Channel Feedback Based on AoD-Adaptive Subspace Codebook in FDD Massive MIMO Systems

In this paper, we consider the problem of Angle of Departure (AoD) based channel feedback in Frequency Division Duplex (FDD) massive Multiple-Input Multiple-Output (MIMO) systems with multiple antennas at the users. We consider the use of Zero-Forcing Block Diagonalization (BD) as the downlink precoding scheme. We consider two different cases; one in which the number of streams intended for a user equals the number of antennas at that user and the other case in which the number of streams is less than the number of user antennas. BD requires the feedback of the subspace spanned by the channel matrix at the user or a subspace of it in the case of having less number of streams than the number of antennas at a specific user. Based on our channel model, we propose a channel feedback scheme that requires less feedback overhead compared to feeding back the whole channel matrix. Then, we quantify the rate gap between the rate of the system with perfect Channel State Information (CSI) at the massive MIMO Basestation (BS) and our proposed channel feedback scheme for a given number of feedback bits. Finally, we design feedback codebooks based on optimal subspace packing in the Grassmannian manifold. We show that our proposed codes achieve performance that is very close to the performance of the system with perfect CSI at the BS.

Massive multiple-input multiple-output (MIMO) is one of the most promising techniques for next generation wireless communications due to its superior capability to provide high spectrum and energy efficiency. Considering the very large number of antennas employed at the base station, however, the pilot overhead for downlink channel estimation becomes unaffordable in frequency division duplex (FDD) multiuser massive MIMO systems. In this paper, we propose an information-theoretic metric to design the pilot for downlink channel estimation in FDD multiuser massive MIMO systems. By exploiting the low-rank nature of the channel covariance matrix, we first derive the minimum number of pilot symbols required to ensure perfect channel recovery, which is much less than the number of antennas at the base station. Further, under a general channel model that the channel vector of each user follows a Gaussian mixture distribution, the pilot symbols are designed by maximizing the weighted sum of the Shannon mutual information between the measurements of the users and their corresponding channel vectors on the complex Grassmannian manifold. Simulation results demonstrate the effectiveness of the proposed information-theoretic pilot design for the downlink channel estimation in FDD massive MIMO systems.

In frequency-division duplexing (FDD) massive multiple-input-multiple-output (MIMO) systems, channel estimation about reducing the training and feedback overhead has always been a hot research area. The previous studies have shown that the method of utilizing channel sparsity in discrete Fourier transform (DFT) domain and angle reciprocity works well in particular channel environment. In this paper, we propose an improved method based on pilot reuse for general channel environment. The proposed method is applied to uplink/downlink channel estimation in FDD massive MIMO systems. Based on practical characteristics of the channel in massive MIMO systems, we modify the original method and propose an improved algorithm in assigning the pilot resources dynamically. The numerical results corroborate that compared to the original method, the improved method is more suitable and performs better in general channel environment. Meanwhile, the proposed algorithm can save the pilot resources and reduce the feedback overhead efficiently.

Accurate downlink channel state information (CSI) is required to be fed back to the base station (BS) in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems in order to achieve maximum antenna diversity and multiplexing. However, downlink CSI feedback overhead scales with the number of transceiver antennas, a major hurdle for practical deployment of FDD massive MIMO systems. To solve this problem, we propose a compressive sampled CSI feedback method based on deep learning (SampleDL). In SampleDL, the massive MIMO channel matrix is sampled uniformly in time/frequency dimension before being fed into neural networks (NNs), which will reduce the computational resource/time at user equipment (UE) as well as enhance the CSI recovery accuracy at the BS. Both theoretical analysis and normalized mean square errors (NMSE) results confirm the advantages of the proposed method in terms of time complexity and recovery accuracy. Besides, a suitable CSI feedback period is explored by link level simulations, which aims to further reduce the overhead of CSI feedback without degrading the communication quality.

Massive multiple-input multiple-output (MIMO) systems are a main enabler of the excessive throughput requirements in 5G and future generation wireless networks as they can serve many users simultaneously with high spectral and energy efficiency. To achieve this massive MIMO systems require accurate and timely channel state information (CSI), which is acquired by a training process that involves pilot transmission, CSI estimation, and feedback. This training process incurs a training overhead, which scales with the number of antennas, users, and subcarriers. Reducing the training overhead in massive MIMO systems has been a major topic of research since the emergence of the concept. Recently, deep learning (DL)-based approaches have been proposed and shown to provide significant reduction in the CSI acquisition and feedback overhead in massive MIMO systems compared to traditional techniques. In this paper, we present an overview of the state-of-the-art DL architectures and algorithms used for CSI acquisition and feedback, and provide further research directions.

Massive multiple-input multiple-output (MIMO) technology for wireless communication is considered a key technology for the future fifth-generation (5G) communication networks. To reduce the propagation loss of channel, MIMO systems with analog or digital hybrid precoders and combiners (HPC) architecture have been used. This review paper presents the various types of analog and digital HPC designs for the massive MIMO communication systems that were investigated within the last decade. The reviewed systems are useful for both single-user (SU) and multi-user MIMO (MU-MIMO) systems. The key parameter of the study was spectral efficiency (SE), signal-to-noise ratio (SNR), signal-to-interference pulse noise ratio (SINR), system sum-rate (SR) performance, computational complexity (CC), co-channel interference (CCI), inter-primary base station interference (IPBSI), multiuser interference (MUI), effective desired channel gain (EDCG), and minimum mean square error (MMSE).

In wireless communications, massive multiple-input multiple-output (MIMO) systems in which the base station (BS) is equipped with a large number of antennas can provide significant spectral and energy efficiency by means of simple signal processing. Therefore, massive MIMO is an attractive technology for next generation wireless communication systems and for green communications. There are two operation modes: time-division duplex (TDD) and frequency-division duplex (FDD) for massive MIMO systems, and the debate on the two modes is still discussed in the literature. The originator of massive MIMO systems, Marzetta, has presented the basic frame structures for both the TDD and the FDD modes. However, the basic frame structures do not carefully take the hardware impairments such as phase noise (PN) into account. In this paper, by taking the PN as the key hardware impairment into account, we recommend new and efficient frame structures for both the TDD and the FDD modes. The corresponding performance comparison between the two modes is also provided by using the data transmission efficiency (DTE) as the performance measurement. The comparison may help determine which mode should be used for massive MIMO systems.

The performance of the hybrid beamforming system based on the full-connected structure is close to that of the full-digital one in millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, due to the high complexity of circuit wiring in practical applications, it has been greatly restricted. This paper investigates the hybrid (analog/digital) beamforming design of a multiuser mmWave massive MIMO system with sub-connected structure. For this system, we focus on a sum-rate maximization probelm. Considering the joint design of the receiver, and transmitter, a two-stage design method is adopted. In the analog stage, the analog beamformer, and combiner are designed by the proposed piecewise dual joint iterative approximation (PDJIA) method, which not only can obtain closed-form solutions but also has linear property. Based on the criterion of avoiding the loss of information, the problem of digital beamforming is solved by exploiting the baseband piecewise successive approximation (BPSA) method, which can effectively increase the number of users served. Simulation results show that the proposed scheme outperforms the state-of-the art MIMO hybrid beamforming design schemes, and more accurately approximates to that of the full-digital system.

Massive multiple-input multiple-output (MIMO) systems hold the potential to be an enabling technology for 5G cellular. Uniform planar array (UPA) antenna structures are a focus of much commercial discussion because of their ability to enable a large number of antennas in a relatively small area. With UPA antenna structures, the base station can control the beam direction in both the horizontal and vertical domains simultaneously. However, channel conditions may dictate that one dimension requires higher channel state information (CSI) accuracy than the other. We propose the use of an additional one bit of feedback information sent from the user to the base station to indicate the preferred domain on top of the feedback overhead of CSI quantization in frequency division duplexing (FDD) massive MIMO systems. Combined with variable-rate CSI quantization schemes, the numerical studies show that the additional one bit of feedback can increase the quality of CSI significantly for UPA antenna structures.

In this work, we propose low-complexity detectors for massive multiple-input multiple-output (MIMO) systems. Particularly, we leverage variants of truncated polynomial expansion (TPE) in order to reduce the computational complexity of the signal detection in the uplink direction. Linear detectors such as zero-forcing (ZF) and minimum mean square error (MMSE) involve expensive matrix-matrix multiplication and matrix inversion operations. TPE-based detectors are appropriate candidates for approximating these linear detectors. However, tuning the normalization factor of TPE-based detectors may require calculating the minimum and the maximum eigenvalues of the channel Gram matrix. These calculations become computationally expensive for some massive MIMO systems, especially for systems with a large ratio of single-antenna user terminals to the number of antennas at the base station, i.e., loading factor. We propose to tune the normalization factor using appropriate approximations for the extreme eigenvalues. The proposed TPE-based detectors exhibit a bit error performance similar to that of the TPE-based detector with the optimal normalization factor. Moreover, our proposed detectors achieve the error performance of ZF and MMSE for different loading factors of spatially correlated and uncorrelated massive MIMO channels. The computational complexity of the proposed detector is proportional to the number of base station antennas and the number of users.

This paper studies the downlink sum-rate and energy efficiency (EE) of massive multiple-input multiple-output (MIMO) systems under the effect of channel aging caused by the movements of users. First, a closed-form expression of the downlink sum-rate where zero-forcing (ZF) precoder is adopted at the base station (BS) is derived. Based on the expression, the power-scaling law that when the number of BS antennas M approaches to infinity, the transmit power of BS can be reduced proportionally to 1/√M is still satisfied in the massive MIMO downlink system. Second, we utilize a general power consumption model to analyze the EE of the system. Both theoretical analysis and Monte-Carlo simulations show that the emergence of channel aging could degrade the sum-rate and the EE of the system.

The base station (BS) density influences the coverage performance of cellular communication system. In massive multiple input multiple output (MIMO) system, each BS is equipped with large scale antenna array. The stochastic geometric model is employed because of its analytical tractability. This paper demonstrates that BS density has to be below a certain bound in order to satisfy the coverage requirement in massive MIMO system. Closed-form expression for the BS density bounded by maximum outage probability is derived using Lambert W function. Moreover, the expression for the upper bound of successful area spectral efficiency (ASE) is also derived. Our study claims that increasing BS density will lead to the deterioration of coverage performance in massive MIMO system.

In cellular systems, deploying a large number of antennas at the base station (BS), also called massive multiple-input multiple-output (MIMO), can offer a huge improvement in system throughput. This performance gain achieved through coherent beamforming highly depends on having accurate channel state information (CSI) at the BS. Initially, massive MIMO was considered promising only for time division duplexing (TDD) systems because the downlink training overhead in frequency division duplexing (FDD) systems could be large. To reduce the overhead in FDD systems, we propose efficient eigenspace training and precoding. In the downlink training, the prebeamforming matrix is designed based on the spatial fading correlation to probe the channel and minimize the mean squared error (MSE) in channel estimation. In data transmission, the precoding matrix is designed based on instantaneous CSI to manage the inter-user interference. Our algorithms achieve significant savings in the downlink training because the overhead is associated with the dimension of prebeamforming matrix and no longer limited by the number of BS antennas. Compared with joint spatial division and multiplexing, our algorithms offer much lower MSE and, under some conditions, higher sum rates.

Accurate channel state information (CSI) at base station (BS) is the key to achieve full multiplexing and diversity gain in traditional multiple-input multiple-output (MIMO) systems. In frequency-division-duplex (FDD) systems, it is obtained through downlink training and uplink feedback. However, the training and feedback overhead in massive MIMO systems is unacceptable for the large number of antennas equipped at BS. To reduce the CSI feedback overhead and improve CSI quantization accuracy, we propose a limited feedback scheme for spatio-temporal correlated massive MIMO channel. The proposed scheme jointly performs Karhunen-Loève transform (KLT) and polar-cap quantization on CSI. For the compactly deployed antennas at BS, there exists spatial correlation in massive MIMO channel. When the user equipment (UE) moves slowly, adjacent channels feature temporal correlation. The high dimensional and spatial correlated CSI is compressed through KLT. Then the compressed CSI is normalized to be isotropic to perform polar-cap quantization. Simulation results show that the proposed scheme is capable of improving the sum-rate performance with limited feedback bits for massive MIMO systems.

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 5G massive MIMO. This paper proposes novel limited feedback algorithms that lift this burden by exploiting the inherent sparsity in double-directional MIMO channel representation using overcomplete dictionaries. These dictionaries are associated with angle of arrival and angle of departure 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 5G 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 5G systems.