Frequency Division Duplex Massive MIMO Research Articles

Modular CSI Quantization for FDD Massive MIMO Communication

We consider high-dimensional MIMO transmissions in frequency division duplexing (FDD) systems. For precoding, the frequency selective channel has to be measured, quantized and fed back to the base station by the users. When the number of antennas is very high this typically leads to prohibitively high quantization complexity and large feedback. In 5G New Radio (NR), a modular quantization approach has been applied for this, where first a low-dimensional subspace is identified for the whole frequency selective channel, and then subband channels are linearly mapped to this subspace and quantized. We analyze how the components in such a modular scheme contribute to the overall quantization distortion. Based on this analysis we improve the technology components in the modular approach and propose an orthonormalized wideband precoding scheme and a sequential wideband precoding approach which provide considerable gains over the conventional method. We compare the performance of the developed quantization schemes to prior art by simulations in terms of the projection distortion, overall distortion and spectral efficiency, in a scenario with a realistic spatial channel model.

Downlink Training Sequence Design Based on Waterfilling Solution for Low-Latency FDD Massive MIMO Communications Systems

Future generations of wireless communications systems are expected to evolve toward allowing massive ubiquitous connectivity and achieving ultra-reliable and low-latency communications (URLLC) with extremely high data rates. Massive multiple-input multiple-output (m-MIMO) is a crucial transmission technique to fulfill the demands of high data rates in the upcoming wireless systems. However, obtaining a downlink (DL) training sequence (TS) that is feasible for fast channel estimation, i.e., meeting the low-latency communications required by future generations of wireless systems, in m-MIMO with frequency-division-duplex (FDD) when users have different channel correlations is very challenging. Therefore, a low-complexity solution for designing the DL training sequences to maximize the achievable sum rate of FDD systems with limited channel coherence time (CCT) is proposed using a waterfilling power allocation method. This achievable sum rate maximization is achieved using sequences produced from a summation of the user’s covariance matrices and then applying a waterfilling power allocation method to the obtained low-complexity training sequence. The results show that the proposed TS outperforms the existing methods in the medium and high SNR regimes while reducing computational complexity. The obtained results signify the proposed TS’s feasibility for practical consideration compared with the existing DL training sequence designs.

Rate Splitting in FDD Massive MIMO Systems Based on the Second Order Statistics of Transmission Channels

In this work, we present new results for the application of rate splitting multiple access (RSMA) to the downlink (DL) of a massive multiple-input-multiple-output system (MIMO) operating in frequency-division-duplex (FDD) mode. We propose a statistical precoding design relying on the channels’ second-order information when one-layer RS is implemented. The advantage of the statistical precoding lies in simplifying the precoder design by basing the optimization objective on the slowly-varying channel covariance matrices instead of the fast-changing instantaneous channel estimates. To this end, we use the so-called bilinear precoder, which was shown in [1] and [2] to have limited performance in the high SNR regime due to the imperfect channel state information (CSI) available at the base station (BS). We formulate the DL throughput maximization problem based on a widely used lower bound on the achievable sum rate and propose an iterative approach to solve the underlying optimization problem. Numerical results demonstrate the benefit of implementing one-layer RS. Furthermore, the proposed iterative approach achieves excellent results in terms of spectral efficiency compared to the state-of-the-art techniques.

A Partial Channel Reciprocity-Based Codebook for Wideband FDD Massive MIMO

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 channel reciprocity (PCR) codebook, inspired by the low-rankness behavior and the fact that the uplink and downlink channels have similar angle-delay distributions. Compared to the latest codebook in 5G, the proposed PCR codebook scheme achieves higher performance, lower complexity at the user side, and requires less feedback. We derive the feedback overhead necessary to achieve asymptotically error-free CSI feedback. Two low-complexity alternatives are also proposed to further reduce the complexity at the base station side. Simulations with the practical 3GPP channel model show the significant gains over the latest 5G codebook, which prove that our proposed methods are practical solutions for 5G and beyond.

A Computationally Efficient Gradient Algorithm for Downlink Training Sequence Optimization in FDD Massive MIMO Systems

Future wireless networks will require advance physical-layer techniques to meet the requirements of Internet of Everything (IoE) applications and massive communication systems. To this end, a massive MIMO (m-MIMO) system is to date considered one of the key technologies for future wireless networks. This is due to the capability of m-MIMO to bring a significant improvement in the spectral efficiency and energy efficiency. However, designing an efficient downlink (DL) training sequence for fast channel state information (CSI) estimation, i.e., with limited coherence time, in a frequency division duplex (FDD) m-MIMO system when users exhibit different correlation patterns, i.e., span distinct channel covariance matrices, is to date very challenging. Although advanced iterative algorithms have been developed to address this challenge, they exhibit slow convergence speed and thus deliver high latency and computational complexity. To overcome this challenge, we propose a computationally efficient conjugate gradient-descent (CGD) algorithm based on the Riemannian manifold in order to optimize the DL training sequence at base station (BS), while improving the convergence rate to provide a fast CSI estimation for an FDD m-MIMO system. To this end, the sum rate and the computational complexity performances of the proposed training solution are compared with the state-of-the-art iterative algorithms. The results show that the proposed training solution maximizes the achievable sum rate performance, while delivering a lower overall computational complexity owing to a faster convergence rate in comparison to the state-of-the-art iterative algorithms.

Improved Downlink Rates for FDD Massive MIMO Systems Through Bayesian Neural Networks-Based Channel Prediction

In frequency-division-duplex (FDD) massive MIMO systems, channel state information (CSI) feedback waiting phase does not get fully exploited since base station needs to wait for the CSI feedback before transmitting downlink data. The proportion of the CSI feedback waiting phase during the downlink transmission would be high as the MIMO system scales up, which sacrifices downlink rates of the FDD massive MIMO systems significantly. In this paper, we first present a channel prediction-aided FDD scheme to utilize the idle waiting time efficiently. Then we propose a novel channel prediction method based on Bayesian neural network (BNN), which can handle the uncertainty in a natural manner and learn regularization from data without painstaking manual pre-tuning of network hyperparameters. Numerical results show that our proposed channel prediction-aided FDD scheme can achieve remarkable performance gains in terms of either achievable downlink rates or bit error rate. Moreover, our proposed BNN-based channel predictor is much more effective and robust in contrast to the state-of-the-art channel prediction techniques such as autoregressive model and recurrent neural network.

Downlink Training Design for FDD Massive MIMO Systems in the Presence of Colored Noise

Massive multiple-input multiple-output (MaMi) systems have attracted much research attention during the last few years. This is because MaMi systems are able to achieve a remarkable improvement in data rate and thus meet the immensely ongoing traffic demands required by the future wireless networks. To date, the downlink training sequence (DTS) for the frequency division duplex (FDD) MaMi communications systems have been designed based on the idealistic assumption of white noise environments. However, it is essential and more practical to consider the colored noise environments when designing an efficient DTS for channel estimation. To this end, this paper proposes a new DTS design by exploring the joint use of spatial channel and noise covariance matrices, when the channel is not reciprocal but the coherence block length remains limited. We derive an analytical solution for the mean square error (MSE) based on the proposed training design with colored noise. In addition, this paper exploits the method of random matrix theory to provide an analytical solution for the downlink (DL) achievable sum rate of the regularized zero forcing beamforming (RZFBF) precoder. Numerical results demonstrate that using the proposed DTS design, the MSE of the channel estimate is significantly reduced compared with the conventional training designs with white noise. Furthermore, the results show that the proposed pilot design markedly improves the DL achievable SR over the conventional training designs, especially at relatively low signal-to-noise-ratio (SNR) levels. This enables FDD MaMi systems to operate under more practical scenarios of colored noise and limited coherence time environments.

CV-3DCNN: Complex-Valued Deep Learning for CSI Prediction in FDD Massive MIMO Systems

In beyond fifth-generation (B5G) era, massive multiple-input multiple-output (M-MIMO) will be a key technology to offer higher network capacities. Due to the different frequency of uplink and downlink channels in FDD systems, the channel state information (CSI) feedback from user terminal to the base station is necessary, but this reduces the spectrum efficiency. This letter proposes a deep learning based solution to predict the downlink CSI in frequency division duplex (FDD) systems, which is termed as complex-valued three dimensional convolutional neural network (CV-3DCNN). The proposed network uses a complex-valued neural network in complex domain to deal with the complex CSI matrices, and adopts three-dimensional convolution operations for feature extraction. The proposed scheme aims to make full use of the hidden information of the complex matrices of the CSI data, and to minimize information loss caused by data processing. The experimental results demonstrate that the proposed architecture can improve accuracy of the downlink CSI prediction by approximately 6 dB.

Efficient Angle-Domain Processing for FDD-Based Cell-Free Massive MIMO Systems

Cell-free massive MIMO communications is an emerging network technology for 5G wireless communications wherein distributed multi-antenna access points (APs) serve many users simultaneously. Most prior work on cell-free massive MIMO systems assume time-division duplexing mode, although frequency-division duplexing (FDD) systems dominate current wireless standards. The key challenges in FDD massive MIMO systems are channel-state information (CSI) acquisition and feedback overhead. To address these challenges, we exploit the so-called angle reciprocity of multipath components in the uplink and downlink, so that the required CSI acquisition overhead scales only with the number of served users, and not the number of AP antennas nor APs. We propose a low complexity multipath component estimation technique and present linear angle-of-arrival (AoA)-based beamforming/combining schemes for FDD-based cell-free massive MIMO systems. We analyze the performance of these schemes by deriving closed-form expressions for the mean-square-error of the estimated multipath components, as well as expressions for the uplink and downlink spectral efficiency. Using semi-definite programming, we solve a max-min power allocation problem that maximizes the minimum user rate under per-user power constraints. Furthermore, we present a user-centric (UC) AP selection scheme in which each user chooses a subset of APs to improve the overall energy efficiency of the system. Simulation results demonstrate that the proposed multipath component estimation technique outperforms conventional subspace-based and gradient-descent based techniques. We also show that the proposed beamforming and combining techniques along with the proposed power control scheme substantially enhance the spectral and energy efficiencies with an adequate number of antennas at the APs.

Downlink Channel Prediction for Time-Varying FDD Massive MIMO Systems

Accurate channel estimation is important for massive multiple-input multiple-output (mMIMO) to ensure good performance. Considering mMIMO application in 5G, frequency division duplexing (FDD) can provide higher data rate and wider coverage than the time division duplexing (TDD) mode. However, since the uplink/downlink channel is not straightforwardly reciprocal, FDD downlink channel estimation requires heavier training and computation than TDD mode due to the massive number of antennas. In addition, fast channel variation renders the real time estimation even more difficult. In this paper, we propose a downlink channel prediction scheme for FDD mMIMO, which requires only the TDD overhead. Specifically, the downlink channel matrix is represented by three components: steering matrix (frequency dependent), fading coefficients (time varying), and time delays (semi-static). By the proposed scheme, these three components can be obtained through uplink training. In addition, fast tracking and prediction is leveraged to obtain the real time channel state information. Simulation results show that accurate channel prediction is obtained via low cost and complexity by the proposed scheme.

A burst-form CSI estimation approach for FDD massive MIMO systems

Pilot and channel state information (CSI) feedback overhead in the downlink and uplink paths are two major implementation challenges in frequency-division duplex (FDD) based massive MIMO systems. When the massive MIMO channel satisfies the burst-sparsity property, we can acquire the channel with compressed pilots and CSI feedback in a more efficient approach. This paper proposes a burst-form estimation approach, referred to as the burst-form least squares (BFLS) algorithm, to fully utilize the burst-sparsity property of massive MIMO channels. The proposed algorithm is based on knowledge of the starting location of each burst at the user side. For situations where the starting locations change quickly or are otherwise initially unknown at the user, a starting point estimation (SPE) algorithm is proposed to provide the position of each burst in the channel vector. Numerical results demonstrate that the BFLS algorithm acquires the channel better than competing approaches and reaches the performance upper bound. It is shown that the SPE algorithm can find the location of bursts with high accuracy and using the estimated values do not significantly degrade the estimation quality.

FDD Massive MIMO via UL/DL Channel Covariance Extrapolation and Active Channel Sparsification

We propose a novel method for massive multiple-input multiple-output (massive MIMO) in frequency division duplexing (FDD) systems. Due to the large frequency separation between uplink (UL) and downlink (DL) in FDD systems, channel reciprocity does not hold. Hence, in order to provide DL channel state information to the base station (BS), closed-loop DL channel probing, and channel state information (CSI) feedback is needed. In massive MIMO, this typically incurs a large training overhead. For example, in a typical configuration with M ≃200 BS antennas and fading coherence block of T ≃ 200 symbols, the resulting rate penalty factor due to the DL training overhead, given by max{0, 1 - M/T }, is close to 0. To reduce this overhead, we build upon the well-known fact that the angular scattering function of the user channels is invariant over frequency intervals whose size is small with respect to the carrier frequency (as in current FDD cellular standards). This allows us to estimate the users' DL channel covariance matrix from UL pilots without additional overhead. Based on this covariance information, we propose a novel sparsifying precoder in order to maximize the rank of the effective sparsified channel matrix subject to the condition that each effective user channel has sparsity not larger than some desired DL pilot dimension T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dl</sub> , resulting in the DL training overhead factor max{0, 1 - T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dl</sub> /T } and CSI feedback cost of Tdl pilot measurements. The optimization of the sparsifying precoder is formulated as a mixed integer linear program, that can be efficiently solved. Extensive simulation results demonstrate the superiority of the proposed approach with respect to the concurrent state-of-the-art schemes based on compressed sensing or UL/DL dictionary learning.

Beam-Time Block Coding With Joint User Grouping and Beamforming for FDD Massive MIMO Systems

A downlink (DL) precoding scheme that needs no DL training nor uplink (UL) feedback for massive MIMO systems operated under frequency-division duplex (FDD) is proposed, whereas most of the schemes in the literature were proposed to compress the overhead of training and feedback. Due to the above advantage, the proposed scheme is suitable for extremely low-latency applications. This scheme exploits angle reciprocity of FDD systems to enable the base station to acquire partial DL channel state information through a previous UL signaling. A joint user grouping and beamforming optimization method without DL training and UL feedback is proposed to enhance spectral efficiency and mitigate interference between multiple UEs during DL data transmission. Simulation results suggest that the proposed scheme possesses a comparable performance to a number of previous grouping-based schemes that require DL training and UL feedback.

Feedback Mechanisms for FDD Massive MIMO With D2D-Based Limited CSI Sharing

Channel state information (CSI) feedback is a challenging issue in frequency division duplexing (FDD) massive MIMO systems. This paper studies a cooperative feedback scheme, where the users first exchange their CSI with each other through device-to-device (D2D) communications, then compute the precoder by themselves, and feedback the precoder to the base station (BS). Analytical results are derived to show that the cooperative precoder feedback is more efficient than the CSI feedback in terms of interference mitigation. To reduce the delays for CSI exchange, we develop an adaptive CSI exchange strategy based on signal subspace projection and optimal bit partition. Numerical results demonstrate that the proposed cooperative precoder feedback scheme with adaptive CSI exchange significantly outperforms the CSI feedback scheme, even under moderate delays for CSI exchange via D2D.

Low-Rank Covariance-Assisted Downlink Training and Channel Estimation for FDD Massive MIMO Systems

We consider the problem of downlink training and channel estimation in frequency division duplex (FDD) massive MIMO systems, where the base station (BS) equipped with a large number of antennas serves a number of single-antenna users simultaneously. To obtain the channel state information (CSI) at the BS in FDD systems, the downlink channel has to be estimated by users via downlink training and then fed back to the BS. For FDD large-scale MIMO systems, the overhead for downlink training and CSI uplink feedback could be prohibitively high, which presents a significant challenge. In this paper, we study the behavior of the minimum mean-squared error (MMSE) estimator when the channel covariance matrix has a low rank or an approximate low-rank structure. Our theoretical analysis reveals that the amount of training overhead can be substantially reduced by exploiting the low-rank property of the channel covariance matrix. In particular, we show that the MMSE estimator is able to achieve exact channel recovery in the asymptotic low-noise regime, provided that the number of pilot symbols in time is no less than the rank of the channel covariance matrix. We also present an optimal pilot design for the single-user case, and an asymptotic optimal pilot design for the multi-user scenario. Last, we develop a simple model-based scheme to estimate the channel covariance matrix, based on which the MMSE estimator can be employed to estimate the channel. The proposed scheme does not need any additional training overhead. Simulation results are provided to verify our theoretical results and illustrate the effectiveness of the proposed estimated covariance-assisted MMSE estimator.

Uplink Downlink Rate Balancing and Throughput Scaling in FDD Massive MIMO Systems

In this work we extend the concept of uplink-downlink rate balancing to frequency division duplex (FDD) massive MIMO systems. We consider a base station with large number antennas serving many single antenna users. We first show that any unused capacity in the uplink can be traded off for higher throughput in the downlink in a system that uses either dirty paper (DP) coding or linear zero-forcing (ZF) precoding. We then also study the scaling of the system throughput with the number of antennas in cases of linear Beamforming (BF) Precoding, ZF Precoding, and DP coding. We show that the downlink throughput is proportional to the logarithm of the number of antennas. While, this logarithmic scaling is lower than the linear scaling of the rate in the uplink, it can still bring significant throughput gains. For example, we demonstrate through analysis and simulation that increasing the number of antennas from 4 to 128 will increase the throughput by more than a factor of 5. We also show that a logarithmic scaling of downlink throughput as a function of the number of receive antennas can be achieved even when the number of transmit antennas only increases logarithmically with the number of receive antennas.

Achievable Rates of FDD Massive MIMO Systems With Spatial Channel Correlation

It is well known that the performance of frequency-division-duplex (FDD) massive MIMO systems with i.i.d. channels is disappointing compared with that of time-division-duplex (TDD) systems, due to the prohibitively large overhead for acquiring channel state information at the transmitter (CSIT). In this paper, we investigate the achievable rates of FDD massive MIMO systems with spatially correlated channels, considering the CSIT acquisition dimensionality loss, the imperfection of CSIT and the regularized-zero-forcing linear precoder. The achievable rates are optimized by judiciously designing the downlink channel training sequences and user CSIT feedback codebooks, exploiting the multiuser spatial channel correlation. We compare our achievable rates with TDD massive MIMO systems, i.i.d. FDD systems, and the joint spatial division and multiplexing (JSDM) scheme, by deriving the deterministic equivalents of the achievable rates, based on popular channel models. It is shown that, based on the proposed eigenspace channel estimation schemes, the rate-gap between FDD systems and TDD systems is significantly narrowed, even approached under moderate number of base station antennas. Compared to the JSDM scheme, our proposal achieves dimensionality-reduction channel estimation without channel pre-projection, and higher throughput for moderate number of antennas and moderate to large channel coherence time, though at higher computational complexity.