive number of unidentified users (only a small fraction of them being active at any given time) are connected to the base station (BS). We introduce a slotted coding scheme for which each active user chooses a slot at random for transmitting its signal, consisting of a pilot part and a randomly spread polar codeword. The proposed decoder operates in two phases. In the first phase, called the RIS configuration phase, the BS detects the transmitted pilots. The detected pilots are then utilized to estimate the corresponding users’ channel state information, using which the BS suitably selects RIS phase shift employing the proposed RIS design algorithms. The proposed channel estimator offers the capability to obtain the channel coefficients of the users whose pilots interfere with each other without prior access to the list of transmitted pilots or the number of active users. In the second phase, called the data phase, transmitted messages of active users are decoded. Moreover, we establish an approximate achievability bound for the RIS-based URA scheme, providing a valuable benchmark. Computer simulations show that the proposed scheme outperforms the state-of-the-art RIS-aided URA.

We investigate the unsourced random access scheme assuming that the base station is equipped with multiple antennas, and propose a high-performing solution utilizing on-off-division multiple access. We assume that each user spreads its pilot sequence and polar codeword to the pilot and data parts of the transmission frame, respectively, based on a transmission pattern. The iterative receiver operation consists of pilot and pattern detection followed by channel vector and symbol estimation, polar decoding, and successive interference cancellation. Numerical findings demonstrate that the proposed scheme has superior performance compared to the state-of-the-art in various antenna settings.

We study the problem of unsourced random access (URA) over Rayleigh block-fading channels with a receiver equipped with multiple antennas. We propose a slotted structure with multiple stages of orthogonal pilots, each of which is randomly picked from a codebook. In the proposed signaling structure, each user encodes its message using a polar code and appends it to the selected pilot sequences to construct its transmitted signal. Accordingly, the transmitted signal is composed of multiple orthogonal pilot parts and a polar-coded part, which is sent through a randomly selected slot. The performance of the proposed scheme is further improved by randomly dividing users into different groups each having a unique interleaver-power pair. We also apply the idea of multiple stages of orthogonal pilots to the case of a single receive antenna. In all the set-ups, we use an iterative approach for decoding the transmitted messages along with a suitable successive interference cancellation technique. The use of orthogonal pilots and the slotted structure lead to improved accuracy and reduced computational complexity in the proposed set-ups, and make the implementation with short blocklengths more viable. Performance of the proposed set-ups is illustrated via extensive simulation results which show that the proposed set-ups with multiple antennas perform better than the existing MIMO URA solutions for both short and large blocklengths, and that the proposed single-antenna set-ups are superior to the existing single-antenna URA schemes.

We examine federated learning (FL) with over-the-air (OTA) aggregation, where mobile users (MUs) aim to reach a consensus on a global model with the help of a parameter server (PS) that aggregates the local gradients. In OTA FL, MUs train their models using local data at every training round and transmit their gradients simultaneously using the same frequency band in an uncoded fashion. Based on the received signal of the superposed gradients, the PS performs a global model update. While the OTA FL has a significantly decreased communication cost, it is susceptible to adverse channel effects and noise. Employing multiple antennas at the receiver side can reduce these effects, yet the path-loss is still a limiting factor for users located far away from the PS. To ameliorate this issue, in this paper, we propose a wireless-based hierarchical FL scheme that uses intermediate servers (ISs) to form clusters in the areas where the MUs are more densely located. Our scheme utilizes OTA cluster aggregations for the communication of the MUs with their corresponding IS, and OTA global aggregations from the ISs to the PS. We present a convergence analysis for the proposed algorithm, and show through numerical evaluations of the derived analytical expressions and experimental results that utilizing ISs results in a faster convergence and a better performance than the OTA FL alone while using less transmit power. We also validate the results on the performance using different numbers of cluster iterations with different datasets and data distributions. We conclude that the best choice of cluster aggregations depends on the data distribution among the MUs and the clusters.

We consider unsourced random access over fading channels with a massive number of antennas at the base station, and propose a simple, yet energy-efficient solution by dividing the transmission frame into slots. We utilize non-orthogonal pilot sequences followed by a polar codeword for transmission in each slot. At the receiver side, we first detect the transmitted pilot sequences by employing a generalized orthogonal matching pursuit algorithm and utilize a linear minimum mean square error solution to estimate the channel vectors. We then perform an iterative decoding based on maximal ratio combining, single-user polar decoding, and successive interference cancellation with re-estimation of the channel vectors to recover the data bits. We also analyze the performance of the proposed scheme using normal approximations and provide a detailed complexity analysis. Numerical examples demonstrate that the proposed scheme either outperforms the existing schemes in the literature or has a competitive performance with a lower complexity. Furthermore, it is suitable for fast-fading scenarios due to its excellent performance in the short blocklength regime.

This paper considers an unsourced random access (URA) setup equipped with a passive reconfigurable intelligent surface (RIS), where a massive number of unidentified users (of which only a small fraction are active at a given time) share the same communication resources. We propose a slotted transmission scheme that operates in two phases. In the first phase, called the RIS configuration phase, the base station (BS) detects the active pilots and estimates their respective channel state information (CSI). Then, using the estimated CSI, the BS suitably selects the phase shifts of the RIS elements. In the second phase, called the data phase, transmitted messages of active users are decoded. The proposed channel estimator offers the capability to estimate the channel coefficients of the users whose pilots interfere with each other without prior access to the list of selected pilots or the number of active users. In this paper, we consider the direct link between the users and the BS to be completely blocked, and show that employing RIS improves the performance of the URA system by creating additional links between the BS and the users. The effectiveness of the proposed algorithms is confirmed through computer simulations.

We consider unsourced random access for which the base station is equipped with a massive number of antennas and there are residual hardware impairments at both the base station and the user equipment. We divide the transmission frame into slots where each user sends a non-orthogonal pilot selected based on part of its message bits followed by its data bits encoded by a polar code. At the receiver side, we first identify the selected pilot sequences by a generalized orthogonal matching pursuit algorithm and estimate the user channels employing a newly developed hardware-impairment aware linear minimum mean-squared error solution. We then perform symbol estimation by maximal ratio combining and data decoding by a single-user polar decoder followed by successive interference cancellation in an iterative fashion. Numerical examples illustrate that hardware impairments degrade the system performance; however, the proposed solution alleviates this loss in terms of both energy efficiency and the number of supported active users.

We develop bounds on the capacity of Poisson-repeat channels (PRCs) for which each input bit is independently repeated according to a Poisson distribution. The upper bounds are obtained by considering an auxiliary channel where the output lengths corresponding to input blocks of a given length are provided as side information at the receiver. Numerical results show that the resulting upper bounds are significantly tighter than the best known one for a large range of the PRC parameter λ (specifically, for λ ≥0.35). We also describe a way of obtaining capacity lower bounds using information rates of the auxiliary channel and the entropy rate of the provided side information.

We consider the downlink of a multiuser system operating in the time-division duplexing mode, for which base station (BS) and users are equipped with multiple antennas, and provide a robust precoding/combining design against imperfect channel state information (CSI) and calibration errors due to hardware mismatch. Towards this end, we first formulate a robust joint precoder and combiner design as a stochastic minimum mean squared error optimization problem. Then, employing an alternating optimization approach, we propose an algorithm to obtain the precoding and combining matrices assuming imperfect CSI and calibration errors at both the BS and the user sides. We also provide asymptotic closed-form expressions for the mean squared error (MSE) and the achievable sum-rate in the massive MIMO regime. The results indicate that while the MSE linearly increases with the calibration errors at the user side, the sum-rate is asymptotically independent of them. Extensive simulation results show that the proposed robust joint precoder/combiner outperforms the existing solutions while having the same order of complexity. Moreover, when the BS sends a quantized version of the combining coefficients to the users, it is observed that the proposed solution is more robust to the quantization errors than the existing algorithms.

We consider federated edge learning among mobile devices that harvest the required energy from their surroundings, and share their updates with the parameter server (PS) through a shared wireless channel. In particular, we consider energy harvesting FL with over-the-air (OTA) aggregation, where the participating devices perform local computations and wireless transmission only when they have the required energy available, and transmit the local updates simultaneously over the same channel bandwidth. In order to prevent bias among the heterogeneous devices, we utilize a weighted averaging with respect to their latest energy arrivals and data cardinalities. We provide a convergence analysis and carry out numerical experiments with different energy arrival profiles, which show that the proposed scheme is robust against heterogeneous energy arrivals in error-free scenarios while having less than 10% performance loss for fading channels.

We consider unsourced random access over fading channels with a massive number of antennas at the base station and propose a simple yet energy-efficient solution by dividing the transmission frame into slots where each slot is also divided into pilot and data parts. We utilize non-orthogonal pilot sequences selected based on part of the information bits, and encode the remaining message bits with a polar code for transmission. At the receiver side, we first detect the transmitted pilot sequences by employing the generalized orthogonal matching pursuit algorithm, and utilize a linear minimum mean square error solution to estimate the channel vectors. We perform symbol estimation by maximal ratio combining, and pass the symbol estimates to a single-user polar decoder to recover the data bits with succes-sive cancellation list decoding, along with successive interference cancellation at the end of each iteration. Numerical examples demonstrate that the proposed scheme either outperforms the existing schemes in the literature, or has a lower complexity while achieving a comparable performance.

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system operating in the time-division duplexing (TDD) mode. In this mode, assuming reciprocity, the channel coefficients estimated during the uplink channel training are utilized by the base station (BS) in the downlink data transmission. However, due to hardware mismatches, the uplink and downlink channels are not exactly the same, and therefore, there are calibration errors, which degrade the system performance. In this paper, our goal is to provide a transceiver design which has a robust performance under imperfect channel reciprocity. To this end, we first formulate a robust joint precoder and combiner design as a stochastic minimum mean square error (MMSE) optimization problem. Then, employing an alternating optimization approach, we propose an algorithm to obtain the precoding and combining matrices assuming imperfect CSI and calibration errors at both the BS and user sides. Extensive simulation results show that the proposed robust joint precoder/combiner outperforms the existing solutions in the literature.

Federated learning (FL) over wireless communication channels, specifically, over-the-air (OTA) model aggregation framework is considered. In OTA wireless setups, the adverse channel effects can be alleviated by increasing the number of receive antennas at the parameter server (PS), which performs model aggregation. However, the performance of OTA FL is severely limited by the presence of mobile users (MUs) located far away from the PS. In this paper, to mitigate this limitation, we propose hierarchical over-the-air federated learning (HOTAFL), which utilizes intermediary servers (IS) to form clusters near MUs. We provide a convergence analysis for the proposed setup, and demonstrate through experimental results that local aggregation in each cluster before global aggregation leads to a better performance and faster convergence than OTA FL.

As a building block toward a simple and scalable solution for massive random access, we introduce collision-resolution algorithms using successive interference cancellation (SIC) based on the received signals, with no need for any coordination or codebook differentiation. We first consider two-user multiple access with the ZigZag algorithm. We prove that the original ZigZag and a modified version of it, calleddouble-zipper ZigZag, attain the same performance as the optimal coordinated time-sharing in the high signal to noise ratio (SNR) regime, even in the presence of channel state information (CSI) errors. We then extend the results to the case of arbitrary number of users employing delay-domain processing. Specifically, we introduce delay-domain zero forcing and its regularized version, which are able to cancel and suppress the interference among users, respectively. By obtaining a post-processing system model and characterizing the accumulated noise during the decoupling process, we also derive bounds on the achievable sum-rates of the proposed algorithm for both cases of perfect and imperfect CSI. Simulation results show that the newly proposed approach have comparable performance with coordinated time-sharing at high SNRs.

As a building block toward a simple and scalable solution to massive random access, we consider two-user multiple access with ZigZag decoding, with no need for any coordination or codebook differentiation. We derive closed-form bounds on the achievable sum-rates of the original ZigZag and a modified version of it, called double-zipper ZigZag, for both cases of perfect and imperfect channel state information (CSI). We also show that performances of both versions of ZigZag approach that of optimal coordinated time-sharing in the high signal to noise ratio regime, even in the presence of CSI errors.

The authors consider downlink transmission in a multi‐cell massive multiple‐input and multiple‐output (MIMO) system and focus on decreasing the feedback overhead caused by cell cooperation in constant envelope precoding (CEP). In the literature, the single‐cell case for CEP with perfect channel state information (CSI) has been studied. Here, considering full cooperation among the cells, they develop CEP for the multi‐cell case. They devise a low overhead centralised construction for CEP which employs limited cooperation among the cells, providing higher system throughput. To achieve the minimum feedback overhead, a distributed realisation of CEP is proposed where each cell locally performs CEP. Furthermore, a new optimisation problem is solved to compensate for the effects of pilot contamination. In addition, to reduce the computational complexity, a relaxed iterative form is presented for the limited cooperation and the distributed scenarios. Numerical results show that in the proposed structures, despite a tremendous decrease in the system overhead, the performance confronts merely an insignificant degradation, <10%, compared to the full‐cooperation case. Moreover, in the presence of imperfect CSI, the performance of the distributed structure whose imperfect CSI is compensated for, approaches the performance of this structure in the perfect CSI scenario.

We consider downlink of a multiuser massive multiple-input multiple-output (MIMO) system and focus on reducing the hardware costs by using a single common power amplifier and separate phase shifters (PSs) for antenna front-ends. In the previous literature, the use of analog PSs in this setup has been considered. Here, we study the use of practical digital PSs, which only support a limited set of discrete phases. Considering the sum of interference powers as a metric, we formulate the corresponding nonlinear discrete optimization problem and solve for the phases to be used during transmission. We devise a low-complexity algorithm, which employs a trellis structure providing suboptimal, but efficient and effective solutions. We demonstrate via examples that the proposed solutions have comparable performance to conventional analog PS-based algorithms. Furthermore, we prove that by utilizing discrete-phase constant envelope precoding, the interference can be made arbitrarily small by increasing the number of antennas. Therefore, the asymptotic gains promised by massive MIMO systems are preserved. We also obtain closed-form expressions for the rate loss due to errors in the phase and amplitude of the PSs, for both low and high SNR regimes.

The effect of large‐scale fading variations over massive multiple input multiple output (MIMO) antenna array on sum‐capacity of massive MIMO system has not been thoroughly investigated in the literature. This study considers a multiuser massive MIMO system with a Rayleigh fading channel that takes into account large‐scale fading variations over base station antenna array. Two scenarios are investigated: distributed antenna base station and linear array base station. In both scenarios, the authors obtain an approximate closed‐form expressions for uplink ergodic sum‐capacity for both low and high signal‐to‐noise ratio (SNR) regimes. It is shown that the proposed closed‐form expressions are accurate in a wide range of practical SNRs; for example, the approximation error is below 10% for SNRs lower than −10 dB and higher than 17 dB for low‐SNR and high‐SNR closed‐form expressions, respectively. It is also shown that the proposed closed‐form expressions are not only valid for massive MIMO scenario but also for a system with a few number of base station antennas. The numerical results show that the proposed closed‐form expressions have much less computational complexity than previous works.