Quantized Channel State Information Research Articles

Channel Customization for Limited Feedback in RIS-Assisted FDD Systems

Reconfigurable intelligent surfaces (RISs) represent a pioneering technology to realize smart electromagnetic environments by reshaping the wireless channel. Jointly designing the transceiver and RIS relies on the channel state information (CSI), whose feedback has not been investigated in multi-RIS-assisted frequency division duplexing systems. In this study, the limited feedback of the RIS-assisted wireless channel is examined by capitalizing on the ability of the RIS in channel customization. By configuring the phase shifters of the surfaces using statistical CSI, we customize a sparse channel in rich-scattering environments, which significantly reduces the feedback overhead in designing the transceiver and RISs. Since the channel is customized in terms of singular value decomposition (SVD) with full-rank, the optimal SVD transceiver can be approached without a matrix decomposition and feeding back the complete channel parameters. The theoretical spectral efficiency (SE) loss of the proposed transceiver and RIS design is derived by considering the limited CSI quantization. To minimize the SE loss, a bit partitioning algorithm that splits the limited number of bits to quantize the CSI is developed. Extensive numerical results show that the channel customization-based transceiver with reduced CSI can achieve satisfactory performance compared with the optimal transceiver with full CSI. Given the limited number of feedback bits, the bit partitioning algorithm can minimize the SE loss by adaptively allocating bits to quantize the channel parameters.

Clustering Algorithm-Based Quantization Method for Massive MIMO CSI Feedback

Deep learning-based channel state information (CSI) feedback can provide high downlink throughput for massive multiple-input multiple-output (MIMO) system in frequency division duplex mode. The compression and quantization of CSI greatly reduce the feedback overhead. However, existing quantization methods design quantization levels without matching the distribution of feedback codewords, which impairs the reconstruction accuracy of CSI. In this letter, we propose a k-means clustering algorithm-based quantizer, named KMQBlock, which can find the appropriate quantization levels according to the distribution of feedback codewords by using scalar and vector quantization. To illustrate the efficacy of KMQBlock, we firstly propose a deep learning-based CSI feedback network MRNet to improve the CSI reconstruction accuracy. Then, we apply KMQBlock to MRNet to quantize the feedback codewords. Experimental results show that KMQBlock can provide at most 8.20 dB performance improvement for MRNet compared with conventional quantization methods.

On Adaptive Transmission for Distributed Detection in Energy Harvesting Wireless Sensor Networks With Limited Fusion Center Feedback

We consider a wireless sensor network tasked with solving a binary distributed detection problem. Sensors communicate directly with a fusion center (FC) over orthogonal fading channels, with additive Gaussian noise. Each sensor can harvest randomly arriving energy units and store them in a battery. Also, it knows its quantized channel state information (CSI), acquired via a limited feedback channel from the FC. Modeling the randomly arriving energy units during a time slot as a Poisson process and the battery dynamics as a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> -state Markov chain (where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> is the battery size), we propose a channel-dependent transmit power control strategy such that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${J}$ </tex-math></inline-formula> -divergence based detection metric is maximized at the FC, subject to an average transmit power per sensor constraint. The proposed strategy is parametrized in terms of the channel gain quantization thresholds and the scale factors corresponding to the quantization intervals. This strategy allows each sensor to adapt its transmit power based on its battery state and its qunatized CSI. Finding optimal strategy requires solving a non-convex optimization problem that is not differentiable with respect to the optimization variables. We propose near-optimal strategies based on random search methods that have a low-computational complexity and provide a close-to-optimal performance.

Deep Learning Based CSI Compression and Quantization With High Compression Ratios in FDD Massive MIMO Systems

Generally, the downlink channel state information (CSI) used for precoding is conveyed back in massive multi-input multi-output (MIMO) systems with frequency division duplex (FDD) mode, which costs too much bandwidth. However, most of CSI compression algorithms including deep learning based schemes show poor performance with high compression ratio (CR) in ourdoor scenery. In this letter, we propose a new neural network that utilizes the deep neural network (DNN) to improve the learning ability of residual network and a novel activation function to adapt the neural network. Simulation results show that the proposed CsiNet+DNN method exhibits better performance than exsiting methods in recovery quality and accuracy, which also achieves remarkable robustness at noise situations.

Flag Manifold-Based Precoder Interpolation Techniques for MIMO-OFDM Systems

The use of channel state information (CSI) at the transmitter significantly enhances the performance of wireless communication systems. However, the requirement of CSI feedback places an undue burden on the reverse link, especially in links that employ multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM), where CSI takes the form of a precoding matrix (precoder) for each subcarrier. Typical deployments use quantization and feedback of CSI at certain subcarriers, with interpolation to fill in missing CSI at the transmitter. Past work has used the orthogonal structure of precoders with Flag manifolds for quantization and interpolation of CSI, although interpolation is complicated due to the absence of analytic expressions for geodesics on Flag manifolds. Other approaches have involved the parameterization of the precoder into scalar parameters that are amenable to quantization and interpolation. In this paper, we present efficient methods to quantize and interpolate on Flag manifolds, using both optimal algorithms as well as simplified suboptimal algorithms. Further, we unify these with the parameterization based approaches and show that these translate directly to low-complexity quantization and interpolation on Flag manifolds. Simulations reveal that the proposed precoder quantization and interpolation effectively enhance achievable rates with limited complexity.

Hybrid Precoder Design With Minimum-Subspace-Distortion Quantization in Multiuser mmWave Communications

Hybrid precoding has been a promising technique in millimeter wave (mmWave) communications, providing a balanced tradeoff between system performance and hardware complexity. Existing hybrid precoding schemes either require full channel state information (CSI) or use codebook-based design, causing large feedback overhead or degraded system performance, respectively. In this paper, we propose a balanced scheme with limited feedback CSI and element-level quantization. Our key idea is to maximize the system sum rate by using an adaptive baseband precoder and an eigenbeam radio frequency (RF) precoder. The adaptive baseband precoder can balance the effective channel gain and the multiuser interference according to the transmitted power. The eigenbeam RF precoder is optimized with only requiring a limited length of feedback vector. Considering the practical constraints on RF precoders, we then propose a quantization algorithm that minimizes the subspace distortion between the optimized eigenbeam RF precoder and the quantized one. The quantization algorithm also works for the case when RF chains are more than users. Extensive simulation results are provided and validate the effectiveness of the proposed hybrid precoding scheme.

Recursive CSI Quantization of Time-Correlated MIMO Channels by Deep Learning Classification

In frequency division duplex (FDD) multiple-input multiple-output (MIMO) wireless communications, limited channel state information (CSI) feedback is a central tool to support advanced single- and multi-user MIMO beamforming/precoding. To achieve a given CSI quality, the CSI quantization codebook size has to grow exponentially with the number of antennas, leading to quantization complexity, as well as, feedback overhead issues for larger MIMO systems. We have recently proposed a multi-stage recursive Grassmannian quantizer that enables a significant complexity reduction of CSI quantization. In this paper, we show that this recursive quantizer can effectively be combined with deep learning classification to further reduce the complexity, and that it can exploit temporal channel correlations to reduce the CSI feedback overhead.

On Optimizing Feedback-Rate Allocation for Downlink MIMO-NOMA With Quantized CSIT

We consider multiple-input multiple output (MIMO) non-orthogonal multiple access (NOMA) downlink channels with zeroforcing beamforming transmission. The base station has multiple transmit antennas while all mobile devices have single receive antenna. With a limited feedback rate, channel direction information (CDI) needs to be quantized and fed back from mobile users to a base station. Thus, the accuracy of the quantized channel state information at the transmitter (CSIT) will depend on the feedback rate. To increase spectral efficiency, 2 active users in some clusters share the same beamforming vector and thus, will interfere fully with each other. Given a total-feedback rate, we analyze the feedback allocation for clusters with single active user and 2 active users. The objective is to either minimize the maximum outage probability or maximize the minimum rate among all active users in a cell. We show that the proposed feedback allocation is close to the optimum. Some numerical examples show that the resulting rate performance with the proposed feedback allocation is increased by 100% over that with the uniform feedback allocation.

On the Accuracy of Quantization Cell Approximation in MIMO Broadcast Systems Based on Limited Feedback

This study investigates the accuracy of quantization cell approximation (QCA) in a multiple-input multiple-output (MIMO) broadcast channel. QCA is an analytical quantization model used to approximate the quantized channel state information (CSI) in limited-feedback-based MIMO systems. It has been widely used in important studies for analytical tractability because it approximates the quantized CSI as a simple beta random variable multiplied by a deterministic value. Moreover, the effect of quantization is solely concentrated on the deterministic value such that the corresponding performance analysis is stochastically independent of the quantization process. Nevertheless, the accuracy of QCA has not been carefully demonstrated in previous studies. In this study, a generalized version of QCA is proposed with a complete analysis. Because the proposed QCA requires the use of a specific distance measure, the validity of the distance measure is first investigated. Based on the proposed distance measure, the accuracy of QCA is estimated by analyzing the difference between the spectral efficiencies achieved using QCA and random matrix quantization (RMQ). The corresponding results show that the difference gradually decreases and converges to zero as the number of feedback bits increases. As QCA and RMQ provide performance upper and lower bounds, respectively, in terms of codebook construction, these results prove the asymptotic validity of QCA with respect to the number of feedback bits. Both analysis and simulation results demonstrate that the difference in spectral efficiencies is also small for a moderate number of feedback bits. In addition, this study also demonstrates an asymptotic difference in spectral efficiencies with respect to the signal-to-noise-ratio (SNR). The difference increases with the SNR, but it is bounded by a finite value. Thus, the difference in the worst case SNR can also be suppressed by increasing the number of feedback bits.

Data-Driven Relay Selection for Physical-Layer Security: A Decision Tree Approach

Conventional optimization-driven secure relay selection relies on maximization algorithm and accurate channel state information (CSI) of both legitimate and eavesdropper channels. Particularly, estimating and collecting accurate eavesdropper CSI is a difficult task. In this paper, we exploit the benefits of machine learning in solving secure relay selection problem from a data-driven perspective. We convert secure relay selection to a multiclass-classification problem and solve it by a decision-tree-based scheme, which is composed of three phases - preparing training data, building decision tree and predicting relay selection. To meet decision tree’s requirement that input features must take discrete values, a feature extraction method is proposed to generate discrete input by quantizing the accurate CSI of legitimate and eavesdropper channels. By this means, the decision-tree-based relay selection only requires quantized CSI feedback which takes substantially fewer bits in predicting phase. For the purpose of optimizing quantization parameters and enhancing decision tree prediction, we further derive three splitting criteria, i.e. information gain, information gain ratio and Gini index. Simulation results show that if the quantization parameters are set properly, the proposed decision-tree-based scheme can achieve satisfactory performance in terms of average secrecy rate while reducing computational complexity and feedback amount.

Reconsidering Design of Multi-Antenna NOMA Systems With Limited Feedback

We provide in this paper a comprehensive solution to the design, performance analysis, and optimization of a multi-antenna non-orthogonal multiple access (NOMA) system for multiuser downlink communications under a general limited channel state information (CSI) feedback framework for frequency division duplex mode. We design a general framework including user clustering, joint power and bits allocation, CSI quantization and feedback, signal superposition coding, transmit beamforming, and successive interference cancellation at receivers. Then, we conduct a mathematically strict performance analysis of the considered system, and obtain a closed-form lower bound on the ergodic rate of each user in terms of transmit power, CSI quantization accuracy and channel conditions. For exploiting the potentials of multiple-antenna techniques in NOMA systems, we jointly optimize two key parameters, i.e., transmit power and the number of feedback bits allocated to each user, and propose low-complexity closed-form solutions. Moreover, through asymptotic analysis, we reveal the interactions between the main system parameters and their impacts on the joint power and feedback bits allocation result, and hence show some guidelines on the system design. Finally, numerical results validate the correctness of our theoretical analysis and demonstrate the advantages of the proposed algorithms over the most related state of the art.

Bit-Level Optimized Neural Network for Multi-Antenna Channel Quantization

Quantized channel state information (CSI) plays a critical role in precoding design which helps reap the merits of multiple-input multiple-output (MIMO) technology. In order to reduce the overhead of CSI feedback, we propose a deep learning based CSI quantization method by developing a joint convolutional residual network (JC-ResNet) which benefits MIMO channel feature extraction and recovery from the perspective of bit-level quantization performance. Experiments show that our proposed method substantially improves the performance.

Grassmannian Product Codebooks for Limited Feedback Massive MIMO With Two-Tier Precoding

In frequency-division duplex full-dimension massive MIMO systems, one of the main challenges is to obtain sufficiently accurate channel state information (CSI) at the transmitter to enable efficient multi-user MIMO transmission. In this paper, we propose a novel dual stage Grassmannian product quantization approach that is suitable for high-dimensional CSI quantization and feedback. We apply the proposed method for outer-tier CSI feedback in two-tier precoding architectures, which employ channel-subspace based outer-tier precoding strategies, such as maximum eigenmode transmission. The proposed method is especially effective if the channel can be decomposed in the angular domain, such that DFT codebooks enable an efficient CSI compression. Our dual stage product codebook quantization approach mitigates the well-known inefficiency of oversampled DFT codebooks for growing codebook sizes, by varying the intermediate quantization dimension of the proposed quantizer.

Delay constrained throughput optimization in multi-hop AF relay networks, using limited quantized CSI

In this paper, we analyze the throughput of multi-hop amplify and forward (AF) relay networks in delay-constrained scenario. Using quantized channel state information (CSI), the transmission rates and powers are discretely adapted with individual average power constraint on each node. A sub-gradient projection-based algorithm is utilized, by which there is no need for probability density functions (PDFs) to solve the optimization problem. Our numerical evaluations show that the sub-gradient projection-based algorithm results in a comparable performance with an analytical approach using PDFs. As shown, a considerably better performance obtained by the designed scheme compared to previous schemes with constant power transmission. More than 70% throughput improvement is achieved by our scheme compared to constant power transmission with just two more feedback bits and a short training time required at the beginning of the transmission.

Artificial-Noise-Aided Nonlinear Secure Transmission for Multiuser Multi-Antenna Systems With Finite-Rate Feedback

We consider a low-complexity transceiver design for secure communications of a multiuser multi-antenna system with an external multi-antenna eavesdropper. We propose to employ Tomlinson–Harashima precoder (THP) to simultaneously transmit message-bearing signals and artificial noise (AN) according to the quantized channel state information (CSI). Based on random vector quantization of the channel vectors, we obtain analytical approximations of the ergodic secrecy rate (ESR) of each legitimate receiver (LR) and the ergodic secrecy sum rate of the system with arbitrary system parameters. Based on the obtained analytical results, the near-optimal power allocation to the information signals and AN can be obtained using a numerical method. We show using an information-theoretical method that, besides the advantage in the ESR over the linear precoding scheme, THP can reduce the supported rate of the eavesdropper’s channel by preventing the eavesdropper from obtaining the legitimate channels’ (quantized) CSI. The ESR loss of each LR compared with the perfect CSI case will increase without bound for a fixed number of feedback bits. We also derive a feedback bit scaling law to solve this problem. Finally, numerical results are provided to verify our analytical results and also the advantage of the proposed secure nonlinear transceiver over the corresponding linear scheme.

Nonlinear-Precoded Multiuser Secure Transmission With Cooperative Jamming and Adaptive Limited Feedback

This paper studies secure transceiver design for multiuser multiantenna systems with an external passive eavesdropper and a cooperative jamming helper. Due to the finite-rate constraint of feedback channels, only quantized channel state information (CSI) of the legitimate users is available at the transmitter and the helper. A nonlinear-precoded secure transmission strategy is proposed using Tomlinson–Harashima precoding at the transmitter and null-space beamforming at the helper based on the quantized CSI. The accurate closed-form expression of an approximation for the ergodic rate of each legitimate user is obtained using quantization cell approximation for random vector quantization of the channels. Assuming the quantized CSI of the legitimate channels and the helper's channel at the eavesdropper, closed-form expression of an upper bound of the ergodic rate of each user's message at the eavesdropper is also derived. Then, a closed-form expression of an approximation for the worst-case ergodic secrecy sum rate follows. We also theoretically show that, besides the advantage in ergodic rate over the linear precoding scheme, when the quantized CSI is not available at the eavesdropper, Tomlinson–Harashima precoding is also more effective in degrading the received signal quality at the eavesdropper, and, thus, is more capable to enhance the secrecy of the systems compared with the linear precoding scheme. Given the total bandwidth constraint of CSI-feedback channels, an adaptive feedback bit allocation algorithm is proposed for each legitimate user to optimize the ergodic secrecy rate performance. Numerical results illustrate that the proposed nonlinear-precoded secure transmission strategy outperforms the corresponding linear precoding scheme, and significant advantage can be achieved by adaptively allocating the total available feedback bits.

Energy Efficient Power Allocation for Carrier Aggregation in Heterogeneous Networks: Partial Feedback and Circuit Power Consumption

The energy-efficient power allocation for carrier aggregation (CA) in heterogeneous networks (HetNets) is studied in this paper. We assume that multiple component carriers belong to HetNets and, thus, inter-band CA is considered, where both full and partial feedback scenarios are investigated. For the latter, we consider quantized channel state information at the transmitter and the corresponding power allocation policies are derived. Next, we derive energy-efficient optimal power allocation policies by assuming circuit power consumption for the transmitter that account for the multiple radio frequency (RF) chains required to support massive inter-band CA. The resulting algorithms are then used in order to investigate the relation between optimal energy efficiency (EE) and design parameters such as the number of frequency bands, antennas and feedback allocation through controlling the quantized information. A greedy optimization algorithm is also introduced to jointly optimize the aforementioned parameters. By carrying out simulations, it is observed that the achievable EE gains for massive CA in HetNets is further limited by either the number of feedback bits or the increase in RF circuits power consumption.

Advanced Quantizer Designs for FDD-Based FD-MIMO Systems Using Uniform Planar Arrays

Massive multiple-input multiple-output (MIMO) systems, which utilize a large number of antennas at the base station, are expected to enhance network throughput by enabling improved multiuser MIMO techniques. To deploy many antennas in reasonable form factors, base stations are expected to employ antenna arrays in both horizontal and vertical dimensions, which is known as full-dimension (FD) MIMO. The most popular two-dimensional array is the uniform planar array (UPA), where antennas are placed in a grid pattern. To exploit the full benefit of massive MIMO in frequency division duplexing (FDD), the downlink channel state information (CSI) should be estimated, quantized, and fed back from the receiver to the transmitter. However, it is difficult to accurately quantize the channel in a computationally efficient manner due to the high dimensionality of the massive MIMO channel. In this paper, we develop both narrowband and wideband CSI quantizers for FD-MIMO taking the properties of realistic channels and the UPA into consideration. To improve quantization quality, we focus on not only quantizing dominant radio paths in the channel, but also combining the quantized beams. We also develop a hierarchical beam search approach, which scans both vertical and horizontal domains jointly with moderate computational complexity. Numerical simulations verify that the performance of the proposed quantizers is better than that of previous CSI quantization techniques.

Power Allocation for Distributed Detection Systems in Wireless Sensor Networks with Limited Fusion Center Feedback

We consider a distributed detection system for a wireless sensor network over slow-fading channels. Each sensor only has knowledge of quantized channel state information (CSI) which is received from the fusion center via a limited feedback channel. We then consider transmit power allocation at each sensor in order to maximize a J-divergence based detection metric subject to a total and individual transmit power constraints. Our aim is to jointly design the quantization regions of all sensors CSI and the corresponding power allocations. A locally optimum solution is obtained by applying the generalized Lloyd algorithm (GLA). To overcome the high computational complexity of the GLA, we then propose a low-complexity near-optimal scheme which performs very close to its GLA based counterpart. This enables us to explicitly formulate the problem and to find the unique solution despite the non-convexity of the optimization problem. An asymptotic analysis is also provided when the number of feedback bits becomes large. Numerical results illustrate that only a small amount of feedback is needed to achieve a detection performance close to the full CSI case.

Impact of Imperfect Source-to-Relay CSI in Amplify-and-Forward Relay Networks

Cooperative communication assisted by relays is regarded as an effective means of achieving spatial diversity. The achievable diversity gain relies on the channel-state information (CSI) that can be acquired at the destination because spatial diversity combining unavoidably requires the disintegrated channel information. To reduce signaling overhead, quantization and compression are applied prior to the delivery of the source-to-relay (SR) CSI to the destination. This paper studies an amplify-and-forward relay network while considering the impact of the quantization of the SR CSI. Several quantization methods relying on the statistics of the SR CSI are investigated. The probability density functions of upper and lower bounds on the signal-to-noise ratio (SNR) and the corresponding symbol-error rate (SER) achieved at the destination are derived analytically. Monte Carlo simulations are performed to compare the simulation results with the analytical results of the SER bounds and to verify the effectiveness of the proposed channel quantizer. A combined method of determining the quantization interval based on equal-probability partitioning and determining the representative quanta based on the minimum-mean-square-error criterion is proposed and is verified to have the lowest quantization error among the noniterative quantization methods compared here. It is shown via the simulations that when using an iterative procedure based on the Lloyd–Max procedure, three bits per dimension are sufficient to achieve negligible SNR degradation.