Optimal Detection Problem Research Articles

Mathematical Formalization and Algorithmization of the Main Modules of Organizational and Technical Systems

The purpose of the research is to develop a generalized structural scheme of organizational and technical systems based on the general theory of management, which contains the necessary and sufficient number of modules and formalize on this basis the main management tasks that act as goals of the behavior of the management object. The main modules that directly implement the management process are the status assessment module of organizational and technical systems and the management module. It is shown that in traditional organizational and technical systems, including the decision-maker, the key module is the state assessment module of organizational and technical systems. In this regard, the key aspect of the work is to study the optimal algorithms for evaluating the state of processes occurring in the organizational and technical systems and develop on this basis the principles of mathematical formalization and algorithmization of the status assessment module. The research method is the application of the principles of the theory of statistical estimates of random processes occurring in the organizational and technical systems against the background of interference and the synthesis of algorithms for the functioning of the status assessment module on this basis. It is shown that a characteristic feature of random processes occurring in organizational and technical systems is their essentially discrete nature and Poisson statistics. A mathematical description of the statistical characteristics of point random processes is formulated, which is suitable for solving the main problems of process evaluation and management in organizational and technical systems. The main results were the definition of state space of the organizational and technical systems, the development of a generalized structural scheme of the organizational and technical systems in state space that includes the modules forming the state variable of the module assessment and module management. This mathematical interpretation of the organizational and technical systems structure allowed us to formalize the main problems solved by typical organizational and technical systems and consider optimal algorithms for solving such problems. The assumption when considering the problems of synthesis of optimal algorithms is to optimize the status assessment module of organizational and technical systems and the control module separately, while the main attention is paid to the consideration of optimal estimation algorithms. The formalization and algorithmization of the organizational and technical systems behavior is undertaken mainly in terms of the Bayesian criterion of optimal statistical estimates. Various methods of overcoming a priori uncertainty typical for the development of real organizational and technical systems are indicated. Methods of adaptation are discussed, including Bayesian adaptation of the decision-making procedure under conditions of a priori uncertainty. Using a special case of the Central limit theorem, an asymptotic statistical relationship between the mentioned point processes and traditional Gaussian processes is established. As an example, a nontrivial problem of optimal detection of Poisson signal against a background of Poisson noise is considered; graphs of the potential noise immunity of this algorithm are calculated and presented. The corresponding references are given to the previously obtained results of estimates of Poisson processes. For automatic organizational and technical systems, the generally accepted criteria for the quality of management of such systems are specified. The result of the review is a classification of methods for formalization and algorithmization of problems describing the behavior of organizational and technical systems.

Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.

A Novel SD-Based Detection for Generalized SCMA Constellations

Sphere decoding (SD) based detection schemes for sparse code multiple access (SCMA) systems have recently received attention due to their promising features. However, the existing SD-based schemes can only be applied to SCMA systems with constellations that possess a certain structure. In this paper, we propose a novel SD-based detection scheme, namely improved SD (ISD), for SCMA that achieves the optimal maximum likelihood detector for any arbitrary regular or irregular constellations. To overcome the rank deficiency problem of the SCMA channel matrix, we fix a portion of the transmitted symbols and obtain an optimal detection problem that is equivalent to the original SCMA detection problem for all types of constellations. Moreover, due to the sparse nature of SCMA, the partial metric at each layer is evaluated in such a way that is independent of users assigned to each resource element. This, in turn, reduces the average complexity of ISD.

Soft-Decision-Based Distributed Detection With Correlated Sensing Channels

Prior works on distributed detection with correlated Gaussian observations primarily dealt with single-bit reports to the fusion center and suboptimal fusion rules. Considering multiple bits and independent reporting channel errors, we formulate the optimal detection problem as a nonlinear integer programming problem for which the genetic algorithm is applied to find a suboptimal solution. The Bayesian probability of error performance of our suboptimal solution, first, for one-bit, is better than the performance of some previously proposed schemes and, second, for multiple bits, approaches that of the centralized detection scheme.

Spectrum sensing based on Bayesian generalised likelihood ratio for cognitive radio systems with multiple antennas

In this paper, the spectrum sensing problem is addressed via using multiple antennas in cognitive radio systems when the noise and the primary user signal are independent. The problem of optimal detection is considered, and an estimation framework is presented where the primary user signal is a complex zero-mean Gaussian distribution. This paper discusses the generalized likelihood ratio detector (GLRT) when the sample size is a finite number and derive the corresponding GLRT detector of the spectrum sensing problem in a multiantenna framework by utilizing the statistics of the received signal, the channel information and the prior information of the noise. The scenario involves the assumption that the noise variance is unknown while the channel matrix gain is known for the secondary user (SU). The simulation results show that the proposed Bayesian GLRT detector is optimal even under a limited number of samples and more importantly also clarify that the proposed detector outperforms other the state-of-the-art detectors.

ANALYTICALLY APPROACH OF A COST FUNCTION TO OPTIMIZE AND ESTIMATE OF EFFICIENCE FOR RADIO- AND ELECTRONIC SYSTEMS

The problem of extending the scope of practical application of the methods of the theory of statistical solutions to problems arising in the design and operation of radio electronic systems is reviewed. Existing methods are applied in advanced systems in a very limited scope. Among the variety of problems causing such limitations the most significant one is a lack of loss functions that could be adequate for practical tasks and the same time, suitable for analytical calculations. Using the example of information-control systems designed for defense purposes and with allowance for the physical specifics of their operation, the structure of the loss function suitable for use in analytical constructions of the theory of statistical solutions and reflecting the physical specifics of the most important applications is proposed. An analytical model of damage in a single-purpose and multi-purpose situation is proposed. A multiplicative model and resulting additive model of damage from many targets are reviewed. A generalization was made for a environment featured by random number and values of target parameters-a random flow of targets. A simple analytical expression for a posteriori average risk is obtained, such risk been defined as a measure of the average expected damage from an arbitrary flow of targets. A model of counteraction with the aim of reducing damage is reviewed. Analytical expressions for the average risk and the value of prevented damage and their dependence on the parameters of counteraction have been obtained, and inter alia, in the presence of a flow of targets. A number of examples have been reviewed that show a possibility for splitting a complex multidimensional problem into parallel problems of a limited dimension, for simultaneous resolution of the problem of optimal detection, measurement and counteraction. Also, additional possibilities are opened for optimizing requirements to characteristics of the subsystems components. The proposed method makes it possible to significantly expand the scope of the theory of statistical solutions and to resolve a number of urgent problems that were previously irresolvable analytically. The proposed method can be applied in other areas as well.

Optimal Quantum Estimation of the Unruh-Hawking Effect

We address on general quantum-statistical grounds the problem of optimal detection of the Unruh-Hawking effect. We show that the effect signatures are magnified up to potentially observable levels if the scalar field to be probed has high mean energy from an inertial perspective: The Unruh-Hawking effect acts like an amplification channel. We prove that a field in a Fock inertial state, probed via photon counting by a noninertial detector, realizes the optimal strategy attaining the ultimate sensitivity allowed by quantum mechanics for the observation of the effect. We define the parameter regime in which the effect can be reliably revealed in laboratory experiments, regardless of the specific implementation.

Detection of Multiple Transient Signals With Unknown Arrival Times

The problem of optimal detection of signal transients with unknown arrival times contaminated by additive Gaussian noise is considered. The transients are assumed to be time continuous and belong to a parameterized family with the uncertainty about the parameters described by means of an a priori distribution. Under the assumption of a negligible probability that the independent transient observations overlap in time, a likelihood ratio is derived for the problem of detecting an unknown number of transients from the family, each transient with unknown arrival time. The uncertainty about the arrival times is assumed to be equal for all transients and is also described by means of a distribution. Numerical simulations of the performance of detecting a particular transient signal family are presented in the form of receiver operating characteristics (ROCs) for both the optimal detector and the classical generalized likelihood ratio test (GLRT). The results show that the optimal detector yields noticeable performance improvements over the GLRT. Moreover, the results show that the optimal detector may still outperform the GLRT when the true and modeled uncertainties about arrival times no longer agree.

CDMA multiuser detection: a nonlinear programming approach

The optimum receiver to detect the bits of multiple code-division multiple access (CDMA) users has an exponential complexity in the number of active users in the system. Consequently, many suboptimum receivers have been developed to achieve good performance with less complexity. We take the approach of approximating the solution of the optimum multiuser detection problem (OMUD) using nonlinear programming relaxations. First, we observe that some popular suboptimum receivers indeed correspond to relaxations of the optimal detection problem. In particular, one proposed approximation method yields to iterative solutions which correspond to previously proposed heuristic nonlinear detectors. Using a nonlinear programming approach, we identify the convergence properties of these iterative detectors. Secondly, we propose a relaxation that yields a receiver which we call the generalized minimum mean squared error detector. We give a simple iterative implementation of the detector. Its performance is evaluated and comparisons to other suboptimum detection schemes are given.

Incorporating uncertainty in ocean acoustics for optimum signal detection

An overview of detection, classification and localization of signals in an uncertain ocean environment is presented from a Bayesian perspective. The Bayesian approach allows one to both model and incorporate, in an optimal way, the inherent uncertainty that often exists in the knowledge of ocean acoustic environmental parameters. The relationship between environmental parameter estimation and signal detection is illustrated, and it is shown how environmental parameter estimation can be viewed as an inherent part of the optimum Bayesian detector. Furthermore, by using the Bayesian approach, one can design optimum detection algorithms that are robust with respect to precise knowledge of environmental parameters. Using the receiver operating characteristic (ROC), one can illustrate the trade-off among detection performance, environmental uncertainty, and signal-to-noise ratio. Several examples are taken from an uncertain shallow water environment to illustrate these trade-offs. Finally, it is shown how depth classification can be viewed as an optimal detection problem. [Work supported by ONR.]

Optimum multiuser detection is tractable for synchronous CDMA systems using m-sequences

The optimum multiuser detection problem was shown to be NP-hard, i.e., its computational complexity increases exponentially with the number of users (Verdu 1986, 1989). In this letter, we show that the optimum multiuser detection problem for a synchronous code-division multiple access (CDMA) system is equivalent to the minimum capacity cut problem in a related network and propose an optimum multiuser detection algorithm with polynomial computational complexity for a certain class of signature sequences. The minimum cut problem is solvable in polynomial time if the capacities of the links not incident to source and sink are nonnegative. This condition in the optimum detection problem is equivalent to all cross correlations between the signature sequences of the users being negative. One example of such a set of signature sequences is obtained when shifted versions of the maximal length sequences (or m-sequences) are used. In this case the cross correlation between users i and j is given as /spl Gamma//sub ij/=-1/G for all i,j, where G is the processing gain.

On recursive optimal detection of linear modulations in the presence of random fading

AbstractIn this paper, the problem of optimal detection of a linearly modulated digital signal transmitted over a fading channel is addressed. First, the issue of preliminary front‐end processing in order to extract a sufficient statistics for information sequence detection from the continuous‐time received signal is considered. Then, recursive algorithms are derived, which approximate optimal detection under the assumption of a linear and noisy channel modeled by a stochastic time‐varying impulse response with arbitrary known statistics. Specific solutions are proposed for the Rayleigh fading channel typical of mobile radio communications. The information symbols are assumed to be grouped into blocks which are preceded and followed by known preamble and postamble, respectively This model encompasses both Time Division Multiple Access (TDMA) schemes and pilot symbol assisted transmission. Two detection schemes are considered and relevant recursive formulations proposed. More specifically, optimal detection in complete absence of Channel State Information (CSI) (blind detection) or in presence of perfect CSI at the beginning of the data block (trained detection) are investigated. It is shown that optimal detection performance may be practically attained by sampling the received signal with few samples per symbol interval and searching a trellis diagram of adequate size by means of a Viterbi algorithm. State‐complexity reduction techniques based on Per‐Survivor Processing (PSP) for both types of detection schemes are also considered.

A system of functional‐differential equations associated with the optimal detection problem for jump‐times of a Poisson process

The value function in the optimal detection problem for jump‐times of a Poisson process satisfies a special system of functional‐differential equations. In this paper, we investigate the system and prove the existence and uniqueness of its solution.

Generalization of the problem of optimal detection of signals in the presence of non-Gaussian passive clutter

We have synthesized asymptotically optimal detectors of weak and strong signals with random noninformative parameters against a background of non-Gaussian passive clutter. A possibility of using an adaptive approach to synthesis has been considered and an appropriate structure of an optimal detector of signals with an unknown initial phase has been found.

Optimal detection of discontinuous changes of signal parameters in discrete time

The problem of optimal detection (discrimination) of signals with random discontinuous parameter changes in discrete time is examined. A recursion algorithm for calculation of the likelihood ratio in real time is obtained. As an example, the problem of optimal detection of a rectangular pulse signal with a random time of appearance, duration, and amplitude is solved. Computer simulation results are presented.

Adaptive two-stage maximum likelihood estimation for cellular radio

The problem of optimal detection over nonselective fading channels for cellular radio is treated from the viewpoint of adaptive two-stage maximum likelihood estimation (MLE). Data for transmission are divided into blocks, each preceded by one or more reference symbols. For selective fading, the receiver consists of an adaptive filter (AF) and a two-stage maximum likelihood estimator (TSMLE). For nonselective fading, TSMLE is preceded by a fixed filter. For quadrature modulation, the complex output of the filter contains two sets of unknowns, the quadrature data symbols (QDS) and the quadrature gains (QG) between transmitter and filter output. Stage I generates MLE estimates of the QG during the reference period and Stage II generates QDS estimates during the data intervals. AF coefficients are adjusted using a QR-decomposition least squares (QRD-LS) algorithm. A likelihood ratio test is performed to produce noise-free data estimates which Stage I in turn can use, in a decision aided manner, to update its gain estimates for the next interval. The quadrature gain estimates can be used to further correct reference carrier phase errors. Nonrecursive and recursive estimation procedures are developed. Bit error rate (BER) expressions are presented for 4-PSK and pi /4-DQPSK. Numerical results show that the scheme meets the North American Digital Cellular (NADC) system performance specifications (IS-54) with a margin. The BER floor is an order of magnitude lower than those of other schemes reported in the literature. For nonselective fading the BER floor is practically eliminated. This, and results reported elsewhere (Haeb and Meyr, 1989), lead us to conclude that schemes performing quadrature gain estimation can be used to lower error probabilities, attractively.

On the theory of importance sampling applied to the analysis of detection systems

Detection systems are designed to operate with optimal or nearly optimal probability of a wrong decision. Analytical solutions of the performance of these systems have been very difficult to obtain. Monte Carlo simulations are often the most tractable method of estimating performance. However, in systems with small probability of error, this technique requires very large amounts of computer time. A technique known as importance sampling substantially reduces the number of simulation trials needed, for a given accuracy, over the standard Monte Carlo method. The theory and application of the importance sampling method in Monte Carlo simulation is considered in a signal detection context. A general method of applying this technique to the optimal detection problem is given. Results show that in cases examined, the gain is approximately proportional to the inverse of the error probability. Applications of the proposed method are not limited to optimum detection systems; analysis, leading to a measure of the gain in using this biasing scheme, shows that in all optimal systems considered, less than 100 trials is needed to achieve estimates with 45% confidence, even for extremely small error probabilities. >

Hypotheses Testing in a Distributed Environment

The problem of optimum detection with n decentralized sensors selecting among m possible signals is considered from the decision theory point of view. The loss function is defined in terms of the decisions made by each observer and the transmitted signal. Then the average of this loss function is minimized. This leads to sets of coupled inequalities in terms of the likelihood ratio of each observer and the decisions made at the other sensors. This determines the structure of the optimum decentralized detection for an arbitrary number of sensors and an arbitrary number of possible signals. These results are valuable in numerous situations that may arise in large-scale and distributed systems.

Optimal Whereabouts Search for a Moving Target

This paper shows that solving the optimal whereabouts search problem for a moving target is equivalent to solving a finite number of optimal detection problems for moving targets. This generalizes the result of Kadane (Kadane, J. B. 1971. Optimal whereabouts search. Opns. Res. 19 894–904.) for stationary targets.

Some lower bounds on signal parameter estimation

New bounds are presented for the maximum accuracy with which parameters of signals imbedded in white noise can be estimated. The bounds are derived by comparing the estimation problem with related optimal detection problems. They are, with few exceptions, independent of the bias and include explicitly the dependence on the a priori interval. The new results are compared with previously known results.