The increasing complexity of 6G networks demands advanced tools for network management and simulation. This demo pioneers the integration of ns-3 and NVIDIA Sienna®RT, laying the foundation for the first multi-Radio Access Technologies (RAT) full-stack, open-source Digital Network Twin (DNT). The introduction of a deterministic ray tracer for an accurate channel modeling into ns-3 enables realistic and site-specific simulation which cannot be achieved via stochastic channel models. Tested in a challenging vehicular urban scenario, the proposed framework demonstrates significant improvements in predicting dynamic wireless channels and its impact at higher network layers.

Localization services for wireless devices play an increasingly important role in our daily lives and a plethora of emerging services and applications already rely on precise position information. Widely used on-device positioning methods, such as the global positioning system, enable accurate outdoor positioning and provide the users with full control over what services and applications are allowed to access their location information. In order to provide accurate positioning indoors or in cluttered urban scenarios without line-of-sight satellite connectivity, powerful off-device positioning systems, which process channel state information (CSI) measured at the infrastructure base stations or access points with deep neural networks, have emerged recently. Such off-device wireless positioning systems inherently link a user’s data transmission with its localization, since accurate CSI measurements are necessary for reliable wireless communication—this not only prevents the users from controlling who can access this information but also enables virtually everyone in the device’s range to estimate its location, resulting in serious privacy and security concerns. We therefore propose on-device attacks against off-device wireless positioning systems in multi-antenna orthogonal frequency-division multiplexing systems while remaining standard compliant and minimizing the impact on quality-of-service, and we demonstrate their efficacy using real-world measured datasets for cellular outdoor and wireless LAN indoor scenarios. We also investigate defenses to counter such attack mechanisms, and we discuss the limitations and implications on protecting location privacy in existing and future wireless communication systems.

This is the second part of a two-part paper that focuses on link-adaptation (LA) and physical layer (PHY) abstraction for multi-user MIMO (MU-MIMO) systems with non-linear receivers. The first part proposes a new metric, called bit-metric decoding rate (BMDR) for a detector, as being the equivalent of post-equalization signal-to-interference-noise ratio (SINR) for non-linear receivers. Since this BMDR does not have a closed form expression, a machine-learning based approach to estimate it effectively is presented. In this part, the concepts developed in the first part are utilized to develop novel algorithms for LA, dynamic detector selection from a list of available detectors, and PHY abstraction in MU-MIMO systems with arbitrary receivers. Extensive simulation results that substantiate the efficacy of the proposed algorithms are presented.

LA is one of the most important aspects of wireless communications where the MCS used by the transmitter is adapted to the channel conditions in order to meet a certain target error-rate. In a SU-SISO system with out-of-cell interference, LA is performed by computing the post-equalization SINR at the receiver. The same technique can be employed in MU-MIMO receivers that use linear detectors. Another important use of post-equalization SINR is for PHY abstraction, where several PHY blocks like the channel encoder, the detector, and the channel decoder are replaced by an abstraction model in order to speed up system-level simulations. However, for MU-MIMO systems with non-linear receivers, there is no known equivalent of post-equalization SINR which makes both LA and PHY abstraction extremely challenging. This important issue is addressed in this two-part paper. In this part, a metric called the BMDR of a detector, which is the proposed equivalent of post-equalization SINR, is presented. Since BMDR does not have a closed form expression that would enable its instantaneous calculation, a machine-learning approach to predict it is presented along with extensive simulation results.

We propose a neural network (NN)-based algorithm for device detection and time of arrival (ToA) and carrier frequency offset (CFO) estimation for the narrowband physical random-access channel (NPRACH) of narrowband internet of things (NB-IoT). The introduced NN architecture leverages residual convolutional networks as well as knowledge of the preamble structure of the 5G New Radio (5G NR) specifications. Benchmarking on a 3rd Generation Partnership Project (3GPP) urban microcell (UMi) channel model with random drops of users against a state-of-the-art baseline shows that the proposed method enables up to 8 dB gains in false negative rate (FNR) as well as significant gains in false positive rate (FPR) and ToA and CFO estimation accuracy. Moreover, our simulations indicate that the proposed algorithm enables gains over a wide range of channel conditions, CFOs, and transmission probabilities. The introduced synchronization method operates at the base station (BS) and, therefore, introduces no additional complexity on the user devices. It could lead to an extension of battery lifetime by reducing the preamble length or the transmit power. Our code is available at: https://github.com/NVlabs/nprach_synch/.

In this paper, we propose an end-to-end deep learning-based joint transceiver design algorithm for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, which consists of deep neural network (DNN)-aided pilot training, channel feedback, and hybrid analog-digital (HAD) precoding. Specifically, we develop a DNN architecture that maps the received pilots into feedback bits at the receiver, and then further maps the feedback bits into the hybrid precoder at the transmitter. To reduce the signaling overhead and channel state information (CSI) mismatch caused by the transmission delay, a two-timescale DNN composed of a long-term DNN and a short-term DNN is developed. The analog precoders are designed by the long-term DNN based on the CSI statistics and updated once in a frame consisting of a number of time slots. In contrast, the digital precoders are optimized by the short-term DNN at each time slot based on the estimated low-dimensional equivalent CSI matrices. A two-timescale training method is also developed for the proposed DNN with a binary layer. We then analyze the generalization ability and signaling overhead for the proposed DNN based algorithm. Simulation results show that our proposed technique significantly outperforms conventional schemes in terms of bit-error rate performance with reduced signaling overhead and shorter pilot sequences.

In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital beamforming is an essential technique for exploiting the potential array gain without using a dedicated radio frequency chain for each antenna. However, due to the large number of antennas, the conventional channel estimation and hybrid beamforming algorithms generally require high computational complexity and signaling overhead. In this work, we propose an end-to-end deep-unfolding neural network (NN) joint channel estimation and hybrid beamforming (JCEHB) algorithm to maximize the system sum rate in time-division duplex (TDD) massive MIMO. Specifically, the recursive least-squares (RLS) algorithm and stochastic successive convex approximation (SSCA) algorithm are unfolded for channel estimation and hybrid beamforming, respectively. In order to reduce the signaling overhead, we consider a mixed-timescale hybrid beamforming scheme, where the analog beamforming matrices are optimized based on the channel state information (CSI) statistics offline, while the digital beamforming matrices are designed at each time slot based on the estimated low-dimensional equivalent CSI matrices. We jointly train the analog beamformers together with the trainable parameters of the RLS and SSCA induced deep-unfolding NNs based on the CSI statistics offline. During data transmission, we estimate the low-dimensional equivalent CSI by the RLS induced deep-unfolding NN and update the digital beamformers. In addition, we propose a mixed-timescale deep-unfolding NN where the analog beamformers are optimized online, and extend the framework to frequency-division duplex (FDD) systems where channel feedback is considered. Simulation results show that the proposed algorithm can significantly outperform conventional algorithms with reduced computational complexity and signaling overhead.

The fourth call for papers of the Series on Machine Learning in Communications and Networks has continued to receive a great number of high-quality papers covering various aspects of intelligent communications, from which we have included 16 original contributions in this issue. In the following, we provide a brief review of these papers according to their topics.

The third call for papers of the Series on Machine Learning in Communications and Networks has continued to receive a great number of high-quality papers covering various aspects of intelligent communications, from which we have included 26 original contributions in this issue. In the following, we provide a brief review of key contributions of papers in this issue according to their topics.

The fourth (and final) call for papers of the Series on Machine Learning in Communications and Networks has continued to receive a great number of high-quality papers covering various aspects of intelligent communications. In addition to those published in the August issue, we include in this issue 16 articles submitted to the call. In the following, we provide a brief review of these articles according to their topics.

We propose a learning-based method for the joint design of a transmit and receive filter, the constellation geometry and associated bit labeling, as well as a neural network (NN)-based detector. The method maximizes an achievable information rate, while simultaneously satisfying constraints on the adjacent channel leakage ratio (ACLR) and peak-to-average power ratio (PAPR). This allows control of the tradeoff between spectral containment, peak power, and communication rate. Evaluation on an additive white Gaussian noise (AWGN) channel shows significant reduction of ACLR and PAPR compared to a conventional baseline relying on quadrature amplitude modulation (QAM) and root-raised-cosine (RRC), without significant loss of information rate. When considering a 3rd Generation Partnership Project (3GPP) multipath channel, the learned waveform and neural receiver enable competitive or higher rates than an orthogonal frequency division multiplexing (OFDM) baseline, while reducing the ACLR by$\mathrm {10~ \text {dB}}$and the PAPR by$\mathrm {2~ \text {dB}}$. The proposed method incurs no additional complexity on the transmitter side and might be an attractive tool for waveform design of beyond-5G systems.

The benefits of end-to-end learning has been demonstrated over AWGN channels but has not yet been quantified over realistic wireless channel models. This work aims to fill this gap by exploring the gains of end-to-end learning over a frequency- and time-selective fading channel using OFDM. With imperfect channel knowledge at the receiver, the shaping gains observed on AWGN channels vanish. Nonetheless, we identify two other sources of performance improvements. The first comes from a neural network-based receiver operating over a large number of subcarriers and OFDM symbols which allows to reduce the number of orthogonal pilots without loss of BER. The second comes from entirely eliminating orthogonal pilots by jointly learning a neural receiver together with either superimposed pilots (SIPs), combined with conventional QAM, or an optimized constellation. The learned constellation works for a wide range of signal-to-noise ratios, Doppler and delay spreads, has zero mean and does hence not contain any form of SIP. Both schemes achieve the same BER as the pilot-based baseline with 7% higher throughput. Thus, we believe that a jointly learned transmitter and receiver are a very interesting component for beyond-5G communication systems which could remove the need and associated overhead for demodulation reference signals.

The advance of deep learning in computer vision has been leveraged for channel estimation in radio receiver since high-resolution full channel response can be reconstructed from raw channel estimate achieved based on sparse pilots. Despite that significant performance gains have been derived by using powerful neural networks (NN) especially in given channel conditions, it is still challenging and crucial to augment NN's robustness in untrained scenarios in terms of user equipments' (UE) locations and velocities. In this paper, we proposed a super-resolution (SR) NN as the backbone structure for high-resolution channel response reconstruction from low-resolution raw estimate based on sparse pilots. On top of that, a specialized sub NN structure is embedded to adaptively combat against vari-ant Doppler-induced diverse phase rotations between orthogonal frequency division multiplexing (OFDM) symbols in time domain. The Sub-NN with semantic information like UEs' velocities as the input can learn multi-path-propagation dependent Doppler decomposition, and compensate the phase rotation accordingly. For the first time, we show how such specially tailored NN with extra information can be used for high-accuracy channel estimation using only 1 demodulation reference signal (DMRS), which is robust to locations and Dopplers that have not even been trained.

Machine learning (ML) starts to be widely used to enhance the performance of multi-user multiple-input multiple-output (MU-MIMO) receivers. However, it is still unclear if such methods are truly competitive with respect to conventional methods in realistic scenarios and under practical constraints. In addition to enabling accurate signal reconstruction on realistic channel models, MU-MIMO receive algorithms must allow for easy adaptation to a varying number of users without the need for retraining. In contrast to existing work, we propose an machine learning (ML)-enhanced MU-MIMO receiver that builds on top of a conventional linear minimum mean squared error (LMMSE) architecture. It preserves the interpretability and scalability of the LMMSE receiver, while improving its accuracy in two ways. First, convolutional neural networks (CNNs) are used to compute an approximation of the second-order statistics of the channel estimation error which are required for accurate equalization. Second, a CNN-based demapper jointly processes a large number of orthogonal frequency-division multiplexing (OFDM) symbols and subcarriers, which allows it to compute better log likelihood ratios (LLRs) by compensating for channel aging. The resulting architecture can be used in the up- and downlink and is trained in an end-to-end manner, removing the need for hard-to-get perfect channel state information (CSI) during the training phase. Simulation results demonstrate consistent performance improvements over the baseline which are especially pronounced in high mobility scenarios.

In the era of the new generation of communication systems, data traffic is expected to continuously strain the capacity of future communication networks. Along with the remarkable growth in data traffic, new applications, such as wearable devices, autonomous systems, and the Internet of Things (IoT), continue to emerge and generate even more data traffic with vastly different requirements. This growth in the application domain brings forward an inevitable need for more intelligent processing, operation, and optimization of future communication networks.

The Second Call for Papers of the Series on Machine Learning in Communications and Networks has continued to receive a great number of high-quality papers covering various aspects of intelligent communication systems. In addition to 23 original contributions in response to the first call for papers, we include in this issue 5 articles submitted to the second call for papers. In the following, we provide a brief review of key contributions of papers in this issue according to their topics.

We provide the reader with an accessible yet rigorous introduction to Bayesian optimisation with Gaussian processes (BOGP) for the purpose of solving a wide variety of radio resource management (RRM) problems. We believe that BOGP is a powerful tool that has been somewhat overlooked in RRM research, although it elegantly addresses pressing requirements for fast convergence, safe exploration, and interpretability. BOGP also provides a natural way to exploit prior knowledge during optimization. After explaining the nuts and bolts of BOGP, we delve into more advanced topics, such as the choice of the acquisition function and the optimization of dynamic performance functions. Finally, we put the theory into practice for the RRM problem of uplink open-loop power control (OLPC) in 5G cellular networks, for which BOGP is able to converge to almost optimal solutions in tens of iterations without significant performance drops during exploration.

We introduce a trainable coded modulation scheme that enables joint optimization of the bit-wise mutual information (BMI) through probabilistic shaping, geometric shaping, bit labeling, and demapping for a specific channel model and for a wide range of signal-to-noise ratios (SNRs). Compared to probabilistic amplitude shaping (PAS), the proposed approach is not restricted to symmetric probability distributions, can be optimized for any channel model, and works with any code rate k/m, m being the number of bits per channel use and k an integer within the range from 1 to m-1. The proposed scheme enables learning of a continuum of constellation geometries and probability distributions determined by the SNR. Additionally, the PAS architecture with Maxwell-Boltzmann (MB) as shaping distribution was extended with a neural network (NN) that controls the MB shaping of a quadrature amplitude modulation (QAM) constellation according to the SNR, enabling learning of a continuum of MB distributions for QAM. Simulations were performed to benchmark the performance of the proposed joint probabilistic and geometric shaping scheme on additive white Gaussian noise (AWGN) and mismatched Rayleigh block fading (RBF) channels.

We propose MMNet, a deep learning MIMO detection scheme that significantly outperforms existing approaches on realistic channels with the same or lower computational complexity. MMNet's design builds on the theory of iterative soft-thresholding algorithms and uses a novel training algorithm that leverages temporal and spectral correlation in real channels to accelerate training. These innovations make it practical to train MMNet online for every realization of the channel. On spatially-correlated channels, MMNet achieves the same error rate as the next-best learning scheme (OAMPNet) at 2.5dB lower signal-to-noise ratio (SNR), and with at least 10× less computational complexity. MMNet is also 4-8dB better overall than the linear minimum mean square error (MMSE) detector.

We consider a trainable point-to-point communication system, where both transmitter and receiver are implemented as neural networks (NNs), and demonstrate that training on the bit-wise mutual information (BMI) allows seamless integration with practical bit-metric decoding (BMD) receivers, as well as joint optimization of constellation shaping and labeling. Moreover, we present a fully differentiable neural iterative demapping and decoding (IDD) structure which achieves significant gains on additive white Gaussian noise (AWGN) channels using a standard 802.11n low-density parity-check (LDPC) code. The strength of this approach is that it can be applied to arbitrary channels without any modifications. Going one step further, we show that careful code design can lead to further performance improvements. Lastly, we show the viability of the proposed system through implementation on software-defined radios (SDRs) and training of the end-to-end system on the actual wireless channel. Experimental results reveal that the proposed method enables significant gains compared to conventional techniques.

Since the seminal paper by Marzetta from 2010, Massive MIMO has changed from being a theoretical concept with an infinite number of antennas to a practical technology. The key concepts are adopted into the 5G New Radio Standard and base stations (BSs) with M = 64 fully digital transceivers have been commercially deployed in sub-6GHz bands. The fast progress was enabled by many solid research contributions of which the vast majority assume spatially uncorrelated channels and signal processing schemes developed for single-cell operation. These assumptions make the performance analysis and optimization of Massive MIMO tractable but have three major caveats: 1) practical channels are spatially correlated; 2) large performance gains can be obtained by multicell processing, without BS cooperation; 3) the interference caused by pilot contamination creates a finite capacity limit, as M → ∞. There is a thin line of papers that avoided these caveats, but the results are easily missed. Hence, this tutorial article explains the importance of considering spatial channel correlation and using signal processing schemes designed for multicell networks. We present recent results on the fundamental limits of Massive MIMO, which are not determined by pilot contamination but the ability to acquire channel statistics. These results will guide the journey towards the next level of Massive MIMO, which we call “Massive MIMO 2.0”.

The explosion of the number of low-power devices in the next decades calls for a re-thinking of wireless network design, namely, unifying wireless transmission of information and power so as to make the best use of the RF spectrum, radiation, and infrastructure for the dual purpose of communicating and energizing. This article provides a novel learning-based approach towards such wireless network design. To that end, a parametric model of a practical energy harvester, accounting for various sources of nonlinearities, is proposed using a nonlinear regression algorithm applied over collected real data. Relying on the proposed model, the learning problem of modulation design for Simultaneous Wireless Information-Power Transmission (SWIPT) over a point-to-point link is studied. Joint optimization of the transmitter and the receiver is implemented using Neural Network (NN)-based autoencoders. The results reveal that by increasing the receiver power demand, the baseband transmit modulation constellation converges to an On-Off keying signalling. Utilizing the observations obtained via learning, an algorithmic SWIPT modulation design is proposed. It is observed via numerical results that the performance loss of the proposed modulations are negligible compared to the ones obtained from learning. Extension of the studied problem to learning modulation design for multi-user SWIPT scenarios and coded modulation design for point-to-point SWIPT are considered. The major conclusion of this work is to utilize learning-based results to design non learning-based algorithms, which perform as well. In particular, inspired by the results obtained via learning, an algorithmic approach for coded modulation design is proposed, which performs very close to its learning counterparts, and is significantly superior due to its high real-time adaptability to new system design parameters.

Traditional symbol detection algorithms either perform poorly or are impractical to implement for Massive Multiple-Input Multiple-Output (MIMO) systems. Recently, several learning-based approaches have achieved promising results on simple channel models (e.g., i.i.d. Gaussian channel coefficients), but as we show, their performance degrades on real-world channels with spatial correlation. We propose MMNet, a deep learning MIMO detection scheme that significantly outperforms existing approaches on realistic channels with the same or lower computational complexity. MMNet's design builds on the theory of iterative soft-thresholding algorithms, and uses a novel training algorithm that leverages temporal and spectral correlation in real channels to accelerate training. These innovations make it practical to train MMNet online for every realization of the channel. On i.i.d. Gaussian channels, MMNet requires two orders of magnitude fewer operations than existing deep learning schemes but achieves near-optimal performance. On spatiallycorrelated channels, it achieves the same error rate as the next-best learning scheme (OAMPNet) at 2.5dB lower signalto-noise ratio (SNR), and with at least 10× less computational complexity. MMNet is also 4-8dB better overall than a classic linear scheme like the minimum mean square error (MMSE) detector.

End-to-end learning of communication systems enables joint optimization of transmitter and receiver, implemented as deep neural network (NN)-based autoencoders, over any type of channel and for an arbitrary performance metric. Recently, an alternating training procedure was proposed which eliminates the need for an explicit channel model. However, this approach requires feedback of real-valued losses from the receiver to the transmitter during training. In this paper, we first show that alternating training works even with a noisy feedback channel. Then, we design a system that learns to transmit real numbers over an unknown channel without a preexisting feedback link. Once trained, this feedback system can be used to communicate losses during alternating training of autoencoders. Evaluations over additive white Gaussian noise (AWGN) and Rayleigh block-fading (RBF) channels show that end-to-end communication systems trained using the proposed feedback system achieve the same performance as when trained with a perfect feedback link.

The idea of end-to-end learning of communication systems through neural network (NN)-based autoencoders has the shortcoming that it requires a differentiable channel model. We present in this paper a novel learning algorithm which alleviates this problem. The algorithm enables training of communication systems with an unknown channel model or with non-differentiable components. It iterates between training of the receiver using the true gradient, and training of the transmitter using an approximation of the gradient. We show that this approach works as well as model-based training for a variety of channels and tasks. Moreover, we demonstrate the algorithm's practical viability through hardware implementation on software defined radios (SDRs) where it achieves state-of-the-art performance over a coaxial cable and wireless channel.

This paper analyzes how the distortion created by hardware impairments in a multiple-antenna base station affects the uplink spectral efficiency (SE), with a focus on massive multiple input multiple output (MIMO). This distortion is correlated across the antennas but has been often approximated as uncorrelated to facilitate (tractable) SE analysis. To determine when this approximation is accurate, basic properties of distortion correlation are first uncovered. Then, we separately analyze the distortion correlation caused by third-order non-linearities and by quantization. Finally, we study the SE numerically and show that the distortion correlation can be safely neglected in massive MIMO when there are sufficiently many users. Under independent identically distributed Rayleigh fading and equal signal-to-noise ratios (SNRs), this occurs for more than five transmitting users. Other channel models and SNR variations have only minor impact on the accuracy. We also demonstrate the importance of taking the distortion characteristics into account in the receive combining.

This paper considers the uplink of a distributed Massive MIMO network where N base stations (BSs), each equipped with M antennas, receive data from K = 2 users. We study the asymptotic spectral efficiency (as M → ∞) with spatial correlated channels, pilot contamination, and different degrees of channel state information (CSI) and statistical knowledge at the BSs. By considering a two-user setup, we can simply derive fundamental asymptotic behaviors and provide novel insights into the structure of the optimal combining schemes. In line with [1], when global CSI is available at all BSs, the optimal minimum-mean squared error combining has an unbounded capacity as M → ∞, if the global channel covariance matrices of the users are asymptotically linearly independent. This result is instrumental to derive a suboptimal combining scheme that provides unbounded capacity as M → ∞ using only local CSI and global channel statistics. The latter scheme is shown to outperform a generalized matched filter scheme, which also achieves asymptotic unbounded capacity by using only local CSI and global channel statistics, but is derived following [2] on the basis of a more conservative capacity bound.

The capacity of cellular networks can be improved by the unprecedented array gain and spatial multiplexing offered by Massive MIMO. Since its inception, the coherent interference caused by pilot contamination has been believed to create a finite capacity limit, as the number of antennas goes to infinity. In this paper, we prove that this is incorrect and an artifact from using simplistic channel models and suboptimal precoding/combining schemes. We show that with multicell MMSE precoding/combining and a tiny amount of spatial channel correlation or large-scale fading variations over the array, the capacity increases without bound as the number of antennas increases, even under pilot contamination. More precisely, the result holds when the channel covariance matrices of the contaminating users are asymptotically linearly independent, which is generally the case. If also the diagonals of the covariance matrices are linearly independent, it is sufficient to know these diagonals (and not the full covariance matrices) to achieve an unlimited asymptotic capacity.

The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Thus, we partition the encoding graph into smaller sub-blocks and train them individually, closely approaching maximum a posteriori (MAP) performance per sub-block. These blocks are then connected via the remaining conventional belief propagation decoding stage(s). The resulting decoding algorithm is non-iterative and inherently enables a highlevel of parallelization, while showing a competitive bit error rate (BER) performance. We examine the degradation through partitioning and compare the resulting decoder to state-of-the art polar decoders such as successive cancellation list and belief propagation decoding.

The decoding performance of polar codes strongly depends on the decoding algorithm used, while also the decoder throughput and its latency mainly depend on the decoding algorithm. In this work, we implement the powerful successive cancellation list (SCL) decoder on a GPU and identify the bottlenecks of this algorithm with respect to parallel computing and its difficulties. The inherent serial decoding property of the SCL algorithm naturally limits the achievable speed-up gains on GPUs when compared to CPU implementations. In order to increase the decoding throughput, we use a hybrid decoding scheme based on the belief propagation (BP) decoder, which can be intra- and inter-frame parallelized. The proposed scheme combines excellent decoding performance and high throughput within the signal-to-noise ratio (SNR) region of interest.

Massive MIMO (multiple-input multiple-output) provides great improvements in spectral efficiency over legacy cellular networks, by coherent combining of the signals over a large antenna array and by spatial multiplexing of many users. Since its inception, the coherent interference caused by pilot contamination has been believed to be an impairment that does not vanish, even with an unlimited number of antennas. In this work, we show that this belief is incorrect and an artifact from using simplistic channel models and suboptimal signal processing schemes. We focus on the uplink and prove that with multicell MMSE combining, the spectral efficiency grows without bound as the number of antennas increases, even under pilot contamination, under a condition of linear independence between the channel covariance matrices. This condition is generally satisfied, except in special cases that are hardly found in practice.

The second-order coding rate of the multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channel is studied. We tackle this problem via an information-spectrum approach and statistical bounds based on recent random matrix theory techniques. We derive a central limit theorem (CLT) to analyze the information density in the regime where the block length n and the number of transmit and receive antennas K and N, respectively, grow simultaneously large. This result leads to the characterization of closed-form upper and lower bounds on the optimal average error probability when the coding rate is within O(1/√(nK)) of the asymptotic capacity.

Assume that a multi-user multiple-input multiple-output (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios.

Assume that a multi-user multiple-input multiple-output (MIMO) communication system must be designed to cover a given area with maximal energy efficiency (bits/Joule). What are the optimal values for the number of antennas, active users, and transmit power? By using a new model that describes how these three parameters affect the total energy efficiency of the system, this work provides closed-form expressions for their optimal values and interactions. In sharp contrast to common belief, the transmit power is found to increase (not decrease) with the number of antennas. This implies that energy efficient systems can operate at high signal-to-noise ratio (SNR) regimes in which the use of interference-suppressing precoding schemes is essential. Numerical results show that the maximal energy efficiency is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve relatively many users using interference-suppressing regularized zero-forcing precoding.

The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little interuser interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipments (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and interuser interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.

We propose a time division duplex (TDD) based network architecture where a macrocell tier with a “massive” multiple-input multiple-output (MIMO) base station (BS) is overlaid with a dense tier of small cells (SCs). In this context, the TDD protocol and the resulting channel reciprocity have two compelling advantages. First, a large number of BS antennas can be deployed without incurring a prohibitive overhead for channel training. Second, the BS can estimate the interference covariance matrix from the SC tier which can be leveraged for downlink precoding. In particular, the BS designs its precoding vectors to transmit independent data streams to its users while being orthogonal to the subspace spanned by the strongest interference directions; thereby minimizing the sum interference imposed on the SCs. In other words, the BS “sacrifices” some of its antennas for interference cancellation while the TDD protocol allows for an implicit coordination across both tiers. Simulation results suggest that, given a sufficiently large number of BS antennas, the proposed scheme can significantly improve the sum-rate of the SC tier at the price of a small macro performance loss.

We study the second-order coding rate of the multiple-input multiple-output (MIMO) Rayleigh block-fading channel via statistical bounds from information spectrum methods and random matrix theory. Based on an asymptotic analysis of the mutual information density which considers the simultaneous growth of the block length n and the number of transmit and receive antennas K and N, we derive closed-form upper and lower bounds on the optimal average error probability when the code rate is within O(1/√nK) of the asymptotic capacity. A Gaussian approximation is then used to establish an upper bound on the error probability for arbitrary code rates which is shown by simulations to be accurate for small N, K, and n.

A well-established capacity lower bound of multiple-input multiple-output (MIMO) single-user fading channels operating with imperfect receiver-side channel-state information (CSI) is improved using a simple rate-splitting and successive-decoding scheme. The potential improvement is shown to increase with the number of allowed decoding steps (layers) to such extent that the best layering strategy is approached in the limit as the number of layers tends to infinity. We give a general analytic expression of this limit, which constitutes a new capacity lower bound that is sharper than the conventional bound. Using large random matrix theory, we derive an asymptotic approximation of this novel bound, which is shown via numerical simulation to be highly accurate over the whole range of signal-to-noise ratios.

We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively.

This article proposes a large system approximation of the ergodic sum-rate (SR) for cellular multi-user multiple-input multiple-output uplink systems. The considered system has various degrees of freedom, such as clusters of base stations (BSs) performing cooperative multi-point processing, randomly distributed user terminals (UTs), and supports arbitrarily configurable antenna gain patterns at the BSs. The approximation is provably tight in the limiting case of a large number of single antenna UTs and antennas at the BSs. Simulation results suggest that the asymptotic analysis is accurate for small system dimensions. Our deterministic SR approximation result is applied to numerically study and optimize the effects of antenna tilting in an exemplary sectorized 3D small cell network topology. Significant SR gains are observed with optimal tilt angles and we provide new insights on the optimal parameterization of cellular networks, along with a discussion of several non-trivial effects.

We consider the downlink of a time-division duplexing (TDD) multicell multiuser MIMO system where the base stations (BSs) are equipped with a very large number of antennas. Assuming channel estimation through uplink pilots, arbitrary antenna correlation and user distributions, we derive approximations of achievable rates with linear precoding techniques, namely eigenbeamforming (BF) and regularized zero-forcing (RZF). The approximations are tight in the large system limit with an infinitely large number of antennas and user terminals (UTs), but match our simulations for realistic system dimensions. We further show that a simple RZF precoding scheme can achieve the same performance as BF with one order of magnitude fewer antennas in both uncorrelated and correlated fading channels.

This paper provides a novel central limit theorem (CLT) for the information density of the MIMO Rayleigh fading channel under white Gaussian inputs, when the data blocklength n and the number of transmit and receive antennas K and N, respectively, are large but of similar order of magnitude. This CLT is used to derive closed-form upper bounds on the error probability via an input-constrained version of Feinstein's lemma by Polyanskiy et al. and the second-order approximation of the coding rate. Numerical evaluations suggest that the normal approximation is tight for reasonably small values of n, K, N.

In this work, we study the performance of random isometric precoders over quasi-static and correlated fading channels. We derive deterministic approximations of the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide simple provably converging fixed-point algorithms for their computation. Although these approximations are only proven exact in the asymptotic regime with infinitely many antennas at the transmitters and receivers, simulations suggest that they closely match the performance of small-dimensional systems. We exemplarily apply our results to the performance analysis of multi-cellular communication systems, multiple-input multiple-output multiple-access channels (MIMO-MAC), and MIMO interference channels. The mathematical analysis is based on the Stieltjes transform method. This enables the derivation of deterministic equivalents of functionals of large-dimensional random matrices. In contrast to previous works, our analysis does not rely on arguments from free probability theory which enables the consideration of random matrix models for which asymptotic freeness does not hold. Thus, the results of this work are also a novel contribution to the field of random matrix theory and applicable to a wide spectrum of practical systems.

We study a multi-cell frequency-selective fading uplink channel from K user terminals (UTs) to B base stations (BSs). The BSs, assumed to be oblivious of the applied encoding scheme, compress and forward their observations to a central station (CS) via capacity limited backhaul links. The CS jointly decodes the messages from all UTs. Since we assume no prior channel state information, the channel needs to be estimated during its coherence time. Based on a lower bound of the ergodic mutual information, we determine the optimal fraction of the coherence time used for channel training. We then study how the optimal training length is impacted by the backhaul capacity. Our analysis is based on large random matrix theory but shown by simulations to be tight for even small system dimensions.

We consider a general wireless channel model for different types of code-division multiple access (CDMA) and space-division multiple-access (SDMA) systems with isometric random signature/precoding matrices over frequency-selective and flat fading channels. We derive deterministic approximations of the Stieltjes transform, the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide a simple fixed-point algorithm for their computation, which is proved to converge. The deterministic approximations are asymptotically tight, almost surely, but shown by simulations to be very accurate for even small system dimensions. Our analysis requires neither arguments from free probability theory nor the asymptotic freeness or the convergence of the spectral distribution of the involved matrices. The results presented in this work are, therefore, also a novel contribution to the field of random matrix theory and might be useful to further applications involving isometric random matrices.

We consider a certain class of large random matrices, composed of independent column vectors with zero mean and different covariance matrices, and derive asymptotically tight deterministic approximations of their moments. This random matrix model arises in several wireless communication systems of recent interest, such as distributed antenna systems or large antenna arrays. Computing the linear minimum mean square error (LMMSE) detector in such systems requires the inversion of a large covariance matrix which becomes prohibitively complex as the number of antennas and users grows. We apply the derived moment results to the design of a low-complexity polynomial expansion detector which approximates the matrix inverse by a matrix polynomial and study its asymptotic performance. Simulation results corroborate the analysis and evaluate the performance for finite system dimensions.

We consider the problem of multi-cell downlink beamforming with N cells and K terminals per cell. Cooperation among base stations (BSs) has been found to increase the system throughput in a multi-cell set up by mitigating inter-cell interference. Most of the previous works assume that the BSs can exchange the instantaneous channel state information (CSI) of all their user terminals (UTs) via high speed backhaul links. However, this approach quickly becomes impractical as N and K grow large. In this work, we formulate a distributed beamforming algorithm in a multi-cell scenario under the assumption that the system dimensions are large. The design objective is the minimize the total transmit power across all BSs subject to satisfying the user SINR constraints while implementing the beamformers in a distributed manner. In our algorithm, the BSs would only need to exchange the channel statistics rather than the instantaneous CSI. We make use of tools from random matrix theory to formulate the distributed algorithm. The simulation results illustrate that our algorithm closely satisfies the target SINR constraints when the number of UTs per cell grows large, while implementing the beamforming vectors in a distributed manner.

We consider a fading version of the dirty-paper problem, as proposed by Grover and Sahai. In this formulation, the various signals involved are complex-valued, and the interference (known only to the transmitter) is multiplied by a random complex-valued coefficient, whose phase is known only to the receiver. We focus on a compound channel formulation, and seek to maximize the worst-case performance. We present an achievable strategy modeled on the lattice-based approach of Erez, Shamai and Zamir and propose heuristic methods to optimize its parameters. We also derive an upper bound on the maximum achievable transmission rates. Our bounds are shown to be tight in some settings, yielding a complete characterization of capacity. We also provide simulation results, indicating the practical effectiveness of our approaches.

Most publications on the capacity and performance of wireless ad hoc networks share the underlying assumption of a uniform random distribution of nodes. In this paper, we study the effects of different node distributions on the local throughput of the slotted ALOHA MAC protocol. The throughput achieved in a network where the nodes are distributed according to a Poisson point process is used as a baseline performance measure for the comparison with other point distributions. Our simulations show that non-uniform random node distributions have a strong impact on the local throughput which is related to the network capacity and performance. This means that the node topology should be taken into account in more detailed analyses and simulations of ad hoc, sensor, and mesh networks.

We analyze the impacts of multi-hop relaying on the quality of service of voice transmission in the downlink OFDMA communication system. It is shown that the system performance in terms of capacity and quality strongly depends on deployment and operating parameters such as the location of relays, traffic loads and the allowable packet error rate. The impact of relaying is less evident when the traffic load is light and the base station can effectively cover the whole cell. In the high traffic load region, multi-hop relaying is most effective in reducing the outage probability while increasing the cell throughput.