Code division multiple-access (CDMA) schemes are widely used in cellular communications system because they provide high quality, reduced interference and result in high system capacity. In CDMA systems since one carrier frequency is being used, a phenomenon known as soft hand off occurs when a user changes radio resources from one base station to another. In this paper, we propose a soft hand off scheme using a two cell and roaming user probability approach, to properly illustrate the hand off process between the cells of interest. The proposed scheme assumes that calls entering the soft region are immediately assigned two channels. This assumption helps to reduce the blocking probability of new calls in the soft region as opposed to other schemes which do not explicitly cater for such calls. A three dimensional Markov process is created to describe and develop the stochastic behavior of the calls in the system. Performance measures such as new call blocking probability, hand off call blocking probability, channel efficiency, total carried traffic are deduced

In this paper we use a WCDMA network simulator to evaluate the different performance criteria. We also simulate a transmit diversity scheme and use the results of the diversity scheme in the simulator to evaluate the QoS (quality of service) enhancements obtained. Further we explore the possibility of a coexistence of a WCDMA network with the WIPAS (wireless IP access system).

The multiple access problem as characterized by infinite user population and a slotted-time channel is examined, and an algorithm that utilizes a control mini-slot is proposed. The stability region of the proposed algorithm is determined and compared to the random access algorithm with the highest known throughput. A break-even point is also given.

Two fundamental distributed decision network structures are considered: the first system consists of finite number of sensors, each collecting asymptotically many data, while the second one employs asymptotically many sensors, each collecting a single datum. For binary hypothesis testing, the Neyman-Pearson criterion is utilized and justified via information theoretic arguments. An asymptotic relative efficiency performance measure is used to establish tradeoffs between the two structures, by comparing the performance characteristics of the decentralized detection systems to their centralized counterparts.>

The problem of binary hypothesis testing is revisited in the context of distributed detection with feedback. Two basic distributed structures with decision feedback are considered. The first structure is the fusion center network, with decision feedback connections from the fusion center element to each one of the subordinate decisionmakers. The second structure consists of a set of detectors that are fully interconnected via decision feedback. Both structures are optimized in the Neyman-Pearson sense by optimizing each decision-maker individually. Then, the time evolution of the power of the tests is derived. Definite conclusions regarding the gain induced by the feedback process and direct comparisons between the two structures and the optimal centralized scheme are obtained through asymptotic studies (that is, assuming the presence of asymptotically many local detectors). The behavior of these structures is also examined in the presence of variations in the statistical description of the hypotheses. Specific robust designs are proposed and the benefits from robust operations are established. Numerical results provide additional support to the theoretical arguments.>

A generalization of the Cramer-Rao (C-R) bound is derived for the p-th moment of any unbiased location parameter estimator. The relationship between the generalized C-R bound and the generalized Gaussian density is examined. A looser bound is also provided for the case of a mixture of generalized Gaussian densities as well as the case of multiple independent generalized Gaussian observations.>

This paper considers the problem of Neyman-Pearson distributed detection. In distributed detection structures, a number of subordinate decision makers decide upon the active hypothesis based on their own data, and then transmit these decisions to one or more primary decision makers. Then the Neyman-Pearson performance criterion is deployed, the objective is to maximize the probability of detection (also known as power probability) induced by the primary decision makers, subject to a given false alarm constraint. In this formulation, the overall optimization problem reduces to the problem of threshold evaluation. This paper deals exactly with this issue. An on-line threshold learning algorithm is proposed that operates directly an data and requires-no explicit knowledge of the underlying probability distributions. The algorithm adapts recursively the pertinent threshold parameters in a way that minimizes the Kullback-Leibler distance between the observed and the desired output distribution. A formal convergence study is carried out and shows that, under some general conditions, the algorithm is strongly consistent; that is, the sequences of the produced threshold estimates converge to the optimal threshold values with probability 1. The rate of convergence is examined, and methods for controlling it are proposed. Simulation results are included and provide additional support to the theoretical arguments.>

Two feedforward neural structures intended for binary hypothesis testing are considered. The first structure, FFS1, is a tandem structure, while the second structure, FFS2, involves cumulative feedforward feedback. Both parametric and robust designs for the two structures are considered and analyzed in terms of induced false alarm and power probabilities. The inferiority of the FFS1 is rigorously proved in terms of the rate with which the induced power probability increases with respect to the number of the neural elements. Asymptotic results are presented, as well as numerical results, with emphasis on the Gaussian and location parameter nominal hypotheses model. Learning algorithms for the parameter involved in the robust network designs are discussed as well.>

Generalized decoding decision rules provide added flexibility in a decoding scheme, and some advantages. In a generalized decoding decision rule, the following possibilities are considered: (1) the decoder has the option of not deciding at all, or rejecting all estimates. This is termed an erasure; (2) the decoder has the option of putting out more than one estimate. The resulting output is called a list. Only if the correct codeword is not on the list is there a list error. Taking into account the lack of exact knowledge of the channel statistics and assuming a mismatch between the true channel transition probabilities and the nominal probabilities used in the decoding metric, error bounds are developed for generalized decision rules. Conditions under which the error probabilities converge to zero exponentially with the block length, in spite of the presence of mismatch, are established.>

The binary signal detection problem is considered, when a distributed system of sensors operates in a decentralized fashion. Local processing at each sensor is performed. Using Chernoff's large deviation theorems, the author considers as a criterion the rate of convergence of the error probability to zero. It is shown that the optimum quantizer of blocks of data under the above criterion is the likelihood ratio quantizer. A lower bound to the error probability is also developed. The question of how many coarsely quantized sensors can replace the infinitely quantized one is also answered. The main result given is the structure of the optimum quantizer, consisting of the calculation of the likelihood ratio concatenated by a scalar quantizer.>

A binary feedback collision resolution algorithm is developed for a multiuser random access communication system with nonhomogeneous user population. The user population is split into two classes with different priorities. The throughput and delay analysis of the proposed algorithm are performed, and numerical results are obtained.>

Existing upper bounds to the error probability in testing between m>2 hypotheses, and H. Chernoff's (1952) asymptotically correct error probability expression for m=2 hypotheses, as the number of observations n to infinity , are discussed. The multidimensional version of Chernoff's bound and its relationship to large deviation theory is presented. Large deviation theory is used to develop new bounds. The new bounds are asymptotically exact, in the sense that as n to infinity , they converge to the correct asymptotic rate, which is guaranteed to be the optimum one by the large deviation theorem. Necessary and sufficient conditions are determined so that asymptotic convergence of the error rates to zero is sustained in the presence of mismatch, which occurs when inaccurate versions of the true probability density functions are utilized in the maximum-likelihood decision rule. The conditions are expressed in terms of informational divergence distances, for Markov chain data and Gaussian multivariate stationary random processes. The results for multisensor data are generalized.>

Bernoulli and first-order Markov processes are used to approximate the output process of a class of slotted multiuser random-access communication networks. The output process is defined as the process of the successfully transmitted packets within the network. The parameters of the approximating processes are analytically calculated for a network operating under a specific random access algorithm. The applied methods are general and can be used to calculate these parameters in the case of any random access algorithm within a class. To evaluate the accuracy of the approximations, a star topology of interconnected multiuser random-access communication networks is considered. The mean time that a packet spends in the central node of the star topology is calculated under the proposed approximations of the output processes of the interconnected networks. The results are compared to simulation results of the actual system. It turns out that the memoryless approximation gives satisfactory results up to a certain per network traffic load. Beyond that per network traffic load, the first-order Markov process performs better.>

The concept of approximating the output process of slotted multiuser random-access communication networks (i.e. the process of the successfully transmitted packets within the networks) by a second-order Markov process is introduced. A method is developed for analytically calculating the parameters of the approximating process for a class of random-access algorithms. The method is illustrated by considering a specific random-access algorithm from that class. The mean time that a packet spends in the central node of a star topology of interconnected networks is incorporated in the evaluation of the accuracy of the proposed approximation. This quantity is calculated under the proposed approximation on the output processes of the interconnected networks and is compared to simulation results from the actual system. Results showing the accuracy of the proposed approximation for networks operating under a specific random-access algorithm are presented.>

The binary signal detection problem is considered, when a distributed system of sensors operates in a decentralized fashion, i.e. local processing is performed at each sensor. Chernoff's large deviation theorem is used, and the rate of convergence of the error probability to zero is taken as a criterion. It is shown that the optimum quantizer of blocks of data under the above criterion is the likelihood ratio quantizer. A lower bound to the error probability is also developed. The monotonicity of performance with refinement of quantization is proved. The question of how many coarsely quantized sensors can replace the infinitely quantized one is also answered.>

A protocol for a multiuser packet radio communication channel is proposed. The basic functions of this protocol are determined by a modified stack-type limited sensing collision resolution algorithm. The protocol is a hybrid of a pure random-access scheme and a reservation scheme. A message consists of a number of packets that are capable of revealing the current activity of the channel. The performance of the system is investigated in terms of throughput and average message delay and analytical results are provided.>

Bernoulli and first-order Markov processes are used to approximate the output process of a class of slotted multiuser random-access communication networks. The parameters of the approximating processes are analytically calculated for a network operating under a specific random-access algorithm. The mean time that a packet spends in the central node of the star topology is calculated under the proposed approximations of the output processes of the interconnected networks. The results are compared with simulation results of the actual system. It turns out that the memoryless approximation gives satisfactory results up to a certain per-network-traffic load. Beyond that point, the first-order Markov processes performs better.>

In this paper we consider the design of robust block quantizers when the number of quantization levels is large. Therth power distortion measure is utilized through the convenient expression developed by Bennett and Gersho. The robust design is formulated as a two-person game, and it is shown that for convex families of signal probability density functions there is a saddle point solution. The evaluation of the robust solution amounts to determining the maximums-norm element in the class of signal densities. We then develop specific solutions for three classes of pdf: a) the class specified by generalized moment contraints, b) the class of εcontaminated densities, which has been a popular model in robust signal detection, and c) the class specified by upper and lower bounds to the probability density function of the signal. For high-quality quantization under fixed output entropy, the quantizer is uniform and the resulting distortion is an increasing function of the source entropy. The least favorable distribution is then the one having maximum entropy. For the ε-contaminated family and the "banded" family(c), we derive the maxentropic distributions.

Noiseless coding of a discrete source with partially known statistics is formulated as a two-person game. The payoff is the average codeword length, using Shannon codes. The code designer picks a source probability distribution for the design of the code, while an opponent picks the actual source probability distribution. It is shown that if the class of probability distributions allowed is convex, then there is a saddle point solution which is determined by the maximum entropy distribution of the convex class. The maximum entropy element is derived for three families of source probability mass functions (pmf): a) the class of c-contaminated pmf's; b) the class of pmf's for which each probability is known only through an upper and lower bound; c) the class of pmf's which is a convex hull of a finite number of known pmf's. An extension of the robust noiseless source coding problem for families of sources modeled as first-order Markov chains is discussed.

A conjecture and corrects some inaccuracies of the convergence bounds that were derived in a previous paper.

A new expression for the Chernoff distance between two continuous-time stationary vector Gaussian processes that contain a common white noise component and have equal means is derived. The expression is given in terms of the spectral density matrices for large observation intervalT. The expression is then used for deriving upper and lower bounds to the Bayes probability of error. Both bounds converge to zero exponentially inT. It is also shown that theI-divergence andJ-divergence can be easily evaluated in the frequency domain by differentiation of the Chernoff distance.

A binary detection problem of the Neymann-Pearson type, in which the probability density functions used are inaccurate versions of the true ones, are considered. The performance of the above suboptimal detection scheme as the number of observations increases is investigated. A necessary and sufficient condition is given for the exponential convergence to zero of the two error probabilities as the number of observations increases. The condition is in terms of an inequality between differences of asymptotic per sample informational divergence expressions.

The performance of a multiclass maximum likelihood decision rule is analyzed, when inaccurate versions of the true probability density functions are used. A general bound to the error probability is developed, and it is valid for both finite observation sizenandn \rightarrow \infty. A necessary and sufficient condition is developed for the bound to be less than one and to converge exponentially to zero, assuming that we exclude the case of equality between informational divergence expressions. The condition is given in terms of the information divergence per sample, both for the finitenand asymptotic case. As long as the inaccurate density lies in a "tolerance region" around the true density of the class, exponential convergence of the error to zero is maintained. Specific expressions for the bounds and informational divergence are obtained for homogeneous Markov chain observations and Gaussian stationary process observations in discrete time. The computational complexity of evaluating the asymptotic bounding expression for thes-dimensional Gaussian process case is shown to beO(ns^{2} + 2n log_{2}n), which is much smaller than the complexityO((sn)^{3})required for the evaluation of the bound for finite sample sizen.

Recursive expressions for certain distance measures between continuous-time stationary vector-Gaussian processes are derived and used to derive upper bounds to the mean square error performance of the Bayes and maximum-likelihood estimates of a parameter, when only a finite-valued parameter set is used. The question of convergence when the true parameter value does not belong to the finite set is also answered.

Using some recently derived spectral expressions for distance measures between vector Gaussian stationary processes, upper bounds are given for the mean-square-error performance of the Bayes estimate of a parameter on the basis of vector Gaussian observations. The result is directly applicable to evaluating the performance of certain adaptive estimation schemes and to finite-state Markov chain systems.

We summarize some new frequency domain expressions of statistical distance measures between stationary vector Gaussian processes recently derived by the authors. Both time-discrete and time-continuous processes are treated. Some of the frequency domain distance measures have been empirically verified to be very useful speech recognition and speech analysis-synthesis.

Let l=f^n(x) be the kernel estimate of a density f(x) from a sample of size n. Wahba [6] has developed an upper bound to E[f(x)-l=f^n(x)]2. In the present paper, we find the kernel function of finite support [m=-T, T] that minimizes Wahba's upper bound. It is Q(y) = (1 + am=-1) (2T)m=-1 [1-m=-a|y|a] where a = 2-pm=-1, p m=ge 1.

The problem of approximating a probability density function by a simpler one is considered from a decision theory viewpoint. Among the family of candidate approximating densities, we seek the one that is most difficult to discriminate from the original. This formulation leads naturaliy to the density at the smallest Bhattacharyya distance. The resulting optimization problem is analyzed in detail.

The idea of finding a low-order approximation to a Markov chain is considered. The approximating process is characterized by a smaller number of parameters than the original one. As a criterion for approximation the lower order process is required to be the most difficult to discriminate from the original one in a decision theoretical context, i.e., achieving maximal Bayes error probability. It is shown that the Hellinger distance metric is closely related to the discrimination performance and provides robust approximation. It is then used to derive the best memoryless approximation, with a possibly reduced number of states, to a first-order Markov chain.

A decision-directed detection scheme for multiple hypotheses is developed and analyzed. It is assumed that the probability density functions\{f_{i}(x)\}under each of them+1hypotheses are known, and the prior probablities\{\pi_{i}\}are unknown and sequentially estimated on the basis of previous decisions. Using a set of nonlinear transformations of the data and applying results from the stochastic approximation theory, improved algorithms are given for achieving asymptotically unbiased estimates and accelerated convergence to the true priors.

The problem of sequential detection between Poisson processes is analyzed and resolved. Wald's results on sequential analysis are used, but a substantial modification is shown to be necessary due to the discontinuous nature of the likelihood ratio. It is shown that, in general, one can take into account the "excess over the boundary" so as to design sequential tests with a given error performance.

A further analysis of maximum likelihood sequence estimation algorithms for Gaussian channels with finite intersymbol interference is presented. It is shown that several maximum likelihood survivor paths cannot occur simultaneously, and hence that searching some of the nodes of the state trellis diagram can be avoided. An efficient algorithm is given that updates the metrics while avoiding redundant parts of the search.

For thek-hypothesis detection problem, it is shown that, among thek-classes of probability density functions withmfixed quantiles, histograms achieve the least favorable performance as measured by the probability of correct detection and Chernoff distance. It is assumed that themcell probabilities are estimated usingntraining samples per class. With the aid of the estimated cell probabilities, new observations are processed. A distribution-free upper bound to the probability of\epsilon-deviation between the actual probability of correct detection and the theoretical (known quantiles) probability is derived as a function of(m,n,\epsilon,k,u_{o}), whereu_{o}is a uniform upper bound to the true class densities. The bound converges exponentially to zero asn \rightarrow \infty. Exponential convergence is obtained by choosingm = n^{\alpha}, 0 < \alpha < 1. Hence, the rulem = n^{\alpha}answers the long standing question of how to relatemandnin a distribution-free manner. The question of the optimal choice of a is also discussed.

The rate of convergence of the conditional error probabilities of the nearest neighbor rule and thekth nearest neighbor rule are investigated.

The problem of finding the linear scalar feature that minimizes the probability of error in discriminating between two Gaussian multivariate hypotheses is comidered. A one-dimensional search algorithm to solve this problem is given, improving upon a previous multidimentional theorem.

When the statistical structure under each of two hypotheses is time varying, the collection of infinitely many observations does not guarantee an error probability that approaches zero. A recursive formula for the Bhattacharyya distance between two Markov chains is derived, and it is used to derive necessary and sufficient conditions for asymptotically perfect detection (APD). It is shown that the use of incorrect prior probabilities in the Bayes detection rulee does not affect AID. The results are also extended to time-continuons finite-state Markov observations. An application is analyzed, in which the behavior of a message buffer is monitored for the purpose of detecting malfunctions in a computer communication network.

The problem of estimating the prior probabilitiesq = (q_{1} \cdots q_{m-1})ofmstatistical classes with known probability density functionsF_{1}(X) \cdots F_{m}(x)on the basis ofnstatistically independent observations(X_{l} \cdots x_{n})is considered. The mixture densityg(x|q) = \sum^{m-1}_{j-1}q_{j}F_{j}(x) + (1 - \sum^{m-1}_{\tau = 1}q_{\tau})F_{m(x)is used to show that the maximum likelihood estimate ofqis asymptotically efficient and weakly consistent under very mild constraints on the set of density functions. A recursive estimate is proposed forq. By using stochastic approximation theory and optimizing the gain sequence, it is shown that the recursive estimate is asymptotically efficient for them = 2class case. Form > 2classes, the rate of convergence is computed and shown to be very close to asymptotic efficiency.

A solution is given to the linear discrimination problem for more than two statistical classes, using a generalized Fisher criterion as the distance measure. Essentially, we find the direction X on which the projections of k > 2 statistical hypotheses make the generalized Fisher criterion maximum. Since the latter depends mainly on the minimum pairwise projected mean difference, the optimal projection direction X maximizes the worst distance. With the use of linear manifold subspaces and decomposition of the optimization problem into a union of simple convex constrained ones, a closed form solution for the optimal X is attained, and no numerical optimization techniques are needed. Such numerical optimization algorithms in high-dimensional spaces were required in previously proposed methods in which other distance measures were used. For the same generalized Fisher distance measure and with similar methodology, we also derive the best set of discriminant vectors.