Bounds on maximum likelihood ratio-part I: application to antenna array detection-estimation with perfect wavefront coherence

The multiple hypothesis testing problem of the detection-estimation of an unknown number of independent Gaussian point sources is adequately addressed by likelihood ratio (LR) maximization over the set of admissible covariance matrix models. We introduce nonasymptotic lower and upper bounds for the maximum LR. Since LR optimization is generally a nonconvex multiextremal problem, any practical solution could now be tested against these bounds, enabling a high probability of recognizing nonoptimal solutions. We demonstrate that in many applications, the lower bound is quite tight, with approximate maximum likelihood (ML) techniques often unable to approach this bound. The introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace-based direction-of-arrival (DOA) estimation techniques. We also demonstrate that by proper LR maximization, we can extend the range of signal-to-noise ratio (SNR) values and/or number of data samples wherein accurate parameter estimates are produced. Yet, when the SNR and/or sample size falls below a certain limit for a given scenario, we show that ML estimation suffers from a discontinuity in the parameter estimates: a phenomenon that cannot be eliminated within the ML paradigm.     

Distributed beamforming in wireless relay networks with quantized feedback

This paper is on quantized beamforming in wireless amplify-and-forward (AF) relay networks. We use the generalized Lloyd algorithm (GLA) to design the quantizer of the feedback information and specifically to optimize the bit error rate (BER) performance of the system. Achievable bounds for different performance measures are derived. First, we analytically show that a simple feedback scheme based on relay selection can achieve full diversity. Unlike the previous diversity analysis on the relay selection scheme, our analysis is not aided by any approximations or modified forwarding schemes. Then, for highrate feedback, we find an upper bound on the average signalto- noise ratio (SNR) loss. Using this result, we demonstrate that both the average SNR loss and the capacity loss decay at least exponentially with the number of feedback bits. In addition, we provide approximate upper and lower bounds on the BER, which can be calculated numerically.We observe that our designs can achieve both full diversity as well as high array gain with only a moderate number of feedback bits. Simulations also show that our approximate BER is a reliable estimation on the actual BER. We also generalize our analytical results to asynchronous networks, where perfect carrier level synchronization is not available among the relays.     

DVB-S2 ACM技术中的信噪比估计

为了在DVB-S2系统自适应编码调制(ACM)技术中实现对信道信噪比的精确、高效估计,提出了一种基于子空间分解的数据辅助类信噪比估计算法。计算机仿真结果表明,在较宽的信噪比范围内,该算法的性能优于数据辅助类的最大似然估计算法和经典的基于子空间分解的ED算法,估计精度高,计算复杂度低,非常适合在DVB-S2系统ACM技术中应用。     

A new method for determining “unknown” worst-casechannels for maximum-likelihood sequence estimation

We derive a series of upper and lower bounds for the minimum distance between two noise-free output sequences over unknown channels with fixed-energy finite-duration impulse responses. Using these bounds, we develop a method for determining the minimum distance. Such distance is crucial for determining the worst possible performance of maximum likelihood sequence estimation (MLSE)     

Bayesian bounds for matched-field parameter estimation

Matched-field methods concern estimation of source locations and/or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation. Because of the nonlinear parameter-dependence of the signal field, the estimate is subject to ambiguities and the sidelobe contribution often dominates the estimation error below a threshold signal-to-noise ratio (SNR). To study the matched-field performance, three Bayesian lower bounds on mean-square error are developed: the Bayesian Crame/spl acute/r-Rao bound (BCRB), the Weiss-Weinstein bound (WWB), and the Ziv-Zakai bound (ZZB). Particularly, for a multiple-frequency, multiple-snapshot random signal model, a closed-form minimum probability of error associated with the likelihood ratio test is derived, which facilitates error analysis in a wide scope of applications. Analysis and example simulations demonstrate that 1) unlike the local CRB, the BCRB is not achieved by the maximum likelihood estimate (MLE) even at high SNR if the local performance is not uniform across the prior parameter space; 2) the ZZB gives the closest MLE performance prediction at most SNR levels of practical interest; 3) the ZZB can also be used to determine the necessary number of independent snapshots achieving the asymptotic performance of the MLE at a given SNR; 4) incoherent frequency averaging, which is a popular multitone processing approach, reduces the peak sidelobe error but may not improve the overall performance due to the increased ambiguity baseline; and finally, 5) effects of adding additional parameters (e.g., environmental uncertainty) can be well predicted from the parameter coupling.     

High SNR sum capacity analysis of BD MIMO BC systems with imperfect CSI

We investigate the sum capacity of Block Diagonalization precoding Multiple Input Multiple Output Broadcast Channels (BD MIMO BC) with imperfect Channel State Information (CSI) at the base station. Since it is difficult to obtain the exact expression, a lower and an upper bounds of the sum capacity under Gaussian channel estimation errors are drived instead. Analyses show that the gap between two bounds is considerably tight at all Signal to Noise Ratio (SNR) region. From the lower bound of the sum capacity, we can see that the multiplexing gain tends to be zero at high SNR region, which indicates that the BD MIMO BC system with channel estimation errors is interference-limited at high SNR.     

Adaptive Transmission with Variable-Rate Turbo Bit-Interleaved Coded Modulation

We study an adaptive transmission scheme based on variable-rate turbo bit-interleaved coded modulation (VR- Turbo-BICM). The proposed coding scheme employs punctured turbo codes. A continuously varying transmission rate can be obtained by changing the code rate through both puncturing of the coded bits and adapting of the modulation constellation size. The main results are elaborated in two parts. First, we derive a closed-form expression for a set of achievable rate bounds (called rate thresholds) for VR-Turbo-BICM by employing recent results on the parallel channel performance of turbo code ensembles and the BICM parallel channel analysis model. The derived rate threshold is expressed as a fraction of the capacity of BICM with Gray mapping, where this fraction is a turbo code weight spectrum parameter. Simulation results illustrate that introduced rate thresholds predict well the rate versus SNR performance of VR-Turbo-BICM for a wide range of codeword error probabilities and codeword lengths. Next, based on a simplified rate threshold, we derive a power, puncturing rate, and modulation constellation size assignment policy for a slow fading channel.     

Multichannel MLSE equalizer with parametric FIR channelidentification

We propose a parametric finite impulse response (FIR) channel identification algorithm, apply the algorithm to a multichannel maximum likelihood sequential estimation (MLSE) equalizer using multiple antennas, and investigate the improvement in the overall bit error rate (BER) performance. By exploring the structure of the specular multipath channels, we are able to reduce the number of channel parameters to provide a better channel estimate for the MLSE equalizer. The analytic BER lower bounds of the proposed algorithm as well as those of several other conventional MLSE algorithms in the specular multipath Rayleigh-fading channels are derived. In the derivation, we consider the channel mismatch caused by the additive Gaussian noise and the finite-length channel approximation error. A handy-to-use simplified BER lower bound is also derived. Simulation results that illustrate the BER performance of the proposed algorithm in the global system for mobile communications (GSM) system are presented and compared to the analytic lower bounds     

一种适合软件无线电的符号定时估计算法

研究了一种适合软件无线电的符号定时估计算法,该算法通过并行方法估计线性和非线性调制方式的符号定时。计算机仿真结果表明,通过设置观测时间间隔数和并行估计样本值的个数,算法可以满足多种调制方式对符号定时估计指标的要求,在误比特率为10-5时,相对于理想的相干解调性能,信噪比最大损失0. 5dB。算法全数字实现,复杂度适中,适合于软件无线电系统中对多种调制方式条件下符号定时估计的需要。     

Gaussian mixture density modeling of non-Gaussian source forautoregressive process

A new approach is taken to model non-Gaussian sources of AR processes using Gaussian mixture densities that are known to be effective for approximating wide varieties of probability distributions. A maximum likelihood estimation algorithm is derived for estimating the AR parameters by solving a generalized normal equation, and a clustering algorithm is used for estimating the parameters of Gaussian mixture density of the source signals. The correlation matrix of the generalized normal equation is not Toeplitz but is symmetric and in general positive definite. Higher order statistics of skewness and kurtosis are used for identifying the source distribution as being Gaussian or non-Gaussian and, consequently, determining the parameter estimation technique between the conventional method and the proposed method. Experiments on non-Gaussian source AR processes demonstrate that under high SNR conditions (SNR⩾20 dB), the proposed algorithm outperforms the conventional AR estimation algorithm and the cumulant-based algorithm by an order-of-magnitude reduction of average estimation errors. The proposed algorithm also has very low estimation errors with short data records. Finally, a maximum likelihood prediction method is formulated for non-Gaussian source AR processes that has shown potential in achieving higher efficiency signal coding than linear predictive coding     

基于G.9960协议的高阶QAM调制与解调

G.9960是国际电信联盟(ITU-T)制定的下一代家用网络标准,采用正交频分复用(OFDM)和高阶QAM调制相结合的技术,实现高速可靠的数据传输.将讨论高阶QAM调制和软解调的算法.偶数阶调制使用方形星座图,将格雷码形式排列的二进制序列,映射成复数点;奇数阶调制使用十字型星座,将格雷码形式的二进制序列映射为复数点后,再依据一定的规则加以旋转.基于Bahl等人提出的逐符号最大后验概率译码算法,推导了对数似然比计算公式;由于对数似然比计算涉及对数运算,因此利用取最大值代替指数对数运算来进行简化.仿真结果表明,在AWGN信道下,信噪比为8 dB时,使用简化的软解调算法,2048QAM-LDPC系统的误码率可达到3×10-5,4096QAM-LDPC系统的误码率可达到5×10-4.简化的软解调算法,计算量较小,误码率低,具有良好的性能.     

Upper bounds on sequential decoding performance parameters

This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, oft-order failure (advance to depthtinto an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric biasGis arbitrary. Upper bounds on the Pareto exponent are also presented. TheG-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. TheG-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices ofGand SNR for a binary-input quantized-output Gaussian additive noise channel.     

A genetic algorithm for the maximum likelihood estimation of the parameters of sinusoids in a noisy environment

An adaptive generic algorithm was developed to solve the optimization problem of the maximum likelihood estimation of the sum of sinusoids in a noisy environment. The algorithm is based on genetic concepts and is extended, with modifications, to this problem. Simulation results were performed to see the effect of different parameters such as permutation and crossover probabilities. The effects of the signal-to-noise ratio (SNR) were also studied. It was found that the key factor for accuracy is the probabilities of permutation and crossover. Thus, we developed an adaptive method to estimate these probabilities, on line, to reduce the error. This was accomplished by considering them as unknown parameters to be estimated with the signal parameters. The mean square error of the frequency estimates was compared favorably to the Cramér-Rao lower bound. Several simulations are shown for SNR values ranging between –7 dB and 20 dB.     

A bound on mean-square estimation error with background parameter mismatch

In typical parameter estimation problems, the signal observation is a function of the parameter set to be estimated as well as some background (environmental/system) parameters assumed known. The assumed background could differ from the true one, leading to biased estimates even at high signal-to-noise ratio (SNR). To analyze this background mismatch problem, a Ziv-Zakai-type lower bound on the mean-square error (MSE) is developed based on the mismatched likelihood ratio test (MLRT). At high SNR, the bound incorporates the increase in MSE due to estimation bias; at low SNR, it includes the threshold effect due to estimation ambiguity. The kernel of the bound's evaluation is the error probability associated with the MLRT. A closed-form expression for this error probability is derived under a random signal model typical of the bearing estimation/passive source localization problem. The mismatch is then analyzed in terms of the related ambiguity functions. Examples of bearing estimation with system (array shape) mismatch demonstrate that the developed bound describes the simulations of the maximum-likelihood estimate well, including the sidelobe-introduced threshold behavior and the bias at high SNR.     

Hybrid SNR-Adaptive Multiuser Detectors for SDMA-OFDM Systems

Multiuser detection (MUD) and channel estimation techniques in space-division multiple-access aided orthogonal frequency-division multiplexing systems recently has received intensive interest in receiver design technologies. The maximum likelihood (ML) MUD that provides optimal performance has the cost of a dramatically increased computational complexity. The minimum mean-squared error (MMSE) MUD exhibits poor performance, although it achieves lower computational complexity. With almost the same complexity, an MMSE with successive interference cancellation (SIC) scheme achieves a better bit error rate performance than a linear MMSE multiuser detector. In this paper, hybrid ML-MMSE with SIC adaptive multiuser detection based on the joint channel estimation method is suggested for signal detection. The simulation results show that the proposed method achieves good performance close to the optimal ML performance at low SNR values and a low computational complexity at high SNR values.     

Distributed Space-Time Trellis Codes for a Cooperative System

In this paper, we propose a novel distributed spacetime trellis code (DSTTC) structure, and analyze its error performance in both slow and quasi-slow Rayleigh fading channels. The protocol adopted is decode-and-forward (DAF) with a single relay between the source and destination. Both scenarios with perfect and imperfect decoding at the relay are investigated. For imperfect decoding at the relay node, we consider an equivalent one-hop link model for the source-relay-destination path, and use it to modify the maximum likelihood detection metric by taking into account the equivalent signal-to-noise ratio (SNR) of the link model. The upper bounds of pairwise error probability (PEP) are derived for slow and quasi-slow Rayleigh fading channels, and the DSTTC design criteria are formulated accordingly. Based on the proposed design criteria, new DSTTCs are constructed by computer search. Simulation results demonstrate the superiority of the designed codes.     

Joint data and channel estimation for TDMA mobile channels

One of the main problems in time-division multiple-access (TDMA) digital mobile communications is the poor performance of the receiver for fast-fading channels. We propose to use a novel joint data and channel estimation (JDCE) technique to improve performance. The basic idea of this method originates from the so-called generalized likelihood ratio (GLR) test of classical detection theory. The technique was combined with the well-known Viterbi algorithm and applied to blind equalization by Seshadri [1]. In this paper, we introduce this technique to TDMA mobile communications. We find that the problems of delayed channel updating and divergence caused by error decision feedback in conventional maximum likelihood sequence estimation with decision delay (MLSE/DD) can be completely solved. An improvement of 4.5 dB can be obtained compared with the MLSE/DD method when it is applied to the Northern American Digital Cellular (NADC) system. The specified IS-54 requirement of 19 dB signal-to-noise ratio (SNR) at a bit error rate (BER) of 3% and a vehicle speed of 100 km/h can be met with a remarkable margin of 8 dB. When the intersymbol interference (ISI) of a channel is not severe, the required computation is moderate. For example, in the NADC system, the computational burden of the JDCE method is twice that of the MLSE/DD method if the least-mean-squares (LMS) algorithm is used for channel tracking.This work was presented in part in the Third International Symposium on Personal, Indoor and Mobile Radio Communications, Boston, MA, October 1992.     

一种非判决辅助前向结构载波频差估计方法

本文从最大似然准则出发,提出一种适于旋转对称星座的非判决辅助前向结构载频偏差估计算法.为了解决相位区间跳变问题,从而扩大估计范围,提出了一种新的相位展开方法.对于2π/M旋转对称星座,该估计算法的估计范围可扩大到±1/2MT.计算机仿真给出了该算法在估计范围、估计精度以及计算复杂度方面的性能.     

基于最大似然法的超分辨率离散谱估计算法

基于最大似然法的交替陷波周期图算法（ＡＮＰＡ）是一种超分辨率的谱估计算法,它同时具有超分辨率、高精度和低信噪比门限的特性。本文提出了一种计算陷波周期图的新算法,它可使运算量和存储容量大幅度下降。计算机仿真结果证明了这种算法在分辨能力和估计精度方面优于己有算法。     

Soft-Decision Decoding of Punctured Convolutional Codes in Asynchronous-CDMA Communications Under Perfect Phase-Tracking Conditions

In this paper, the performance of punctured convolutional codes of short constraint lengths is discussed. The punctured codes are used to provide error protection to a particular user in an asynchronous CDMA system. A perfect phase reference is assumed to be available throughout this paper. A slow fading Rician channel is assumed. Maximum likelihood decoding through a Viterbi algorithm is used to decode the information symbols. Soft-decision decoding of punctured convolutional codes is considered in this paper. The upper bounds with Viterbi decoding are derived and plotted for the various punctured codes considered. The simulated results are found to agree very well with their upper and lower bounds.