Closed-Loop Compressive CSIT Estimation in FDD Massive MIMO Systems With 1 Bit Feedback

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.

Cell-free system where a group of base stations (BSs) cooperatively serves users has received much attention as a promising technology for the future wireless systems. In order to maximize the cooperation gain in the cell-free systems, acquisition of downlink channel state information (CSI) at the BSs is crucial. While this task is relatively easy for the time division duplexing (TDD) systems due to the channel reciprocity, it is not easy for the frequency division duplexing (FDD) systems due to the CSI feedback overhead. This issue is even more pronounced in the cell-free systems since the user needs to feed back the CSIs of multiple BSs. In this paper, we propose a novel feedback reduction technique for the FDD-based cell-free systems. Key feature of the proposed technique is to choose a few dominating paths and then feed back the path gain information (PGI) of the chosen paths. By exploiting the property that the angles of departure (AoDs) are quite similar in the uplink and downlink channels (this property is referred to as angle reciprocity), the BSs obtain the AoDs directly from the uplink pilot signal. From the extensive simulations, we observe that the proposed technique can achieve more than 60% reduction in feedback overhead over the conventional CSI feedback scheme.

Channel feedback is essential in frequency division duplexing (FDD) massive\nmultiple-input multiple-output (MIMO) systems. Unfortunately, previous work on\nmultiuser MIMO has shown that the codebook size for channel feedback should\nscale exponentially with the number of base station (BS) antennas, which is\ngreatly increased in massive MIMO systems. To reduce the codebook size and\nfeedback overhead, we propose an angle-of-departure (AoD)-adaptive subspace\ncodebook for channel feedback in FDD massive MIMO systems. Our key insight is\nto leverage the observation that path AoDs vary more slowly than the path\ngains. Within the angle coherence time, by utilizing the constant AoD\ninformation, the proposed AoD-adaptive subspace codebook is able to quantize\nthe channel vector in a more accurate way. We also provide performance analysis\nof the proposed codebook in the large-dimensional regime, where we prove that\nto limit the capacity degradation within an acceptable level, the required\nnumber of feedback bits only scales linearly with the number of resolvable\n(path) AoDs, which is much smaller than the number of BS antennas. Moreover, we\ncompare quantized channel feedback using the proposed AoD-adaptive subspace\ncodebook with analog channel feedback. Extensive simulations that verify the\nanalytical results are provided.\n

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.

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.

The compressive sensing (CS)-based sparse channel estimator is recognized as the most effective solution to the excessive pilot overhead in massive MIMO systems. However, due to the complex signal processing in the wireless communication systems, the measurement matrix in the CS-based channel estimation is sometimes “unfriendly” to the channel recovery. To overcome this problem, in this paper, the state-of-the-art sparse Bayesian learning using approximate message passing with unitary transformation (UTAMP-SBL), which is robust to various measurement matrices, is leveraged to address the multi-user uplink channel estimation for hybrid architecture millimeter wave massive MIMO systems. Specifically, the sparsity of channels in the angular domain is exploited to reduce the pilot overhead. Simulation results demonstrate that the UTAMP-SBL is able to achieve effective performance improvement than other competitors with low pilot overhead.

Massive MIMO has been proposed as a means of achieving huge spectral efficiency in cellular networks. However, its implementation is usually based on linear precoding schemes using Channel State Information (CSI). For this reason, the use of the Time Division Duplex (TDD) mode is typically assumed since it removes the dependence on the number of antennas at the transmitter to acquire CSI. Unfortunately, most of the cellular network operate in the Frequency Division Duplex (FDD) mode in which the acquisition of CSI depends proportionally to the number of transmit antennas. For this reason, the implementation of Massive MIMO is handicapped to few transmit antennas for the current cellular networks. In this paper we study the use of reconfigurable antennas that can switch among a set of preset modes, i.e., radiation patterns, through Blind Interference Alignment schemes. We show that it is a solution to exploit a very large number of antennas at the transmit side, overcoming the bottleneck that today constitutes the acquisition of CSI in Massive MIMO systems operating in FDD mode.

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.

Massive multiple-input multiple-output (MIMO) is believed to deliver unrepresented spectral efficiency gains for 5G and beyond. However, a practical challenge arises during its commercial deployment, which is known as the “curse of mobility”. The performance of massive MIMO drops alarmingly when the velocity level of user increases. In this paper, we tackle the problem in frequency division duplex (FDD) massive MIMO with a novel Channel State Information (CSI) acquisition framework. A joint angle-delay-Doppler (JADD) wideband precoder is proposed for channel training. Our idea consists in the exploitation of the partial channel reciprocity of FDD and the angle-delay-Doppler channel structure. More precisely, the base station (BS) estimates the angle-delay-Doppler information of the UL channel based on UL pilots using Matrix Pencil (MP) method. It then computes the wideband JADD precoders according to the extracted parameters. Afterwards, the user estimates and feeds back some scalar coefficients for the BS to reconstruct the predicted DL channel. Asymptotic analysis shows that the CSI prediction error converges to zero when the number of BS antennas and the bandwidth increases. Numerical results with industrial channel model demonstrate that our framework can well adapt to high speed (350 km/h), large CSI delay (10 ms) and channel sample noise.

In order to unlock the full advantages of massive multiple input multiple output (MIMO) in the downlink, channel state information (CSI) is required at the base station (BS) to optimize the beamforming matrices. In frequency division duplex (FDD) systems, full channel reciprocity does not hold, and CSI acquisition generally requires downlink pilot transmission followed by uplink feedback. Prior work proposed the end-to-end design of pilot transmission, feedback, and CSI estimation via deep learning. In this work, we introduce an enhanced end-to-end design that leverages partial uplink-downlink reciprocity and temporal correlation of the fading processes by utilizing jointly downlink and uplink pilots. The proposed method is based on a novel deep learning architecture – HyperRNN – that combines hypernetworks and recurrent neural networks (RNNs) to optimize the transfer of long-term channel features from uplink to downlink. Simulation results demonstrate that the HyperRNN achieves a lower normalized mean square error (NMSE) performance, and that it reduces requirements in terms of pilot lengths.

In this paper, we propose a novel method for efficient implementation of a massive Multiple-Input Multiple- Output (massive MIMO) system with Frequency Division Duplexing (FDD) operation. Our main objective is to reduce the large overhead incurred by Downlink (DL) common training and Uplink (UL) feedback needed to obtain channel state information (CSI) at the base station. Our proposed scheme relies on the fact that the underlying angular distribution of a channel vector, also known as the angular scattering function, is a frequency-invariant entity yielding a ULDL reciprocity and has a limited angular support. We estimate this support from UL CSI and interpolate it to obtain the corresponding angular support of the DL channel. Finally we exploit the estimated support of the DL channel of all the users to design an efficient channel probing and feedback scheme that maximizes the total spectral efficiency of the system. Our method is different from the existing compressed-sensing (CS) based techniques in the literature. Using support information helps reduce the feedback overhead from O(s logM) in CS techniques to O(s) in our proposed method, with s andM being sparsity order of the channel vectors and the number of base station antennas, respectively. Furthermore, in order to control the channel sparsity and therefore the DL common training and UL feedback overhead, we introduce the novel concept of active channel sparsification. In brief, when the fixed pilot dimension is less than the required amount for reliable channel estimation, we introduce a pre-beamforming matrix that artificially reduces the effective channel dimension of each user to be not larger than the DL pilot dimension, while maximizing both the number of served users and the number of probed angles. We provide numerical experiments to assess the performance of our method and compare it with the state-of-the-art CS technique.

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.

High-speed train (HST) communication has emerged as a prominent area of research, given its critical role in meeting the demanding requirements of high mobility scenarios like auto-driving and mission-critical train control signaling. The provision of these services relies heavily on the accurate acquisition of channel state information (CSI). However, traditional methods of channel estimation are inadequate for massive multiple-input multiple-output (MIMO) HST channels due to their extremely short channel coherence time, typically in the microsecond range. In this paper, we propose a dynamic grid-based joint uplink/downlink (UL/DL) channel tracking scheme in the angular domain, specifically designed to address fast time-varying channels in HST communication. The spatial reciprocity between UL and DL channels in frequency division duplex (FDD) systems and fuzzy spatial information are exploited to ensure the consistency of UL/DL supports and improve the tracking performance of the line-of-sight (LOS) channel, respectively. Then, we formulate a sparse Bayesian learning (SBL) problem and adopt a block majorization-minimization (MM) algorithm, where a significant gradient-based fast search (SGFS) algorithm is devised to solve the non-convex maximum a posteriori (MAP) problem for the angle of arrivals/departures (AoAs/AoDs) estimation. Finally, simulations verify the superiority of joint UL/DL channel tracking and show that the proposed scheme converges quickly with more accurate tracking results.

In compressive sensing (CS), the restricted isometry property (RIP) is an important condition on measurement matrices which guarantees the recovery of sparse signals with undersampled measurements. It has been proved in the prior works that both random (e.g., i.i.d. Gaussian, Bernoulli, $\ldots$ ) and Toeplitz matrices satisfy the RIP with high probability. However, structured matrices, such as banded Toeplitz matrices have drawn more attention since their structures have the advantage of fast matrix multiplication which may decrease the computational complexity of recovery algorithms. In this paper, we show that banded block Toeplitz matrices satisfy the RIP condition with high probability. Banded block Toeplitz matrices can be used in the sparse multi-channel source separation. The banded block Toeplitz matrices decrease the computational complexity while they have fewer number of non-zero entries in comparison to the same dimensional banded Toeplitz matrices. Furthermore, our simulation results show that banded block Toeplitz matrices outperform banded Toeplitz matrices in signal estimation. The analytical RIP bound for banded block Toeplitz matrices is provided in this paper and the RIP bound of sparse Gaussian matrices is also obtained as an upper bound for banded block Toeplitz matrices. Our simulation and analytical results show that sparse Gaussian random matrices do satisfy the RIP condition with high probability. The probability of satisfying the RIP depends on the probability of zero entries.

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.