Efficient Downlink Channel Probing and Uplink Feedback in FDD Massive MIMO Systems

Massive Multiple-Input Multiple-Output (massive MIMO) is a variant of multi-user MIMO in which the number of antennas at each Base Station (BS) is very large and typically much larger than the number of users simultaneously served. Massive MIMO can be implemented with Time Division Duplexing (TDD) or Frequency Division Duplexing (FDD) operation. FDD massive MIMO systems are particularly desirable due to their implementation in current wireless networks and their efficiency in situations with symmetric traffic and delay-sensitive applications. However, implementing FDD massive MIMO systems is known to be challenging since it imposes a large feedback overhead in the Uplink (UL) to obtain channel state information for the Downlink (DL). In recent years, a considerable amount of research is dedicated to developing methods to reduce the feedback overhead in such systems. In this paper, we use the sparse spatial scattering properties of the environment to achieve this goal. The idea is to estimate the support of the continuous, frequency-invariant scattering function from UL channel observations and use this estimate to obtain the support of the DL channel vector via appropriate interpolation. We use the resulting support estimate to design an efficient DL probing and UL feedback scheme in which the feedback dimension scales proportionally with the sparsity order of DL channel vectors. Since the sparsity order is much less than the number of BS antennas in almost all practically relevant scenarios, our method incurs much less feedback overhead compared with the currently proposed methods in the literature, such as those based on compressed-sensing. We use numerical simulations to assess the performance of our probing-feedback algorithm and compare it with these methods.Comment: 24 pages, 10 figure

Joint Channel Training and Feedback for FDD Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) is widely recognized as a promising technology for future 5G wireless communication systems. To achieve the theoretical performance gains in massive MIMO systems, accurate channel state information at the transmitter (CSIT) is crucial. Due to the overwhelming pilot signaling and channel feedback overhead, however, conventional downlink channel estimation and uplink channel feedback schemes might not be suitable for frequency-division duplexing (FDD) massive MIMO systems. In addition, these two topics are usually separately considered in the literature. In this paper, we propose a joint channel training and feedback scheme for FDD massive MIMO systems. Specifically, we firstly exploit the temporal correlation of time-varying channels to propose a differential channel training and feedback scheme, which simultaneously reduces the overhead for downlink training and uplink feedback. We next propose a structured compressive sampling matching pursuit (S-CoSaMP) algorithm to acquire a reliable CSIT by exploiting the structured sparsity of wireless MIMO channels. Simulation results demonstrate that the proposed scheme can achieve substantial reduction in the training and feedback overhead

Distributed Compressive CSIT Estimation and Feedback for FDD Multi-user Massive MIMO Systems

To fully utilize the spatial multiplexing gains or array gains of massive MIMO, the channel state information must be obtained at the transmitter side (CSIT). However, conventional CSIT estimation approaches are not suitable for FDD massive MIMO systems because of the overwhelming training and feedback overhead. In this paper, we consider multi-user massive MIMO systems and deploy the compressive sensing (CS) technique to reduce the training as well as the feedback overhead in the CSIT estimation. The multi-user massive MIMO systems exhibits a hidden joint sparsity structure in the user channel matrices due to the shared local scatterers in the physical propagation environment. As such, instead of naively applying the conventional CS to the CSIT estimation, we propose a distributed compressive CSIT estimation scheme so that the compressed measurements are observed at the users locally, while the CSIT recovery is performed at the base station jointly. A joint orthogonal matching pursuit recovery algorithm is proposed to perform the CSIT recovery, with the capability of exploiting the hidden joint sparsity in the user channel matrices. We analyze the obtained CSIT quality in terms of the normalized mean absolute error, and through the closed-form expressions, we obtain simple insights into how the joint channel sparsity can be exploited to improve the CSIT recovery performance.Comment: 16 double-column pages, accepted for publication in IEEE Transactions on Signal Processin

High-Dimensional CSI Acquisition in Massive MIMO: Sparsity-Inspired Approaches

Massive MIMO has been regarded as one of the key technologies for 5G wireless networks, as it can significantly improve both the spectral efficiency and energy efficiency. The availability of high-dimensional channel side information (CSI) is critical for its promised performance gains, but the overhead of acquiring CSI may potentially deplete the available radio resources. Fortunately, it has recently been discovered that harnessing various sparsity structures in massive MIMO channels can lead to significant overhead reduction, and thus improve the system performance. This paper presents and discusses the use of sparsity-inspired CSI acquisition techniques for massive MIMO, as well as the underlying mathematical theory. Sparsity-inspired approaches for both frequency-division duplexing and time-division duplexing massive MIMO systems will be examined and compared from an overall system perspective, including the design trade-offs between the two duplexing modes, computational complexity of acquisition algorithms, and applicability of sparsity structures. Meanwhile, some future prospects for research on high-dimensional CSI acquisition to meet practical demands will be identified.Comment: 15 pages, 3 figures, 1 table, submitted to IEEE Systems Journal Special Issue on 5G Wireless Systems with Massive MIM

FDD Massive MIMO via UL/DL Channel Covariance Extrapolation and Active Channel Sparsification

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.Comment: 30 pages, 7 figures - Further simulation results and comparisons with the state-of-the-art techniques, compared to the previous versio

A Block Sparsity Based Estimator for mmWave Massive MIMO Channels with Beam Squint

Multiple-input multiple-output (MIMO) millimeter wave (mmWave) communication is a key technology for next generation wireless networks. One of the consequences of utilizing a large number of antennas with an increased bandwidth is that array steering vectors vary among different subcarriers. Due to this effect, known as beam squint, the conventional channel model is no longer applicable for mmWave massive MIMO systems. In this paper, we study channel estimation under the resulting non-standard model. To that aim, we first analyze the beam squint effect from an array signal processing perspective, resulting in a model which sheds light on the angle-delay sparsity of mmWave transmission. We next design a compressive sensing based channel estimation algorithm which utilizes the shift-invariant block-sparsity of this channel model. The proposed algorithm jointly computes the off-grid angles, the off-grid delays, and the complex gains of the multi-path channel. We show that the newly proposed scheme reflects the mmWave channel more accurately and results in improved performance compared to traditional approaches. We then demonstrate how this approach can be applied to recover both the uplink as well as the downlink channel in frequency division duplex (FDD) systems, by exploiting the angle-delay reciprocity of mmWave channels

Channel correlation-based approach for feedback overhead reduction in massive MIMO

For frequency-division duplex multiple-input-multiple-output (MIMO) systems, the channel state information at the transmitter is usually obtained by sending pilots or reference signals from all elements of the antenna array. The channel is then estimated by the receiver and communicated back to the transmitter. However, for massive MIMO, this periodical estimation of the full transfer matrix can lead to prohibitive overhead. To reduce the amount of data, we propose to estimate the updated channel matrix from the knowledge of the full correlation matrix at the transmitter made during some initialization time and the instantaneous measured channel matrix of smaller size, characterizing the link between the user and a limited number of reference array elements. The proposed algorithm is validated with measured massive MIMO channel transfer functions at 3.5GHz between a $9 \times 9$ uniform rectangular array and different user positions. Since measurements were made in static conditions, the criteria chosen for evaluating the performance of the algorithm are based on a comparison of the predicted channel capacity calculated from either the measured or estimated channel matrix

Downlink Achievable Rate Analysis for FDD Massive MIMO Systems

Multiple-Input Multiple-Output (MIMO) systems with large-scale transmit antenna arrays, often called massive MIMO, are a very promising direction for 5G due to their ability to increase capacity and enhance both spectrum and energy efficiency. To get the benefit of massive MIMO systems, accurate downlink channel state information at the transmitter (CSIT) is essential for downlink beamforming and resource allocation. Conventional approaches to obtain CSIT for FDD massive MIMO systems require downlink training and CSI feedback. However, such training will cause a large overhead for massive MIMO systems because of the large dimensionality of the channel matrix. In this dissertation, we improve the performance of FDD massive MIMO networks in terms of downlink training overhead reduction, by designing an efficient downlink beamforming method and developing a new algorithm to estimate the channel state information based on compressive sensing techniques. First, we design an efficient downlink beamforming method based on partial CSI. By exploiting the relationship between uplink direction of arrivals (DoAs) and downlink direction of departures (DoDs), we derive an expression for estimated downlink DoDs, which will be used for downlink beamforming. Second, By exploiting the sparsity structure of downlink channel matrix, we develop an algorithm that selects the best features from the measurement matrix to obtain efficient CSIT acquisition that can reduce the downlink training overhead compared with conventional LS/MMSE estimators. In both cases, we compare the performance of our proposed beamforming method with traditional methods in terms of downlink achievable rate and simulation results show that our proposed method outperform the traditional beamforming methods

Principal Component Analysis (PCA)-based Massive-MIMO Channel Feedback

Channel-state-information (CSI) feedback methods are considered, especially for massive or very large-scale multiple-input multiple-output (MIMO) systems. To extract essential information from the CSI without redundancy that arises from the highly correlated antennas, a receiver transforms (sparsifies) a correlated CSI vector to an uncorrelated sparse CSI vector by using a Karhunen-Loeve transform (KLT) matrix that consists of the eigen vectors of covariance matrix of CSI vector and feeds back the essential components of the sparse CSI, i.e., a principal component analysis method. A transmitter then recovers the original CSI through the inverse transformation of the feedback vector. Herein, to obtain the covariance matrix at transceiver, we derive analytically the covariance matrix of spatially correlated Rayleigh fading channels based on its statistics including transmit antennas' and receive antennas' correlation matrices, channel variance, and channel delay profile. With the knowledge of the channel statistics, the transceiver can readily obtain the covariance matrix and KLT matrix. Compression feedback error and bit-error-rate performance of the proposed method are analyzed. Numerical results verify that the proposed method is promising, which reduces significantly the feedback overhead of the massive-MIMO systems with marginal performance degradation from full-CSI feedback (e.g., feedback amount reduction by 80%, i.e., 1/5 of original CSI, with spectral efficiency reduction by only 2%). Furthermore, we show numerically that, for a given limited feedback amount, we can find the optimal number of transmit antennas to achieve the largest spectral efficiency, which is a new design framework.Comment: 10 pages, 5 figure

Limited Feedback Channel Estimation in Massive MIMO with Non-uniform Directional Dictionaries

Channel state information (CSI) at the base station (BS) is crucial to achieve beamforming and multiplexing gains in multiple-input multiple-output (MIMO) systems. State-of-the-art limited feedback schemes require feedback overhead that scales linearly with the number of BS antennas, which is prohibitive for $5$G massive MIMO. This work proposes novel limited feedback algorithms that lift this burden by exploiting the inherent sparsity in double directional (DD) MIMO channel representation using overcomplete dictionaries. These dictionaries are associated with angle of arrival (AoA) and angle of departure (AoD) that specifically account for antenna directivity patterns at both ends of the link. The proposed algorithms achieve satisfactory channel estimation accuracy using a small number of feedback bits, even when the number of transmit antennas at the BS is large -- making them ideal for $5$G massive MIMO. Judicious simulations reveal that they outperform a number of popular feedback schemes, and underscore the importance of using angle dictionaries matching the given antenna directivity patterns, as opposed to uniform dictionaries. The proposed algorithms are lightweight in terms of computation, especially on the user equipment side, making them ideal for actual deployment in $5$G systems