Frequency Division Duplexing Massive Massive Multiple-input Multiple-output Systems Research Articles

Tracking FDD Massive MIMO Downlink Channels by Exploiting Delay and Angular Reciprocity

The massive multiple-input multiple-output (MIMO) technology considerably enhances the spectral efficiency of a wireless communication system. However, it suffers from substantial performance degradation caused by the movement of users and the difficulty in acquiring downlink channel state information when combined with frequency division duplexing (FDD). This paper addresses these two fundamental problems by proposing a downlink channel tracking scheme that traces the multiuser downlink time-varying channel of an FDD massive MIMO system. By leveraging the delay and angular reciprocity between the uplink and downlink, a low-complexity module initially traces the frequency-independent parameters in each user's channel in the uplink. With the tracing results in previous instances, the module can efficiently trace the parameters of the existing paths, find paths that disappeared, and detect new paths from sparse uplink sounding reference signals. Then, in the downlink, a low-overhead module estimates the downlink gains for each user from a limited amount of cell-common sparse pilots. The K-means clustering algorithm is utilized to design these pilots and restrict them within a predefined amount. Accurate downlink channel tracking results can be obtained by using the frequently updated frequency-independent parameters and downlink gains, thereby compensating the performance degradation caused by movement. The numerical results validate the effectiveness and robustness of the proposed tracking scheme and suggest that we should frequently apply this scheme to ensure a high multiuser sum spectral efficiency performance.

Information-Theoretic Pilot Design for Downlink Channel Estimation in FDD Massive MIMO Systems

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.

Sparsity-aided codebook for limited feedback in FDD massive MIMO system

Channel state information at transmitter (CSIT) is vital for massive multiple-input-multiple-output (MIMO) system to achieve unprecedented improvement in capacity and spectral efficiency. Unfortunately, CSIT is acquired via channel feedback in frequency-division duplexing (FDD) system, which suffers from large volume of feedback overhead and size of codebook, since they increase with the number of antennas at transmitter. In this paper, by exploiting the channel sparsity in virtual angular domain, a sparsity-aided codebook is proposed for FDD massive MIMO system to alleviate the channel feedback overhead and codebook size. Specifically, a sparsity aided limited channel feedback model is proposed, where the high dimensional channel is decomposed to the limited linear combination with channel coefficients in virtual angular domain. Then, the high dimensional channel can be quantized by the proposed codebook in a more precise way with significantly small codebook size and fed back in low overhead within virtual coherence time. Furthermore, the upper bound of inter-user interference and the per user rate loss incurred by the proposed sparsity-aided codebook are theoretically analyzed, in which the required quantization bits only increase linearly with the channel sparsity level rather than number of BS antennas when the rate loss is limited to a constant level.

Compressed Sensing-Aided Downlink Channel Training for FDD Massive MIMO Systems

There is much discussion in industry and academia about possible technical solutions to address the growth in demand for wireless broadband. Massive multiple-input multiple-output (MIMO) systems are one of the most popular solutions to addressing this broadband demand in fifth generation (5G) cellular systems. Massive MIMO systems employ tens or hundreds of antennas at the base station to enable advanced multiuser MIMO communications. To reap the massive MIMO throughput gain, coherent transmission exploiting accurate channel state information at the transmitter is required. While it is expected that many 5G systems will employ frequency division duplexing (FDD), channel sounding for FDD systems requires a large pilot overhead, which usually scales proportionally to the number of transmit antennas. To resolve this problem, a compressed sensing (CS)-aided channel estimation scheme is proposed, which exploits the observation that the channel statistics change slowly in time. By utilizing a conventional least squares approach and a CS technique simultaneously, the proposed scheme reduces the pilot overhead. Simulation results show that the proposed scheme can estimate the channel with a reduced pilot overhead even when conventional CS cannot be applied.

Beam-Domain Channel Estimation for FDD Massive MIMO Systems With Optimal Thresholds

Massive multiple-input multiple-output (MIMO) systems are expected to operate in the frequency-division duplex (FDD) mode, which is feasible in the channel environment with limited scattering. Since accurate channel estimation is critical for gaining unprecedented capacity, we investigate beam-domain channel estimation and feedback for FDD massive MIMO systems. In particular, we focus on the threshold-based method for channel estimation, where an enhanced estimator is proposed to exploit the common support among all beam-domain channels. For threshold-based estimation, we derive its closed-form mean-squared error (MSE) expression, and obtain an optimal threshold as a function of sparsity, noise variance, and channel variance, and a simplified threshold, which is a function of noise variance only. For the enhanced estimator, we present a threshold to identify the common support, with which an algorithm is designed to improve the estimation accuracy. As for channel feedback, we suggest to feed back only significant elements (above the given threshold) in the beam domain. Numerical results validate our derived MSE expression and demonstrate the superior performance of proposed threshold-based estimators.

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

Channel feedback is essential in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. Unfortunately, prior work on multiuser MIMO has shown that the feedback overhead scales linearly with the number of base station (BS) antennas, which is large in massive MIMO systems. To reduce the 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 path gains. Within the angle coherence time, by utilizing the constant AoD information, the proposed AoD-adaptive subspace codebook is able to quantize the channel vector in a more accurate way. From the performance analysis, we show that the feedback overhead of the proposed codebook only scales linearly with a small number of dominant (path) AoDs instead of the large number of BS antennas. Moreover, we compare the proposed quantized feedback technique using the AoD-adaptive subspace codebook with a comparable analog feedback method. Extensive simulations show that the proposed AoD-adaptive subspace codebook achieves good channel feedback quality, while requiring low overhead.

Quantization and Feedback of Spatial Covariance Matrix for Massive MIMO Systems With Cascaded Precoding

In this paper, we investigate the quantization and the feedback of downlink spatial covariance matrix for massive multiple-input multiple-output (MIMO) systems with cascaded precoding. Massive MIMO has gained a lot of attention recently because of its ability to significantly improve the network performance. To reduce the overhead of downlink channel estimation and uplink feedback in frequency-division duplex massive MIMO systems, cascaded precoding has been used to convert high-dimensional physical channels into low-dimensional effective channels. For the cascaded precoding, the inner precoder is determined by the downlink spatial covariance matrix, which is unknown in the base station (BS). To address this issue, we propose a spatial spectrum-based approach for the quantization and the feedback of the spatial covariance matrix. In this manner, the BS can obtain partial information on the downlink spatial covariance matrix. Our result shows that the inner precoder based on the proposed approach can be viewed as modulated discrete prolate spheroidal sequences and thus achieves much smaller spatial leakage than the traditional discrete Fourier transform submatrix-based precoding. Practical issues for the application of the proposed approach are also addressed in this paper.

User Grouping and Scheduling for Joint Spatial Division and Multiplexing in FDD Massive MIMO System

Massive multiple-input multiple-output (MIMO) is a key technology for the 5th Generation wireless communication systems. Joint spatial division and multiplexing (JSDM) method can reduce the cost of downlink training and feedback for CSIT of frequency-division duplexing (FDD) system. In this paper, we studied user grouping and user scheduling problems based on JSDM, and proposed an improved greedy user scheduling algorithm with lower complexity. Numerical results show that the user grouping and scheduling based on the proposed improved algorithm have much lower computational complexity while resulting in only a slight loss in system performance.

Projection-based Differential Feedback for FDD Massive MIMO Systems

Channel state information at the transmitter (CSIT) plays a key role in achieving potential gain of massive multiple-input–multiple-output (MIMO) systems. In frequency-division duplex (FDD) systems, CSIT can be obtained through feedback from the receiver. Conventional limited feedback schemes, which have been designed for small-scale MIMO systems, suffer from a prohibitive amount of feedback requirement and encoding complexity when the number of transmit antennas becomes massive. In this paper, a projection-based differential feedback (PBDF) protocol is proposed for FDD massive MIMO systems. In the PBDF framework, the difference between original and predicted vectors is projected, and quantization is performed in a smaller dimensional subspace. With an appropriate projection exploiting spatial and temporal correlation of massive MIMO channels, the feedback amount and encoding complexity can be significantly reduced. The simulation results show that the proposed scheme achieves a large portion of potential throughput gain of massive MIMO systems with a small amount of channel feedback.

Codebook Design of Generalized Space Shift Keying for FDD Massive MIMO Systems in Spatially Correlated Channels

The massive multiple-input multiple-output (MIMO) system is one of the most promising techniques for beyond fourth-generation (B4G) wireless communication systems. However, supporting a downlink (DL) frequency-division duplex (FDD) massive MIMO system for backward compatibility might be a bottleneck problem because the number of feedback bits for the FDD system is proportionate to the number of transmit antennas. In this perspective, the well-known generalized space-shift keying (GSSK) can be a suitable candidate to support the DL FDD massive MIMO system. In this paper, the GSSK activating all transmit antennas at once is named as port modulation (PM). PM has enormous potential to utilize the spatial resources of the massive MIMO system by linking precoding and the well-known spatial modulation (SM). In this paper, we propose a codebook design for PM, which makes it possible to improve the average bit error probability (ABEP) of PM without instantaneous channel state information (CSI) at the transmitter (CSIT) or additional efforts to design shaping filters. Simulation results show that when the base station consists of a large number of spatially correlated transmit antennas, the proposed codebook design offers lower ABEP than other limited feedback or open-loop systems, such as spacen‐time-block-coded SM (STBC-SM).

Downlink Training Techniques for FDD Massive MIMO Systems: Open-Loop and Closed-Loop Training With Memory

The concept of deploying a large number of antennas at the base station, often called massive multiple-input multiple-output (MIMO), has drawn considerable interest because of its potential ability to revolutionize current wireless communication systems. Most literature on massive MIMO systems assumes time division duplexing (TDD), although frequency division duplexing (FDD) dominates current cellular systems. Due to the large number of transmit antennas at the base station, currently standardized approaches would require a large percentage of the precious downlink and uplink resources in FDD massive MIMO be used for training signal transmissions and channel state information (CSI) feedback. To reduce the overhead of the downlink training phase, we propose practical open-loop and closed-loop training frameworks in this paper. We assume the base station and the user share a common set of training signals in advance. In open-loop training, the base station transmits training signals in a round-robin manner, and the user successively estimates the current channel using long-term channel statistics such as temporal and spatial correlations and previous channel estimates. In closed-loop training, the user feeds back the best training signal to be sent in the future based on channel prediction and the previously received training signals. With a small amount of feedback from the user to the base station, closed-loop training offers better performance in the data communication phase, especially when the signal-to-noise ratio is low, the number of transmit antennas is large, or prior channel estimates are not accurate at the beginning of the communication setup, all of which would be mostly beneficial for massive MIMO systems.

User Grouping for Massive MIMO in FDD Systems: New Design Methods and Analysis

The massive multiple-input multiple-output (MIMO) system has drawn increasing attention recently as it is expected to boost the system throughput and result in lower costs. Previous studies mainly focus on time division duplexing (TDD) systems, which are more amenable to practical implementations due to channel reciprocity. However, there are many frequency division duplexing (FDD) systems deployed worldwide. Consequently, it is of great importance to investigate the design and performance of FDD massive MIMO systems. To reduce the overhead of channel estimation in FDD systems, a two-stage precoding scheme was recently proposed to decompose the precoding procedure into intergroup precoding and intragroup precoding. The problem of user grouping and scheduling thus arises. In this paper, we first propose three novel similarity measures for user grouping based on weighted likelihood, subspace projection, and Fubini-Study, respectively, as well as two novel clustering methods, including hierarchical and K-medoids clustering. We then propose a dynamic user scheduling scheme to further enhance the system throughput once the user groups are formed. The load balancing problem is considered when few users are active and solved with an effective algorithm. The efficacy of the proposed schemes are validated with theoretical analysis and simulations.