Function Of Error Probability Research Articles

Transmit Antenna Selection and Power Allocation for Joint Multi-Target Localization and Discrimination in MIMO Radar with Distributed Antennas under Deception Jamming

In this paper, with the aim of performing joint multi-target localization and discrimination tasks, a performance-driven resource allocation scheme is proposed. In the first, by establishing the signal model under deception jamming and utilizing the maximum likelihood (ML) estimator, the estimation information of targets can be obtained. Secondly, the Cramer–Rao lower bound (CRLB) for the transmit antenna selection and power allocation is derived. Then, to fully utilize the difference in spatial distribution between true and false targets, a false target discriminator based on the CRLB of the distance deception parameter is utilized. By introducing the nondimensionalization mechanism, we build an optimal objective function of target localization error and discrimination probability. Subsequently, a joint multi-target localization and discrimination optimization model has been established, which is mathematically a non-smooth and non-convex problem. By introducing an auxiliary variable, we propose a three-step solution strategy for solving this problem. Simulation results demonstrate that the proposed algorithm can improve the performance of joint localization accuracy and discrimination ability (JLADA) by more than 30% compared with the algorithms only for localization or discrimination. Meanwhile, by utilizing the proposed algorithm, the composite indicators of JLADA can decrease more than 70% compared with the uniform allocation scheme.

A Closed-Form Minimum BER Precoder for Orthogonal Time Frequency Space Systems

This letter devises a closed-form precoder for Orthogonal Time Frequency Space (OTFS) systems with linear equalization to minimize the bit error rate (BER). The precoder is developed by optimally allocating the power to adapt to the equivalent channel in the delay-Doppler domain. To achieve the minimum BER precoder design, we convert the minimization of the average BER into the minimization of its lower bound subject to a transmission power constraint. By exploiting the convexity, a closed-form minimum BER precoder is designed, which actually achieves the lower bound. As such, the unified bit error probability function for both the zero-forcing (ZF) and minimum mean square error (MMSE) equalizations is derived and verified with their numerical counterparts. Simulation results demonstrate that the designed precoders can provide lower BER than the existing linear equalizations without precoding.

Placement and sizing of EESS bundled with uncertainty modeling by two-stage stochastic search based on improved shark smell optimization algorithm in micro-grids

Microgrids are low voltage small-scale grids which are used for supplying the thermal and electric loads in small areas or locations without access to the main grid. A microgrids can be a proper solution for power generation considering the environmental and economic problems of these locations. In this paper, the optimum size and placement of electric energy storage is presented considering the uncertainties associated with renewable energy resources and fault in the microgrid lines as well as impact of responsive loads in a microgrid. The studied hybrid system is composed of wind turbines and fuel cells. Basically, the wind energy is not certainly accessible and the newly suggested method is based on a two-stage stochastic search (TSSS) model for modeling the impact of uncertainty in the power generated by the wind generation resources by considering the wind energy prediction error as the main stochastic parameter in the planning. The standard probability distribution function is used for showing the error variation. With respect to continuity of this function, the prediction error probability function is discretized using a new method and a certain number of scenarios with specific probability are extracted. Finally, the studied problem is converted to an optimization problem and the developed shark smell optimization (SSO) algorithm is used to solve it. Numerous case studies show and approve the performance of the proposed model.

Effective Energy Efficiency of Ultrareliable Low-Latency Communication

Effective capacity (EC) defines the maximum communication rate subject to a specific delay constraint, while effective energy efficiency (EEE) indicates the ratio between EC and power consumption. We analyze the EEE of ultrareliable networks operating in the finite-blocklength regime. We obtain a closed-form approximation for the EEE in quasistatic Nakagami- m (and Rayleigh as subcase) fading channels as a function of power, error probability, and latency. Furthermore, we characterize the quality-of-service constrained EEE maximization problem for different power consumption models, which shows a significant difference between finite and infinite-blocklength coding with respect to EEE and optimal power allocation strategy. As asserted in the literature, achieving ultrareliability using one transmission consumes a huge amount of power, which is not applicable for energy limited Internet-of-Things devices. In this context, accounting for empty buffer probability in machine-type communication (MTC) and extending the maximum delay tolerance jointly enhances the EEE and allows for adaptive retransmission of faulty packets. Our analysis reveals that obtaining the optimum error probability for each transmission by minimizing the nonempty buffer probability approaches EEE optimality, while being analytically tractable via Dinkelbach's algorithm. Furthermore, the results illustrate the power saving and the significant EEE gain attained by applying adaptive retransmission protocols, while sacrificing a limited increase in latency.

Statistical Delay and Error-Rate Bounded QoS Provisioning Over mmWave Cell-Free M-MIMO and FBC-HARQ-IR Based 6G Wireless Networks

As a new and dominating 6G mobile-networks’ service class for time-sensitive traffics, massive ultra-reliable and low latency communications (mURLLC) has received tremendous attention. One of key 6G enabling-techniques for achieving mURLLC lies in how to efficiently support statistical delay and error-rate bounded quality-of-services (QoS) provisioning for real-time data-transmissions over time-varying wireless networks. Towards this end, several emerging wireless techniques, including finite blocklength coding (FBC), hybrid automatic repeat request with incremental redundancy (HARQ-IR) protocol, millimeter wave (mmWave), cell-free (CF) massive multiple-input multiple-output (m-MIMO), etc., have been shown to be 6G promising enablers to significantly improve various QoS performances. However, integrating these techniques with the statistical delay and error-rate bounded QoS provisioning theory for mURLLC has imposed many new difficulties not encountered before. To overcome these challenges, in this paper we propose the statistical delay-and-error-rate-bounded QoS provisioning system architecture over mmWave user-centric CF m-MIMO and FBC-HARQ-IR based 6G wireless networks. First, we establish the comprehensive system models by accurately characterizing the integrations of above-described 6G promising techniques with statistical QoS provisioning theory. Then, we integrate FBC with HARQ-IR protocol to derive the channel capacity as a function of error probability. Finally, we obtain the closed-form expressions for effective capacities under our proposed schemes. We also conduct a set of simulations to validate and evaluate our proposed FBC-HARQ-IR based mmWave user-centric CF m-MIMO schemes.

METHODS OF FACTORIAL CODING OF SPEECH SIGNALS

Context. The paper outlines the methods of factorial coding of speech signals using a factorial code to provide integrated information security and to maintain a receiver and transmitter clock phase. By integrated information security, for the methods proposed in this article, we mean data protection from effects of noise in communication channel and attempts of data unauthorized access in open multiple access telecommunication networks. Objective. The goal of the research is to provide integrated protection of real-time speech signals based on factorial coding. For this, the methods for factorial coding of speech signals and building speech codecs have been developed. These methods are based on the properties of factorial codes to keep synchronism with the working signal, to detect a significant part of errors caused by the action of noise, natural or created intentionally, to provide the ability to correct all detected errors with a finite accuracy, as well as to provide cryptographic protection against voice message unauthorized listening by hiding the law of converting speech signal samples into a permutation. Method. The main idea of the proposed methods is to choose permutations for information transferring with a specific set of properties and features that provide the ability to correct errors detected by code and to recover speech signal samples with a finite degree of accuracy (with a nonzero aperture). Results. The procedures for information coding/decoding have been determined. The results of the experimental evaluation of the model of such systems when working on a communication channel with both independent and multiple bit errors are presented. The magnitude of decoding noise due to the finite accuracy of speech signal samples recovery is determined as a function of bit error probability in a communication channel. Conclusions. The proposed methods of factorial coding of a speech signal provide integrated information security and recovery with finite accuracy of speech signal samples deformed by noise in communication channel. The requirements to the quality of communication channel (to the value of bit error probability) for comfortable speech perception are determined.

Optimal design methods for a digital human-computer interface based on human reliability in a nuclear power plant: Part 2: The optimization design method for component quantity

This is the second in a series of papers describing the optimal design method for a digital human-computer interface of nuclear power plant (Npp) from three different points based on human reliability. The purpose of this series is to explore different optimization methods from varying perspectives. This present paper mainly discusses the optimal design method for quantity of components of the same factor.In monitoring process, quantity of components has brought heavy burden to operators, thus, human errors are easily triggered. To solve the problem, the authors propose an optimization process, a quick convergence search method and an affinity error probability mapping function. Two balanceable parameter values of the affinity error probability function are obtained by experiments. The experimental results show that the affinity error probability mapping function about human-computer interface has very good sensitivity and stability, and that quick convergence search method for fuzzy segments divided by component quantity has better performance than general algorithm.

Antenna selection for N R‐STAR‐ M QAM spatial modulation

A new multiple-ring star- M -ary quadrature amplitude modulation-aided spatial modulation ( N R-STAR- M QAM-SM) scheme is proposed. The aim is to minimise the average bit error probability (ABEP) of the system. Then in the interest of further minimising the ABEP, the authors formulate a low-complexity algorithm to achieve the optimum radii of N R-STAR- M QAM-SM. This algorithm is based on a specific multiple-input multiple-output configuration and the pairwise error probability function. To validate the results of the proposed scheme, a closed-form union-bound theoretical ABEP expression is derived. Finally, to improve the error performance of N R-STAR- M QAM-SM, the authors propose a low-complexity Euclidean distance-based antenna selection (EDAS) algorithm for N R-STAR- M QAM-SM (EDAS- N R-STAR- M QAM-SM). Since all amplitude/phase modulation schemes are considered to have rotational symmetry and symmetric constellation points have the same EDAS solution, the authors achieve EDAS- N R-STAR- M QAM-SM by searching only one constellation point per symmetric constellation set. The EDAS- N R-STAR- M QAM-SM solution exhibits a significant reduction in the computational complexity compared with the conventional EDAS solution.

Extremal Characteristics of Statistical Criteria with Given Total Variation Distances between Hypotheses

We consider extremal values of the characteristics of nonrandomized statistical criteria in the following case: there are $n$ hypotheses with given total variation distances. It is shown that finding the extremal values of a function of error probabilities may be reduced to solving a finite-dimensional linear programming problem. We found exact formulas for extreme values of the sum of all error probabilities in the case n=3.

An Analytic Formulation of PMD-Induced Pulse Distortion

AbstractWe systematically analyze the pulse distortion resulting from polarization mode dispersion (PMD) by deriving an analytic expression for the characteristic function of the system bit error probability (BEP) density in terms of the lowest-order moments of the Fourier transformed input pulse shape. We determine the range of validity of our technique, which implements a second-order expansion of the Jones matrix, by comparing our results for chirped and unchirped input pulses with direct numerical simulations. Our method may be easily applied to analyze the role of the first- and second-order PMD in the interference between adjacent pulses.

On Two Strong Converse Theorems for Discrete Memoryless Channels

In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R > C. Subsequently, in 1979, Dueck and Korner determined the optimal exponent of correct decoding. Arimoto's bound has been said to be equal to the bound of Dueck and Korner. However its rigorous proof has not been presented so far. In this paper we give a rigorous proof of the equivalence of Arimoto's bound to that of Dueck and Korner.

Optimal opportunistic routing and network coding for bidirectional wireless flows

There is growing interest in recent years in routing methods for wireless networks that leverage the broadcast nature of the wireless medium and the ability of nodes to overhear their neighbors’ transmissions. Such methods include opportunistic routing (OR), which generally choose the next hop on a routing path only after the outcome of the previous transmission is known; and wireless network coding (NC), which linearly combines packets from different flows coexisting in the network. In this paper, we study the potential benefits of forwarding schemes that combine elements from both the OR and NC approaches, when traffic on a bidirectional unicast connection between two nodes is relayed by multiple common neighbors. We present a theoretically optimal scheme that provides a lower bound on the expected number of transmissions required to communicate a packet in both directions as a function of link error probabilities, and demonstrate that this bound can be up to 20% lower than with either OR or NC employed alone even in a small network. Using simulation, we further explore the control overhead in a direct implementation of the scheme with a simple coordination mechanism and show that the optimal bound can be closely approached for a wide range of link error rates.

Lane decoupling for improving the timing-error resiliency of wide-SIMD architectures

A significant portion of the energy dissipated in modern integrated circuits is consumed by the overhead associated with timing guardbands that ensure reliable execution. Timing speculation, where the pipeline operates at an unsafe voltage with any rare errors detected and resolved by the architecture, has been demonstrated to significantly improve the energy-efficiency of scalar processor designs. Unfortunately, applying the same timing-speculative approach to wide-SIMD architectures, such as those used in highly-efficient GPUs, may not provide similar gains. In this work, we make two important contributions. The first is a set of models describing a parametrized general error probability function that is based on measurements of a fabricated chip and the expected efficiency benefits of timing speculation in a SIMD context. The second contribution is a decoupled SIMD pipeline that more effectively utilizes timing speculation and recovery, when compared with a standard SIMD design that uses only conventional timing speculation. The proposed lane decoupling enables each SIMD lane to tolerate timing errors independent of other adjacent lanes, resulting in higher throughput and improved scalability. We validate our models and evaluate our design using a cycle-based GPU simulator, describe the conditions where efficiency improvements can be obtained, and explore the benefits of decoupling across a wide range of parameters. Our results show that timing speculation can achieve up to 10.3% improvement in efficiency.

Maximum error modeling for fault-tolerant computation using maximum a posteriori (MAP) hypothesis

The application of current generation computing machines in safety-centric applications like implantable biomedical chips and automobile safety has immensely increased the need for reviewing the worst-case error behavior of computing devices for fault-tolerant computation. In this work, we propose an exact probabilistic error model that can compute the maximum error over all possible input space in a circuit-specific manner and can handle various types of structural dependencies in the circuit. We also provide the worst-case input vector, which has the highest probability to generate an erroneous output, for any given logic circuit. We also present a study of circuit-specific error bounds for fault-tolerant computation in heterogeneous circuits using the maximum error computed for each circuit. We model the error estimation problem as a maximum a posteriori (MAP) estimate [28,29], over the joint error probability function of the entire circuit, calculated efficiently through an intelligent search of the entire input space using probabilistic traversal of a binary Join tree using Shenoy–Shafer algorithm [20,21]. We demonstrate this model using MCNC and ISCAS benchmark circuits and validate it using an equivalent HSpice model. Both results yield the same worst-case input vectors and the highest percentage difference of our error model over HSpice is just 1.23%. We observe that the maximum error probabilities are significantly larger than the average error probabilities, and provides a much tighter error bounds for fault-tolerant computation. We also find that the error estimates depend on the specific circuit structure and the maximum error probabilities are sensitive to the individual gate failure probabilities.

The noise immunity of a mobile radio communication line with correlated Rayleigh fadings of the signal level

The noise immunity of signal reception in a communication line, consisting of two consecutively-connected intervals, is analyzed and the probability density distribution of the signal level, its variance, its mean value, its mean square, the signal/noise ratio probability distribution, and the error probability of the reception of signals at the output of the second communication-line interval are determined. It is shown that, by measuring the correlation coefficient of consecutive intervals, one can uniquely determine the error probability function characteristic from the mean signal/noise ratio.

Simulation Evaluation of BER Characteristics for M-PSK and M-QAM Modulations used in the Reverse Channel of Cable TV Nets

A profile is drawn for the various types of square modulations, which are used in transmitting digital signals in the reverse channel of cable TV networks (CATV). The latter are attacked by disturbances, which deteriorate the quality of transmitted signals and cause errors in the digital flow. 32, 64, 128-QAM are also analyzed. Signal to noise ratio is calculated as a function of error probability. Based on the obtained results, it is possible to establish the dependence of the cable length sector on the transmission speed featured by different types of cables provided we have an allowable error coefficient. Simulation and experimental results are compared. Ill. 6, bibl. 12 (in English; summaries in English, Russian and Lithuanian).

On convexity of MQAM's and MPAM's bit error probability functions

AbstractFor MQAM and MPAM with practical values of M and Gray mapping, we provide a rigorous proof that the associated bit error probability (BEP) functions are convex of the signal‐to‐noise ratio per symbol. The proof employs Taylor series expansions of the BEP functions' second derivatives and term‐by‐term comparisons between positive and negative terms. Convexity results are useful for optimizing communication systems as in optimizing adaptive transmission policies. Copyright © 2009 John Wiley & Sons, Ltd.

P-Value calculation for multi-stage additive tests

Multi-stage additive tests are commonly used in applications. Appropriate definition of its test decisions, however, turns out to be challenging. There are a number of existing methods for this purpose, mainly by combining p-values of individual tests using a conditional error probability function. Although these methods are flexible enough to use in most applications, their results depend on the conditional error probability function and selection of this function is often subjective. Motivated by a research problem regarding comparison of two survival hazard rate functions, in this paper, we suggest using an alternative and simpler definition of the overall p-value of a multi-stage additive testing procedure. By this definition, no conditional error probability function needs to be chosen, the entire testing procedure is easy to interpret, and the overall p-value has an explicit formula for a general multi-stage additive testing procedure.

Error Probability Bounds for Bit-Interleaved Space–Time Trellis Coding Over Block-Fading Channels

In this correspondence, we investigate the error probability bounds of a bit-interleaved space-time trellis coding (BISTTC) scheme, which concatenates bit-interleaved coded modulation (BICM) with a space-time trellis code (STTC). We focus on general block-fading channels, wherein each data packet or frame spans a number of independent fading blocks. BICM applied to such channel environments can effectively exploit both time and frequency selectivity, while a STTC maximizes the spacial diversity order. The exact pairwise error probability (PEP) and weight enumeration function (WEF) of BISTTC are used to evaluate the error bound. Due to the concatenation of an outer error correction code (ECC) and a STTC, the overall WEF of BISTTC is obtained by combining the WEF of the outer code with that of the STTC through an uniform interleaver. The main challenge here is to compute the WEF of a STTC for block-fading channels with reasonable complexity. We rely on constructing a composite state transition matrix based on a number of single-step virtual trellises, each corresponding to an independent fading block within a frame. We discuss how this approach reduces storage and computational requirements in the bound analysis, compared to the existing method of obtaining the state transition matrix through accumulation of single-step transition matrices. The derived bound is applicable to both spatially uncorrelated and correlated channels as well as to both flat and frequency-selective block-fading channels. The bound is shown to provide a reasonably close estimate of the simulated performance based on the turbo equalizer-like iterative processing of soft information between the STTC decoder and the ECC decoder.

Sufficient Conditions for Monotonicity of the Undetected Error Probability for Large Channel Error Probabilities

The performance of a linear error-detecting code in a symmetric memoryless channel is characterized by its probability of undetected error, which is a function of the channel symbol error probability, involving basic parameters of a code and its weight distribution. However, the code weight distribution is known for relatively few codes since its computation is an NP-hard problem. It should therefore be useful to have criteria for properness and goodness in error detection that do not involve the code weight distribution. In this work we give two such criteria. We show that a binary linear code C of length n and its dual code C ? of minimum code distance d ? are proper for error detection whenever d ? ? ?n/2? + 1, and that C is proper in the interval [(n + 1 ? 2d ?)/(n ? d ?); 1/2] whenever ?n/3? + 1 ? d ? ? ?n/2?. We also provide examples, mostly of Griesmer codes and their duals, that satisfy the above conditions.