Random Vector Quantization Research Articles

Optimization of resource allocation in FDD massive MIMO systems

The performance of massive MIMO systems relies heavily on the availability of Channel State Information at the Transmitter (CSIT). A large amount of work has been devoted to reducing the CSIT acquisition overhead at the pilot training and/or CSI feedback stage. In fact, the downlink communication generally includes three stages, i.e., pilot training, CSI feedback, and data transmission. These three stages are mutually related and jointly determine the overall system performance. Unfortunately, there exist few studies on the reduction of CSIT acquisition overhead from the global point of view. In this paper, we integrate the Minimum Mean Square Error (MMSE) channel estimation, Random Vector Quantization (RVQ) based limited feedback and Maximal Ratio Combining (MRC) precoding into a unified framework for investigating the resource allocation problem. In particular, we first approximate the covariance matrix of the quantization error with a simple expression and derive an analytical expression of the received Signal-to-Noise Ratio (SNR) based on the deterministic equivalence theory. Then the three performance metrics (the spectral efficiency, energy efficiency, and total energy consumption) oriented problems are formulated analytically. With practical system requirements, these three metrics can be collaboratively optimized. Finally, we propose an optimization solver to derive the optimal partition of channel coherence time. Experiment results verify the benefits of the proposed resource allocation schemes under three different scenarios and illustrate the tradeoff of resource allocation between three stages.

Environment Knowledge-Aided Massive MIMO Feedback Codebook Enhancement Using Artificial Intelligence

The autoencoder empowered by artificial intelligence has shown considerable potential in solving channel state information (CSI) feedback problems in frequency-division duplexing systems. However, this method needs to completely change the existing feedback schemes, which is difficult to deploy in the next few years. This paper proposes an environment knowledge-aided codebook-based CSI feedback framework, which retains the existent codebook-based scheme while introducing environment knowledge to feedback process through neural networks (NNs) at the base station. Only an NN-based refining operation is added after the common standardized feedback approach. The NNs learn to automatically extract environment features and utilize the channel statistics through large volumes of recorded data. The NNs also use the partial correlation between bidirectional channels to further improve feedback performance. In addition, to deal with downlink channel estimation errors, we propose two strategies to reduce their effects using an NN-based denoise module. The proposed framework can be easily embedded in most existing codebook-based feedback methods, such as random vector quantization. Two channel datasets generated by QuaDRiGa and measured in practical systems are adopted to evaluate the proposed methods. Results show that the proposed method offers over 100% increase in the throughput compared with the baseline codebook because of more accurate feedback.

Closed-Form Sum-Rate Analysis of Interference Alignment with Limited Feedback Based on Scalar Quantization and Random Vector Quantization

Interference alignment (IA) is a promising interference management technique to achieve the theoretical optimal degree of freedom (DoF) performance in multi-user cooperation scenarios. However, the effective achievable sum-rate performance of IA is largely affected by the feedback overhead and accuracy of channel state information (CSI) and decoding information (DI). Therefore, it is critical to establish the exact relationship between feedback overhead and the achievable sum-rate of IA to obtain the optimal effective performance. Most existing IA performance analysis approaches focus on the vector quantization (VQ)-based feedback strategy, but the implementation complexity of VQ will be excessive when more quantization bits are required to achieve the expected quantization accuracy for larger-sized matrices or higher signal-to-noise ratio (SNR) regimes. Moreover, the obtained achievable sum-rate formulas are too complicated for quick performance evaluation. In this paper, a new sum-rate performance analysis method for IA under different quantization and feedback strategies is proposed to achieve a trade-off between accuracy and complexity, and the closed-form achievable sum-rate expressions are derived. First, in the IA case with random vector quantization (RVQ)-based CSI feedback, the quantization error of RVQ is transformed into the equivalent VQ error of the Gaussian channel error, based on which the achievable sum-rate formula is obtained. Second, in the IA case with scalar quantization (SQ)-based CSI feedback, the relationship between the effective sum-rate and SQ bits is established. Third, in the IA case with SQ-based CSI feedback and RVQ-based DI feedback, the achievable sum-rate formula is derived by combining these two kinds of quantization errors. Finally, the simulation results confirm that the theoretical results are accurate enough, which can help to determine the optimal CSI feedback overhead in practical channel conditions. Moreover, the theoretical and simulation results demonstrate that RVQ may be more applicable to IA scenarios with fewer receiving antennas and low SNR regimes.

Efficient Channel Feedback Scheme for Multi-User MIMO Hybrid Beamforming Systems.

This paper proposes an efficient channel information feedback scheme to reduce the feedback overhead of multi-user multiple-input multiple-output (MU-MIMO) hybrid beamforming systems. As massive machine type communication (mMTC) was considered in the deployments of 5G, a transmitter of the hybrid beamforming system should communicate with multiple devices at the same time. To communicate with multiple devices in the same time and frequency slot, high-dimensional channel information should be used to control interferences between the receivers. Therefore, the feedback overhead for the channels of the devices is impractically high. To reduce the overhead, this paper uses common sparsity of channel and nonlinear quantization. To find a common sparse part of a wide frequency band, the proposed system uses minimum mean squared error orthogonal matching pursuit (MMSE-OMP). After the search of the common sparse basis, sparse vectors of subcarriers are searched by using the basis. The sparse vectors are quantized by a nonlinear codebook that is generated by conditional random vector quantization (RVQ). For the conditional RVQ, the Linde–Buzo–Gray (LBG) algorithm is used in conditional vector space. Typically, elements of sparse vectors are sorted according to magnitude by the OMP algorithm. The proposed quantization scheme considers the property for the conditional RVQ. For feedback, indices of the common sparse basis and the quantized sparse vectors are delivered and the channel is recovered at a transmitter for precoding of MU-MIMO. The simulation results show that the proposed scheme achieves lower MMSE for the recovered channel than that of the linear quantization scheme. Furthermore, the transmitter can adopt analog and digital precoding matrix freely by the recovered channel and achieve higher sum rate than that of conventional codebook-based MU-MIMO precoding schemes.

Reduced Complexity Recursive Grassmannian Quantization

We propose a novel recursive multi-stage approach to Grassmannian quantization. Compared to the commonly employed single-stage quantization, our method has the advantage of significantly decreasing the number of codebook searches required for quantization and, thus, reducing the complexity. On the downside, the multi-stage approach causes a slight rate-distortion degradation compared to single-stage quantization. We analyze the rate-distortion performance of the proposed recursive quantization approach, considering random vector quantization within the individual stages. We furthermore propose a bit-allocation optimization amongst the stages of the quantizer, given a constraint on the total number of quantization bits.

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.

NOVEL PRE-PROCESSING FRAMEWORK TO IMPROVE CLASSIFICATION ACCURACY IN OPINION MINING

The growth of information technology led to the Internet development that in turn helped people in many ways. The major one is to express their views about the products and services through reviews, blogs, feedback, and comments on the website and in social media. The buyers are forced to go through investigation on these reviews/blogs, before choosing any product or service. Out of all online services, Mobile learning app places a vital role to increase the thirst for knowledge. But to identify the suitable mobile learning app, the opinions of the existing customers need to be mined. This research paper analyzes the mobile learning reviews which are available in the corpus. A novel preprocessing framework is proposed in this paper to improve classification accuracy in the dataset - mobile learning app review dataset. The corpus dimension is reduced using SVD through which, the data is prepared for mining. The classification accuracy is evaluated by applying Multinomial Naïve Bayes, Random Forest data mining algorithms and Learning Vector Quantization (LVQ), Elman Neural Network (ENN), Feed Forward Neural Network (FFNN) algorithms with the dataset obtained by the proposed processing method.

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.

Hybrid Precoding Architecture for Massive Multiuser MIMO With Dissipation: Sub-Connected or Fully Connected Structures?

In this paper, we study the hybrid precoding structures over limited feedback channels for massive multiuser multiple-input multiple-output (MIMO) systems. We focus on the system performance of hybrid precoding under a more realistic hardware network model, particularly, with inevitable dissipation. The effect of quantized analog and digital precoding is characterized. We investigate the spectral efficiencies of two typical hybrid precoding structures, i.e., the sub-connected structure and the fully-connected structure. It is revealed that increasing signal power can compensate the performance loss incurred by quantized analog precoding. In addition, by capturing the nature of the effective channels for hybrid processing, we employ a channel correlation-based codebook and demonstrate that the codebook shows a great advantage over the conventional random vector quantization (RVQ) codebook. It is also discovered that, if the channel correlation-based codebook is utilized, the sub-connected structure always outperforms the fully-connected structure in either massive MIMO or low signal-to-noise ratio (SNR) scenarios; otherwise, the fully-connected structrue achieves better performance. Simulation results under both Rayleigh fading channels and millimeter wave (mmWave) channels verify the conclusions above.

Analyzing Coverage Probability of Multitier Heterogeneous Networks Under Quantized Multiuser ZF Beamforming

In this paper, we analyze the coverage probability of a large-scale heterogenous cellular network (HetNet) where base stations (BSs) are equipped with multiantennas, serving a number of single-antenna user equipments (UEs) in the downlink—space division multiple access (SDMA). Adopting the tool of stochastic geometry, we analyze the coverage probability under the quantized zero-forcing beamforming (ZFBF). This analysis, however, intricate as a typical UE in a given cell experiences: i) a residual inter-user interference (IUI) rendered by the quantization error; ii) quantization-driven statistical correlation between its attending signal power and IUI; iii) Nakagami-type fading environment, induced by postprocessing ZFBF; and iv) intercell interference (ICI). Current related literature has not effectively accounted for issues (i), (ii), and (iv) and commonly resorted to simplifying scenarios of full SDMA (i.e., exponential fading), independency of IUI and attending signal power, approximating IUI via an exponential random variable, and the quantization cell approximation (QCA). Our analysis relaxes such limiting assumptions; it includes the more relevant random vector quantization (RVQ) method, and compared to the literature, does not resort to the evaluation of a higher order differentiation for the evaluation of the coverage probability by exploiting our previously developed method. We further introduce three novel approximations of the coverage probability: RVQ-M , RVG-G , and QCA , which the first two approximations are given in semi-closed-form formulas (requiring a simple integration step) and the last approximation is in a closed-form expression. All approximations are numerically affordable, and we confirm the RVG-G approximation is the most accurate one. Finally, we exploit our analysis to study several practically insightful issues to shed some lights on: 1) for given feedback capacity and number of UEs, when desification becomes beneficial; 2) how multitierness of HetNets can be exploited for substantially reducing feedback capacity; and 3) an adaptive share of feedback capacity for the purpose of CDI as well as channel quality information (CQI) feedbacks, when there is an uplink penalty subjected for the feedback procedure and the scheduled data rate at each BS is specified adaptively based on the quantized CQI.

MMSE-Based Precoding for Rate Splitting Systems With Finite Feedback

In this letter, to tackle the inevitable effects of imperfect channel state information caused by finite feedback, we investigate a rate splitting transmission scheme proposed recently, which splits one symbol into a common part and a private part, and transmits signals simultaneously after superposition. First, we propose a minimum mean square error precoding to further suppress the imperfectness of the channel, in which random vector quantization is considered and a closed-form expression is derived. Then, utilizing an approximate expression of the quantization error, we develop a modified power allocation scheme for different parts of symbols by minimizing the sum-rate loss. Numerical results demonstrate the performance gains of the proposed schemes.

Efficient Uniform Channel Quantization of Sparse CIR for Downlink OFDM Systems

Channel state information at the transmitter side is an important issue for wireless communications systems, namely when precoding techniques are employed. Recent works explored random vector quantization (RVQ) as a solution for limited feedback for multi-user systems equipped with multiple antennas. Despite of being a good option for narrowband channels, this method requires large complexity and is not efficient for sparse channels. To overcome these drawbacks we consider a strategy based on uniform quantization, denoted partial uniform quantization (P-UQ), where just part of channel frequency response is quantized. This allows an efficient feedback of channel frequency response from the receivers to the transmitter, by using a reduced number of quantization bits. The comparison between the proposed P-UQ-based method and RVQ performed in this paper leads to the conclusion that the most advantageous method for sparse channels is the P-UQ.

Limited-Feedback Massive MISO Systems With Trellis-Coded Quantization for Correlated Channels

In this paper, we propose trellis coded quantization (TCQ) based limited feedback techniques for massive multiple-input single-output (MISO) frequency division duplexing (FDD) systems in temporally and spatially correlated channels. We exploit the correlation present in the channel to effectively quantize channel direction information (CDI). For multiuser (MU) systems with matched-filter (MF) precoding, we show that the number of feedback bits required by the random vector quantization (RVQ) codebook to match even a small fraction of the perfect CDI signal-to-interference-plus-noise ratio (SINR) performance is large. With such large numbers of bits, the exhaustive search required by conventional codebook approaches make them infeasible for massive MISO systems. Motivated by this, we propose a differential TCQ scheme for temporally correlated channels that transforms the source constellation at each stage in a trellis using 2D translation and scaling techniques. We derive a scaling parameter for the source constellation as a function of the temporal correlation and the number of BS antennas. We also propose a TCQ based limited feedback scheme for spatially correlated channels where the channel is quantized directly without performing decorrelation at the receiver. Simulation results show that the proposed TCQ schemes outperform the existing noncoherent TCQ (NTCQ) schemes, by improving the spectral efficiency and beamforming gain of the system. The proposed differential TCQ also reduces the feedback overhead of the system compared to the differential NTCQ method.

Channel Magnifying Limited Feedback Technique for FDD Massive MIMO Systems

A limited feedback system, so-called, channel magnifying (CM) is proposed for a downlink (DL) frequency-division duplex (FDD) massive multiple-input multiple-output (MIMO) system. Although massive MIMO system has received significant research interest as a key technology for beyond 4G wireless communications systems, it has a number of issues that needs to be technically addressed. Among such issues is the difficulty of acquiring channel state information at transmitter for an FDD massive MIMO system which cannot exploit channel reciprocity as in a time-division duplex system. The proposed CM technique makes it possible to support a few user equipments in DL FDD massive MIMO system by finding a balance between spatial resources and channel quantization error (CQE). By choosing a subchannel with low CQE, CM can secure multiplexing gain at high SNR based on a fixed size codebook. Two types of subchannel indicator alignment (SIA) schemes are introduced for efficient interference nulling for the proposed CM technique. Specifically, we discuss how to maximize the sumrate of CM through genie added SIA and minimum CQE based SIA. Simulation results show that the sum rate of the proposed CM has a higher multiplexing gain than that of random vector quantization, especially when the number of transmit antennas is sufficiently large.

On Performance and Feedback Strategy of Secure Multiuser Communications With MMSE Channel Estimate

In this paper, we investigate a multiuser MIMO downlink with imperfect channel state information (CSI) from the physical-layer security provision. In a classical transmitter (Alice)–legitimate receiver (Bob)–eavesdropper (Eve) model using artificial noise to disturb Eve’s reception, we consider a general scenario where all nodes are equipped with multiple antennas, and Bob’s CSI is acquired by pilot-assisted channel estimation. For designing the secure transmit beamforming, we utilize random matrix quantization (RMQ) to quantize Bob’s channel estimate, and then Bob feeds it back to Alice. Due to the effects of imperfect CSI at Alice, the secrecy performance is upper bounded in the high signal-to-noise ratio (SNR) regions. In order to avoid the interference-limited phenomenon, we present a scaled strategy for the secrecy system utilizing derived upper bound on the secrecy rate loss. Moreover, it is shown that our derived results can be easily extended to a special case where both legitimate and eavesdropping receivers equip a single antenna each, where random vector quantization (RVQ) is utilized instead. By employing our proposed feedback strategy, the secrecy rate increases with transmit power, and the certain secrecy requirement can be guaranteed.

Sensitivity Analysis for RVQ-Based Tomlinson–Harashima Precoded MIMO Systems

Tomlinson-Harashima precoded (THP) multiple-input-multiple-output (MIMO) systems are developed to cancel the intersymbol interference (ISI) at the transmitter. However, the THP at least requires perfect channel direction information (CDI) to completely mitigate the interference at the transmitter, which is not practical in the real world. The limited feedback systems are then practically developed to convey the quantized CDI to the transmitter. Using the quantized CDI to conduct the THP, an unavoidable interference degrades the performance at the receiver. In this paper, we investigate the performance degradation resulted from the random vector quantization (RVQ), which is a kind of CDI-based limited feedback mechanism. Here, we measure the performance degradation as the excess mean-squared error (EMSE). Since the formulation of the EMSE is a complicated function of the quantization error, we proposed using the second-order Taylor expansion to derive an analytical result. Simulation results have also verified our proposed analysis, showing that the derived analysis can match the actual EMSE.

Interference Alignment With Quantized Grassmannian Feedback in the K-User Constant MIMO Interference Channel

A simple channel state information (CSI) feedback scheme is proposed for interference alignment (IA) over the K-user constant multiple-input-multiple-output interference channel (MIMO IC). The proposed technique relies on the identification of invariants in the IA equations, which enables the reformulation of the CSI quantization problem as a single quantization on the Grassmann manifold at each receiver. The scaling of the number of feedback bits with the transmit power sufficient to preserve the multiplexing gain that can be achieved under perfect CSI is established. We show that the CSI feedback requirements of the proposed technique are better (lower) than what is required when using previously published methods (including state-of-the-art codebook-based as well as analog feedback techniques), for system dimensions (number of users and antennas) of practical interest. Furthermore, we show through simulations that this advantage persists at low SNR, in the sense that the proposed technique yields a higher sum-rate performance for a given number of feedback bits. Finally, to complement our analysis, we introduce a statistical model that faithfully captures the properties of the quantization error obtained for random vector quantization (RVQ) on the Grassmann manifold for large codebooks; this enables the numerical (Monte Carlo) analysis of general Grassmannian RVQ schemes for codebook sizes that would be impractically large to simulate.

Coordinated Regularized Zero-Forcing Precoding for Multicell MISO Systems with Limited Feedback

We investigate coordinated regularized zero-forcing precoding for limited feedback multicell multiuser multiple-input single-output systems. We begin by deriving an approximation to the expected signal-to-interference-plus-noise ratio for the proposed scheme with perfect channel direction information (CDI) at the base station (BS). We also derive an expected SINR approximation for limited feedback systems with random vector quantization (RVQ) based codebook CDI at the BS. Using the expected interference result for the RVQ based limited feedback CDI, we propose an adaptive feedback bit allocation strategy to minimize the expected interference by partitioning the total number of bits between the serving and out-of-cell interfering channels. Numerical results show that the proposed adaptive feedback bit allocation method offers a spectral efficiency gain over the existing coordinated zero-forcing scheme.

Codebook Size Design for RVQ-Based Tomlinson–Harashima Precoded MIMO Broadcast Channels

In this paper, we study the codebook size design strategies in the multiple-input–multiple-output (MIMO) broadcast channel (BC) systems. We adopt the nonlinear Tomlinson–Harashima precoder (THP), which is designed by the imperfect channel direction information (CDI) acquired from the random vector quantization (RVQ) feedback mechanism. Under the limitation of the total feedback rate, we flexibly allocate the size of each user's codebook so that the overall channel capacity is maximized. Since the design problem is not convex, directly finding out the optimum allocation of codebook size is not attainable. However, by sophisticatedly using the discrete majorization theory, we can derive the codebook size allocation strategies for the high- and the low-signal-to-noise-ratio (SNR) regions. Interestingly, the results show that the equal size codebook is preferable in the low-SNR region, whereas the codebook allocates the whole available codebook size to a single user in the high-SNR region. Simulations certify the theoretical result of our design.

Guaranteeing Positive Secrecy Capacity for MIMOME Wiretap Channels With Finite-Rate Feedback Using Artificial Noise

While the impact of finite-rate feedback on the capacity of fading channels has been extensively studied in the literature, not much attention has been paid to this problem under secrecy constraint. In this work, we study the ergodic secret capacity of a multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channel with quantized channel state information (CSI) at the transmitter and perfect CSI at the legitimate receiver, under the assumption that only the statistics of eavesdropper CSI is known at the transmitter. We refine the analysis of Lin et al. 's random vector quantization (RVQ) based artificial noise (AN) scheme, where a heuristic upper bound on the secrecy rate loss (compared to the perfect CSI case) was given. We propose a lower bound on the ergodic secrecy capacity. We show that the lower bound and the secrecy capacity with perfect CSI coincide asymptotically as the number of feedback bits and the AN power go to infinity. For practical applications, we propose a very efficient quantization codebook construction method for the two transmit antennas case.