Grassmannian beamforming for MIMO amplify-and-forward relaying

We consider the problem of beamforming codebook design for limited feedback half-duplex multiple-input multiple output (MIMO) amplify-and-forward (AF) relay system. In the first part of the paper, the direct link between the source and the destination is ignored. Assuming perfect channel state information (CSI), we show that the source and the relay should map their signals to the dominant right singular vectors of the source-relay and relay-destination channels. For the limited feedback scenario, we prove the appropriateness of Grassmannian codebooks as the source and relay beamforming codebooks based on the distributions of the optimal source and relay beamforming vectors. In the second part of the paper, the direct link is considered in the problem model. Assuming perfect CSI, we derive the optimization problem that identifies the optimal source beamforming vector and show that the solution to this problem is uniformly distributed on the unit sphere for independent and identically distributed (i.i.d) Rayleigh channels. For the limited feedback scenario, we justify the appropriateness of Grassmannian codebooks for quantizing the optimal source beamforming vector based on its distribution. Finally, a modified quantization scheme is presented, which introduces a negligible penalty in the system performance but significantly reduces the required number of feedback bits.     

Constrained-storage vector quantization with a universal codebook

Many image compression techniques require the quantization of multiple vector sources with significantly different distributions. With vector quantization (VQ), these sources are optimally quantized using separate codebooks, which may collectively require an enormous memory space. Since storage is limited in most applications, a convenient way to gracefully trade between performance and storage is needed. Earlier work addressed this problem by clustering the multiple sources into a small number of source groups, where each group shares a codebook. We propose a new solution based on a size-limited universal codebook that can be viewed as the union of overlapping source codebooks. This framework allows each source codebook to consist of any desired subset of the universal code vectors and provides greater design flexibility which improves the storage-constrained performance. A key feature of this approach is that no two sources need be encoded at the same rate. An additional advantage of the proposed method is its close relation to universal, adaptive, finite-state and classified quantization. Necessary conditions for optimality of the universal codebook and the extracted source codebooks are derived. An iterative design algorithm is introduced to obtain a solution satisfying these conditions. Possible applications of the proposed technique are enumerated, and its effectiveness is illustrated for coding of images using finite-state vector quantization, multistage vector quantization, and tree-structured vector quantization.     

On transceiver design and channel quantization for downlink multiuser MIMO systems with limited feedback

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments.     

The Effect of Finite Rate Feedback on CDMA Signature Optimization and MIMO Beamforming Vector Selection

We analyze the effect of finite rate feedback on code-division multiple-access (CDMA) signature optimization and multiple-input multiple-output (MIMO) beamforming vector selection. In CDMA signature optimization, for a particular user, the receiver selects a signature vector from a codebook to best avoid interference from other users, and then feeds the corresponding index back to the specified user. For MIMO beamforming vector selection, the receiver chooses a beamforming vector from a given codebook to maximize the instantaneous information rate, and feeds back the corresponding index to the transmitter. These two problems are dual: both can be modeled as selecting a unit norm vector from a finite size codebook to ldquomatchrdquo a randomly generated Gaussian matrix. Assuming that the feedback link is rate limited, our main result is an exact asymptotic performance formula where the length of the signature/beamforming vector, the dimensions of interference/channel matrix, and the feedback rate approach infinity with constant ratios. The proof rests on the large deviations of the underlying random matrix ensemble. Further, we show that random codebooks generated from the isotropic distribution are asymptotically optimal not only on average, but also in probability.     

Residual vector quantization using a multilayer competitive neuralnetwork

This paper presents a new technique for designing a jointly optimized residual vector quantizer (RVQ). In conventional stage-by-stage design procedure, each stage codebook is optimized for that particular stage distortion and does not consider the distortion from the subsequent stages. However, the overall performance can be improved if each stage codebook is optimized by minimizing the distortion from the subsequent stage quantizers as well as the distortion from the previous stage quantizers. This can only be achieved when stage codebooks are jointly designed for each other. In this paper, the proposed codebook design procedure is based on a multilayer competitive neural network where each layer of this network represents one stage of the RVQ. The weight connecting these layers form the corresponding stage codebooks of the RVQ. The joint design problem of the RVQ's codebooks (weights of the multilayer competitive neural network) is formulated as a nonlinearly constrained optimization task which is based on a Lagrangian error function. This Lagrangian error function includes all the constraints that are imposed by the joint optimization of the codebooks. The proposed procedure seeks a locally optimal solution by iteratively solving the equations for this Lagrangian error function. Simulation results show an improvement in the performance of an RVQ when designed using the proposed joint optimization technique as compared to the stage-by-stage design, where both generalized Lloyd algorithm (GLA) and the Kohonen learning algorithm (KLA) were used to design each stage codebook independently, as well as the conventional joint-optimization technique     

Low complexity codebook search method in massive MIMO system

In Massive MIMO systems for 5G networks,precoding technology is one of the key technologies.Aiming at user side codebook search method of the discrete Fourier transform (DFT) rotation codebook,a low complexity search algorithm was proposed.In this algorithm,all horizontal and vertical codebooks were grouped separately according to the characteristics that the precoding vectors with the same column of DFT rotation codebooks had the smallest chordal distance and the smaller chordal distance have the stronger correlation,and then the optimal horizontal and vertical codewords with maximum channel gain were obtained to form 3D precoding code-books.The simulation results indicate that the searching complexity of the proposed method is significantly reduced under conditions of insuring the system performance,moreover,this advantage becomes greater with the number of antennas increasing.     

基于BD-DFT扩展的大规模MIMO码本设计

考虑到大规模多输入多输出（Multiple Input Multiple Output, MIMO）阵列尺寸及外形等因素的限制,本文提出了一种适用于基站采用交叉极化天线面阵的大规模MIMO（Massive MIMO）码本设计方法。该方法综合考虑交叉极化信道的对角化特点和相邻天线之间的相关性,首先设计出与采用交叉极化线阵匹配的码本,进而利用垂直维度天线间的相关性对其进行扩展,最终生成与交叉极化面阵相匹配的码本。仿真结果表明该码本设计方法可使大规模MIMO系统的传输速率和误码率性能得到明显地提升。     

Block transform image coding by multistage vector quantization withoptimal bit allocation

A multistage vector quantization with optimal bit allocation (MVQ-OBA) in the transform domain is presented. A set of bit allocation planes is first obtained by slicing a (scalar) optimal bit allocation map where the number of bits assigned to each coefficient is proportional to the coefficient variance. The set of bit allocation planes determines the coefficients to be used and the codebook size at each stage. The vector dimensionalities are restricted to small values and relatively small codebooks are used, thus reducing both the overhead required for transmitting the codebooks and the complexity in codebook design. The computer simulation results demonstrate that MVQ-OBA is competitive with many other transform coding techniques including variable length transform coding. MVQ-OBA is well suited for progressive transmission     

Partial distortion sensitive competitive learning algorithm foroptimal codebook design

An effective competitive learning algorithm based on the partial distortion theorem is proposed for optimal codebook design. Compared with some representative learning algorithms for codebook design, the proposed algorithm has consistently shown the best performance for designing codebooks of different sizes, especially large size codebooks     

Linear feedback shift registers as vector quantisation codebooks

Linear feedback shift registers with fixed initial conditions can be used as codebooks for vector quantisation data compression methods, avoiding the need to store codebooks at the encoder and decoder. Suboptimal search procedures can be used to effectively search the codebook space with lower complexity, with only modest coding performance penalties     

Image compression based on fuzzy algorithms for learning vectorquantization and wavelet image decomposition

This paper evaluates the performance of an image compression system based on wavelet-based subband decomposition and vector quantization. The images are decomposed using wavelet filters into a set of subbands with different resolutions corresponding to different frequency bands. The resulting subbands are vector quantized using the Linde-Buzo-Gray (1980) algorithm and various fuzzy algorithms for learning vector quantization (FALVQ). These algorithms perform vector quantization by updating all prototypes of a competitive neural network through an unsupervised learning process. The quality of the multiresolution codebooks designed by these algorithms is measured on the reconstructed images belonging to the training set used for multiresolution codebook design and the reconstructed images from a testing set.     

Linearly constrained generalized Lloyd algorithm for reducedcodebook vector quantization

As linearly constrained vector quantization (LCVQ) is efficient for block-based compression of images that require low complexity decompression, it is a “de facto” standard for three-dimensional (3-D) graphics cards that use texture compression. Motivated by the lack of an efficient algorithm for designing LCVQ codebooks, the generalized Lloyd (1982) algorithm (GLA) for vector quantizer (VQ) codebook improvement and codebook design is extended to a new linearly constrained generalized Lloyd algorithm (LCGLA). This LCGLA improves VQ codebooks that are formed as linear combinations of a reduced set of base codewords. As such, it may find application wherever linearly constrained nearest neighbor (NN) techniques are used, that is, in a wide variety of signal compression and pattern recognition applications that require or assume distributions that are locally linearly constrained. In addition, several examples of linearly constrained codebooks that possess desirable properties such as good sphere packing, low-complexity implementation, fine resolution, and guaranteed convergence are presented. Fast NN search algorithms are discussed. A suggested initialization procedure halves iterations to convergence when, to reduce encoding complexity, the encoder considers the improvement of only a single codebook for each block. Experimental results for image compression show that LCGLA iterations significantly improve the PSNR of standard high-quality lossy 6:1 LCVQ compressed images     

Fast Image Coding Algorithm Using Indirect-Index Codebook Based on SMVQ

Side-match vector quantization (SMVQ) achieves better compression performance than vector quantization (VQ) in image coding due to its exploration of the dependence of adjacent pixels. However, SMVQ has the disadvantage of requiring excessive time during the process of coding. Therefore, this paper proposes a fast image coding algorithm using indirect-index codebook based on SMVQ (ⅡC-SMVQ) to reduce the coding time. Two codebooks, named indirect-index codebook (Ⅱ-codebook) and entire-state codebook (ES-codebook), are trained and utilized. The Ⅱ-codebook is trained by using the Linde-Buzo-Gray (LBG) algorithm from side-match information, while the ES-codebook is generated from the clustered residual blocks on the basis of the Ⅱ-codebook. According to the relationship between these two codebooks, the codeword in the Ⅱ-codebook can be regarded as an indicator to construct a fast search path, which guides in quickly determining the state codebook from the ES-codebook to encode the to-be-encoded block. The experimental results confirm that the coding time of the proposed scheme is shorter than that of the previous SMVQ.     

Fast image colourisation based on twin-codebook vector quantisation

A novel colourisation scheme for grey-level images based on twincodebook vector quantisation (TBVQ) is presented. Different from the traditional vector quantiser with the same codebook in the encoding and decoding processes, the proposed TBVQ adopts two different but related codebooks in the encoder and decoder, respectively. During the colourisation process, the target image is first encoded by the greyscale codebook and then decoded by the related chromatic codebook. Experimental results demonstrate the effectiveness and efficiency of the proposed algorithm.     

Multiplication free vector quantization usingL1 distortion measure and its variants

The author considers vector quantization that uses the L (1) distortion measure for its implementation. A gradient-based approach for codebook design that does not require any multiplications or median computation is proposed. Convergence of this method is proved rigorously under very mild conditions. Simulation examples comparing the performance of this technique with the LBG algorithm show that the gradient-based method, in spite of its simplicity, produces codebooks with average distortions that are comparable to the LBG algorithm. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. Once again, by appropriate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. The author applies the techniques in predictive vector quantization of images and demonstrates the viability of multiplication-free predictive vector quantization of image data.     

Vector quantization using tree-structured self-organizing featuremaps

In this paper, we propose a binary-tree structure neural network model suitable for structured clustering. During and after training, the centroids of the clusters in this model always form a binary tree in the input pattern space. This model is used to design tree search vector quantization codebooks for image coding. Simulation results show that the acquired codebook not only produces better-quality images but also achieves a higher compression ratio than conventional tree search vector quantization. When source coding is applied after VQ, the new model performs better than the generalized Lloyd algorithm in terms of distortion, bits per pixel, and encoding complexity for low-detail and medium-detail images     

SCMA codebook design based on resource block constellation

Aiming at the problems of typical sparse code multiple access codebook design scheme based on multidimensional mother constellation that the complexity is high and the minimum Euclidean distance between constellation points on resource blocks is difficult to determine,a SCMA codebook design scheme based on resource block constellation was proposed.By converting the design of multidimensional mother constellation into the design of two-dimensional resource block constellation,the design complexity of constellation was reduced.And the codebook design scheme starting from resource block constellation could maximize the minimum Euclidean distance between constellation points on resource blocks,which was better than the design method in which user codebooks were obtained from multi-dimensional mother constellation.Simulation results show that the proposed SCMA codebook design scheme based on resource block constellation can significantly improve the BER performance of system compared with the typical codebook design scheme based on multidimensional mother constellation.     

基于二维格星座对SCMA码本的一种设计方法

现有的SCMA(稀疏码分多址)码本采用高维复数星座和映射矩阵相结合的设计方法,存在高维复数星座设计过程复杂,且任意时频资源星座图星座点间的最小欧式距离难以控制的问题.针对上述问题提出了 一种基于时频资源星座的码本设计方法.首先设计一个二维格星座,然后通过星座优化和扩频得到特定用户的码本.所提方法不仅可以获得最大成形增益...     

Variable-length constrained-storage tree-structured vectorquantization

Constrained storage vector quantization, (CSVQ), introduced by Chan and Gersho (1990, 1991) allows for the stagewise design of balanced tree-structured residual vector quantization codebooks with low encoding and storage complexities. On the other hand, it has been established by Makhoul et al. (1985), Riskin et al. (1991), and by Mahesh et al. (see IEEE Trans. Inform. Theory, vol.41, p.917-30, 1995) that variable-length tree-structured vector quantizer (VLTSVQ) yields better coding performance than a balanced tree-structured vector quantizer and may even outperform a full-search vector quantizer due to the nonuniform distribution of rate among the subsets of its input space. The variable-length constrained storage tree-structured vector quantization (VLCS-TSVQ) algorithm presented in this paper utilizes the codebook sharing by multiple vector sources concept as in CSVQ to greedily grow an unbalanced tree structured residual vector quantizer with constrained storage. It is demonstrated by simulations on test sets from various synthetic one dimensional (1-D) sources and real-world images that the performance of VLCS-TSVQ, whose codebook storage complexity varies linearly with rate, can come very close to the performance of greedy growth VLTSVQ of Riskin et al. and Mahesh et al. The dramatically reduced size of the overall codebook allows the transmission of the code vector probabilities as side information for source adaptive entropy coding.