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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.

Massive MIMO is a variant of multiuser MIMO in which the number of antennas at the base station (BS) M is very large and typically much larger than the number of served users (data streams) K. Recent research has widely investigated the system-level advantages of massive MIMO and, in particular, the beneficial effect of increasing the number of antennas M . These benefits, however, come at the cost of a dramatic increase in hardware and computational complexity. This is partly due to the fact that the BS needs to compute precoding/receiving vectors in order to coherently transmit/detect data to/from each user, where the resulting complexity grows proportionally to the number of antennas M and the number of served users K. Recently, different algorithms based on tools from asymptotic random matrix theory and/or approximated message passing have been proposed to reduce such complexity. The underlying assumption in all these techniques, however, is that the exact statistics (covariance matrix) of the channel vectors of the users is a priori known. This is far from being realistic, especially taking into account that, in the high-dim regime of M ≫ 1, estimating the channel covariance matrices of the users is also challenging in terms of both computation and storage requirements. In this paper, we propose a novel technique for computing the precoder/detector in a massive MIMO system. Our method is based on the randomized Kaczmarz algorithm and does not require a priori knowledge of the statistics of the users channel vectors. We analyze the performance of our proposed algorithm theoretically and compare its performance with that of other techniques based on random matrix theory and approximate message

We propose a novel method for massive Multiple-Input Multiple-Output (massive MIMO) in Frequency Division Duplexing (FDD) systems. Due to the large frequency separation between Uplink (UL) and Downlink (DL), in FDD systems channel reciprocity does not hold. Hence, in order to provide DL channel state information to the Base Station (BS), closed-loop DL channel probing and Channel State Information (CSI) feedback is needed. In massive MIMO this incurs typically a large training overhead. For example, in a typical configuration with M 200 BS antennas and fading coherence block of T 200 symbols, the resulting rate penalty factor due to the DL training overhead, given by max{0, 1 − M/T }, is close to 0. To reduce this overhead, we build upon the well-known fact that the Angular Scattering Function (ASF) of the user channels is invariant over frequency intervals whose size is small with respect to the carrier frequency (as in current FDD cellular standards). This allows to estimate the users' DL channel covariance matrix from UL pilots without additional overhead.Based on this covariance information, we propose a novel sparsifying precoder in order to maximize the rank of the effective sparsified channel matrix subject to the condition that each effective user channel has sparsity not larger than some desired DL pilot dimension T dl , resulting in the DL training overhead factor max{0, 1 − T dl /T } and CSI feedback cost of T dl pilot measurements. The optimization of the sparsifying precoder is formulated as a Mixed Integer Linear Program, that can be efficiently solved. Extensive simulation results demonstrate the superiority of the proposed approach with respect to concurrent state-of-the-art schemes based on compressed sensing or UL/DL dictionary learning. Index TermsFDD massive MIMO, downlink covariance estimation, active channel sparsification. I. INTRODUCTIONMultiuser Multiple-Input Multiple-Output (MIMO) consists of exploiting multiple antennas at the Base Station (BS) side, in order to multiplex over the spatial domain multiple data streams to multiple users sharing the same time-frequency transmission resource (channel bandwidth and time slots). For a block-fading channel with spatially independent fading and coherence block of T symbols, 1 the high-SNR sum-capacity behaves aswhere M * = min{M, K, T /2}, M denotes the number of BS antennas, and K denotes the number of single-antenna users [2][3][4]. When M and the number of users are potentially very large, the system pre-log factor 2 is maximized by serving K = T /2 data streams (users). While any number M ≥ K of BS antennas yields the same (optimal) pre-log factor, a key observation made in [6] is that, when training a very large number of antennas comes at no additional overhead cost, it is indeed convenient to use M K antennas at the BS. In this way, at the cost of some additional hardware complexity, very significant benefits at the system level can be achieved. These include: i) energy efficiency (due to the large beamforming gain); ii) inter-cell inte...

Massive MIMO is a variant of multiuser MIMO where the number of base-station antennas M is very large (typically ≈ 100), and generally much larger than the number of spatially multiplexed data streams (typically ≈ 10). The benefits of such approach have been intensively investigated in the past few years, and all-digital experimental implementations have also been demonstrated. Unfortunately, the front-end A/D conversion necessary to drive hundreds of antennas, with a signal bandwidth of the order of 10 to 100 MHz, requires very large sampling bitrate and power consumption.In order to reduce such implementation requirements, Hybrid Digital-Analog architectures have been proposed. In particular, our work in this paper is motivated by one of such schemes named Joint Spatial Division and Multiplexing (JSDM), where the downlink precoder (resp., uplink linear receiver) is split into the product of a baseband linear projection (digital) and an RF reconfigurable beamforming network (analog), such that only a reduced number m M of A/D converters and RF modulation/demodulation chains is needed. In JSDM, users are grouped according to similarity of their channel dominant subspaces, and these groups are separated by the analog beamforming stage, where multiplexing gain in each group is achieved using the digital precoder. Therefore, it is apparent that extracting the channel subspace information of the M -dim channel vectors from snapshots of m-dim projections, with m M , plays a fundamental role in JSDM implementation.In this paper, we develop novel efficient algorithms that require sampling only m = O(2 √ M ) specific array elements according to a coprime sampling scheme, and for a given p M , return a p-dim beamformer that has a performance comparable with the best p-dim beamformer that can be designed from the full knowledge of the exact channel covariance matrix. We assess the performance of our proposed estimators both analytically and empirically via numerical simulations. We also demonstrate by simulation that the proposed subspace estimation methods provide near-ideal performance for a massive MIMO JSDM system, by comparing with the case where the user channel covariances are perfectly known.