| 1. |
- Durisi, Giuseppe, 1977, et al.
(författare)
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Short-packet transmission
- 2021
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Ingår i: Information Theoretic Perspectives on 5G Systems and Beyond. - 9781108416474
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- 5G, a new generation of cellular technology under deployment worldwide, can provide about 100 times faster communications than current 4G technology. But a higher speed is not the sole differentiating factor: 5G is also more reliable, secure, and capable of ubiquitously connecting a massively large number of devices. Ultra-reliable, low-delay, omni-present 5G networks hold the promise of enabling a range of new applications, including self-driving cars, highly automatized industrial tasks, virtual reality gaming, as well as of providing the connectivity platform for the Internet of Things (IoT). Since its introduction in 1948, information theory has underpinned the mathematical foundations of communication systems, including 5G networks, and it will impact the design of cellular systems beyond 5G. The theoretical insights obtained by information theory point to the optimal system performance under a given model, offering strong guidelines and benchmarks for the design and validation of modern communication technologies. Information Theoretic Perspectives on 5G Systems and Beyond provides a comprehensive overview of the state-of-art information-theoretic approaches that led to realization of 5G. Three main areas are discussed, namely network architecture, coding and modulation, and network protocols. Examples of covered topics include cloud/fog radio access networks (a central component in future 6G (beyond 5G) cell-less structure), device-to-device communications, caching, energy harvesting, polar coding, Massive MIMO, short-packet transmission, NOMA, 5G protocols, interference management, content delivery, and cooperative and confidential communications. Information Theoretic Perspectives on 5G Systems and Beyond is the result of a grand effort by more than 40 experts in the field of information theory. It includes 19 chapters, offering a detailed introduction to advanced topics in information theory, and it took several years in making. We are extremely excited that the book is now available. We hope that it can serve as a tool for researchers and graduate students in the fields of information theory and wireless communications, as well as for practitioners in the telecommunications industry.
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| 2. |
- Rezazadeh, Arezou, 1987, et al.
(författare)
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Conditional Mutual Information-Based Generalization Bound for Meta Learning
- 2021
-
Ingår i: IEEE International Symposium on Information Theory - Proceedings. - 2157-8095. ; 2021-July, s. 1176-1181
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Konferensbidrag (refereegranskat)abstract
- Meta-learning optimizes an inductive bias—typically in the form of the hyperparameters of a base-learning algorithm—by observing data from a finite number of related tasks. This paper presents an information-theoretic bound on the generalization performance of any given meta-learner, which builds on the conditional mutual information (CMI) framework of Steinke and Zakynthinou (2020). In the proposed extension to meta-learning, the CMI bound involves a training meta-supersample obtained by first sampling 2N independent tasks from the task environment, and then drawing 2M independent training samples for each sampled task. The meta-training data fed to the meta-learner is modelled as being obtained by randomly selecting N tasks from the available 2N tasks and M training samples per task from the available 2M training samples per task. The resulting bound is explicit in two CMI terms, which measure the information that the meta-learner output and the base-learner output provide about which training data are selected, given the entire meta-supersample. Finally, we present a numerical example that illustrates the merits of the proposed bound in comparison to prior information-theoretic bounds for meta-learning
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| 3. |
- Aabel, Lise, et al.
(författare)
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A TDD Distributed MIMO Testbed Using a 1-bit Radio-Over-Fiber Fronthaul Architecture
- 2024
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Ingår i: IEEE Transactions on Microwave Theory and Techniques. - 0018-9480 .- 1557-9670. ; In Press
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Tidskriftsartikel (refereegranskat)abstract
- We present the uplink and downlink of a time-division duplex distributed multiple-input multiple-output (D-MIMO) testbed, based on a 1-bit radio-over-fiber architecture, which is low cost and scalable. The proposed architecture involves a central unit (CU) that is equipped with 1-bit digital-to-analog and analog-to-digital converters, operating at 10 GS/s. The CU is connected to multiple single-antenna remote radio heads (RRHs) via optical fibers, over which a binary radio frequency (RF) waveform is transmitted. In the uplink, a binary RF waveform is generated at the RRHs by a comparator, whose inputs are the received RF signal and a suitably designed dither signal. In the downlink, a binary RF waveform is generated at the CU via bandpass sigma-delta modulation. Our measurement results show that low error-vector magnitude (EVM) can be achieved in both the uplink and the downlink, despite 1-bit sampling at the CU. Specifically, for point-to-point over-cable transmission between a single user equipment (UE) and a CU equipped with a single RRH, we report, for a 10-MBd signal using single-carrier (SC) 16 quadratic-amplitude modulation (QAM) modulation, an EVM of 3.3% in the downlink, and of 4.5% in the uplink. We then consider a CU connected to three RRHs serving over the air two UEs, and show that, after over-the-air reciprocity calibration, a downlink zero-forcing precoder designed on the basis of uplink channel estimates at the CU achieves an EVM of 6.4% and 10.9% at UE 1 and UE 2, respectively. Finally, we investigate the ability of the proposed architecture to support orthogonal frequency-division multiplexing (OFDM) waveforms, and its robustness against both in-band and out-of-band interference.
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| 4. |
- Aabel, Lise, 1992, et al.
(författare)
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Distributed Massive MIMO via all-Digital Radio Over Fiber
- 2020
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Ingår i: Conference Record - Asilomar Conference on Signals, Systems and Computers. - 1058-6393. ; 2020-November, s. 319-323
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Konferensbidrag (refereegranskat)abstract
- A crucial challenge in the implementation of distributed massive multiple-input multiple-output (MIMO) architectures is to provide phase coherence while, at the same time, limit the complexity of the remote-radio heads (RRHs), which is important for cost-efficient scalability. To address this challenge, we present in this paper a phase-coherent distributed MIMO architecture, based on off-the-shelf, low-cost components. In the proposed architecture, up- and down-conversion are carried out at the central unit (CU). The RRHs are connected to the CU by means of optical fibers carrying oversampled radio-frequency (RF) 1-bit signals. In the downlink, the 1-bit signal is generated via sigma-delta modulation. At the RRH, the RF signal is recovered from the 1-bit signal through a bandpass filter and a power amplifier, and then fed to an antenna. In the uplink, the 1-bit signal is generated by a comparator whose inputs are the low-noise-amplified received RF signal and a suitably designed dither signal. The performance of the proposed architecture is evaluated with satisfactory results both via simulation and measurements from a testbed.
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| 5. |
- Atzeni, Italo, et al.
(författare)
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Low-Resolution Massive MIMO Under Hardware Power Consumption Constraints
- 2021
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Ingår i: Conference Record - Asilomar Conference on Signals, Systems and Computers. - 1058-6393. - 9781665458283
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Konferensbidrag (refereegranskat)abstract
- We consider a fully digital massive multipleinput multiple-output architecture with low-resolution analogto-digital/digital-to-analog converters (ADCs/DACs) at the base station (BS) and analyze the performance trade-off between the number of BS antennas, the resolution of the ADCs/DACs, and the bandwidth. Assuming a hardware power consumption constraint, we determine the relationship between these design parameters by using a realistic model for the power consumption of the ADCs/DACs and the radio frequency chains. Considering uplink pilot-aided channel estimation, we build on the Bussgang decomposition to derive tractable expressions for uplink and downlink ergodic achievable sum rates. Numerical results show that the ergodic performance is boosted when many BS antennas with very low resolution (i.e., 2 to 3 bits) are adopted in both the uplink and the downlink.
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| 6. |
- Castaneda, Oscar, et al.
(författare)
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Finite-alphabet MMSE equalization for all-digital massive MU-MIMO mmWave communications
- 2020
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Ingår i: IEEE Journal on Selected Areas in Communications. - 0733-8716 .- 1558-0008. ; 38:9, s. 2128 -2141
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Tidskriftsartikel (refereegranskat)abstract
- We propose finite-alphabet equalization, a new paradigm that restricts the entries of the spatial equalization matrix to low-resolution numbers, enabling high-throughput, low-power, and low-cost hardware equalizers. To minimize the performance loss of this paradigm, we introduce FAME, short for finite-alphabet minimum mean-square error (MMSE) equalization, which is able to significantly outperform a naïve quantization of the linear MMSE matrix. We develop efficient algorithms to approximately solve the NP-hard FAME problem and showcase that near-optimal performance can be achieved with equalization coefficients quantized to only 1-3 bits for massive multi-user multiple-input multiple-output (MU-MIMO) millimeter-wave (mmWave) systems. We provide very-large scale integration (VLSI) results that demonstrate a reduction in equalization power and area by at least a factor of 3.9× and 5.8×, respectively.
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| 7. |
- Castañeda, Oscar, et al.
(författare)
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Hardware-Friendly Two-Stage Spatial Equalization for All-Digital mmWave Massive MU-MIMO
- 2020
-
Ingår i: Conference Record - Asilomar Conference on Signals, Systems and Computers. - 1058-6393. ; 2020-November, s. 388-392
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Konferensbidrag (refereegranskat)abstract
- Next generation wireless communication systems are expected to combine millimeter-wave communication with massive multi-user multiple-input multiple-output technology. All-digital base-station implementations for such systems need to process high-dimensional data at extremely high rates, which results in excessively high power consumption. In this paper, we propose two-stage spatial equalizers that first reduce the problem dimension by means of a hardware-friendly, low-resolution linear transform followed by spatial equalization on a lower-dimensional signal. We consider adaptive and non-adaptive dimensionality reduction strategies and demonstrate that the proposed two-stage spatial equalizers are able to approach the performance of conventional linear spatial equalizers that directly operate on high-dimensional data, while offering the potential to reduce the power consumption of spatial equalization.
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| 8. |
- Castañeda, Oscar, et al.
(författare)
-
High-Bandwidth Spatial Equalization for mmWave Massive MU-MIMO with Processing-in-Memory
- 2020
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Ingår i: IEEE Transactions on Circuits and Systems II: Express Briefs. - 1549-7747 .- 1558-3791. ; 67:5, s. 891-895
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Tidskriftsartikel (refereegranskat)abstract
- All-digital basestation (BS) architectures enable superior spectral efficiency compared to hybrid solutions in massive multi-user MIMO systems. However, supporting large bandwidths with all-digital architectures at mmWave frequencies is challenging as traditional baseband processing would result in excessively high power consumption and large silicon area. The recently-proposed concept of finite-alphabet equalization is able to address both of these issues by using equalization matrices that contain low-resolution entries to lower the power and complexity of high-throughput matrix-vector products in hardware. In this brief, we explore two different finite-alphabet equalization hardware implementations that tightly integrate the memory and processing elements: (i) a parallel array of multiply-accumulate (MAC) units and (ii) a bit-serial processing-in-memory (PIM) architecture. Our all-digital VLSI implementation results in 28nm CMOS show that the bit-serial PIM architecture reduces the area and power consumption up to a factor of 2× and 3×, respectively, when compared to a parallel MAC array that operates at the same throughput.
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| 9. |
- Castañeda, Oscar, et al.
(författare)
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Resolution-Adaptive All-Digital Spatial Equalization for mmWave Massive MU-MIMO
- 2021
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Ingår i: IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC. ; , s. 386-390
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Konferensbidrag (refereegranskat)abstract
- All-digital basestation (BS) architectures for millimeter-wave (mmWave) massive multi-user multiple-input multiple-output (MU-MIMO), which equip each radio-frequency chain with dedicated data converters, have advantages in spectral efficiency, flexibility, and baseband-processing simplicity over hybrid analog-digital solutions. For all-digital architectures to be competitive with hybrid solutions in terms of power consumption, novel signal-processing methods and baseband architectures are necessary. In this paper, we demonstrate that adapting the resolution of the analog-to-digital converters (ADCs) and spatial equalizer of an all-digital system to the communication scenario (e.g., the number of users, modulation scheme, and propagation conditions) enables orders-of-magnitude power savings for realistic mmWave channels. For example, for a 256-BS-antenna 16-user system supporting 1 GHz bandwidth, a traditional baseline architecture designed for a 64-user worst-case scenario would consume 23 W in 28 nm CMOS for the ADC array and the spatial equalizer, whereas a resolution-adaptive architecture is able to reduce the power consumption by 6.7×.
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| 10. |
- Castañeda, Oscar, et al.
(författare)
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Soft-Output Finite Alphabet Equalization for mmWave Massive MIMO
- 2020
-
Ingår i: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. - 1520-6149. ; 2020-May, s. 1764-1767
-
Konferensbidrag (refereegranskat)abstract
- Nxt-generation wireless systems are expected to combine millimeter-wave (mmWave) and massive multi-user multiple-input multiple-output (MU-MIMO) technologies to deliver high data-rates. These technologies require the basestations (BSs) to process high-dimensional data at extreme rates, which results in high power dissipation and system costs. Finite-alphabet equalization has been proposed recently to reduce the power consumption and silicon area of uplink spatial equalization circuitry at the BS by coarsely quantizing the equalization matrix. In this work, we improve upon finite-alphabet equalization by performing unbiased estimation and soft-output computation for coded systems. By simulating a massive MU-MIMO system that uses orthogonal frequency-division multiplexing and per-user convolutional coding, we show that soft-output finite-alphabet equalization delivers competitive error-rate performance using only 1 to 3 bits per entry of the equalization matrix, even for challenging mmWave channels.
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| 11. |
- Erkip, Elza, et al.
(författare)
-
Editorial Issue on 'Information Theoretic Foundations of Future Communication Systems'
- 2022
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Ingår i: IEEE Journal on Selected Areas in Information Theory. - 2641-8770. ; 3:1, s. 2-4
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Information theory, starting with Shannon’s groundbreaking work, has fundamentally shaped the way communication systems are designed and operated. Information theoretic principles form the underpinnings of modern communication networks. This issue explores how new advances in information theory can impact future communication systems. Several papers address issues at the heart of next generation wireless and wired networks: Multiple access, including access by a massive number of devices, multi-hop, large antenna arrays, communication security, and timeliness of information. Others consider new applications such as joint communication and sensing, communication for learning and inference, wireless imaging, and new storage mediums such as DNA, thereby providing the information theoretic foundations of modalities beyond human-to-human communications.
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| 12. |
- Ettefagh, Yasaman, 1989, et al.
(författare)
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Performance of Quantized Massive MIMO with Fronthaul Rate Constraint over Quasi-Static Channels
- 2023
-
Ingår i: IEEE Access. - 2169-3536 .- 2169-3536. ; 11, s. 56935-56950
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Tidskriftsartikel (refereegranskat)abstract
- We provide a rigorous framework for characterizing and numerically evaluating the error probability achievable in the uplink and downlink of a fully digital quantized multiuser multiple-input multiple-output (MIMO) system. We assume that the system operates over a quasi-static channel that does not change across the finite-length transmitted codewords, and only imperfect channel state information (CSI) is available at the base station (BS) and at the user equipments. The need for the novel framework developed in this paper stems from the fact that, for the quasi-static scenario, commonly used signal-to-interference-and-distortion-ratio expressions that depend on the variance of the channel estimation error are not relatable to any rigorous information-theoretic achievable-rate bound. We use our framework to investigate how the performance of a fully digital massive MIMO system subject to a fronthaul rate constraint, which imposes a limit on the number of samples per second produced by the analog-to-digital and digital-to-analog converters (ADCs and DACs), depends on the number of BS antennas and on the precision of the ADCs and DACs. In particular, we characterize, for a given fronthaul constraint, the trade-off between the number of antennas and the resolution of the data converters, and discuss how this trade-off is influenced by the accuracy of the available CSI. Our framework captures explicitly the cost, in terms of spectral efficiency, of pilot transmission—an overhead that the outage capacity, the classic asymptotic metric used in this scenario, cannot capture. We present extensive numerical results that validate the accuracy of the proposed framework and allow us to characterize, for a given fronthaul constraint, the optimal number of antennas and the optimal resolution of the converters as a function of the transmitted power and of the available CSI.
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| 13. |
- Hellström, Fredrik, 1993, et al.
(författare)
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Evaluated CMI Bounds for Meta Learning: Tightness and Expressiveness
- 2022
-
Ingår i: Advances in Neural Information Processing Systems. - 1049-5258. - 9781713871088 ; 35
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Konferensbidrag (refereegranskat)abstract
- Recent work has established that the conditional mutual information (CMI) framework of Steinke and Zakynthinou (2020) is expressive enough to capture generalization guarantees in terms of algorithmic stability, VC dimension, and related complexity measures for conventional learning (Harutyunyan et al., 2021, Haghifam et al., 2021). Hence, it provides a unified method for establishing generalization bounds. In meta learning, there has so far been a divide between information-theoretic results and results from classical learning theory. In this work, we take a first step toward bridging this divide. Specifically, we present novel generalization bounds for meta learning in terms of the evaluated CMI (e-CMI). To demonstrate the expressiveness of the e-CMI framework, we apply our bounds to a representation learning setting, with $n$ samples from $\hat n$ tasks parameterized by functions of the form $f_i \circ h$. Here, each $f_i \in \mathcal F$ is a task-specific function, and $h \in \mathcal H$ is the shared representation. For this setup, we show that the e-CMI framework yields a bound that scales as $\sqrt{ \mathcal C(\mathcal H)/(n\hat n) + \mathcal C(\mathcal F)/n} $, where $\mathcal C(\cdot)$ denotes a complexity measure of the hypothesis class. This scaling behavior coincides with the one reported in Tripuraneni et al. (2020) using Gaussian complexity.
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| 14. |
- Hellström, Fredrik, 1993, et al.
(författare)
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Fast-Rate Loss Bounds via Conditional Information Measures with Applications to Neural Networks
- 2021
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Ingår i: IEEE International Symposium on Information Theory - Proceedings. - 2157-8095. ; 2021-July, s. 952-957
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Konferensbidrag (refereegranskat)abstract
- We present a framework to derive bounds on the test loss of randomized learning algorithms for the case of bounded loss functions. Drawing from Steinke Zakynthinou (2020), this framework leads to bounds that depend on the conditional information density between the output hypothesis and the choice of the training set, given a larger set of data samples from which the training set is formed. Furthermore, the bounds pertain to the average test loss as well as to its tail probability, both for the PAC-Bayesian and the single-draw settings. If the conditional information density is bounded uniformly in the size n of the training set, our bounds decay as 1/n, This is in contrast with the tail bounds involving conditional information measures available in the literature, which have a less benign 1/√n dependence. We demonstrate the usefulness of our tail bounds by showing that they lead to nonvacuous estimates of the test loss achievable with some neural network architectures trained on MNIST and Fashion-MNIST.
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| 15. |
- Hellström, Fredrik, 1993, et al.
(författare)
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Generalization Bounds via Information Density and Conditional Information Density
- 2020
-
Ingår i: IEEE Journal on Selected Areas in Information Theory. - 2641-8770. ; 1:3, s. 824-839
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Tidskriftsartikel (refereegranskat)abstract
- We present a general approach, based on an exponential inequality, to derive bounds on the generalization error of randomized learning algorithms. Using this approach, we provide bounds on the average generalization error as well as bounds on its tail probability, for both the PAC-Bayesian and single-draw scenarios. Specifically, for the case of sub-Gaussian loss functions, we obtain novel bounds that depend on the information density between the training data and the output hypothesis. When suitably weakened, these bounds recover many of the information-theoretic bounds available in the literature. We also extend the proposed exponential-inequality approach to the setting recently introduced by Steinke and Zakynthinou (2020), where the learning algorithm depends on a randomly selected subset of the available training data. For this setup, we present bounds for bounded loss functions in terms of the conditional information density between the output hypothesis and the random variable determining the subset choice, given all training data. Through our approach, we recover the average generalization bound presented by Steinke and Zakynthinou (2020) and extend it to the PAC-Bayesian and singledraw scenarios. For the single-draw scenario, we also obtain novel bounds in terms of the conditional α-mutual information and the conditional maximal leakage.
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| 16. |
- Hellström, Fredrik, 1993, et al.
(författare)
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Generalization Error Bounds via mth Central Moments of the Information Density
- 2020
-
Ingår i: IEEE International Symposium on Information Theory - Proceedings. - 2157-8095. ; 2020-June, s. 2741-2746
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Konferensbidrag (refereegranskat)abstract
- We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both for the case in which a new hypothesis is randomly generated every time the algorithm is used - as often assumed in the probably approximately correct (PAC)-Bayesian literature - and in the single-draw case, where the hypothesis is extracted only once.For this last scenario, we present a novel bound that is explicit in the central moments of the information density. The bound reveals that the higher the order of the information density moment that can be controlled, the milder the dependence of the generalization bound on the desired confidence level.Furthermore, we use tools from binary hypothesis testing to derive a second bound, which is explicit in the tail of the information density. This bound confirms that a fast decay of the tail of the information density yields a more favorable dependence of the generalization bound on the confidence level.
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| 17. |
- Hellström, Fredrik, 1993, et al.
(författare)
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New Family of Generalization Bounds Using Samplewise Evaluated CMI
- 2022
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Ingår i: Advances in Neural Information Processing Systems. - 1049-5258. ; 35
-
Konferensbidrag (refereegranskat)abstract
- We present a new family of information-theoretic generalization bounds, in which the training loss and the population loss are compared through a jointly convex function. This function is upper-bounded in terms of the disintegrated, samplewise, evaluated conditional mutual information (CMI), an information measure that depends on the losses incurred by the selected hypothesis, rather than on the hypothesis itself, as is common in probably approximately correct (PAC)-Bayesian results. We demonstrate the generality of this framework by recovering and extending previously known information-theoretic bounds. Furthermore, using the evaluated CMI, we derive a samplewise, average version of Seeger's PAC-Bayesian bound, where the convex function is the binary KL divergence. In some scenarios, this novel bound results in a tighter characterization of the population loss of deep neural networks than previous bounds. Finally, we derive high-probability versions of some of these average bounds. We demonstrate the unifying nature of the evaluated CMI bounds by using them to recover average and high-probability generalization bounds for multiclass classification with finite Natarajan dimension.
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| 18. |
- Hu, Anzhong, et al.
(författare)
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EVM Analysis of Distributed Massive MIMO with 1-Bit Radio-Over-Fiber Fronthaul
- 2024
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Ingår i: IEEE Transactions on Communications. - 0090-6778 .- 1558-0857. ; In Press
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the uplink performance of a distributed massive multiple-input multiple-output (MIMO) architecture in which the remotely located access points (APs) are connected to a central processing unit via a fiber-optical fronthaul carrying a dithered and 1-bit quantized version of the received radio-frequency (RF) signal. The innovative feature of the proposed architecture is that no down-conversion is performed at the APs. This eliminates the need to equip the APs with local oscillators, which may be difficult to synchronize. Under the assumption that a constraint is imposed on the amount of data that can be exchanged across the fiber-optical fronthaul, we investigate the tradeoff between spatial oversampling, defined in terms of the total number of APs, and temporal oversampling, defined in terms of the oversampling factor selected at the central processing unit, to facilitate the recovery of the transmitted signal from 1-bit samples of the RF received signal. Using the so-called error-vector magnitude (EVM) as performance metric, we shed light on the optimal design of the dither signal, and quantify, for a given number of APs, the minimum fronthaul rate required for our proposed distributed massive MIMO architecture to outperform a standard co-located massive MIMO architecture in terms of EVM.
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| 19. |
- Jose, Sharu Theresa, et al.
(författare)
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Transfer Meta-Learning: Information-Theoretic Bounds and Information Meta-Risk Minimization
- 2022
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 68:1, s. 474-501
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Tidskriftsartikel (refereegranskat)abstract
- Meta-learning automatically infers an inductive bias by observing data from a number of related tasks. The inductive bias is encoded by hyperparameters that determine aspects of the model class or training algorithm, such as initialization or learning rate. Meta-learning assumes that the learning tasks belong to a task environment, and that tasks are drawn from the same task environment both during meta-training and meta-testing. This, however, may not hold true in practice. In this paper, we introduce the problem of transfer meta-learning, in which tasks are drawn from a target task environment during meta-testing that may differ from the source task environment observed during meta-training. Novel information-theoretic upper bounds are obtained on the transfer meta-generalization gap, which measures the difference between the meta-training loss, available at the meta-learner, and the average loss on meta-test data from a new, randomly selected, task in the target task environment. The first bound, on the average transfer meta-generalization gap, captures the meta-environment shift between source and target task environments via the KL divergence between source and target data distributions. The second, PAC-Bayesian bound, and the third, single-draw bound, account for this shift via the log-likelihood ratio between source and target task distributions. Furthermore, two transfer meta-learning solutions are introduced. For the first, termed Empirical Meta-Risk Minimization (EMRM), we derive bounds on the average optimality gap. The second, referred to as Information Meta-Risk Minimization (IMRM), is obtained by minimizing the PAC-Bayesian bound. IMRM is shown via experiments to potentially outperform EMRM.
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| 20. |
- Kislal, Ahmet Oguz, 1993, et al.
(författare)
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Efficient evaluation of the error probability for pilot-assisted finite-blocklength transmission
- 2022
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Ingår i: Conference Record - Asilomar Conference on Signals, Systems and Computers. - 1058-6393. ; 2022-October, s. 1038-1044
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Konferensbidrag (refereegranskat)abstract
- We propose a numerically efficient method for evaluating the random-coding union bound with parameter s on the error probability achievable in the finite-blocklength regime by a pilot-assisted transmission scheme employing Gaussian code-books and operating over a memoryless block-fading channel. Our method relies on the saddlepoint approximation, which, differently from previous results reported for similar scenarios, is performed with respect to the number of fading blocks (a.k.a. diversity branches) spanned by each codeword, instead of the number of channel uses per block. This different approach avoids a costly numerical averaging of the error probability over the realizations of the fading process and of its pilot-based estimate at the receiver and yields a significant reduction of the number of channel realizations required to estimate the error probability via Monte-Carlo simulation. For example, in a single-input single-output scenario, when four or more diversity branches are available, an error probability of 10-4can be estimated accurately using our method by using less than 3000 samples. In contrast, the conventional saddlepoint approach requires around 106samples.
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| 21. |
- Kislal, Ahmet Oguz, 1993, et al.
(författare)
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Efficient evaluation of the error probability for pilot-assisted URLLC with Massive MIMO
- 2023
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Ingår i: IEEE Journal on Selected Areas in Communications. - 0733-8716 .- 1558-0008. ; 41:7, s. 1969-1981
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Tidskriftsartikel (refereegranskat)abstract
- We propose a numerically efficient method for evaluating the random-coding union bound with parameter s on the error probability achievable in the finite-blocklength regime by a pilot-assisted transmission scheme employing Gaussian code-books and operating over a memoryless block-fading channel. Our method relies on the saddlepoint approximation, which, differently from previous results reported for similar scenarios, is performed with respect to the number of fading blocks (a.k.a. diversity branches) spanned by each codeword, instead of the number of channel uses per block. This different approach avoids a costly numerical averaging of the error probability over the realizations of the fading process and of its pilot-based estimate at the receiver and results in a significant reduction of the number of channel realizations required to estimate the error probability accurately. Our numerical experiments for both single-antenna communication links and massive multiple-input multiple-output (MIMO) networks show that, when two or more diversity branches are available, the error probability can be estimated accurately with the saddlepoint approximation with respect to the number of fading blocks using a numerical method that requires about two orders of magnitude fewer Monte-Carlo samples than with the saddlepoint approximation with respect to the number of channel uses per block.
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| 22. |
- Lancho Serrano, Alejandro, 1991, et al.
(författare)
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A Finite-Blocklength Analysis for URLLC with Massive MIMO
- 2021
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Ingår i: IEEE International Conference on Communications. - 1550-3607. ; June 2021
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Konferensbidrag (refereegranskat)abstract
- This paper presents a rigorous finite-blocklength framework for the characterization and the numerical evaluation of the packet error probability achievable in the uplink and downlink of Massive MIMO for ultra-reliable low-latency communications (URLLC). The framework encompasses imperfect channel-state information, pilot contamination, spatially correlated channels, and arbitrary linear signal processing. For a practical URLLC network setup involving base stations with M = 100 antennas, we show by means of numerical results that a target error probability of 10-5 can be achieved with MMSE channel estimation and multicell MMSE signal processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. For the same setting, an alternative solution with lower computational complexity, based on least-squares channel estimation and regularized zero-forcing signal processing, does not suffice unless M is increased significantly.
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| 23. |
- Lancho Serrano, Alejandro, 1991, et al.
(författare)
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Cell-Free Massive MIMO for URLLC: A Finite-Blocklength Analysis
- 2023
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Ingår i: IEEE Transactions on Wireless Communications. - 1558-2248 .- 1536-1276. ; 22:12, s. 8723-8735
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Tidskriftsartikel (refereegranskat)abstract
- We present a general framework for the characterization of the packet error probability achievable in cell-free Massive multiple-input multiple output (MIMO) architectures deployed to support ultra-reliable low-latency (URLLC) traffic. The framework is general and encompasses both centralized and distributed cell-free architectures, arbitrary fading channels and channel estimation algorithms at both network and user-equipment (UE) sides, as well as arbitrary combing and precoding schemes. The framework is used to perform numerical experiments on specific scenarios, which illustrate the superiority of cell-free architectures compared to cellular architectures in supporting URLLC traffic in uplink and downlink. Also, these numerical experiments provide the following insights into the design of cell-free architectures for URLLC: i) minimum mean square error (MMSE) spatial processing must be used to achieve the URLLC targets; ii) for a given total number of antennas per coverage area, centralized cell-free solutions involving single-antenna access points (APs) offer the best performance in the uplink, thereby highlighting the importance of reducing the average distance between APs and UEs in the URLLC regime; iii) this observation applies also to the downlink, provided that the APs transmit precoded pilots to allow the UEs to estimate accurately the precoded channel.
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| 24. |
- Lancho Serrano, Alejandro, 1991, et al.
(författare)
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Cell-free Massive MIMO with Short Packets
- 2021
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Ingår i: IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC. ; , s. 416-420
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Konferensbidrag (refereegranskat)abstract
- In this paper, we adapt to cell-free Massive MIMO (multiple-input multiple-output) the finite-blocklength framework introduced by Ostman et al. (2020) for the charac- ¨ terization of the packet error probability achievable with Massive MIMO, in the ultra-reliable low-latency communications (URLLC) regime. The framework considered in this paper encompasses a cell-free architecture with imperfect channelstate information, and arbitrary linear signal processing performed at a central-processing unit connected to the access points via fronthaul links. By means of numerical simulations, we show that, to achieve the high reliability requirements in URLLC, MMSE signal processing must be used. Comparisons are also made with both small-cell and Massive MIMO cellular networks. Both require a much larger number of antennas to achieve comparable performance to cell-free Massive MIMO.
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| 25. |
- Lancho Serrano, Alejandro, 1991, et al.
(författare)
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On Joint Detection and Decoding in Short-Packet Communications
- 2021
-
Ingår i: Proceedings - IEEE Global Communications Conference, GLOBECOM. - 2334-0983 .- 2576-6813.
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Konferensbidrag (refereegranskat)abstract
- We consider a communication problem in which the receiver must first detect the presence of an information packet and, if detected, decode the message carried within it. We present general nonasymptotic upper and lower bounds on the maximum coding rate that depend on the blocklength, the probability of false alarm, the probability of misdetection, and the packet error probability. The bounds, which are expressed in terms of binary-hypothesis-testing performance metrics, generalize finiteblocklength bounds derived previously for the scenario when a genie informs the receiver whether a packet is present. The bounds apply to detection performed either jointly with decoding on the entire data packet, or separately on a dedicated preamble. The results presented in this paper can be used to determine the blocklength values at which the performance of a communication system is limited by its ability to perform packet detection satisfactorily, and to assess the difference inperformance between preamblebased detection, and joint detection and decoding. Numerical results pertaining to the binary-input AWGN channel are provided.
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| 26. |
- Lancho Serrano, Alejandro, 1991, et al.
(författare)
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On single-antenna Rayleigh block-fading channels at finite blocklength
- 2020
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 66:1, s. 496-519
-
Tidskriftsartikel (refereegranskat)abstract
- This article concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation of the maximum coding rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals $L$ over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate at SNR values above 15dB and when the number of coherence intervals is 10 or more.
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| 27. |
- Lancho Serrano, Alejandro, 1991, et al.
(författare)
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Saddlepoint Approximations for Short-Packet Wireless Communications
- 2020
-
Ingår i: IEEE Transactions on Wireless Communications. - 1558-2248 .- 1536-1276. ; 19:7, s. 4831-4846
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Tidskriftsartikel (refereegranskat)abstract
- In recent years, the derivation of nonasymptotic converse and achievability bounds on the maximum coding rate as a function of the error probability and blocklength has gained attention in the information theory literature. While these bounds are accurate for many scenarios of interest, they need to be evaluated numerically for most wireless channels of practical interest, and their evaluation is computationally demanding. This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB and blocklengths of 168 channel uses or more.
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| 28. |
- Marti, Gian, et al.
(författare)
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Hybrid Jammer Mitigation for All-Digital mmWave Massive MU-MIMO
- 2021
-
Ingår i: Conference Record - Asilomar Conference on Signals, Systems and Computers. - 1058-6393. - 9781665458283
-
Konferensbidrag (refereegranskat)abstract
- Low-resolution analog-to-digital converters (ADCs) simplify the design of millimeter-wave (mmWave) massive multi-user multiple-input multiple-output (MU-MIMO) base-stations, but increase vulnerability to jamming attacks. As a remedy, we propose HERMIT (short for Hybrid jammER MITigation), a method that combines a hardware-friendly adaptive analog transform with a corresponding digital equalizer: The analog transform removes most of the jammer’s energy prior to data conversion; the digital equalizer suppresses jammer residues while detecting the legitimate transmit data. We provide theoretical results that establish the optimal analog transform as a function of the user equipments' and the jammer’s channels. Using simulations with mmWave channel models, we demonstrate the superiority of HERMIT compared both to purely digital jammer mitigation as well as to a recent hybrid method that mitigates jammer interference with a nonadaptive analog transform.
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| 29. |
- Munari, Andrea, et al.
(författare)
-
An Age of Information Characterization of Frameless ALOHA
- 2021
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Ingår i: Conference Record - Asilomar Conference on Signals, Systems and Computers. - 1058-6393. ; 2021-October, s. 1488-1495
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Konferensbidrag (refereegranskat)abstract
- We provide a characterization of the peak age of information (AoI) achievable in a random-access system operating according to the frameless ALOHA protocol. Differently from previous studies, our analysis accounts for the fact that the number of terminals contending the channel may vary over time, as a function of the duration of the previous contention period. The exact characterization of the AoI provided in this paper, which is based on a Markovian analysis, reveals the impact of some key protocol parameters such as the maximum length of the contention period, on the average peak AoI. Specifically, we show that setting this parameter so as to maximize the throughput may result in an AoI degradation.
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| 30. |
- Munari, Andrea, et al.
(författare)
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The Dynamic Behavior of Frameless ALOHA: Drift Analysis, Throughput, and Age of Information
- 2023
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Ingår i: IEEE Transactions on Communications. - 0090-6778 .- 1558-0857. ; 71:12, s. 6914-6927
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Tidskriftsartikel (refereegranskat)abstract
- We study the dynamic behavior of frameless ALOHA, both in terms of throughput and age of information (AoI). In particular, differently from previous studies, our analysis accounts for the fact that the number of terminals contending the channel may vary over time, as a function of the duration of the previous contention period. The stability of the protocol is analyzed via a drift analysis, which allows us to determine the presence of stable and unstable equilibrium points. We also provide an exact characterization of the AoI performance, through which we determine the impact of some key protocol parameters, such as the maximum length of the contention period, on the average AoI. Specifically, we show that configurations of parameters that maximize the throughput may result in a degradation of the AoI performance.
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| 31. |
- Ngo, Khac-Hoang, 1992, et al.
(författare)
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Age of Information in Prioritized Random Access
- 2021
-
Ingår i: Conference Record - Asilomar Conference on Signals, Systems and Computers. - 1058-6393. - 9781665458283
-
Konferensbidrag (refereegranskat)abstract
- Age of information (AoI) is a performance metric that captures the freshness of status updates. While AoI has been studied thoroughly for point-to-point links, the impact of modern random-access protocols on this metric is still unclear. In this paper, we extend the recent results by Munari to prioritized random access where devices are divided into different classes according to different AoI requirements. We consider the irregular repetition slotted ALOHA protocol and analyze the AoI evolution by means of a Markovian analysis following similar lines as in Munari (2021). We aim to design the protocol to satisfy the AoI requirements for each class while minimizing the power consumption. To this end, we optimize the update probability and the degree distributions of each class, such that the probability that their AoI exceeds a given threshold lies below a given target and the average number of transmitted packets is minimized.
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| 32. |
- Ngo, Khac-Hoang, 1992, et al.
(författare)
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Age of Information in Slotted ALOHA With Energy Harvesting
- 2023
-
Ingår i: Proceedings - IEEE Global Communications Conference, GLOBECOM. - 2334-0983 .- 2576-6813. ; , s. 3579-3584
-
Konferensbidrag (refereegranskat)abstract
- We examine the age of information (AoI) of a status update system that incorporates energy harvesting and uses the slotted ALOHA protocol. We derive analytically the average AoI and the probability that the AoI exceeds a given threshold. Via numerical results, we investigate two strategies to minimize the age of information (AoI): transmitting a new update whenever possible to exploit every chance to reduce the AoI, and transmitting only when sufficient energy is available to increase the chance of successful delivery. The two strategies are beneficial for low and high update generation rates, respectively. However, an optimized approach that balances the two strategies outperforms them significantly in terms of both AoI and throughput.
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| 33. |
- Ngo, Khac-Hoang, 1992, et al.
(författare)
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Irregular Repetition Slotted ALOHA Over the Binary Adder Channel
- 2023
-
Ingår i: IEEE International Conference on Communications. - 1550-3607. ; 2023-May, s. 5346-5351
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Konferensbidrag (refereegranskat)abstract
- We propose an irregular repetition slotted ALOHA (IRSA) based random-access protocol for the binary adder channel (BAC). The BAC captures important physical-layer concepts, such as packet generation, per-slot decoding, and information rate, which are neglected in the commonly considered collision channel model. We divide a frame into slots and let users generate a packet, to be transmitted over a slot, from a given codebook. In a state-of-the-art scheme proposed by Paolini et al. (2022), the codebook is constructed as the parity-check matrix of a BCH code. Here, we construct the codebook from independent and identically distributed binary symbols to obtain a random-coding achievability bound. Our per-slot decoder progressively discards incompatible codewords from a list of candidate codewords, and can be improved by shrinking this list across iterations. In a regime of practical interests, our scheme can resolve more colliding users in a slot and thus achieves a higher average sum rate than the scheme in Paolini et al. (2022).
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| 34. |
- Ngo, Khac-Hoang, 1992, et al.
(författare)
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Massive Uncoordinated Access with Random User Activity
- 2021
-
Ingår i: IEEE International Symposium on Information Theory - Proceedings. - 2157-8095. ; 2021-July, s. 3014-3019
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Konferensbidrag (refereegranskat)abstract
- We extend the seminal work by Polyanskiy (2017) on massive uncoordinated access to the case where the number of active users is random and unknown a priori. We define a random-access code accounting for both misdetection (MD) and false-alarm (FA), and derive a random-coding achievability bound for the Gaussian multiple access channel. Our bound captures the fundamental trade-off between MD and FA probabilities. It suggests that lack of knowledge of the number of active users entails a small penalty in power efficiency. For a typical scenario, to achieve both MD and FA probabilities below 0.1, the required energy per bit predicted by our bound is 0.5-0.7 dB higher than that predicted by the bound in Polyanskiy (2017) for a known number of active users. Taking both MD and FA into account, we use our bound to benchmark the energy efficiency of some recently proposed massive random access schemes.
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| 35. |
- Ngo, Khac-Hoang, 1992, et al.
(författare)
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Unsourced Multiple Access for Heterogeneous Traffic Requirements
- 2022
-
Ingår i: Conference Record - Asilomar Conference on Signals, Systems and Computers. - 1058-6393. ; 2022-October, s. 687-691
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Konferensbidrag (refereegranskat)abstract
- We investigate the coexistence of critical and massive Internet of Things (IoT) services in the context of the unsourced multiple access (UMA) framework, introduced by Polyanskiy (2017). We consider the standard UMA setup in which all users employ a common codebook and the receiver returns an unordered list of codewords. To model the critical IoT service, we assume that the users can also communicate a common alarm message. We further assume that the number of active users in each transmission attempt is random and unknown. We derive a random-coding bound for the Gaussian multiple access channel and demonstrate that orthogonal network slicing enables the two traffic types to coexist with high energy efficiency.
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| 36. |
- Ngo, Khac-Hoang, 1992, et al.
(författare)
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Unsourced Multiple Access With Common Alarm Messages: Network Slicing for Massive and Critical IoT
- 2024
-
Ingår i: IEEE Transactions on Communications. - 0090-6778 .- 1558-0857. ; 72:2, s. 907-923
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the coexistence of massive and critical Internet of Things (IoT) services in the context of the unsourced multiple access (UMA) framework introduced by Polyanskiy (2017), where all users employ a common codebook and the receiver returns an unordered list of decoded codewords. This setup is suitably modified to introduce heterogeneous traffic. Specifically, to model the massive IoT service, we assume that a standard message originates independently from each IoT device as in the standard UMA setup. To model the critical IoT service, we assume the generation of alarm messages that are common for all devices. This setup requires a significant redefinition of the error events, i.e., misdetections and false positives. We further assume that the number of active users in each transmission attempt is random and unknown. We derive a random-coding achievability bound on the misdetection and false positive probabilities of both standard and alarm messages on the Gaussian multiple access channel. Using our bound, we demonstrate that orthogonal network slicing enables massive and critical IoT to coexist under the requirement of high energy efficiency. On the contrary, we show that nonorthogonal network slicing is energy inefficient due to the residual interference from the alarm signal when decoding the standard messages.
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| 37. |
- Ngo, Khac-Hoang, 1992, et al.
(författare)
-
Unsourced Multiple Access With Random User Activity
- 2023
-
Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 69:7, s. 4537-4558
-
Tidskriftsartikel (refereegranskat)abstract
- To account for the massive uncoordinated random access scenario, which is relevant for the Internet of Things, Polyanskiy (2017) proposed a novel formulation of the multiple-access problem, commonly referred to as unsourced multiple access, where all users employ a common codebook and the receiver decodes up to a permutation of the messages. In this paper, we extend this seminal work to the case where the number of active users is random and unknown a priori. We define a random-access code accounting for both misdetection (MD) and false alarm (FA), and derive a random-coding achievability bound for the Gaussian multiple access channel. Our bound captures the fundamental trade-off between MD and FA probabilities. It suggests that the lack of knowledge of the number of active users entails a small penalty in energy efficiency when the target MD and FA probabilities are high. However, as the target MD and FA probabilities decrease, the energy efficiency penalty becomes more significant. For example, in a typical IoT scenario with framelength 19200 complex channel uses and 25–300 active users in average, the required energy per bit to achieve both MD and FA probabilities below 10-1, predicted by our bound, is only 0.5–0.7 dB higher than that predicted by the bound in Polyanskiy (2017) for a known number of active users. This gap increases to 3–4 dB when the target MD probability and/or FA probability is below 10-3. Taking both MD and FA into account, we use our bound to benchmark the energy efficiency of slotted-ALOHA with multi-packet reception, of a decoder that simply treats interference as noise, and of some recently proposed unsourced multiple access schemes. Numerical results suggest that, when the target MD and FA probabilities are high, it is effective to estimate the number of active users, then treat this estimate as the true value, and use a coding scheme that performs well for the case of known number of active users. However, this approach becomes energy inefficient when the requirements on MD and FA probabilities are stringent.
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| 38. |
- Sezgin, Ibrahim Can, 1992, et al.
(författare)
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All-Digital, Radio-over-Fiber, Communication Link Architecture for Time-Division Duplex Distributed Antenna Systems
- 2021
-
Ingår i: Journal of Lightwave Technology. - 0733-8724 .- 1558-2213. ; 39:9, s. 2769-2779
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Tidskriftsartikel (refereegranskat)abstract
- Radio-over-fiber is a popular technique to establish communication links between a central location and many remote antenna units. Many different architectures are available for the downlink, i.e., for the communication link from the central unit to the remote antennas. On the contrary, the low-cost and low-complexity requirement of the remote units makes it difficult to devise architectures suitable for the uplink, i.e., for the communication link from the remote antennas to the central unit. In this paper, we address this and propose a low-complexity, all-digital, time-division-duplex communication architecture. For the downlink, a band-pass sigma-delta-over-fiber is employed. In the receive mode, the uplink includes an all-digital pulse-width-modulation technique. The received radio frequency (RF) signal is quantized into a binary stream through comparison with a tailored reference signal provided by the central unit. The direct quantization of the RF signal eliminates any need for local-oscillator and mixer stages at the remote units. The performance of the proposed architecture is investigated through extensive simulations and measurements. For instance, the all-digital, time-division duplex communication link provides -30.0 dB and -25.5 dB normalized mean square error signal quality through downlink and uplink communication with 20-MHz, 64-quadrature amplitude modulation signals centered at 2.365-GHz, respectively.
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| 39. |
- Tsaloli, Georgia, 1993, et al.
(författare)
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WiP: Verifiable, Secure and Energy-Efficient Private Data Aggregation in Wireless Sensor Networks
- 2022
-
Ingår i: Proceedings of ACM Symposium on Access Control Models and Technologies, SACMAT. - New York, NY, USA : ACM. ; , s. 61-66
-
Konferensbidrag (refereegranskat)abstract
- Large amounts of data are collected by IoT devices, and transmitted wirelessly to cloud servers for aggregation. These data are often sensitive and need to remain secret. Moreover, the employed servers might be untrustworthy, and maliciously alter their results. To address this, public verifiability must be provided, i.e., anyone can check the result's correctness. Nevertheless, any such protocol must also cope with the limited battery capacity of the IoT devices. We investigate the problem of verifiable, privacy-preserving aggregation and how to accommodate the IoT energy-efficiency requirements, in the context of a 5G wireless communication setting. We revisit the verifiable additive homomorphic secret sharing (VAHSS), which computes the sum of K sensors' data. We propose a threshold secure and private VAHSS protocol where only a subset of the servers is needed for computing the sum. This sum is publicly verifiable thanks to a proof created during the protocol. We provide an energy efficiency analysis, including the trade-off between the sensors' transmitted power and the protocol's failure probability due to decoding errors in the wireless transmission phase.
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| 40. |
- Östman, Johan, 1989, et al.
(författare)
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Short-packet Transmission via Variable-Length Codes in the Presence of Noisy Stop Feedback
- 2021
-
Ingår i: IEEE Transactions on Wireless Communications. - 1558-2248 .- 1536-1276. ; 20:1, s. 214-227
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Tidskriftsartikel (refereegranskat)abstract
- We present an upper bound on the error probability achievable using variable-length stop feedback (VLSF) codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently from the bound proposed in Polyanskiy et al. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant setup in which the feedback link is noisy. Numerical evaluation of our bound suggests that, for fixed latency and reliability constraints, noise in the feedback link may increase the minimum average service time for the VLSF scheme considered in this paper, to the extent that fixed-length codes without feedback may be preferable in some scenarios.
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| 41. |
- Östman, Johan, 1989, et al.
(författare)
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URLLC with Massive MIMO: Analysis and Design at Finite Blocklength
- 2021
-
Ingår i: IEEE Transactions on Wireless Communications. - 1558-2248 .- 1536-1276. ; 20:10, s. 6387-6401
-
Tidskriftsartikel (refereegranskat)abstract
- The fast adoption of Massive MIMO for high-throughput communications was enabled by many research contributions mostly relying on infinite-blocklength information-theoretic bounds. This makes it hard to assess the suitability of Massive MIMO for ultra-reliable low-latency communications (URLLC) operating with short-blocklength codes. This paper provides a rigorous framework for the characterization and numerical evaluation (using the saddlepoint approximation) of the error probability achievable in the uplink and downlink of Massive MIMO at finite blocklength. The framework encompasses imperfect channel state information, pilot contamination, spatially correlated channels, and arbitrary linear spatial processing. In line with previous results based on infinite-blocklength bounds, we prove that, with minimum mean-square error (MMSE) processing and spatially correlated channels, the error probability at finite blocklength goes to zero as the number M of antennas grows to infinity, even under pilot contamination. However, numerical results for a practical URLLC network setup involving a base station with M = 100 antennas, show that a target error probability of 10-5 can be achieved with MMSE processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. Maximum ratio processing does not suffice.
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