Extremely large-scale multiple-input multiple-output (XL-MIMO) promises to provide ultrahigh data rates in millimeter-wave (mmWave) and Terahertz (THz) spectrum. However, the spherical-wavefront wireless transmission caused by large aperture array presents huge challenges for channel state information (CSI) acquisition and beamforming. Two independent parameters (physical angles and transmission distance) should be simultaneously considered in XL-MIMO beamforming, which brings severe overhead consumption and beamforming degradation. To address this problem, we exploit the near-field channel characteristic and propose two low-overhead hierarchical beam training schemes for near-field XL-MIMO system. Firstly, we project near-field channel into spatial-angular domain and slope-intercept domain to capture detailed representations. Then we point out three critical criteria for XL-MIMO hierarchical beam training. Secondly, a novel spatial-chirp beam-aided codebook and corresponding hierarchical update policy are proposed. Thirdly, given the imperfect coverage and overlapping of spatial-chirp beams, we further design an enhanced hierarchical training codebook via manifold optimization and alternative minimization. Theoretical analyses and numerical simulations are also displayed to verify the superior performances on beamforming and training overhead.
Beam training based on hierarchical codebook for millimeter wave (mmWave) massive MIMO is investigated. Unlike the existing work using the same hierarchical codebook to estimate different multi-path components (MPCs), dynamic hierarchical codebooks which are updated according to the estimated MPCs are adopted. Firstly, a generalized hierarchical codebook design method is proposed. Then based on this method, a beam training method which dynamically updates the hierarchical codebook by removing the contribution of the estimated MPCs from the codebook is proposed. Simulation results verify the ef…
Codebook design is one of the core technologies in limited feedback multi-input multi-output (MIMO) communication systems. However, the conventional codebook designs usually assume MIMO vectors are uniformly distributed or isotropic. Motivated by the excellent classfication and analysis ability of clustering algorithms, we propose a K-means clustering based codebook design. First, large amounts of channel state information (CSI) is stored as the input data of the clustering, and finally divided into N clusters according to the minimal distance. The clustering centroids are used as the statisti…
In this work, we study codebook designs for full-dimension multiple-input multiple-output (FD-MIMO) systems with a multi-panel array (MPA). We propose novel codebooks which allow precise beam structures for MPA FD-MIMO systems by investigating the physical properties and alignments of the panels. We specifically exploit the characteristic that a group of antennas in a vertical direction exhibit more correlation than those in a horizontal direction. This enables an economical use of feedback bits while constructing finer beams compared to conventional codebooks. The codebook is further improved…
Scaling the number of antennas up is a key characteristic of current and future wireless communication systems. The hardware cost and power consumption, however, motivate large-scale MIMO systems, especially at millimeter wave (mmWave) bands, to rely on analog-only or hybrid analog/digital transceiver architectures. With these architectures, mmWave base stations normally use pre-defined beamforming codebooks for both initial access and data transmissions. Current beam codebooks, however, generally adopt single-lobe narrow beams and scan the entire angular space. This leads to high beam trainin…
Communications system with analog or hybrid analog/digital architectures usually relies on a pre-defined codebook to perform beamforming. With the increase in the size of the antenna array, the characteristics of the spherical wavefront in the near-field situation are not negligible. Therefore, it is necessary to design a codebook that is adaptive to near-field scenarios. In this letter, we investigate the hierarchical codebook design method in the near-field situation. We develop a steering beam gain calculation method and design the lower-layer codebook to satisfy the coverage of the Fresnel…
Next generation wireless communications rely on multiple input multiple output (MIMO) techniques to achieve high data rates. Feedback of channel information can be used in MIMO precoding to fully activate the strongest channel modes and improve MIMO performance. Unfortunately, the bandwidth of the control channel via which the feedback is conveyed is severely limited. An important issue is how to improve the MIMO precoding performance with minimal feedback. In this letter, we present a method that uses a rotating codebook technique to effectively improve the precoding performance without the n…
This correspondence proposes a new rotated codebook for three-dimensional (3D) multi-input-multi-output (MIMO) system under spatially correlated channel. To avoid the problem of high dimensionality led by large antenna array, the rotation matrix in the rotated codebook is proposed to be decomposed by Tucker decomposition into three lowdimensional units, i.e., statistical channel direction information in horizontal and vertical directions respectively, and statistical channel power in the joint horizontal and vertical direction. A closed-form suboptimal solution is provided to reduce the comput…
In this paper, we consider limited feedback systems for FDD large-scale (massive) MIMO. A new codebook-based framework for multiuser (MU) MIMO downlink systems is introduced and then compared with an ideal non-codebook based system. We are particularly interested in the less-known finite-rate feedback regime where the number $M$ of transmit antennas and the number of users are of the same order of magnitude and $M$ is large but finite, which is a typical scenario of large-scale MIMO. We provide new findings in this regime and identify some benefits of the new framework in terms of scheduling g…
The acquisition of channel state information (CSI) in Frequency Division Duplex (FDD) massive MIMO has been a formidable challenge. In this paper, we address this problem with a novel CSI feedback framework enabled by the partial reciprocity of uplink and downlink channels in the wideband regime. We first derive the closed-form expression of the rank of the wideband massive MIMO channel covariance matrix for a given angle-delay distribution. A low-rankness property is identified, which generalizes the well-known result of the narrow-band uniform linear array setting. Then we propose a partial …
In this paper, we investigate a radio frequency (RF) lens-embedded massive multiple-input multiple-output (MIMO) system and evaluate the system performance of limited feedback by utilizing a technique for generating a suitable codebook for the system. We fabricate an RF lens that operates on a 77 GHz (mmWave) band. Experimental results show a proper value of amplitude gain and an appropriate focusing property. In addition, using a simple numerical technique--beam propagation method (BPM)--we estimate the power profile of the RF lens and verify its accordance with experimental results. We also …
Channel feedback is essential in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. Unfortunately, previous work on multiuser MIMO has shown that the codebook size for channel feedback should scale exponentially with the number of base station (BS) antennas, which is greatly increased in massive MIMO systems. To reduce the codebook size and feedback overhead, we propose an angle-of-departure (AoD)-adaptive subspace codebook for channel feedback in FDD massive MIMO systems. Our key insight is to leverage the observation that path AoDs vary more slowly than…
The number of radio frequency (RF) chains can be reduced through beam selection in lens-based millimeter-wave (mmWave) massive MIMO systems, where the equivalent channel between RF chains and multiple users is required at the BS to achieve the multi-user multiplexing gain. However, to the best of our knowledge, there is no dedicated codebook for the equivalent channel feedback in such systems. In this paper, we propose the dimension-reduced subspace codebook, which achieves a significant reduction of the feedback overhead and codebook size. Specifically, we firstly utilize the limited scatteri…
Millimeter wave (mmWave) and massive MIMO systems are intrinsic components of 5G and beyond. These systems rely on using beamforming codebooks for both initial access and data transmission. Current beam codebooks, however, generally consist of a large number of narrow beams that scan all possible directions, even if these directions are never used. This leads to very large training overhead. Further, these codebooks do not normally account for the hardware impairments or the possible non-uniform array geometries, and their calibration is an expensive process. To overcome these limitations, thi…
A codebook based limited feedback strategy is a practical way to obtain partial channel state information at the transmitter in a precoded multiple-input multiple-output (MIMO) wireless system. Conventional codebook designs use Grassmannian packing, equiangular frames, vector quantization, or Fourier based constructions. While the capacity and error rate performance of conventional codebook constructions have been extensively investigated, constructing these codebooks is notoriously difficult relying on techniques such as nonlinear search or iterative algorithms. Further, the resulting codeboo…
It is of great interest to develop efficient ways to acquire accurate channel state information (CSI) for frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems for backward compatibility. It is theoretically well known that the codebook size for CSI quantization should be increased as the number of transmit antennas becomes larger, and 3GPP long term evolution (LTE) and LTE-Advanced codebooks also follow this trend. Thus, in massive MIMO, it is hard to apply the conventional approach of using pre-defined vector-quantized codebooks for CSI quantization mainly …
This paper develops an efficient procedure for designing low-complexity codebooks for precoding in a full-dimension (FD) multiple-input multiple-output (MIMO) system with a uniform planar array (UPA) antenna at the transmitter (Tx) using tensor learning. In particular, instead of using statistical channel models, we utilize a model-free data-driven approach with foundations in machine learning to generate codebooks that adapt to the surrounding propagation conditions. We use a tensor representation of the FD-MIMO channel and exploit its properties to design quantized version of the channel pre…
XL-MIMO promises to provide ultrahigh data rates in Terahertz (THz) spectrum. However, the spherical-wavefront wireless transmission caused by large aperture array presents huge challenges for channel state information (CSI) acquisition. Two independent parameters (physical angles and transmission distance) should be simultaneously considered in XL-MIMO beamforming, which brings severe overhead consumption and beamforming degradation. To address this problem, we exploit the near-field channel characteristic and propose one low-overhead hierarchical beam training scheme for near-field XL-MIMO s…
We describe in details the interplay between binary symplectic geometry and quantum computation, with the ultimate goal of constructing highly structured codebooks. The Binary Chirps (BCs) are Complex Grassmannian Lines in $N = 2^m$ dimensions used in deterministic compressed sensing and random/unsourced multiple access in wireless networks. Their entries are fourth roots of unity and can be described in terms of second order Reed-Muller codes. The Binary Subspace Chirps (BSSCs) are a unique collection of BCs of $\textit{ranks}$ ranging from $r=0$ to $r = m$, embedded in $N$ dimensions accordi…
Millimeter wave (mmWave) and terahertz MIMO systems rely on pre-defined beamforming codebooks for both initial access and data transmission. Being pre-defined, however, these codebooks are commonly not optimized for specific environments, user distributions, and/or possible hardware impairments. This leads to large codebook sizes with high beam training overhead which increases the initial access/tracking latency and makes it hard for these systems to support highly mobile applications. To overcome these limitations, this paper develops a deep reinforcement learning framework that learns how t…
In this paper, we focus on the design of the hybrid analog/digital precoding in millimeter wave multiple-input multiple-output (MIMO) systems. To reduce the feedback overhead, we propose two non-uniform quantization (NUQ) codebook based hybrid precoding schemes for two main hybrid precoding implementations, i.e., the full-connected structure and the sub-connected structure. Specifically, we firstly group the angles of the arrive/departure (AOAs/AODs) of the scattering paths into several spatial lobes by exploiting the sparseness property of the millimeter wave in the angular domain, which divi…
A virtual multiple-input multiple-output (MIMO) wireless system using the receiver-side cooperation with the compress-and-forward (CF) protocol, is an alternative to a point-to-point MIMO system, when a single receiver is not equipped with multiple antennas. It is evident that the practicality of CF cooperation will be greatly enhanced if an efficient source coding technique can be used at the relay. It is even more desirable that CF cooperation should not be unduly sensitive to carrier frequency offsets (CFOs). This paper presents a practical study of these two issues. Firstly, codebook desig…
This paper focuses on the design of beamforming codebooks that maximize the average normalized beamforming gain for any underlying channel distribution. While the existing techniques use statistical channel models, we utilize a model-free data-driven approach with foundations in machine learning to generate beamforming codebooks that adapt to the surrounding propagation conditions. The key technical contribution lies in reducing the codebook design problem to an unsupervised clustering problem on a Grassmann manifold where the cluster centroids form the finite-sized beamforming codebook for th…
Hybrid precoding design is challenging for millimeter-wave (mmWave) massive MIMO. Most prior hybrid precoding schemes are designed to maximize the sum spectral efficiency (SSE), while seldom investigate the bit-error-rate (BER). Therefore, we propose an over-sampling codebook (OSC)-based hybrid minimum sum-mean-square-error (min-SMSE) precoding scheme for mmWave multi-user three-dimensional (3D)-MIMO systems to optimize the BER, where multi-user transmission with multiple data streams for each user is considered. Specifically, given the effective baseband channel consisting of the real channel…
Extremely large-scale massive multiple-input-multiple-output (XL-MIMO) is regarded as a promising technology for next-generation communication systems. In order to enhance the beamforming gains, codebook-based beam training is widely adopted in XL-MIMO systems. However, in XL-MIMO systems, the near-field domain expands, and near-field codebook should be adopted for beam training, which significantly increases the pilot overhead. To tackle this problem, we propose a deep learning-based beam training scheme where the near-field channel model and the near-field codebook are considered. To be spec…
We present and analyze a new robust feedback and transmit strategy for multiuser MIMO downlink communication systems, termed Rate Approximation (RA). RA combines the flexibility and robustness needed for reliable communications with the user terminal under a limited feedback constraint. It responds to two important observations. First, it is not so significant to approximate the channel but rather the rate, such that the optimal scheduling decision can be mimicked at the base station. Second, a fixed transmit codebook at the transmitter is often better when therefore the channel state informat…
This paper proposes a codebook for jointly quantizing channel direction information (CDI) of spatially correlated three-dimensional (3D) multi-input-multi-output (MIMO) channels. To reduce the dimension for quantizing the CDI of large antenna arrays, we introduce a special structure to the codewords by using Tucker decomposition to exploit the unique features of 3D MIMO channels. Specifically, the codeword consists of four parts each with low dimension individually targeting at a different type of information: statistical CDIs in horizontal direction and in vertical direction, statistical powe…
Imperfect channel state information degrades the performance of multiple-input multiple-output (MIMO) communications; its effect on single-user (SU) and multi-user (MU) MIMO transmissions are quite different. In particular, MU-MIMO suffers from residual inter-user interference due to imperfect channel state information while SU-MIMO only suffers from a power loss. This paper compares the throughput loss of both SU and MU MIMO on the downlink due to delay and channel quantization. Accurate closed-form approximations are derived for the achievable rates for both SU and MU MIMO. It is shown that …
The low complexity quantization of channel state information (CSI) and the utilization of vertical freedom of three dimension (3D) channels are two critical issues in the limited feedback design of the \emph{full dimension multi-input-multi-output} (FD-MIMO) systems. In this paper, we propose an effective limited feedback scheme. We first employ Kronecker product based codebook (KPC) to explore the vertical freedom of 3D channels, extending the limited feedback from two dimension (2D) to 3D. Fruthermore, we use noncoherent sequence detection (NCSD) to quantify the CSI which includes both the v…
In network MIMO systems, channel state information is required at the transmitter side to multiplex users in the spatial domain. Since perfect channel knowledge is difficult to obtain in practice, \emph{limited feedback} is a widely accepted solution. The {\em dynamic number of cooperating BSs} and {\em heterogeneous path loss effects} of network MIMO systems pose new challenges on limited feedback design. In this paper, we propose a scalable limited feedback design for network MIMO systems with multiple base stations, multiple users and multiple data streams for each user. We propose a {\em l…
The channel feedback overhead for massive MIMO systems with a large number of base station (BS) antennas is very high, since the number of feedback bits of traditional codebooks scales linearly with the number of BS antennas. To reduce the feedback overhead, an effective codebook based on channel statistics has been designed, where the required number of feedback bits only scales linearly with the rank of the channel correlation matrix. However, this attractive conclusion was only intuitively explained and then verified through simulation results in the literature, while no rigorous theoretica…
In this paper, we investigate the energy-efficient resource allocation problem in an uplink non-orthogonal multiple access (NOMA) millimeter wave system, where the fully-connected-based sparse radio frequency chain antenna structure is applied at the base station (BS). To relieve the pilot overhead for channel estimation, we propose a codebook-based analog beam design scheme, which only requires to obtain the equivalent channel gain. On this basis, users belonging to the same analog beam are served via NOMA. Meanwhile, an advanced NOMA decoding scheme is proposed by exploiting the global infor…
In this paper, we study the hybrid precoding structures over limited feedback channels for massive multiuser multiple-input multiple-output (MIMO) systems. We focus on the system performance of hybrid precoding under a more realistic hardware network model, particularly, with inevitable dissipation. The effect of quantized analog and digital precoding is characterized. We investigate the spectral efficiencies of two typical hybrid precoding structures, i.e., the sub-connected structure and the fully-connected structure. It is revealed that increasing signal power can compensate the performance…
Achieving high channel estimation accuracy and reducing hardware cost as well as power dissipation constitute substantial challenges in the design of massive multiple-input multiple-output (MIMO) systems. To resolve these difficulties, sophisticated pilot designs have been conceived for the family of energy-efficient hybrid analog-digital (HAD) beamforming architecture relying on adaptive-resolution analog-to-digital converters (RADCs). In this paper, we jointly optimize the pilot sequences, the number of RADC quantization bits and the hybrid receiver combiner in the uplink of multiuser massiv…
We analyze the effect of finite rate feedback on CDMA (code-division multiple access) signature optimization and MIMO (multi-input-multi-output) beamforming vector selection. In CDMA signature optimization, for a particular user, the receiver selects a signature vector from a codebook to best avoid interference from other users, and then feeds the corresponding index back to the specified user. For MIMO beamforming vector selection, the receiver chooses a beamforming vector from a given codebook to maximize throughput, and feeds back the corresponding index to the transmitter. These two proble…
Employing large antenna arrays is a key characteristic of millimeter wave (mmWave) and terahertz communication systems. Due to the hardware constraints and the lack of channel knowledge, codebook based beamforming/combining is normally adopted to achieve the desired array gain. However, most of the existing codebooks focus only on improving the gain of their target user, without taking interference into account. This can incur critical performance degradation in dense networks. In this paper, we propose a sample-efficient online reinforcement learning based beam pattern design algorithm that l…
A 2D antenna array introduces a new level of control and additional degrees of freedom in multiple-input-multiple-output (MIMO) systems particularly for the so-called "massive MIMO" systems. To accurately assess the performance gains of these large arrays, existing azimuth-only channel models have been extended to handle 3D channels by modeling both the elevation and azimuth dimensions. In this paper, we study the channel correlation matrix of a generic ray-based 3D channel model, and our analysis and simulation results demonstrate that the 3D correlation matrix can be well approximated by a K…
Millimeter wave (mmWave) and terahertz MIMO systems rely on pre-defined beamforming codebooks for both initial access and data transmission. However, most of the existing codebooks adopt pre-defined beams that focus mainly on improving the gain of their target users, without taking interference into account, which could incur critical performance degradation in dense networks. To address this problem, in this paper, we propose a sample-efficient digital twin-assisted beam pattern design framework that learns how to form the beam pattern to reject the signals from the interfering directions. Th…
The theory of multiple-input multiple-output (MIMO) technology has been well-developed to increase fading channel capacity over single-input single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. Th…
The ensemble properties of Random Vector Quantization (RVQ) codebooks for limited-feedback beamforming in multi-input multi-output (MIMO) systems are studied with the metrics of interest being the received SNR loss and mutual information loss, both relative to a perfect channel state information (CSI) benchmark. The simplest case of unskewed codebooks is studied in the correlated MIMO setting and these loss metrics are computed as a function of the number of bits of feedback ($B$), transmit antenna dimension ($N_t$), and spatial correlation. In particular, it is established that: i) the loss m…
This study proposes a novel precoding scheme for multiuser multiple-input multiple-output (MIMO) relay systems in the presence of imperfect channel state information (CSI). The base station (BS) and the MIMO relay station (RS) are both equipped with the same codebook of unitary matrices. According to each element of the codebook, we create a latent precoding matrix pair, namely a BS precoding matrix and an RS precoding matrix. The RS precoding matrix is formed by multiplying the appropriate unitary matrix from the codebook by a power scaling factor. Based on the given CSI and a block of transm…
The problem of beam alignment (BA) in a cell-free massive multiple-input multiple-output (CF-mMIMO) system operating at millimeter wave (mmWaves) carrier frequencies is considered in this paper. Two estimation algorithms are proposed, in association with a protocol that permits simultaneous estimation, on a shared set of frequencies, for each user equipment (UE), of the direction of arrival and departure of the radio waves associated to the strongest propagation paths from each of the surrounding access points (APs), so that UE-AP association can take place. The proposed procedure relies on th…
We consider the design of multiple-input multiple-output communication systems with a linear precoder at the transmitter, zero-forcing decision feedback equalization (ZF-DFE) at the receiver, and a low-rate feedback channel that enables communication from the receiver to the transmitter. The channel state information (CSI) available at the receiver is assumed to be perfect, and based on this information the receiver selects a suitable precoder from a codebook and feeds back the index of this precoder to the transmitter. Our approach to the design of the components of this limited feedback sche…
