On Adaptive Tree Polling Algorithms

This paper proposes three different algorithms for polling a finite set of users to determine the binary state of each user. The states are assumed to be described by i.i.d. Bernoulli random variables with parameterp. The algorithms differ in the responses offered by the users to queries and how the responses from several users are combined by the channel to produce a composite feedback signal which is received by all users. For each algorithm, the average number of transmissions required to determine the states of all users is determined as a function of the parameterp.     

A decorrelation-based Monte Carlo simulation—Its application to yield statistics of charge-redistribution A/D converters

A Monte Carlo method for yield estimation in charge-redistribution A/D converters is described, where the capacitances are random variables with finite correlation among themselves. The symmetric property of the resultant covariance matrix was exploited to decorrelate the random variables into another set of independent random variables.     

Blind identifiability of a quadratic stochastic system

Quadratic systems appear in various fields of signal processing, in particular in detection and estimation. In this paper, we establish some conditions to determine the order and identify the coefficients of any discrete and finite extent quadratic system driven by a sequence of independent and identically distributed random variables. The input sequence is assumed unobservable and the conditions are based on some properties of the output cumulant functions up to the third order. Necessary and sufficient conditions ensuring the determination of the order are given. A sufficient condition of uniqueness to recover the parameters is presented. Lastly, some examples are given     

Generalized Entropy Power Inequalities and Monotonicity Properties of Information

New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of n independent random variables to the information contained in sums over subsets of the random variables, for an arbitrary collection of subsets. As a consequence, a simple proof of the monotonicity of information in central limit theorems is obtained, both in the setting of independent and identically distributed (i.i.d.) summands as well as in the more general setting of independent summands with variance-standardized sums.     

Unconditionally secure key agreement and the intrinsic conditionalinformation

This paper is concerned with secret-key agreement by public discussion. Assume that two parties Alice and Bob and an adversary Eve have access to independent realizations of random variables X, Y, and Z, respectively, with joint distribution P_XYZ. The secret-key rate S(X;Y∥Z) has been defined as the maximal rate at which Alice and Bob can generate a secret key by communication over an insecure, but authenticated channel such that Eve's information about this key is arbitrarily small. We define a new conditional mutual information measure, the intrinsic conditional mutual information between S and Y when given Z, denoted by I(X;Y↓Z), which is an upper bound on S(X;Y∥Z). The special scenarios are analyzed where X, Y, and Z are generated by sending a binary random variable R, for example a signal broadcast by a satellite, over independent channels, or two scenarios in which Z is generated by sending X and Y over erasure channels. In the first two scenarios it can be shown that the secret-key rate is strictly positive if and only if I(X;Y↓Z) is strictly positive. For the third scenario, a new protocol is presented which allows secret-key agreement even when all the previously known protocols fail     

On the distribution of positive-definite Gaussian quadratic forms

Quadratic signal processing is used in detection and estimation of random signals. To describe the performance of quadratic signal processing, the probability distribution of the output of the processor is needed. Only positive-definite Gaussian quadratic forms are considered. The quadratic form is diagonalized in terms of independent Gaussian variables and its mean, moment-generating function, and cumulants are computed; conditions are given for the quadratic form to bechi^{2}distributed and distributed like a sum of independent random variables having a Gamma distribution. A new method is proposed to approximate its probability distribution using an expansion in Laguerre polynomials for the central case and in generalizedchi^{2}distributions in the noncentral case. The series coefficients and bounds on truncation error are evaluated. Some applications in average power and power spectrum estimation and in detection illustrate our method.     

On the Utility of Laguerre Series for the Envelope PDF in Multipath Fading Channels

It is well known that multipath fading significantly affects the performance of communication systems. In order to incorporate the impact of this random phenomenon on system analysis and design, in many cases, we need to calculate the probability density function (pdf) of the received signal envelope in multipath fading channels. In this paper, we consider a general multipath fading channel with arbitrary number of paths, where the amplitudes of multipath components are arbitrary correlated positive random variables, independent of phases, whereas the phases are independent and identically distributed random variables with uniform distributions. Since the integral form of the envelope pdf for such a general channel model is too complicated to be used for analytic calculations, we propose two infinite expansions for the pdf: a Laguerre series and a power series. Based on the tight uniform upper bounds on the truncation error of these two infinite series, we show that the Laguerre series is superior to the power series due to the fact that for a fixed number of terms, it yields a smaller truncation error. This Laguerre series with a finite number of terms, which expresses the envelope pdf just in terms of simple polynomial–exponential kernels, is particularly useful for mathematical performance prediction of communication systems in those indoor and outdoor multipath propagation environments, where the number of strong multipath components is small.      

两个独立复高斯随机变量乘积的相位精确分布

针对两个高斯随机变量相乘经常出现在雷达和通信系统信号处理中的情况,研究了两个独立的具有任意均值和方差的复高斯随机变量乘积的相位分布。将该相位的概率密度函数表达为一个包含Kummer函数的无穷级数,分析了该概率密度函数的收敛性及收敛速度。利用所得结果分析信道状态信息不完美情况下单天线多进制相移键控通信系统的性能,推导了该系统的符号错误率,并通过数值实验对所得结果进行了验证。     

Exact closed-form performance analysis of optimum combining with multiple cochannel interferers and Rayleigh fading

A new closed-form expression is derived for the exact bit-error probability (BEP) for optimum combining with binary phase-shift keying. The exact BEP expression is for multiple, equal power, cochannel interferers and multiple reception branches. It is assumed that the aggregate interference and noise is Gaussian and that both the desired signal and interference are subject to Rayleigh fading. The derivation starts by expressing the optimum combining decision statistic as a sum of quadratic forms of Gaussian random variables and it proceeds to average over the fading interference. The new BEP expression has low complexity as it contains only finite sums and products.     

Optimum detection of a weak signal with minimal knowledge of dependency

The optimum nonlinearity is defined for detection of a weak signal when minimal knowledge of the dependency structure of the observations is available. Specifically, it is assumed that the observations form a one-dependent strictly stationary sequence of random variables and that only a finite number of moments of the marginal density and the correlation coefficient between consecutive observations are known. It is assumed that the bivariate densities involved can be represented as diagonal series, using orthonormal polynomials. Using efficacy as a performance measure, the optimum nonlinearity is required to satisfy a saddle-point condition over this class of bivariate densities.     

有限域上独立随机变量和的极限分布定理及其在流密码中的应用

利用有限域上随机变量的特征函数，本文得到了有限域上独立随机变量和的极限分布定理，作为这一定理的应用，本文研究了有限域上非线性组合函数的构造，给出了有限域上一类与任何线性函数都有较小相关性的非线性组合函数的结构。     

Protocol Validation by Maximal Progress State Exploration

We discuss an efficient variation of state exploration for two communicating finite state machines. In particular, we propose to divide the task of generating all reachable states into two independent subtasks. In each subtask, only the states reachable by forcing maximal progress for one machine are generated. Since the two subtasks are completely independent, and since in most instances the time and storage requirements for each subtask are less than those for the original task, maximal Progress state exploration can save time and/or storage over conventional state exploration.     

The piling-up approximation in linear cryptanalysis

One of the key identities in linear cryptanalysis is the piling-up lemma, which allows one to compute the probability distribution of a sum modulo 2 of binary random variables, when the probability that these are zero is known. However, the lemma holds only for independent random variables. In linear cryptanalysis, one often (mis)uses this identity without knowing whether the random variables are independent or not. This paper investigates the problems that may arise when using this identity for dependent random variables. In particular, it is shown that the identity holds in almost all cases if one replaces equality by an approximation sign. The amplitude of departure from equality is also given     

On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays

This paper is concerned with the fault detection problem for a class of discrete-time systems with randomly occurring nonlinearities, mixed stochastic time-delays as well as measurement quantizations. The nonlinearities are assumed to occur in a random way. The mixed time-delays comprise both the multiple discrete time-delays and the infinite distributed delays that occur in a random way as well. A sequence of stochastic variables is introduced to govern the random occurrences of the nonlinearities, discrete time-delays and distributed time-delays, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fault detection filter such that, in the presence of measurement quantization, the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fault detection filters, and then the explicit expression of the desired filter gains is derived by means of the feasibility of certain matrix inequalities. Also, the optimal performance index for the addressed fault detection problem can be obtained by solving an auxiliary convex optimization problem. A practical example is provided to show the usefulness and effectiveness of the proposed design method.     

Linear and quadratic estimation using uncertain observations from multiple sensors with correlated uncertainty

In this paper, filtering algorithms are derived for the least-squares linear and quadratic estimation problems in linear systems with uncertain observations coming from multiple sensors with different uncertainty characteristics. It is assumed that, at each sensor, the state is measured in the presence of additive white noise and that the Bernoulli random variables describing the uncertainty are correlated at consecutive sampling times but independent otherwise. The least-squares linear estimation problem is solved by using an innovation approach, and the quadratic estimation problem is reduced to a linear estimation one in a suitable augmented system. The performance of the linear and quadratic estimators is illustrated by a numerical simulation example wherein a scalar signal is estimated from correlated uncertain observations coming from two sensors with different uncertainty characteristics.     

Computer generation of correlated Gaussian random variables

This paper Presents a means of generating a set of N correlated Gaussian random variables from N or fewer independent Gaussian random variables. In computer generation of pseudorandom variables, this technique sometimes has computational advantages over the more straightforward inverse Gram-Schmidt procedure. As an example, application of the technique in simulation of a pulse frequency modulation (PFM) receiver is discussed.     

一种基带GMSK信号相关器及其输出概率分布

该文提出一种基带GMSK信号相关器,并从GMSK解调信号的相位概率分布函数以及独立同分布随机变量和的概率分布函数出发,给出了该相关器的自相关峰和互相关峰的概率分布函数。从概率论与数理统计出发,推导了一种统一的数字相关器(数字匹配滤波器)的自相关峰和互相关峰的概率分布函数。数值计算结果表明,在相同条件下,该基带GMSK信号相关器的误检概率比数字相关器的低近一个数量级。     

Performance of Coherent Direct-Sequence Spread-Spectrum Communications Over Specular Multipath Fading Channels

The performance of coherent direct-sequence spread-spectrum communications over specular multipath fading channels is investigated. The average probability of error of the correlation receiver is derived for an arbitrary number of paths with deterministic or random gain coefficients. The gain coefficients, delays, and phase angles of any two distinct paths are modeled as mutually independent random variables. Numerical results for several values of the system and channel parameters are presented.     

Signal‐Dependent Chaotic‐State‐Modulated Digital Secure Communication

In this letter, a discrete state, discrete time chaotic pseudo random number generator (CPRNG) is presented for stream ciphering of text, audio, or image data. The CPRNG is treated as a finite state machine, and its state is modulated according to the input bit sequence of the signal to be encrypted. The modulated state sequence obtained can be transmitted as a spread spectrum or encrypted data.     

Probability density functions of amplitude-modulated random signals

The probability density function arising from multiplication of two independent random variables has been extensively treated by statisticians, yet some common signal processing product situations have not been analysed. An important example of this omission is the amplitude modulation of a Gaussian process. Here, a little-known Hankel transform-based procedure provides a ready solution for this problem and many other types of random modulation signals. Several new modulation results are tabulated in graphical form and it is also shown that half-amplitude sinusoidal processes added yield the same distribution as their (unit-amplitude) product