A multiscale relaxation algorithm for SNR maximization innonorthogonal subband coding

Develops a technique for improving the applicability of complete, nonorthogonal, multiresolution transforms to image coding. As is well known, the L(2) norm of the quantization errors is not preserved by nonorthogonal transforms, so the L(2) reconstruction error may be unacceptably large. However, given the quantizers and synthesis filters, the authors show that this artifact can be eliminated by formulating the coding problem as that of minimizing the L(2) reconstruction error over the set of possible encoded images. With this new formulation, the coding problem becomes a high-dimensional, discrete optimization problem and features a coupling between the redundancy-removing and quantization operations. A practical solution to the optimization problem is presented in the form of a multiscale relaxation algorithm, using inter- and intrascale quantization noise feedback filters. Bounds on the coding gain over the standard coding technique are derived. A simple extension of the algorithm allows for the use of a weighted L(2) error criterion and deadband (non-MMSE) quantizers. Experiments using biorthogonal spline filter banks demonstrate appreciable SNR gains over the standard coding technique, and comparable visual improvements.     

Perfect reconstruction versus MMSE filter banks in source coding

Classically, the filter banks (FBs) used in source coding schemes have been chosen to possess the perfect reconstruction (PR) property or to be maximally selective quadrature mirror filters (QMFs). This paper puts this choice back into question and solves the problem of minimizing the reconstruction distortion, which, in the most general case, is the sum of two terms: a first one due to the non-PR property of the FB and the other being due to signal quantization in the subbands. The resulting filter banks are called minimum mean square error (MMSE) filter banks. Several quantization noise models are considered. First, under the classical white noise assumption, the optimal positive bit rate allocation in any filter bank (possibly nonorthogonal) is expressed analytically, and an efficient optimization method of the MMSE filter banks is derived. Then, it is shown that while in a PR FB, the improvement brought by an accurate noise model over the classical white noise one is noticeable, it is not the case for the MMSE FB. The optimization of the synthesis filters is also performed for two measures of the bit rate: the classical one, which is defined for uniform scalar quantization, and the order-one entropy measure. Finally, the comparison of rate-distortion curves (where the distortion is minimized for a given bit rate budget) enables us to quantify the SNR improvement brought by MMSE solutions     

Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design     

Analysis of Multiple Antenna Systems With Finite-Rate Channel Information Feedback Over Spatially Correlated Fading Channels

This paper employs a high resolution quantization framework to study the effects of finite-rate quantization of the channel state information (CSI) on the performance of MISO systems over correlated fading channels. The contributions of this paper are twofold. First, as an application of the general distortion analysis, tight lower bounds on the capacity loss of correlated MISO systems due to the finite-rate channel quantization are provided. Closed-form expressions for the capacity loss in high-signal-to-noise ratio (SNR) and low-SNR regimes are also provided, and their analysis reveals that the capacity loss of correlated MISO channels is related to that of i.i.d. fading channels by a simple multiplicative factor which is given by the ratio of the geometric mean to the arithmetic mean of the eigenvalues of the channel covariance matrix. Second, this paper extends the general asymptotic distortion analysis to the important practical problem of suboptimal quantizers resulting from mismatches in the distortion functions, source statistics, and quantization criteria. As a specific application, two types of mismatched MISO CSI quantizers are investigated: quantizers whose codebooks are designed with minimum mean square error (MMSE) criterion but the distortion measure is the ergodic capacity loss (i.e., mismatched design criterion), and quantizers with codebook designed with a mismatched channel covariance matrix (i.e., mismatched statistics). Bounds on the channel capacity loss of the mismatched codebooks are provided and compared to that of the optimal quantizers. Finally, numerical and simulation results are presented and they confirm the tightness of theoretical distortion bounds.     

Finite Precision Analysis for Space-Time Decoding

Low complexity optimal (or nearly optimal) decoders for space-time codes have recently been under intensive investigation. For example, recent works by Sirianunpiboon and others show that the Silver code and the Golden code can be decoded optimally (or nearly optimally) with quadratic decoding complexity. Fast decodability makes them very attractive in practice. In implementing these decoders, floating-point to fixed-point conversion (FFC) needs to be carefully undertaken to minimize hardware cost while retaining decoding performance. The process of quantization for fixed-point representations is often ignored by research community and lacks investigation, and so FFC is often conducted heuristically based on simulations. This paper studies the effects of quantization to space-time coded systems from an information theoretic perspective. It shows the analytical relationship between quantization error and decoding performance deterioration. This paper also proposes a general finite precision implementation methodology including two FFC criteria for space-time coded systems within an integer optimization framework. As a particular example, this paper examines the finite precision implementation of the quadratic optimal decoding algorithm of the Silver code. However, our methodology and techniques can be applied to general space-time codes.      

单载波频域均衡系统中基于信道频域响应的密钥生成机制研究

单载波频域均衡(SC-FDE)系统中,信道的频域响应可以作为随机源来生成密钥。为了提高密钥容量,该文提出一种利用多径瑞利信道的频域响应来生成密钥的机制(CFR-Key)。首先研究了CFR-Key机制的原理和密钥生成速率,通过互信息理论推导出了CFR-Key的密钥容量;进而研究了CFR-Key机制中算法的量化等级的影响因素,推导验证了量化等级的选择只与信噪比有关,当信噪比确定的情况下通过选择最优的量化等级可以得到最大的密钥生成速率;与基于信道冲激响应生成密钥机制(CIR-Key)对比,证实了CFR-Key机制可大幅提高密钥容量。     

无线传感器网络中基于多比特量化的极大似然分布式估计方法

在无线传感器网络背景下的分布式估计中,由于传输网络对发送功率和传输带宽的限制,压缩信源冗余、降低通信数据量便成为一个重要的课题.为此,本文提出了一种基于多比特量化观测的分布式估计方法（MQS）,利用渐进性能作为优化准则构造量化阈值优化问题,运用粒子群算法对其进行求解得到最优量化阈值,给出了克拉美罗下界的解析表达式,并与均匀量化方法（UQS）和未量化方法（NQS）进行对比.理论分析和仿真实验表明,MQS的性能优于UQS.当量化深度增大到3时,MQS的估计性能十分接近NQS的估计性能.     

On spatial quantization of color images

Image quantization and digital halftoning, two fundamental image processing problems, are generally performed sequentially and, in most cases, independent of each other. Color reduction with a pixel-wise defined distortion measure and the halftoning process with its local averaging neighborhood typically optimize different quality criteria or, frequently, follow a heuristic approach without reference to any quantitative quality measure. In this paper, we propose a new model to simultaneously quantize and halftone color images. The method is based on a rigorous cost-function approach which optimizes a quality criterion derived from a simplified model of human perception. It incorporates spatial and contextual information into the quantization and thus overcomes the artificial separation of quantization and halftoning. Optimization is performed by an efficient multiscale procedure which substantially alleviates the computational burden. The quality criterion and the optimization algorithms are evaluated on a representative set of artificial and real-world images showing a significant image quality improvement compared to standard color reduction approaches. Applying the developed cost function, we also suggest a new distortion measure for evaluating the overall quality of color reduction schemes.     

人工噪声辅助安全传输中的反馈比特数研究人工噪声辅助安全传输中的反馈比特数研究

本文主要研究了人工噪声辅助的多输入单输出（Multiple-input Single-output, MISO）物理层安全传输系统中的最小反馈比特数问题。论文对信道方向信息采用基于随机矢量量化（Random Vector Quantization, RVQ）的码本反馈方法,首先定量分析了RVQ量化导致的系统保密速率损失,充分考虑不同发送信噪比条件与量化误差的特点,推导出了所需最小反馈比特数的闭合表达式。分析表明为保持恒定的遍历保密容量损失,反馈比特数应随对数信噪比及(Nt-1)线性变化（Nt为发送天线数）。理论分析和仿真结果表明,依据本文得到的闭合表达式调整反馈比特数,可以满足系统的安全性能要求。现有研究没有考虑信噪比较低的情况,而本文的结论适用于各种信噪比情况,对于人工噪声辅助的物理层安全传输策略实用化具有指导意义。      

On optimum power allocation for the V-BLAST

A unified analytical framework for optimum power allocation in the unordered V-BLAST algorithm and its comparative performance analysis are presented. Compact closed-form approximations for the optimum power allocation are derived, based on average total and block error rates. The choice of the criterion has little impact on the power allocation and, overall, the optimum strategy is to allocate more power to lower step transmitters and less to higher ones. High-SNR approximations for optimized average block and total error rates are given. The SNR gain of optimization is rigorously defined and studied using analytical tools, including lower and upper bounds, high and low SNR approximations. The gain is upper bounded by the number of transmit antennas, for any modulation format and type of fading channel. While the average optimization is less complex than the instantaneous one, its performance is almost as good at high SNR. A measure of robustness of the optimized algorithm is introduced and evaluated. The optimized algorithm is shown to be robust to perturbations in individual and total transmit powers. Based on the algorithm robustness, a pre-set power allocation is suggested as a low-complexity alternative to the other optimization strategies, which exhibits only a minor loss in performance over the practical SNR range.     

Distance criterion-based quantizer design for cooperative spectrum sensing

In terms of sensing node’s energy and reporting channel’s bandwidth constrains problem for cooperative spectrum sensing in cognitive radio networks,an optimal quantizer design method based on distance criterion was proposed.First of all,the Bhattacharyya distance of received quantized data at the fusion center (FC) was calculated as performance criteria,the optimization mathematical model of the quantizer was constructed,and the optimum quantization thresholds were obtained by using particle swarm optimization algorithm.According to received sensing nodes’ quantized data at the FC,a log-likelihood ratio detector was constructed to decide the presence or absence of primary user signal,the upper bound to sensing performance of energy detector that without quantization was derived.Compared with the existing methods in literatures,the performance of proposed 3-bit quantization method approaches to the upper bound performance of energy detector,under the premise of obtaining comparable detection performance,the requirement of communication bandwidth is reduced.     

Computation reduction for standard-based video encoders based on the energy preservation property of DCT

Based on the energy preservation property of DCT, an optimization technique for motion estimation (ME), DCT, and quantization for standard-based video encoders is developed. First, a stopping criterion for ME is proposed to reduce the number of checking points in finding the motion vectors, and save the computations. The advantage of introducing such a stopping criterion lies in its adaptability to the quantization parameter and applicability to various fast ME algorithms. Then, the DCT and quantization are jointly optimized by tracing the remaining signal energy and removing unnecessary calculations in the process of DCT and quantization. A pruned 2-D DCT based on Huang's fast DCT algorithm is presented to demonstrate the superiority of this algorithm to the full DCT and an existing all-zero block detection method. Although proved to be computationally efficient, the algorithms introduce no obvious quality loss.     

Maximum likelihood estimation and Cramer-Rao bounds for directionof arrival parameters of a large sensor array

A maximum likelihood (ML) method is developed for estimation of direction of arrival (DOA) and associated parameters of narrowband signals based on the Taylor's series expansion of the inverse of the data covariance matrix R for large M, M specifying number of sensors in the array. The stochastic ML criterion function can thus be simplified resulting in a computationally efficient algorithm for DOA estimation. The more important result is the derivation of asymptotic (large M) expressions for the Cramer-Rao lower bound (CRB) on the covariance matrix of all unknown DOA angles for the general D source case. The derived bound is expressed explicitly as a function of snapshots, signal-to-noise ratio (SNR), sensors, separation, and correlation between signal sources. Using the condition of positive definiteness of the Fisher information matrix a resolution criterion is proposed which gives a tight lower limit on the minimum resolvable angle     

12位Sigma-Delta模数转换器的降采样滤波器设计

一种由SNR（信噪比）驱动的滤波器设计,用于12位Sigma-Delta模数转换器。Sigma-Delta模数转换器包括Sigma-Delta调制器和降采样滤波器两部分,首先用Sigma-Delta调制器对信号进行过采样率量化,然后通过降采样滤波器进行数字信号处理,将信号还原到原始采样率并去除量化噪声。和传统的模数转换器相比,Sigma-Delta模数转换器具有采样率高、精度高、面积小等优点。Sigma-Delta模数转换器的滤波器设计有降采样率和滤波性能两个指标要求,该设计方法由SNR驱动并采用了两种滤波器方案,设计结果在MATLAB里进行了仿真,其SNR大于74 dB,达到12位Sigma-Delta模数转换器的要求。     

Optimum spreading bandwidth for selective RAKE reception overRayleigh fading channels

Building on the developments in the performance analysis of generalized selection combining (GSC), this paper examines the optimum spreading bandwidth for a fixed-complexity GSC diversity receiver operating over independent identically distributed Rayleigh paths. For this purpose, the study considers three performance criteria: (1) average combined signal-to-noise ratio (SNR) at the GSC output; (2) average bit error probability (BEP); and (3) outage probability of the instantaneous combined SNR at the GSC output. For the average BEP criterion, results are presented for both coherent and noncoherent combining. For the average combined SNR and some instances of the average BEP optimization problem, an accurate approximate estimate of this optimum bandwidth in the form of a solution of a transcendental equation is provided. In other cases, where the optimization is not easily tractable in an analytic fashion, a numeric-search procedure is used to find this optimum bandwidth for different performance criteria and system parameters of interest. Finally, simplified rule-of-thumb-type formulas are also presented as a good reference for picking the optimum spreading bandwidth given a set of system parameters and a particular performance criterion of interest     

Rate-distortion optimization of scalable video codecs

In this paper joint optimization of layers in the layered video coding is investigated. Through theoretical analysis and simulations, it is shown that, due to higher interactions between the layers in a SNR scalable codec, this type of layering technique benefits most from joint optimization of the layers. A method for joint optimization is then proposed, and its compression efficiency is contrasted against the separate optimization and an optimized single layer coder. It is shown that, in joint optimization of SNR scalable coders when the quantization step size of the enhancement layer is larger than half the step size of the base layer, an additional improvement is gained by not sending the enhancement zero valued quantized coefficients, provided they are quantized at the base-layer. This will result in a non-standard bitstream syntax and as an alternative for standard syntax, one may skip the inter coded enhancement macroblocks. Through extensive tests it is shown that while separate optimization of SNR coders is inferior to single layer coder by more than 2 dB, with joint optimization this gap is reduced to 0.3–0.5 dB. We have shown that through joint optimization quality of the base layer video is also improved over the separate optimization. It is also shown that spatial scalability like SNR scalability does benefit from joint optimization, though not being able to exploit the relation between the quantizer step sizes. The amount of improvement depends on the interpolation artifacts of upsampled base-layer and the residual quantization distortion of this layer. Hence, the degree of improvement depends on image contents as well as the bit rate budget. Simulation results show that joint optimization of spatial scalable coders is about 0.5–1 dB inferior to the single layer optimized coder, where its separate optimization counterpart like SNR scalability is more than 2 dB worse.     

The asymptotic closed-loop approach to predictive vector quantizerdesign with application in video coding

The basic vector quantization (VQ) technique employed in video coding belongs to the category of predictive vector quantization (PVQ), as it involves quantization of the (motion compensated) frame prediction error. It is well known that the design of PVQ suffers from fundamental difficulties, due to the prediction loop, which have an impact on the convergence and the stability of the design procedure. We propose an approach to PVQ design that enjoys the stability of open-loop design while it ensures ultimate optimization of the closed-loop system. The method is derived for general predictive quantization, and we demonstrate it on video compression at low bit rates, where it provides substantial improvement over standard open and closed loop design techniques. Further, the approach outperforms standard DCT-based video coding.     

Blocking effect reduction of compressed images using classification-based constrained optimization

In this paper we propose an adaptive image restoration algorithm using block-based edge-classification for reducing block artifacts in compressed images. In order to efficiently reduce block artifacts, edge direction of each block is classified by using model-fitting criterion, and the constrained least-squares (CLS) filter with corresponding direction is used for restoring the block. The proposed restoration filter is derived based on the observation that the quantization operation in a series of coding processes is a nonlinear and many-to-one mapping operator. Then we propose an approximated version of a constrained optimization technique as a restoration process for removing the nonlinear and space-varying degradation operator. For real-time implementation, the proposed restoration filter can be realized in the form of a truncated FIR filter, which is suitable for postprocessing reconstructed images in digital TV, video conferencing systems, etc.     

Power allocation of data dependent superimposed training

Data Dependent Superimposed Training （DDST） scheme outperforms the traditional superimposed training by fully canceling the effects of unknown data in channel estimator. In DDST, however, the channel estimation accuracy and the data detection or channel equalization performance are affected significantly by the amount of power allocated to data and superimposed training sequence, which is the motivation of this research. In general, for DDST, there is a tradeoff between the channel estimation accuracy and the data detection reliability, i.e., the more accurate the channel estimation, the more reliable the data detection; on the other hand, the more accurate the channel estimation, the more demanding on the power consumption of training sequence, which in turn leads to the less reliable data detection. In this paper, the relationship between the Signal-to-Noise Ratio （SNR） of the data detector and the training sequence power is analyzed. The optimal power allocation of the training sequence is derived based on the criterion of maximizing SNR of the detector. Analysis and simulation results show that for a fixed transmit power, the SNR and the Symbol Error Rate （SER） of detector vary nonlinearly with the increasing of training sequence power, and there exists an optimal power ratio which accords with the derived optimal power ratio, among the data and training sequence.     

Channel Adaptive Quantization for Limited Feedback MIMO Beamforming Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining techniques. In the absence of full channel knowledge at the transmitter, the transmit beamforming vector can be quantized at the receiver and sent to the transmitter using a low-rate feedback channel. In the literature, quantization algorithms for the beamforming vector are designed and optimized for a particular channel distribution, commonly the uncorrelated Rayleigh distribution. When the channel is not uncorrelated Rayleigh, however, these quantization strategies result in a degradation of the receive signal-to-noise ratio (SNR). In this paper, switched codebook quantization is proposed where the codebook is dynamically chosen based on the channel distribution. The codebook adaptation enables the quantization to exploit the spatial and temporal correlation inherent in the channel. The convergence properties of the codebook selection algorithm are studied assuming a block-stationary model for the channel. In the case of a nonstationary channel, it is shown using simulations that the selected codebook tracks the distribution of the channel resulting in improvements in SNR. Simulation results show that in the case of correlated channels, the SNR performance of the link can be significantly improved by adaptation, compared with nonadaptive quantization strategies designed for uncorrelated Rayleigh-fading channels