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...

In this paper, we study the problem of multi-band (frequency-variant) covariance interpolation with a particular emphasis towards massive MIMO applications. In a massive MIMO system, the communication between each BS with M 1 antennas and each single-antenna user occurs through a collection of scatterers in the environment, where the channel vector of each user at BS antennas consists in a weighted linear combination of the array responses of the scatterers, where each scatterer has its own angle of arrival (AoA) and complex channel gain. The array response at a given AoA depends on the wavelength of the incoming planar wave and is naturally frequency dependent. This results in a frequency-dependent distortion where the second order statistics, i.e., the covariance matrix, of the channel vectors varies with frequency. In this paper, we show that although this effect is generally negligible for a small number of antennas M , it results in a considerable distortion of the covariance matrix and especially its dominant signal subspace in the massive MIMO regime where M → ∞, and can generally incur a serious degradation of the performance especially in frequency division duplexing (FDD) massive MIMO systems where the uplink (UL) and the downlink (DL) communication occur over different frequency bands. We propose a novel UL-DL covariance interpolation technique that is able to recover the covariance matrix in the DL from an estimate of the covariance matrix in the UL under a mild reciprocity condition on the angular power spread function (PSF) of the users (this is in contrast with the UL-DL reciprocity of the instantaneous realization of the channel vectors which does not generally hold). We analyze the performance of our proposed scheme mathematically and prove its robustness under a sufficiently large spatial oversampling of the array. We also propose several simple off-the-shelf algorithms for UL-DL covariance interpolation and evaluate their performance via numerical simulations.Index Terms-UL-DL reciprocity, UL-DL reciprocity of the power spectral function, massive MIMO system.

We study the problem of indoor localization using commodity WiFi channel state information (CSI) measurements. The accuracy of methods developed to address this problem is limited by the overall bandwidth used by the WiFi device as well as various types of signal distortions imposed by the underlying hardware. In this paper, we propose a localization method that performs channel impulse response (CIR) estimation by splicing measured CSI over multiple WiFi bands. In order to overcome hardware-induced phase distortions, we propose a phase retrieval (PR) scheme that only uses CSI magnitude values to estimate the CIR. To achieve high localization accuracy, the PR scheme involves a sparse recovery step, which exploits the fact that the CIR is sparse over the delay domain, due to the small number of contributing signal paths in an indoor environment. Simulation results indicate that our approach outperforms the state of the art by an order of magnitude (cm-level localization accuracy) for more than 90% of the trials and for various SNR regimes.Index Terms-Indoor localization, ranging, multi-band splicing, phase retrieval, sparse channel impulse response estimation.

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