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In this paper, we study the problem of activity detection (AD) in a massive MIMO setup, where the Base Station (BS) has M 1 antennas. We consider a block fading channel model where the M -dim channel vector of each user remains almost constant over a coherence block (CB) containing Dc signal dimensions. We study a setting in which the number of potential users Kc assigned to a specific CB is much larger than the dimension of the CB Dc (Kc Dc) but at each time slot only Ac Kc of them are active. Most of the previous results, based on compressed sensing, require that Ac ≤ Dc, which is a bottleneck in massive deployment scenarios such as Internetof-Things (IoT) and Device-to-Device (D2D) communication. In this paper, we show that one can overcome this fundamental limitation when the number of BS antennas M is sufficiently large. More specifically, we derive a scaling law on the parameters (M, Dc, Kc, Ac) and also Signal-to-Noise Ratio (SNR) under which our proposed AD scheme succeeds. Our analysis indicates that with a CB of dimension Dc, and a sufficient number of BS antennas M with Ac/M = o(1), one can identify the activity of Ac = O(D 2 c / log 2 ( Kc Ac )) active users, which is much larger than the previous bound Ac = O(Dc) obtained via traditional compressed sensing techniques. In particular, in our proposed scheme one needs to pay only a poly-logarithmic penalty O(log 2 ( Kc Ac )) for increasing the number of potential users Kc, which makes it ideally suited for AD in IoT setups. We propose low-complexity algorithms for AD and provide numerical simulations to illustrate our results. We also compare the performance of our proposed AD algorithms with that of other competitive algorithms in the literature.

The fifth generation of cellular communication systems is foreseen to enable a multitude of new applications and use cases with very different requirements. A new 5G multiservice air interface needs to enhance broadband performance as well as provide new levels of reliability, latency and supported number of users. In this paper we focus on the massive Machine Type Communications (mMTC) service within a multi-service air interface. Specifically, we present an overview of different physical and medium access techniques to address the problem of a massive number of access attempts in mMTC and discuss the protocol performance of these solutions in a common evaluation framework.

and safety-critical real world applications remains limited. The main factors responsible for this limitation are• the lack of expressiveness and transparency of a deep neural network's inference model, which makes it difficult to trust their outcomes [2],• the inability to distinguish between in-domain and out-ofdomain samples [11], [12] and the sensitivity to domain shifts [13],• the inability to provide reliable uncertainty estimates for a deep neural network's decision [14] and frequently occurring overconfident predictions [15], [16],• the sensitivity to adversarial attacks that make deep neural networks vulnerable for sabotage [17], [18], [19].

As it becomes increasingly apparent that 4G will not be able to meet the emerging demands of future mobile communication systems, the question what could make up a 5G system, what are the crucial challenges and what are the key drivers is part of intensive, ongoing discussions. Partly due to the advent of compressive sensing, methods that can optimally exploit sparsity in signals have received tremendous attention in recent years. In this paper we will describe a variety of scenarios in which signal sparsity arises naturally in 5G wireless systems. Signal sparsity and the associated rich collection of tools and algorithms will thus be a viable source for innovation in 5G wireless system design. We will discribe applications of this sparse signal processing paradigm in MIMO random access, cloud radio access networks, compressive channel-source network coding, and embedded security. We will also emphasize important open problem that may arise in 5G system design, for which sparsity will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces

We investigate recovery of nonnegative vectors from non-adaptive compressive measurements in the presence of noise of unknown power. In the absence of noise, existing results in the literature identify properties of the measurement that assure uniqueness in the non-negative orthant. By linking such uniqueness results to nullspace properties, we deduce uniform and robust compressed sensing guarantees for nonnegative least squares. No 1-regularization is required. As an important proof of principle, we establish that m × n random i.i.d. 0/1-valued Bernoulli matrices obey the required conditions with overwhelming probability provided that m = O(s log(n/s)). We achieve this by establishing the robust nullspace property for random 0/1-matrices-a novel result in its own right. Our analysis is motivated by applications in wireless network activity detection. I. INTRODUCTIONRecovery of lower complexity objects by observations far below the Nyquist rate has applications in physics, applied math, and many engineering disciplines. Moreover, it is one of the key tools for facing challenges in data processing (like big data and the Internet of Things), wireless communications (the 5th generation of the mobile cellular network) and large scale network control. Compressed Sensing (CS), with its original goal of recovering sparse or compressible vectors, has, in particular, stimulated the research community to investigate further in this direction. The aim is to identify compressibility and low-dimensional structures which allow the recovery from low-rate samples with efficient algorithms. In many applications, the objects of interest exhibit further structural constraints which should be exploited in reconstruction algorithms. Take, for instance, the following setting which appears naturally in communication protocols: The components of sparse information carrying vectors are taken from a finite alphabet, or the data vectors are lying in specific subspaces. Similarly, in network traffic estimation and anomaly detection from end-to-end measurements, the parameters are restricted to particular low-dimensional domains. Finally, the signals occurring in imaging problems are typically constrained to non-negative intensities.Our work is partially inspired by the task of identifying sparse network activation patterns in a large-scale asynchronous wireless network: Suppose that, in order to indicate its presence, each active device node transmits an individual sequence into a noisy wireless channel. All such sequences are multiplied with individual, but unknown, This paper has been presented in part at the 2016 IEEE Information Theory Workshop -ITW 2016,

This paper studies the optimal achievable performance of compressed sensing based unsourced random-access communication over the real AWGN channel. "Unsourced" means, that every user employs the same codebook. This paradigm, recently introduced by Polyanskiy, is a natural consequence of a very large number of potential users of which only a finite number is active in each time slot. The idea behind compressed sensing based schemes is that each user encodes his message into a sparse binary vector and compresses it into a real or complex valued vector using a random linear mapping. When each user employs the same matrix this creates an effective binary inner multiple-access channel. To reduce the complexity to an acceptable level the messages have to be split into blocks. An outer code is used to assign the symbols to individual messages. This division into sparse blocks is analogous to the construction of sparse regression codes (SPARCs), a novel type of channel codes, and we can use concepts from SPARCs to design efficient random-access codes. We analyze the asymptotically optimal performance of the inner code using the recently rigorized replica symmetric formula for the free energy which is achievable with the approximate message passing (AMP) decoder with spatial coupling. An upper bound on the achievable rates of the outer code is derived by classical Shannon theory. Together this establishes a framework to analyse the trade-off between SNR, complexity and achievable rates in the asymptotic infinite blocklength limit. Finite blocklength simulations show that the combination of AMP decoding, with suitable approximations, together with an outer code recently proposed by Amalladinne et. al. outperforms state of the art methods in terms of required energy-per-bit at lower decoding complexity.