Error Probability Constraint Research Articles

Downlink Transmission With Heterogeneous URLLC Services: Discrete Signaling With Single-User Decoding

The problem of designing downlink transmission schemes for supporting heterogeneous ultra-reliable low-latency communications (URLLC) and/or with other types of services is investigated. We consider the broadcast channel, where the base station sends superimposed signals to multiple users. Under heterogeneous blocklength constraints, strong users who are URLLC users cannot wait to receive the entire transmission frame and perform successive interference cancellation (SIC) due to stringent latency requirements, in contrast to the conventional infinite blocklength cases. Even if SIC is feasible, SIC may be imperfect under finite blocklength constraints. To cope with the heterogeneity in latency and reliability requirements, we propose a practical downlink transmission scheme with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">discrete signaling</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">single-user decoding (SUD), i.e., without SIC</i> . We carefully design the discrete input distributions to enable efficient SUD by exploiting the structural interference. Furthermore, we derive the second-order achievable rate under heterogenous blocklength and error probability constraints and use it to guide the design of channel coding and modulations. It is shown that in terms of achievable rate under short blocklength, the proposed scheme with regular quadrature amplitude modulations and SUD can operate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">extremely close</i> to the benchmark schemes that assume perfect SIC with Gaussian signaling.

Precoding Design for Multi-Group MIMO-NOMA Scheme With SIC Residual Analysis

This paper presents a precoder design for multiple-input multiple-output (MIMO) uplink communications with a multi-group non-orthogonal multiple access (NOMA) scheme. In this scheme, QR-decomposition-based detection is used to decode user signals of each group under imperfect successive interference cancellation (SIC). In the uplink, transmitted signals are encoded with the constellation of a symmetric quadrature amplitude modulation (QAM), and SIC residual errors are generated from symbol demodulation. The statistics of the SIC errors are derived, with which expressions of approximate SIC-residual-power coefficient and signal-to-interference-plus-noise ratio (SINR) are developed. Consequently, the effect of the SIC errors can be explicitly addressed in the precoder design for minimizing the total transmit power subject to users' symbol error probability (SEP) constraints. A suboptimal design algorithm with efficient “logarithmic” golden-section search is developed. Simulation results show the effectiveness of the design criterion and algorithm, and validate the detection error analysis. Unlike the conventional fractional-SIC-error model that suffers from underestimation/overestimation of SIC errors and infeasibility, our SIC error model can provide accurate effect of the SIC errors in the SINR analysis and enable the proposed method to give design solutions to satisfy the SEP constraints.

Joint Symbol Level Precoding and Receive Beamforming Optimization for Multiuser MIMO Downlink

Consider a multi-casting system where a multi-antenna base station (BS) sends multiple data streams to multiple users via symbol-level precoding (SLP). Unlike most of the existing literature which assume single-antenna users, we consider joint SLP and linear receive beamforming (SLP-RBF) design, to investigate the performance boost brought by multi-antenna users. The SLP-RBF problem minimizes the total transmission power subject to the user symbol error probability (SEP) constraints. It turns out that, due to the RBF, the problem involves a large number of non-convex bilinear terms and is much more challenging to handle. In this paper, our goal is to develop computationally efficient algorithms to tackle the SLP-RBF problem. We first introduce several convex approximation forms for the bilinear terms and develop a successive convex approximation (SCA) based algorithm. Furthermore, by exploiting the problem structure and a rank-reduction transformation (RDT), we equivalently write the problem as a dimension-reduced problem with simple box constraints. The reformulated problem enables us to develop a highly efficient iterative algorithm based on accelerated gradient descent methods. We also extend the study to the SLP-RBF problem with one-bit transmission constraints. Since the RDT is no longer applicable, we develop an algorithm based on successive upper-bound minimization (SUM) and alternating direction method of multipliers (ADMM). Simulation results show that the joint SLP-RBF design offers significant power efficiency gains over SLP methods, and the proposed algorithms is time efficient and can handle a large scale system.

Power Distribution for an OFDM-Based Dual-Function Radar-Communication Sensor

This letter investigates the problem of power distribution along with the word error probability (WEP) constraint for the orthogonal frequency division multiplexing based (OFDM) dual-function radar and communication sensor. First, we optimize the radar signal-to-noise ratio (SNR) with the constraints of the WEP requirement and total transmit power. Second, we propose an alternating direction sequential relaxation programming algorithm that involves solving a sequence of approximation convex version of the original nonconvex problem. Finally, simulation results are provided to evaluate the effect of different WEP requirements on the radar SNR, and a significant gain in the radar SNR can be achieved, compared to the average power allocation case.

Privacy-Aware Distributed Hypothesis Testing.

A distributed binary hypothesis testing (HT) problem involving two parties, a remote observer and a detector, is studied. The remote observer has access to a discrete memoryless source, and communicates its observations to the detector via a rate-limited noiseless channel. The detector observes another discrete memoryless source, and performs a binary hypothesis test on the joint distribution of its own observations with those of the observer. While the goal of the observer is to maximize the type II error exponent of the test for a given type I error probability constraint, it also wants to keep a private part of its observations as oblivious to the detector as possible. Considering both equivocation and average distortion under a causal disclosure assumption as possible measures of privacy, the trade-off between the communication rate from the observer to the detector, the type II error exponent, and privacy is studied. For the general HT problem, we establish single-letter inner bounds on both the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs. Subsequently, single-letter characterizations for both trade-offs are obtained (i) for testing against conditional independence of the observer’s observations from those of the detector, given some additional side information at the detector; and (ii) when the communication rate constraint over the channel is zero. Finally, we show by providing a counter-example where the strong converse which holds for distributed HT without a privacy constraint does not hold when a privacy constraint is imposed. This implies that in general, the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs are not independent of the type I error probability constraint.

Searching for Anomalies Over Composite Hypotheses

The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose value lies in normal or abnormal parameter spaces, depending on its state. The objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint. We develop a deterministic search algorithm with the following desired properties. First, when no additional side information on the process states is known, the proposed algorithm is asymptotically optimal in terms of minimizing the detection delay as the error probability approaches zero. Second, when the parameter value under the null hypothesis is known and equal for all normal processes, the proposed algorithm is asymptotically optimal as well, with better detection time determined by the true null state. Third, when the parameter value under the null hypothesis is unknown, but is known to be equal for all normal processes, the proposed algorithm is consistent in terms of achieving error probability that decays to zero with the detection delay. Finally, an explicit upper bound on the error probability under the proposed algorithm is established for the finite sample regime. Extensive experiments on synthetic dataset and DARPA intrusion detection dataset are conducted, demonstrating strong performance of the proposed algorithm over existing methods.

Sequential Hypothesis Test With Online Usage-Constrained Sensor Selection

This paper investigates the sequential hypothesis testing problem with online sensor selection and sensor usage constraints. That is, in a sensor network, the fusion center sequentially acquires samples by selecting one “most informative” sensor at each time until a reliable decision can be made. In particular, the sensor selection is carried out in the online fashion since it depends on all the previous samples at each time. Our goal is to develop the sequential test (i.e., stopping rule and decision function) and sensor selection strategy that minimize the expected sample size subject to the constraints on the error probabilities and sensor usages. To this end, we first recast the usage-constrained formulation into a Bayesian optimal stopping problem with different sampling costs for the usage-contrained sensors. The Bayesian problem is then studied under both finite- and infinite-horizon setups, based on which, the optimal solution to the original usage-constrained problem can be readily established. Moreover, by capitalizing on the structures of the optimal solution, a lower bound is obtained for the optimal expected sample size. In addition, we also propose algorithms to approximately evaluate the parameters in the optimal sequential test so that the sensor usage and error probability constraints are satisfied. Finally, numerical experiments are provided to illustrate the theoretical findings, and compare with the existing methods.

Distributed Detection in Ad Hoc Networks Through Quantized Consensus

We study asymptotic performance of distributed detection in large scale connected sensor networks. Contrasting to the canonical parallel network where a single node has access to local decisions from all other nodes, each node can only exchange information with its direct neighbors in the present setting. We establish that, with each node employing an identical one-bit quantizer for local information exchange, a novel consensus reaching approach can achieve the optimal asymptotic performance of centralized detection as the network size scales. The statement is true under three different detection frameworks: the Bayesian criterion where the maximum a posteriori detector is optimal, the Neyman-Pearson criterion with a constant type-I error probability constraint, and the Neyman-Pearson criterion with an exponential type-I error probability constraint. Leveraging recent development in distributed consensus reaching using bounded quantizers with possibly unbounded data (which are log-likelihood ratios of local observations in the context of distributed detection), we design a one-bit deterministic quantizer with controllable threshold that leads to desirable consensus error bounds. The obtained bounds are key to establishing the optimal asymptotic detection performance. In addition, we examine non-asymptotic performance of the proposed approach, and show that the type-I and type-II error probabilities at each node can be made arbitrarily close to the centralized ones simultaneously when a continuity condition is satisfied.

Spectrum Sharing Network With Wireless Energy Harvesting at Finite Blocklength Regime

In this paper, a spectrum sharing communication system with wireless energy harvesting is investigated at finite blocklength regime over Rayleigh quasi-static block-fading channels. We analyze the error probability and average delay of the secondary user (SU). The closed-form approximations for the SU error probability and average delay are derived, as functions of the number of channel uses in its information transfer phrase. Under the error probability constraint of the primary user (PU), we investigate the power constraint on the SU. Meanwhile, the error probability and energy supply constraints on the SU are also explored. Numerical results demonstrate that the approximation is very tight for a wide range of signal-to-noise ratio (SNRs). The existence of an optimum number of channel uses for SU information transfer is also verified. Moreover, under the error probability constraint of PU, the SU maximum transmit power is validated to increase with the length of an entire block. In addition, for a given target error probability, we show that the SU error probability constraint can be satisfied within the boundary numbers of channel uses in its information transfer phrase. Finally, the energy supply probability is shown as the harvested energy in each channel use with independent and exponential distribution.

Reciprocally-Benefited Secure Transmission for Spectrum Sensing-Based Cognitive Radio Sensor Networks.

The rapid proliferation of independently-designed and -deployed wireless sensor networks extremely crowds the wireless spectrum and promotes the emergence of cognitive radio sensor networks (CRSN). In CRSN, the sensor node (SN) can make full use of the unutilized licensed spectrum, and the spectrum efficiency is greatly improved. However, inevitable spectrum sensing errors will adversely interfere with the primary transmission, which may result in primary transmission outage. To compensate the adverse effect of spectrum sensing errors, we propose a reciprocally-benefited secure transmission strategy, in which SN’s interference to the eavesdropper is employed to protect the primary confidential messages while the CRSN is also rewarded with a loose spectrum sensing error probability constraint. Specifically, according to the spectrum sensing results and primary users’ activities, there are four system states in this strategy. For each state, we analyze the primary secrecy rate and the SN’s transmission rate by taking into account the spectrum sensing errors. Then, the SN’s transmit power is optimally allocated for each state so that the average transmission rate of CRSN is maximized under the constraint of the primary maximum permitted secrecy outage probability. In addition, the performance tradeoff between the transmission rate of CRSN and the primary secrecy outage probability is investigated. Moreover, we analyze the primary secrecy rate for the asymptotic scenarios and derive the closed-form expression of the SN’s transmission outage probability. Simulation results show that: (1) the performance of the SN’s average throughput in the proposed strategy outperforms the conventional overlay strategy; (2) both the primary network and CRSN benefit from the proposed strategy.

A 2-SPRT Based Approach to Multiple-Model Hypothesis Testing for Multi-Distribution Detection

This paper presents an approach to multiple-model hypothesis testing (MMHT) based on 2-SPRT (2-MMSRPT) for detecting unknown events that may have multiple possible distributions. The sequential probability ratio test (SPRT) based MMHT method (MMSPRT) is promising because of its efficiency and theoretical validity. However, it may suffer from SPRT’s lack of an upper bound on its stopping time, especially in the mis-specified case. The proposed 2-MMSPRT algorithm not only copes with this problem, but also is in a setting that can provide efficient detection in the sense of minimizing the maximum expected sample size subject to error probability constraints. Specifically, we prove the theoretical validity of 2-SPRT for the problem of testing hypotheses with multivariate normal densities. Moreover, we present a technique of forced independence and identical distribution (i.i.d.) to map the non-i.i.d. likelihood ratio sequence to an i.i.d. one, which enables us to apply the SPRT and 2-SPRT effectively to the dynamic case (under the linear-Gaussian assumption) with a non-identical distribution. Also, 2-MMSPRT’s detection efficiency under some assumptions/approximations is verified. Performance of 2-MMSPRT is evaluated for signal detection and model-set selection problems in several scenarios. Simulation results demonstrate the detection efficiency of the proposed 2-MMSPRT compared with the MMSPRT and some traditional tests.

Active Hypothesis Testing for Anomaly Detection

The problem of detecting a single anomalous process among a finite number M of processes is considered. At each time, a subset of the processes can be observed, and the observations from each chosen process follow two different distributions, depending on whether the process is normal or abnormal. The objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint. This problem can be considered as a special case of active hypothesis testing first considered by Chernoff where a randomized strategy, referred to as the Chernoff test, was proposed and shown to be asymptotically (as the error probability approaches zero) optimal. For the special case considered in this paper, we show that a simple deterministic test achieves asymptotic optimality and offers better performance in the finite regime. We further extend the problem to the case where multiple anomalous processes are present. In particular, we examine the case where only an upper bound on the number of anomalous processes is known.

Group Testing-Based Spectrum Hole Search for Cognitive Radios

This paper investigates the use of adaptive group testing to find a spectrum hole of a specified bandwidth in a given wideband of interest. We propose a group testing-based spectrum hole search algorithm that exploits sparsity in the primary spectral occupancy by testing a group of adjacent subbands in a single test. This is enabled by a simple and easily implementable sub-Nyquist sampling scheme for signal acquisition by the cognitive radios (CRs). The sampling scheme deliberately introduces aliasing dur- ing signal acquisition, resulting in a signal that is the sum of signals from adjacent subbands. Energy-based hypothesis tests are used to provide an occupancy decision over the group of subbands, and this forms the basis of the proposed algorithm to find contiguous spectrum holes of a specified bandwidth. We extend this frame- work to a multistage sensing algorithm that can be employed in a variety of spectrum sensing scenarios, including noncontiguous spectrum hole search. Furthermore, we provide the analytical means to optimize the group tests with respect to the detection thresholds, number of samples, group size, and number of stages to minimize the detection delay under a given error probability constraint. Our analysis allows one to identify the sparsity and SNR regimes where group testing can lead to significantly lower detection delays compared with a conventional bin-by-bin energy detection scheme; the latter is, in fact, a special case of the group test when the group size is set to 1 bin. We validate our analytical results via Monte Carlo simulations.

Performance Analysis of Distributed Decision Fusion Using A Multilevel Censoring Scheme in Wireless Sensor Networks

Sensor-censoring schemes have been widely applied to distributed detection to achieve the goal of energy saving in limited-energy wireless sensor networks (WSNs). In the traditional censoring scheme, the sensor transmits data to the fusion center (FC) only when the reliability is beyond a specified threshold, and hereby, energy saving is achieved. To further exploit the energy-efficiency capability of the censoring decision scheme, this paper proposes a new multilevel sensor-censoring scheme. As opposed to our earlier proposed three-region censoring scheme, the number of censoring levels in the proposed scheme is not restricted. A criterion on computing the reliability of the observation in each region is quantitatively determined, which controls the power of the signal transmitted to the FC. When the observation falls within the region with high reliability, the power of the transmitted signal is high, and vice versa. Both soft- and hard-decision fusion rules under the considered multilevel censoring strategy are investigated. For a given fusion rule, the main problem of this work is to minimize the error probability of the global decisions made by the FC by obtaining the best region allocation on the observation, which corresponds to the optimum multilevel censoring regions. The performance of the proposed multilevel censoring scheme is examined in terms of both energy saving and error performance. We compare the multilevel censoring scheme with the conventional scheme, which censors no sensor observations. The results show that the multilevel censoring scheme not only offers us a more flexible design of the censoring strategy but consumes much less energy as well, compared with the conventional scheme when the same error probability constraint is given. In addition, the obtained result shows that the superiority of the multilevel censoring scheme becomes more remarkable when the signal strength of the sensor observations is small.

Performance Analysis of Distributed Decision Fusion Using a Censoring Scheme in Wireless Sensor Networks

Sensor-censoring schemes have been widely applied to distributed detection to achieve the goal of energy saving in limited-energy wireless sensor networks (WSNs). In the traditional censoring scheme, the sensor transmits data to the fusion center (FC) only when the reliability is beyond a specified threshold, and hereby, energy saving is achieved. To further exploit the energy-efficiency capability of the censoring decision scheme, this paper proposes a new multilevel sensor-censoring scheme. As opposed to our earlier proposed three-region censoring scheme, the number of censoring levels in the proposed scheme is not restricted. A criterion on computing the reliability of the observation in each region is quantitatively determined, which controls the power of the signal transmitted to the FC. When the observation falls within the region with high reliability, the power of the transmitted signal is high, and vice versa. Both soft- and hard-decision fusion rules under the considered multilevel censoring strategy are investigated. For a given fusion rule, the main problem of this work is to minimize the error probability of the global decisions made by the FC by obtaining the best region allocation on the observation, which corresponds to the optimum multilevel censoring regions. The performance of the proposed multilevel censoring scheme is examined in terms of both energy saving and error performance. We compare the multilevel censoring scheme with the conventional scheme, which censors no sensor observations. The results show that the multilevel censoring scheme not only offers us a more flexible design of the censoring strategy but consumes much less energy as well, compared with the conventional scheme when the same error probability constraint is given. In addition, the obtained result shows that the superiority of the multilevel censoring scheme becomes more remarkable when the signal strength of the sensor observations is small.

Optimal group‐sequential designs for simultaneous testing of superiority and non‐inferiority

Confirmatory clinical trials comparing the efficacy of a new treatment with an active control typically aim at demonstrating either superiority or non-inferiority. In the latter case, the objective is to show that the experimental treatment is not worse than the active control by more than a pre-specified non-inferiority margin. We consider two classes of group-sequential designs that combine the superiority and non-inferiority objectives: non-adaptive designs with fixed group sizes and adaptive designs where future group sizes may be based on the observed treatment effect. For both classes, we derive group-sequential designs meeting error probability constraints that have the lowest possible expected sample size averaged over a set of values of the treatment effect. These optimized designs provide an efficient means of reducing expected sample size under a range of treatment effects, even when the separate objectives of proving superiority and non-inferiority would require quite different fixed sample sizes. We also present error spending versions of group-sequential designs that are easily implementable and can handle unpredictable group sizes or information levels. We find the adaptive choice of group sizes to yield some modest efficiency gains; alternatively, expected sample size may be reduced by adding another interim analysis to a non-adaptive group-sequential design.

Power-efficient wireless OFDMA using limited-rate feedback

Emerging applications involving low-cost wireless sensor networks motivate well optimization of multi-user orthogonal frequency-division multiple access (OFDMA) in the power-limited regime. In this context, the present paper relies on limited-rate feedback (LRF) sent from the access point to terminals to minimize the total average transmit-power under individual average rate and error probability constraints. Along with the characterization of optimal bit, power and subcarrier allocation policies based on LRF, suboptimal yet simple schemes are developed for channel quantization. The novel algorithms proceed in two phases: (i) an off-line phase to construct the channel quantizer as well as the rate and power codebooks with moderate complexity; and (ii) an on-line phase to obtain, based on quantized channel state information, the optimum, rate, power and user-subcarrier allocation with linear complexity. Numerical examples corroborate the analytical claims and reveal that significant power savings result even with suboptimal schemes based on practically affordable LRF.

Optimizing power efficiency of OFDM using quantized channel state information

Emerging applications involving low-cost wireless sensor networks motivate well optimization of orthogonal frequency-division multiplexing (OFDM) in the power-limited regime. To this end, the present paper develops loading algorithms to minimize transmit-power under rate and error probability constraints, using three types of channel state information at the transmitter (CSIT): deterministic (per channel realization) for slow fading links, statistical (channel mean) for fast fading links, and quantized (Q), whereby a limited number of bits are fed back from the transmitter to the receiver. Along with optimal bit and power loading schemes, quantizer designs and reduced complexity alternatives with low feedback overhead are developed to obtain a suite of Q-CSIT-based OFDM transceivers with desirable complexity versus power-consumption tradeoffs. Numerical examples corroborate the analytical claims and reveal that significant power savings result even with a few bits of Q-CSIT

A synchronous fiber-optic CDMA system using adaptive optical hardlimiter

In this paper, we propose a new synchronous fiber-optic code-division multiple-access (CDMA) system using adaptive optical hardlimiter and modified prime sequence code. At the receiver, the energy in one bit duration is estimated and used to adjust the threshold value of the adaptive optical hardlimiter which is placed after the optical correlator. The bit error probability of the system is analyzed with the consideration of thermal noise, shot noise, and dark current noise of the photodetector. The results show that this system can support a larger number of simultaneous users than other systems also using modified prime sequence code under the same bit error probability constraint.

Sequential Equivalence Testing and Repeated Confidence Intervals, with Applications to Normal and Binary Responses

We propose group sequential tests of the equivalence of two treatments based on ideas related to repeated confidence intervals. These tests adapt readily to unpredictable group sizes, to the possibility of continuing even though a boundary has been crossed, and to nonnormal observations. In comparing two binomial distributions, the required sample size depends strongly on the average success probability and an adaptive choice of group size is needed to produce an efficient test meeting specified error probability constraints. A special case is the experiment where interim analyses are performed, not for the purpose of early termination but simply to adjust the sample size so that nominal error rates will be guaranteed, despite the presence of a nuisance parameter.