Cloud RAN (C-RAN) is a promising enabler for distributed massive MIMO systems, yet is vulnerable to its fronthaul congestion. To cope with the limited fronthaul capacity, this paper proposes a hybrid analog-digital precoding design that adaptively adjusts fronthaul compression levels and the number of active radio-frequency (RF) chains out of the entire RF chains in a downlink distributed massive MIMO system based on C-RAN architecture. Following this structure, we propose an analog beamformer design in pursuit of maximizing multi-user sum average data rate (sum-rate). Each element of the analog beamformer is constructed based on a weighted sum of spatial channel covariance matrices, while the size of the analog beamformer, i.e. the number of active RF chains, is optimized so as to maximize the large-scale approximated sum-rate. With these analog beamformer and RF chain activation, a regularized zero- forcing (RZF) digital beamformer is jointly optimized based on the instantaneous effective channel information observed through the given analog beamformer. The effectiveness of the proposed hybrid precoding algorithm is validated by simulation, and its design criterion is clarified by analysis.
One promising approach to resolve this precoding design problem under limited fronthaul capacity is to utilize spatial covariance of the channel instead of instantaneous CSI, which has been investigated in @cite_15 @cite_29 . Spatial covariance matrix is less frequently changing than instantaneous CSI, and can thus be estimated more easily as shown by @cite_22 @cite_7 @cite_17 @cite_5 @cite_6 . The precoding design based on spatial covariance matrix becomes more effective in massive MIMO systems in C-RAN architecture where their large number of antennas lead to huge amount of CSI to be estimated. As the number of antennas increases, it has been shown by @cite_8 @cite_9 that the instantaneous signal-to-interference-plus-noise ratio ( @math ) asymptotically converges to a deterministic value that is only a function of spatial covariance matrices. Such a deterministic equivalent can be regarded as the large-scale approximation and be exploited for precoding design that is no longer depending on instantaneous CSI @cite_21 @cite_1 @cite_3 .
@cite_22 @cite_7 @cite_8 @cite_29 @cite_9 @cite_21 @cite_1 @cite_6 @cite_3 @cite_5 @cite_15 @cite_17
2145013959 2085098436 2611749634 2084304524 2952850327 2536912378 1632803383 2725094597 2275567740 2015301486 2092397817
This paper addresses the problem of channel estimation in multi-cell interference-limited cellular networks. We consider systems employing multiple antennas and are interested in both the finite and large-scale antenna number regimes (so-called "massive MIMO"). Such systems deal with the multi-cell interference by way of per-cell beamforming applied at each base station. Channel estimation in such networks, which is known to be hampered by the pilot contamination effect, constitutes a major bottleneck for overall performance. We present a novel approach which tackles this problem by enabling a low-rate coordination between cells during the channel estimation phase itself. The coordination makes use of the additional second-order statistical information about the user channels, which are shown to offer a powerful way of discriminating across interfering users with even strongly correlated pilot sequences. Importantly, we demonstrate analytically that in the large-number-of-antennas regime, the pilot contamination effect is made to vanish completely under certain conditions on the channel covariance. Gains over the conventional channel estimation framework are confirmed by our simulations for even small antenna array sizes. Next-generation cellular standards may leverage the large bandwidth available at millimeter wave (mmWave) frequencies to provide gigabit-per-second data rates in outdoor wireless systems. A main challenge in realizing mmWave cellular is achieving sufficient operating link margin, which is enabled via directional beamforming with large antenna arrays. Due to the high cost and power consumption of high-bandwidth mixed-signal devices, mmWave beamforming will likely include a combination of analog and digital processing. In this paper, we develop an iterative hybrid beamforming algorithm for the single user mmWave channel. The proposed algorithm accounts for the limitations of analog beamforming circuitry and assumes only partial channel knowledge at both the base and mobile stations. The precoding strategy exploits the sparse nature of the mmWave channel and uses a variant of matching pursuit to provide simple solutions to the hybrid beamforming problem. Simulation results show that the proposed algorithm can approach the rates achieved by unconstrained digital beamforming solutions. We propose a new hybrid precoding technique for massive multi-input multi-output (MIMO) systems using spatial channel covariance matrices in the analog precoder design. Applying a regularized zero-forcing precoder for the baseband precoding matrix, we find an unconstrained analog precoder that maximizes signal-to-leakage-plus-noise ratio (SLNR) while ignoring analog phase shifter constraints. Subsequently, we develop a technique to design a constrained analog precoder that mimics the obtained unconstrained analog precoder under phase shifter constraints. The main idea is to adopt an additional baseband precoding matrix, which we call a compensation matrix. We analyze the SLNR loss due to the proposed hybrid precoding compared to fully digital precoding, and determine which factors have a significant impact on this loss. In the simulations, we show that if the channel is spatially correlated and the number of users is smaller than the number of RF chains, the SLNR loss becomes negligible compared to fully digital precoding. The main benefit of our method stems from the use of spatial channel matrices in such a way that not only is each user's desired signal considered, but also the inter-user interference is incorporated in the analog precoder design. We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively. Obtaining accurate Channel State Information (CSI) at the transmitters (TX) is critical to many cooperation schemes such as Network MIMO, Interference Alignment etc. Practical CSI feedback and limited backhaul-based sharing inevitably creates degradations of CSI which are specific to each TX, giving rise to a distributed form of CSI. In the Distributed CSI (D-CSI) broadcast channel setting, the various TXs design elements of the precoder based on their individual estimates of the global multiuser channel matrix, which intuitively degrades performance when compared with the commonly used centralized CSI assumption. This paper tackles this challenging scenario and presents a first analysis of the rate performance for the distributed CSI multi-TX broadcast channel setting, in the large number of antenna regime. Using Random Matrix Theory (RMT) tools, we derive deterministic equivalents of the Signal to Interference plus Noise Ratio (SINR) for the popular regularized Zero-Forcing (ZF) precoder, allowing to unveil the price of distributedness for such cooperation methods. The tremendous bandwidth available in the millimeter wave frequencies above 10 GHz have made these bands an attractive candidate for next-generation cellular systems. However, reliable communication at these frequencies depends critically on beamforming with very high-dimensional antenna arrays. Estimating the channel sufficiently accurately to perform beamforming can be challenging due to both low coherence time and a large number of antennas. Also, the measurements used for channel estimation may need to be made with analog beamforming, where the receiver can “look” in only one direction at a time. This paper presents a novel method for estimation of the receive-side spatial covariance matrix of a channel from a sequence of power measurements made in different angular directions. It is shown that maximum likelihood estimation of the covariance matrix reduces to a non-negative matrix completion problem. We show that the non-negative nature of the covariance matrix reduces the number of measurements required when the matrix is low-rank. The fast iterative methods are presented to solve the problem. Simulations are presented for both single-path and multi-path channels using models derived from real measurements in New York City at 28 GHz. The Interfering Broadcast Channel (IBC) applies to the downlink of (cellular and or heterogeneous) multi-cell networks, which are limited by multi-user (MU) interference. The interference alignment (IA) concept has shown that interference does not need to be inevitable. In particular spatial IA in the MIMO IBC allows for low latency transmission. However, IA requires perfect and typically global Channel State Information at the Transmitter(s) (CSIT), whose acquisition does not scale well with network size. Also, the design of transmitters (Txs) and receivers (Rxs) is coupled and hence needs to be centralized (cloud) or duplicated (distributed approach). CSIT, which is crucial in MU systems, is always imperfect in practice. We consider the joint optimal exploitation of mean (channel estimates) and covariance Gaussian partial CSIT. Indeed, in a Massive MIMO (MaMIMO) setting (esp. when combined with mmWave) the channel covariances may exhibit low rank and zero-forcing might be possible by just exploiting the covariance subspaces. But the question is the optimization of beamformers for the expected weighted sum rate (EWSR) at finite SNR. We propose explicit beamforming solutions and indicate that existing large system analysis can be extended to handle optimized beamformers with the more general partial CSIT considered here. Channel covariance is emerging as a critical ingredient of the acquisition of instantaneous channel state information (CSI) in multi-user Massive MIMO systems operating in frequency division duplex (FDD) mode. In this context, channel reciprocity does not hold, and it is generally expected that covariance information about the downlink channel must be estimated and fed back by the user equipment (UE). As an alternative CSI acquisition technique, we propose to infer the downlink covariance based on the observed uplink covariance. This inference process relies on a dictionary of uplink downlink covariance matrices, and on interpolation in the corresponding Riemannian space; once the dictionary is known, the estimation does not rely on any form of feedback from the UE. In this article, we present several variants of the interpolation method, and benchmark them through simulations. We propose joint spatial division and multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional channel state information at the transmitter (CSIT). JSDM achieves significant savings both in the downlink training and in the CSIT uplink feedback, thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing (FDD) systems, for which uplink downlink channel reciprocity cannot be exploited. In the proposed scheme, the multiuser MIMO downlink precoder is obtained by concatenating a prebeamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional “effective” channel matrix. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is approached in the large number of antennas limit. For this case, we use Szego's asymptotic theory of Toeplitz matrices to show that a DFT-based prebeamforming matrix is near-optimal, requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a 2-D base station antenna array, with 3-D beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max-min fairness criteria, showing extremely attractive performance. Our numerical results are obtained via asymptotic random matrix theory, avoiding lengthy Monte Carlo simulations and providing accurate results for realistic (finite) number of antennas and users. Hybrid multiple input multiple output (MIMO) systems consist of an analog beamformer with large antenna arrays followed by a digital MIMO processor. Channel estimation for hybrid MIMO systems in millimeter wave (mm-wave) communications is challenging because of the large antenna array and the low signal-to-noise ratio (SNR) before beamforming. In this paper, we propose an open-loop channel estimator for mm-wave hybrid MIMO systems exploiting the sparse nature of mm-wave channels. A sparse signal recovery problem is formulated for channel estimation and solved by the orthogonal matching pursuit (OMP) based methods. A modification of the OMP algorithm, called the multi-grid (MG) OMP, is proposed. It is shown that the MG-OMP can significantly reduce the computational load of the OMP method. A process for designing the training beams is also developed. Specifically, given the analog training beams the baseband processor for beam training is designed. Simulation results demonstrate the advantage of the OMP based methods over the conventional least squares (LS) method and the efficiency of the MG-OMP over the original OMP.