Federated learning (FL) has attracted great attention lately due to many advantages it provides. The community has noted that FL performance can be greatly degraded by heterogeneous data or any data that is unsuitable for the learning problem under consideration. Here we focus on the gradient descent and heavy ball algorithms in a worker-server architecture and describe a simple but effective approach to reject data from workers with unsuitable data that would significantly harm the training performance. The approach uses a very short pre-training phase where only a few workers who have known suitable data are involved. Using the theory of order statistics, this pre-training allows accurate estimation of the range of gradient directions that should be present during the initial iterations of training, allowing workers with unsuitable data to be recognized. The approach is tested on real data sets and shows promising results for all cases tested.

This article proposes a data-driven dynamic state-estimation (DSE) approach designed for photovoltaic (PV) energy conversion systems (single stage and two stage) that are subjected to both process and measurement noise. The proposed framework follows a two-phase methodology encompassing “data-driven model identification” and “state-estimation.” In the initial model identification phase, state feedback is gathered to elucidate the dynamics of the PV systems using a nonlinear sparse regression technique. Following the identification of the PV dynamics, the nonlinear data-driven model will be utilized to estimate the dynamics of the PV system for monitoring and protection purposes. To account for incomplete measurements, inherent uncertainties, and noise, we employ an “unscented Kalman filter,” which facilitates the state estimation by processing the noisy output data. Ultimately, this article substantiates the efficacy of the proposed sparse regression-based unscented Kalman filter through simulation results, providing a comparative analysis with a physics-based DSE.

Target velocity estimation is investigated for a cooperative multiple-input multiple-output (MIMO) integrated radar and communications (IRC) system employing quantized measurements. To reduce the communications burden, the local receivers quantize the local measurements, and then transmit the quantized measurements to the fusion center (FC). This paper discusses two distributed parameter estimation strategies, one directly quantizes the received signals at each local sensor and sends them to the FC for velocity estimation, while the other first estimates the Doppler frequency at each local sensor and then sends it to the FC after quantization. The FC estimates the target velocity utilizing the quantized measurements from all local receivers for both strategies. We derive the corresponding distributed maximum likelihood (ML) estimators and Cramér-Rao bounds (CRBs). It is demonstrated that for small signal to clutter-plus-noise ratio (SCNR), the Doppler frequency quantization-based strategy has better estimation performance, while for large SCNR the received signal quantization-based strategy performs better.

Data-driven anomaly detection over time series data is studied from the perspective of separating data anomalies—corresponding to sensor failures—from process anomalies—that arise from equipment or operational failures. A semi-supervised approach is proposed that utilizes two predictive models trained on non-anomalous data using two different sensor groups as inputs, and a nested hypothesis test to reliably classify data or process anomalies. Conditions are derived on choice of sensor groups to guarantee reliable detection, and a case study is presented to demonstrate the proposed classification approach.

This paper investigates the secret key-authenticated-capacity region, where information-theoretic authentication is defined by the ability of the decoder to accept and decode messages originating from a valid encoder while rejecting messages from other invalid sources. The model considered here consists of a valid encoder-decoder pairing that can communicate through a channel controlled by an adversary who is also able to eavesdrop on the encoder’s transmissions. Prior to the encoder’s transmission, the adversary decides whether or not to replace the decoder’s observation with an arbitrary one of the adversary’s choosing, with the adversary’s objective being to have the decoder accept and decode their observation to a valid message (different from that of the encoder). To combat the adversary, the encoder and decoder share a secret key. The secret key-authenticated-capacity region is defined as the region of jointly achievable message rate, authentication rate (a to be defined per symbol measure that will generally represent the likelihood that an adversary can fool the decoder), and the key-consumption rate (how many bits of secret key are needed per symbol sent). This is the second of a two-part study, with the parts differing in their measure of the authentication rate. For this second study, the probability of false authentication is considered as a function of the system state, where the system state is defined by the message being transmitted, the value of the secret key, the adversary’s channel observations, and the adversary’s (possibly stochastic) choice for the decoder’s observation. Termed the typical-authentication rate, the authentication measure considered here corresponds to an upper bound on the probability of false authentication for the majority of system states. For this measure, we derive matching inner and outer bounds for the secret key-enabled authenticated capacity region in terms of traditional information-theoretic measures. In doing so, it is shown that the typical-authentication rate and the message rate exhibit a one-to-one trade-off in the capacity region.

This paper investigates the secret-key-authenticated-capacity region, where information-theoretic authentication is defined by the ability of the decoder to accept and decode messages originating from a valid encoder while rejecting messages from other invalid sources. The model considered here consists of a valid encoder-decoder pairing that can communicate through a channel controlled by an adversary who is also able to eavesdrop on the encoder’s transmissions. Over multiple rounds of communication, the adversary first decides whether or not to replace the decoder’s observation with an arbitrary one of the adversary’s choosing, with the goal of the adversary being to have the decoder accept and decode their observation as a valid message (different from that of the encoder). To combat the adversary, the encoder and decoder share a secret key. The secret-key-authenticated-capacity region here is then defined as the region of jointly achievable message rate, authentication rate (a to be defined per symbol measure that will generally represent the likelihood that an adversary can fool the decoder), and the key-consumption rate (how many bits of secret key are needed per symbol sent). This is the first of a two-part study, with the parts differing in their measure of the authentication rate. In this first study, the authentication rate is the exponent of blocklength-normalized exponent of the expected probability of false authentication. For this metric, we provide an inner bound which improves on those existing in the literature. This is achieved by adopting and merging different classical techniques in novel ways. Within these classical secret-key-based authentication techniques, one technique derives authentication capability from secure channel coding to send the secret key with the message, and the other technique derives its authentication capability directly from obscuring the source.

Natural gas pipeline system operations rely heavily on Supervisory Control and Data Acquisition (SCADA) systems. While the SCADA systems introduce many advantages, they also introduce more vulnerabilities by providing opportunities for malicious cyber-attackers. If the cyber-attacks properly modify pressures, flows, and the topology the operator believes is present simultaneously, the cyber-attacks can be undetectable. While this topic has received attention for electrical grids, other cyber-physical systems have seen much less study on this topic. Natural gas networks are employed extensively to power generators in the electrical grid, so attacks on natural gas networks are very important. We have not seen any research on this topic for natural gas networks yet. The particular nonlinear equations which model natural gas networks make the analysis much more difficult. In this paper, we study undetectable attacks on natural gas networks in a signal processing perspective by describing the steady-state mathematical model and sensor measurements. We propose a countermeasure to eliminate undetectable attacks by protecting sensors in specific locations. We present an example that describes how an operator can be misled if the proposed countermeasure is not applied. In such cases, the operator could apply inappropriate control which could damage the system or cause a loss of critical gas supply to customers.

Fingerprint embedding at the physical layer is a highly tunable authentication framework for wireless communication that achieves information-theoretic security by hiding a traditional HMAC tag in noise. In a multiantenna scenario, artificial noise (AN) can be transmitted to obscure the tag even further. The AN strategy, however, relies on perfect knowledge of the channel state information (CSI) between the legitimate users. When the CSI is not perfectly known, the added noise leaks into the receiver's observations. In this article, we explore whether AN still improves security in the fingerprint embedding authentication framework with only imperfect CSI available at the transmitter and receiver. Specifically, we discuss and design detectors that account for AN leakage and analyze the adversary's ability to recover the key from observed transmissions. We compare the detection and security performance of the optimal perfect CSI detector with the imperfect CSI robust matched filter test and a generalized likelihood ratio test (GLRT). We find that utilizing AN can greatly improve security, but suffers from diminishing returns when the quality of CSI knowledge is poor. In fact, we find that in some cases allocating additional power to AN can begin to decrease key security.

Sensor-equipped connected vehicle networks (SECVNs) have the potential to enable substantially safer driving by improved object tracking, which is an important basic building block in SECVNs. Unfortunately, cyber-attacks on SECVNs pose a very serious threat which could lead to unacceptable outcomes, including fatalities. Recently there has been increasing focus on malicious attack detection and mitigation in SECVNs, and some of this work has considered attacks on sensor data to impact object tracking. Unfortunately, low complexity mitigation approaches which do not compromise performance are lacking. This paper describes an efficient machine-learning enhanced approach for tracking under cyber-attacks. By proper selection of some variances related to the sensor and prior probability density functions, under some assumptions the performance can be made as close as desired to a bound on the best possible performance. However, the complexity of this new approach is dramatically lower than the best existing published low complexity approach, which provides performance which is substantially inferior to that provided by the new approach. The new approach also provides much better scaling with the size of the SECVN. In particular, the complexity increases linearly in the number of sensors, while the best low complexity published approach has a complexity which grows quadratically in the number of sensors. The new approach is also applicable to other tracking applications.

Secrecy by design is examined as an approach to information-theoretic secrecy. The main idea behind this approach is to design an information processing system from the ground up to be perfectly secure with respect to an explicit secrecy constraint. The principal technical contributions are decomposition bounds that allow the representation of a random variable$X$as a deterministic function of$({S},{Z})$, where$S$is a given fixed random variable and$Z$is constructed to be independent of$S$. Using the problems of privacy and lossless compression as examples, the utility cost of applying secrecy by design is investigated. Privacy is studied in the setting of the privacy funnel function previously introduced in the literature and new bounds for the regime of zero information leakage are derived. For the problem of lossless compression, it is shown that strong information-theoretic guarantees can be achieved using a reduced secret key size and a quantifiable penalty on the compression rate. The fundamental limits for both problems are characterized with matching lower and upper bounds when the secret$S$is a deterministic function of the information source$X$.

In this letter, we derive the exact joint probability density function (pdf) of the amplitude and phase of the product of two correlated non-zero mean complex Gaussian random variables with arbitrary variances. This distribution is useful in many problems, for example radar and communication systems. We determine the joint pdf in terms of an infinite summation of modified Bessel functions of the first and second kinds, which generalizes the existing results. The truncation error is also studied when a truncated sum is employed. Finally, we evaluate the derived expressions through numerical experiments.

IEEE 1588, built on the classical two-way message exchange scheme, is a popular clock synchronization protocol for packet-switched networks. Due to the presence of random queuing delays in a packet-switched network, the joint recovery of the clock skew and offset from the timestamps of the exchanged synchronization packets can be treated as a statistical estimation problem. In this paper, we address the problem of clock skew and offset estimation for IEEE 1588 in the presence of possible unknown asymmetries between the deterministic path delays of the forward master-to-slave path and reverse slave-to-master path, which can result from incorrect modeling or cyber-attacks. First, we develop lower bounds on the mean square estimation error for a clock skew and offset estimation scheme for IEEE 1588 assuming the availability of multiple master-slave communication paths and complete knowledge of the probability density functions (pdf) describing the random queuing delays. Approximating the pdf of the random queuing delays by a mixture of Gaussian random variables, we then present a robust iterative clock skew and offset estimation scheme that employs the space alternating generalized expectation-maximization (SAGE) algorithm for learning all the unknown parameters. Numerical results indicate that the developed robust scheme exhibits a mean square estimation error close to the lower bounds.

Accurate knowledge of natural gas network topology is critical for the proper operation of natural gas networks. Failures, physical attacks, and cyber attacks can cause the actual natural gas network topology to differ from what the operator believes to be present. Incorrect topology information misleads the operator to apply inappropriate control causing damage and lack of gas supply. Several methods for verifying the topology have been suggested in the literature for electrical power distribution networks, but we are not aware of any publications for natural gas networks. In this paper, we develop a useful topology verification algorithm for natural gas networks based on modifying a general known statistics-based approach to eliminate serious limitations for this application while maintaining good performance. We prove that the new algorithm is equivalent to the original statistics-based approach for a sufficiently large number of sensor observations. We provide new closed-form expressions for the asymptotic performance that are shown to be accurate for the typical number of sensor observations required to achieve reliable performance.

In this work, we study coexisting MIMO radar and MIMO communication systems, where the two systems work cooperatively. The radar shares its antenna positions and transmitted signals with the communication system. The communication system informs the radar about the antenna locations, as well as the statistics of the communication signals. Previous work has presented a performance gain for both the radar and communication systems in terms of target localization performance and mutual information. With the removal of the assumption about completely decoded communication signals at the radar receiver, this paper analyzes the performance metrics and shows that there is still a significant gain obtained through cooperation.

The framework of secrecy by design is introduced and the fundamental limits of lossless data compression are characterized for this setting. The main idea behind secrecy by design is to begin with an operational secrecy constraint, which is modeled by a secrecy function fs, and then to derive fundamental limits for the performance of the resulting secrecy system. In the setting of lossless compression, it is shown that strong information-theoretic secrecy guarantees can be achieved using a reduced secret key size and a modular two-part coding strategy. Focusing on the non-asymptotic fundamental limits of lossless compression, variable-length lossless compression is studied. It is noted that completely lossless compression is not possible when perfect secrecy is required; however, it becomes meaningful under partial secrecy constraints. Moreover, although it is well known that the traditional fundamental limits of variable-length and almost lossless fixed-length compression are intimately related, this relationship collapses once the secrecy constraint is incorporated.

In this letter, the coexistence of a multiple-input multiple-output (MIMO) radar and a distributed MIMO communication systems is studied. Target returns contributed from both the radar transmitters and communication transmitters are employed to complete the radar task, leading to a hybrid active-passive MIMO radar network. For the communication task, not only are the communication signals received directly from communication transmitters, but also those bounced off from the target are exploited to extract useful information. The target localization Cramer-Rao bound and mutual information are derived for the radar and communication systems, respectively. It is shown that there is a performance gain due to the cooperation between the radar and communication systems.

This paper addresses the problem of clock skew and offset estimation (CSOE) for the IEEE 1588 precision time protocol. Built on the classical two-way message exchange scheme, IEEE 1588 is a prominent synchronization protocol for packet switched networks. Due to the presence of random queuing delays in a packet switched network, the joint recovery of clock skew and offset from the received packet timestamps can be viewed as a statistical estimation problem. Recently, assuming perfect clock skew information, minimax optimum clock offset estimators were developed for IEEE 1588. Building on this work, we first develop joint optimum invariant clock skew and offset estimators for IEEE 1588 for known queuing delay statistics and unlimited computational complexity. We then show that the developed estimators are minimax optimum, i.e., these estimators minimize the maximum skew normalized mean square estimation error over all possible values of the unknown parameters. Minimax optimum estimators that utilize information from past timestamps to improve accuracy are also introduced. The developed optimum estimators provide useful fundamental limits for evaluating the performance of CSOE schemes. These performance limits can aid system designers to develop algorithms with the desired computational complexity that achieve performance close to the performance of the optimum estimators. If a designer finds an approach with a complexity they find acceptable and which provides performance close to the optimum performance, they can use it and know they have near optimum performance. This is precisely the approach used in communications when comparing to capacity.

This paper proposes an energy-efficient counting rule for distributed detection by ordering sensor transmissions in wireless sensor networks. In the counting rule-based detection in an N-sensor network, the local sensors transmit binary decisions to the fusion center, where the number of all N local-sensor detections are counted and compared to a threshold. In the ordering scheme, sensors transmit their unquantized statistics to the fusion center in a sequential manner; highly informative sensors enjoy higher priority for transmission. When sufficient evidence is collected at the fusion center for decision making, the transmissions from the sensors are stopped. The ordering scheme achieves the same error probability as the optimum unconstrained energy approach (which requires observations from all the N sensors) with far fewer sensor transmissions. The scheme proposed in this paper improves the energy efficiency of the counting rule detector by ordering the sensor transmissions: each sensor transmits at a time inversely proportional to a function of its observation. The resulting scheme combines the advantages offered by the counting rule (efficient utilization of the network's communication bandwidth, since the local decisions are transmitted in binary form to the fusion center) and ordering sensor transmissions (bandwidth efficiency, since the fusion center need not wait for all the N sensors to transmit their local decisions), thereby leading to significant energy savings. As a concrete example, the problem of target detection in large-scale wireless sensor networks is considered. Under certain conditions the ordering-based counting rule scheme achieves the same detection performance as that of the original counting rule detector with fewer than N/2 sensor transmissions; in some cases, the savings in transmission approaches (N-1).

This paper studies reduced complexity target detection using multiple-input-multiple-output (MIMO) radar with lower complexity. To reduce either hardware or software complexity, some parts of the test statistic are eliminated in the proposed method. For the general case where clutter-plus-noise and reflection coefficients are correlated, the test statistic requires the computation of a set of matched filters (MF-s). These MFs correlate the clutter-plus-noise-free signal received at one receiver due to the signal transmitted from some transmit antenna with the signal received at another receiver. For a special case of uncorrelated clutter-pIus-noise and reflection coefficients and orthogonal waveforms, the proposed method is equivalent to choosing a subset of transmitters to maximize detection probability. In this case we prove that selecting the transmitters at each receiver corresponding to the largest signal-to-clutter-plus-noise ratio (SCNRs) leads to the best detection performance. In the more general case our algorithm picks the best of these MFs to implement under the constraint that the total number of these MFs that one can implement at each receiver is limited.

The rate regions of many variations of the standard and wire-tap channels have been thoroughly explored. Secrecy capacity characterizes the loss of rate required to ensure that the adversary gains no information about the transmissions. Authentication does not have a standard metric, despite being an important counterpart to secrecy. While some results have taken an information-theoretic approach to the problem of authentication coding, the full rate region and accompanying trade-offs have yet to be characterized. In this paper, we provide an inner bound of achievable rates with an average authentication and reliability constraint. The bound is established by combining and analyzing two existing authentication schemes for both noisy and noiseless channels. We find that our coding scheme improves upon existing schemes.

In this letter, we address the problem of target detection in passive multiple-input multiple-output radar networks. A generalized likelihood ratio test is derived, assuming prior knowledge of the signal format used in the noncooperative transmit stations. The performance of the generalized likelihood ratio test in the known signal format case is often significantly more favorable when compared to the case that does not exploit this information. Further, the performance improves with increasing number of samples per symbol and for a sufficiently large number of samples per symbol, the performance closely approximates that of an active radar with a known transmitted signal.

The impact of random compression on the Fisher information matrix (FIM) and the Cramér-Rao bound (CRB) is studied when estimating unknown complex parameters in the perturbed linear model. A random compression matrix is considered whose elements are i.i.d. standard complex normal random variables. The FIM averaged over compression is equal to a scalar of the FIM before compression plus an additional term. The upper and lower bounds of the CRB averaged over the random compression matrix are also given. Finally, numerical results are conducted to verify our theoretical results.

This paper addresses the problem of robust clock phase offset estimation for the IEEE 1588 precision time protocol in the presence of unknown asymmetric network path delays. The presence of an unknown asymmetry between the path delays can lead to significant degradation in the performance of a phase offset estimation scheme. Assuming multiple master-slave communication paths are available, we first provide lower bounds on the best achievable performance for a phase offset estimation scheme in the presence of asymmetric master-slave communication paths. We then present a novel phase offset estimation scheme that employs the expectation-maximization algorithm to identify the asymmetric master-slave communication paths. After discarding information from these paths, we employ the minimax optimum vector location parameter estimator for estimating the phase offset. Simulation results are presented to show that the proposed phase offset estimation scheme exhibits performance close to the lower bounds in a wide variety of network scenarios.

Authentication via fingerprint embedding at the physical layer utilizes noise in the wireless channel to attain a certain degree of information theoretic security that traditional HMAC methods cannot provide. Fingerprint embedding refers to a key-aided process of superimposing a low-power tag to the primary message waveform for the purpose of authenticating the transmission. The tag is uniquely created from the message and key and successful authentication is achieved when the correct tag is detected by the receiver. This paper generalizes a framework for embedding physical layer fingerprints to create an authenticated side-channel for minimal cost. Side-channel information is conveyed to the receiver through the transmitter's choice of tag from a secret codebook generated by the primary message and a shared secret key. In addition, a new linear coding scheme is introduced which enhances the ability to trade off the performance goals of authentication, side-channel rate, secrecy, and privacy.

It is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system. A critical quantity called inestimable dimension for quantized data (IDQD) is introduced, which does not depend on the quantization regions and the statistical models of the observations but instead depends only on the number of sensors and on the precision of the vector quantizers employed by the system. It is shown that the IDQD describes a quantization-induced fundamental limitation on the estimation capabilities of the system. To be specific, if the dimension of the desired vector parameter is larger than the IDQD of the quantized estimation system, then the Fisher information matrix for estimating the desired vector parameter is singular, and, moreover, there exist infinitely many nonidentifiable vector parameter points in the vector parameter space. Furthermore, it is shown that under some common assumptions on the statistical models of the observations and the quantization system, a smaller IDQD can be obtained, which can specify an even more limiting quantization induced fundamental limitation on the estimation capabilities of the system.

In modern heterogeneous sensor networks huge volumes of information rapidly flow across the system, and it is often too difficult or costly to associate data to the sensors that produced them. Then, the set of observations appears to be unlabeled: What comes from whom? We study the classical problem of detecting a known signal embedded in Gaussian noise, but under the peculiar assumption that the signal samples have been scrambled (e.g., in time or space) in an unknown way. Our study sheds light on questions like: How much detection performance is contained in the samples' values and how much in their ordering? Are there nicely-performing detectors with affordable computational complexity?

Estimation of an unknown deterministic vector from quantized sensor data is considered in the presence of spoofing and man-in-the-middle attacks. First, asymptotically optimum processing, which identifies and categorizes the attacked sensors into different groups according to distinct types of attacks, is outlined in the face of man-in-the-middle attacks. Necessary and sufficient conditions are provided under which utilizing the attacked sensor data will lead to better estimation performance when compared to approaches where the attacked sensors are ignored. Next, necessary and sufficient conditions are provided under which spoofing attacks provide a guaranteed attack performance in terms of the Cramer-Rao Bound regardless of the processing the estimation system employs. It is shown that it is always possible to construct such a highly desirable attack by properly employing an attack vector parameter having a sufficiently large dimension relative to the number of quantization levels employed, which was not observed previously. For unattacked quantized estimation systems, a general limitation on the dimension of a vector parameter which can be accurately estimated is uncovered.

In this paper, the downlink channel estimation for millimeter wave (mmWave) MIMO systems over frequency selective channels is considered, where both the base station (BS) and the mobile station (MS) are equipped with massive number of antennas. We assume hybrid analog and digital beamforming structures are employed at BS and MS. To overcome the frequency selective fading, we employ orthogonal frequencydivision multiplexing (OFDM) in transmission. By exploiting the sparse scattering nature of mmWave channels, we propose a CANDECOMP/PARAFAC (CP) decomposition-based method for downlink channel estimation. Our analysis reveals that the uniqueness of the CP decomposition can be guaranteed even when the size of the tensor is small. Hence the proposed method has the potential to achieve substantial training overhead reduction. Simulation results show that the proposed method presents a clear advantage over the compressed sensing-based method in terms of both estimation accuracy and computational complexity.

We consider the problem of downlink channel estimation for millimeter wave (mmWave) MIMO-OFDM systems, where both the base station (BS) and the mobile station (MS) employ large antenna arrays for directional precoding/beamforming. Hybrid analog and digital beamforming structures are employed in order to offer a compromise between hardware complexity and system performance. Different from most existing studies that are concerned with narrowband channels, we consider estimation of wideband mmWave channels with frequency selectivity, which is more appropriate for mmWave MIMO-OFDM systems. By exploiting the sparse scattering nature of mmWave channels, we propose a CANDECOMP/PARAFAC (CP) decomposition-based method for channel parameter estimation (including angles of arrival/departure, time delays, and fading coefficients). In our proposed method, the received signal at the MS is expressed as a third-order tensor. We show that the tensor has the form of a low-rank CP, and the channel parameters can be estimated from the associated factor matrices. Our analysis reveals that the uniqueness of the CP decomposition can be guaranteed even when the size of the tensor is small. Hence the proposed method has the potential to achieve substantial training overhead reduction. We also develop Cramér-Rao bound (CRB) results for channel parameters and compare our proposed method with a compressed sensing-based method. Simulation results show that the proposed method attains mean square errors that are very close to their associated CRBs and present a clear advantage over the compressed sensing-based method.

A harvest-use-store power splitting (PS) relaying strategy with distributed beamforming is proposed for wireless-powered multi-relay cooperative networks in this paper. Different from the conventional battery-free PS relaying strategy, harvested energy is prioritized to power information relaying while the remainder is accumulated and stored for future usage with the help of a battery in the proposed strategy, which supports an efficient utilization of harvested energy. However, PS affects throughput at subsequent time slots due to the battery operations including the charging and discharging. To this end, PS and battery operations are coupled with distributed beamforming. A throughput optimization problem to incorporate these coupled operations is formulated though it is intractable. To address the intractability of the optimization, a layered optimization method is proposed to achieve the optimal joint PS and battery operation design with non-causal channel state information (CSI), in which the PS and the battery operation can be analyzed in a decomposed manner. Then, a general case with causal CSI is considered, where the proposed layered optimization method is extended by utilizing the statistical properties of CSI. To reach a better tradeoff between performance and complexity, a greedy method that requires no information about subsequent time slots is proposed. Simulation results reveal the upper and lower bound on performance of the proposed strategy, which are reached by the layered optimization method with non-causal CSI and the greedy method, respectively. Moreover, the proposed strategy outperforms the conventional PS-based relaying without energy accumulation and time switching-based relaying strategy.

Ambiguity functions are important design tools that characterize the response of radar detectors to mismatched targets. Recently, the authors proposed a new definition of the ambiguity function for radars that perform non-coherent processing. In this paper, this new ambiguity function definition is utilized to optimize frequency hopping waveforms for MIMO radars with arbitrary antenna separations. To this end, ambiguity function expressions for a general MIMO radar with arbitrary antenna separation are derived, and further simplified for frequency-hopping waveforms. Next, a scalar cost function is proposed that expresses the desirability of the ambiguity function associated with any frequency-hopping waveform. Simulation results demonstrate that this cost function can be optimized via heuristic optimization techniques to yield improvements in ambiguity performance.

To realize an efficient utilization of harvested energy and improve throughput with the help of a battery, a harvest-use-store power splitting (PS) relaying strategy with distributed beamforming is proposed for the wireless-powered multi-relay scenario in this paper. To this end, harvested energy via PS can be accumulated and stored for future usage, which affects throughput at subsequent time slots due to the battery operations including the charging and discharging. As a result, PS and battery operations are coupled with distributed beamforming, such that the throughput optimization problem is intractable looking. To address the intractability of the optimization, a layered optimization method with an ideal non-causal channel state information (CSI) assumption is proposed. As a result, the optimal joint PS and battery operation design in the proposed strategy is derived in a decoupled manner. Simulation results confirm the accuracy of the proposed method, and revealed that the proposed strategy has significant performance gains over the conventional designs.

State estimation of a power grid under undetected power injection attacks is considered. With a known prior probabilistic description of the state variables, the maximum a posteriori probability (MAP) estimator is adopted. Undetected attacks lead to model mismatch, which may greatly degrade the estimation performance. The mean square error (MSE) of the MAP estimate under model mismatch is derived. Considering the case where we are able to protect a limited number of nodes under power injection attacks, we formulate and solve an optimization problem to select which nodes to protect to minimize the MSE degradation that the attacker can provide.

This letter investigates the usefulness of quantized data for estimation problems in which unquantized data is already available. A worst case scenario is considered in which a fusion center has access to continuous and binary-valued measurements of the same uniformly distributed parameter observed in Gaussian noise. The difference in mean squared error between a minimum mean squared error estimate using unquantized data and a minimum mean squared error estimate using both quantized and unquantized data is used to quantify the value of fusing the two kinds of data. Discussion of the Cramér-Rao Bound predicts how noise in the quantized data affects the reduction in estimate mean squared error from fusing the data types. It is then determined that the maximum reduction in estimate mean squared error from fusion can be approximated as a rational function of the ratio of the standard deviations of the measurement noise in the two data types. Finally, similarities between the approximation to the reduction in estimate mean squared error for the most favorable uniform prior width and a closed form expression based on the Cramér-Rao Bound are discussed.

In this paper, we describe new lower bounds on error variance of phase offset estimation schemes used in IEEE 1588 based synchronization. The motivation for this study is to determine the feasibility of providing microsecond-level time synchronization over mobile backhaul networks for the backend in 4G cellular systems. Many packet filtering/selection techniques for phase offset estimation have been proposed in synchronization literature, however, lower limits on the performance of such estimators have not yet been described. In this paper, we re-derive two Bayesian estimation bounds, namely the Ziv-Zakai and Weiss-Weinstien bounds, for use under a non-Bayesian formulation. This enables us to apply these bounds to the problem of phase offset estimation. Simulation results compare the performance of existing estimation schemes against these lower bounds under a variety of different network scenarios.

The IEEE 1588 protocol has received recent interest as a means of delivering sub-microsecond level clock phase synchronization over packet-switched mobile backhaul networks. Due to the randomness of the end-to-end delays in packet networks, the recovery of clock phase from packet timestamps in IEEE 1588 must be treated as a statistical estimation problem. A number of estimators for this problem have been suggested in the literature, but little is known about the best achievable performance. In this paper, we describe new minimax estimators for this problem, that are optimum in terms of minimizing the maximum mean squared error over all possible values of the unknown parameters. Minimax estimators that utilize information from past timestamps to improve accuracy are also introduced. Simulation results indicate that significant performance gains over conventional estimators can be obtained via such optimum processing techniques. These minimax estimators also provide fundamental limits on the performance of phase offset estimation schemes.

In packet-based time synchronization protocols such as IEEE 1588, clock phase offsets are determined via two-way message exchanges between a master and a slave. Since the end-to-end delays in packet networks are inherently stochastic in nature, the recovery of phase offsets from message exchanges must be treated as a statistical estimation problem. Recently, minimax estimators for this problem were proposed by the authors, which are optimum in terms of minimizing the mean-squared estimation error over all values of the unknown parameters. In this paper, we consider a restricted class of estimators referred to as L-estimators, which are linear functions of order statistics. The problem of designing optimum L-estimators is studied under several hitherto unconsidered criteria of optimality. Our results address the case where the queuing delay distributions are fully known, as well as the case where network model uncertainty exists. Optimum L-estimators that utilize information from past observation windows to improve performance are also described. The derived L-estimators have a much lower computational complexity than minimax estimators, and also require lesser statistical knowledge of the queuing delays. Simulation results indicate that L-estimators exhibit a mean-squared estimation error very close to minimax estimators under many network scenarios.

Taking into account the existence of multipath ionospheric propagation (MIP), this paper develops the received signal model for a non-point target for multiple-input multiple-output skywave over-the-horizon (MIMO-OTH) radar for the first time. The model describes the ionospheric state, the number of propagation paths between a radar antenna and the target center, as well as the statistics of the reflection coefficients. It is shown that varying system parameters, such as antenna positions and signal frequencies, can result in causing the model to change from a case with highly correlated reflection coefficients to a case with virtually uncorrelated reflection coefficients. The proposed model is used to solve a target detection problem. It is shown that it is possible to exploit the MIP to improve the detection performance of the MIMO-OTH radar.

Ionospheric information is required when estimating target parameters in skywave over-the-horizon (OTH) radar. Unlike the traditional OTH radar which uses only the measurements of ionospheric parameters obtained from an ionosonde to estimate the target parameters, the multiple-input multiple-output skywave OTH (MIMO-OTH) radar studied in this paper estimates the ionospheric and target parameters jointly by exploiting the data received by both the ionosonde and the radar receivers. Two scenarios where the prior distribution of the ionospheric parameters is either known or unknown are considered. For the case when ionospheric parameter prior distribution is unknown, the joint maximum likelihood (JML) estimator is investigated and the Cramér-Rao bound (CRB) is derived. For the case when the ionospheric parameter prior distribution is known, the hybrid maximum likelihood and the maximum a posteriori (ML/MAP) estimator is studied and the hybrid Cramér-Rao bound (HCRB) is developed.

We study the waveform design problem for a multiple-input multiple-output over-the-horizon (MIMO-OTH) radar system faced with a combination of additive Gaussian noise and signal dependent clutter. Considering the operational frequency of the MIMO-OTH radar is generally limited to a certain frequency band due to propagation and implementation issues, the waveform transmitted at each antenna is constructed as a weighted sum of discrete prolate spheroidal (DPS) sequences which have good orthogonal and band-limited properties. Optimum waveforms (possibly nonorthogonal) are designed to maximize the target detection performance of the MIMO-OTH radar system with the constraint of fixed total transmitted energy. The performance of the proposed waveforms is analyzed.

Bolstered by the growing interest in building wireless sensor and ad hoc networks with applications ranging across different engineering disciplines, distributed consensus algorithms have recently seen a new revival since their inception in the early 1980s. Of particular interest is the recently developed broadcast-based consensus algorithm, which is one special type of randomized consensus algorithms and is amenable to practical implementation in wireless networks. This paper focuses on the performance analysis of this broadcast-based consensus algorithm in the presence of non-zero-mean stochastic perturbations. It is demonstrated that as the algorithm proceeds, the deviation of the node states from their average will converge, in expectation, to a fixed value, which is determined by the Laplacian matrix of the network, the mixing parameter, and the mean of the stochastic perturbations. Asymptotic upper and lower bounds on the total mean-square deviation are derived, which describe the range of distances over which the node states deviate from consensus. These bounds can facilitate evaluation of the applicability of this algorithm in practice. Results are also provided on the algorithm's ε-converging time, i.e., the earliest time at which the deviation is ε close to its steady value, and on the mean and mean-square behaviors of the displacement of node states from their initial states at large iteration number. As a special case study, performance of the broadcast-based consensus algorithm under zero-mean stochastic disturbances is analyzed, and results regarding its convergence, mean-square deviation, and mean-square displacement are given. The theoretical results presented in this study hold true regardless of the statistics of the stochastic disturbances, and are valid for arbitrary network topology as long as the topology is connected.

In order to reduce the number of transmissions between a set of sensors and a fusion center in signal detection applications, we propose an algorithm based on ordering and halting the transmissions wisely, which can reduce the data transmission, and thus expended energy and data rate, without sacrificing signal detection performance. Here we consider the specific case of noncoherent signal detection, where the log-likelihood ratio turns out to be nonnegative, with independent observations form sensor to sensor. For this specific case, we design a new ordering algorithm which provides very large savings for some example MIMO radar systems considered for almost all false alarm probabilities and signal-to-noise ratios (SNRs). While these savings are demonstrated numerically, we also prove analytically that savings of (N - 1)/N × 100% are achieved for sufficiently small or large false alarm probabilities and sufficiently large distance measures, a generalization of SNR, for a very large class of signal detection problems which employ N total sensors.

A discretized version of a continuous optimization problem is considered for the case where data is obtained from a set of dispersed sensor nodes and the overall metric is a sum of individual metrics computed at each sensor. An example of such a problem is maximum likelihood estimation based on statistically independent sensor observations. By ordering transmissions from the sensor nodes, a method for achieving a saving in the average number of sensor transmissions is described. While the average number of sensor transmissions is reduced, the approach always yields the same solution as the optimum approach where all sensor transmissions occur. Further, for cases with N sufficiently well designed sensors with sufficiently large signal-to-interference-plus-noise ratios, the average percentage of transmissions saved approaches 100 percent as the number of discrete grid points in the optimization problem Q becomes significantly large. In these same cases, the average percentage of transmissions saved approaches (Q−1)/Q×100 percent as the number of sensors N in the network becomes significantly large.

The diversity gain of a multiple-input multiple-output (MIMO) system adopting the Neyman-Pearson (NP) criterion is derived for a signal-present versus signal-absent scalar hypothesis test statistic and for a vector signal-present versus signal-absent hypothesis testing problem. The results are applied to a MIMO radar system with M transmit and N receive antennas, used to detect a target composed of Q random scatterers with possibly non-Gaussian reflection coefficients in the presence of possibly non-Gaussian clutter-plus-noise. It is found that the diversity gain for the MIMO radar system is dependent on the cumulative distribution function (cdf) of the reflection coefficients while invariant to the cdf of the clutter-plus-noise under some reasonable conditions. If the noise-free received waveforms at each receiver span a space of dimension M' ≤ M, the largest possible diversity gain is controlled by min (N M', Q) and the cdf of the magnitude square of a linear transformed version of the reflection coefficient vector. It is shown that properly chosen nonorthogonal waveforms can achieve the same diversity gain as orthogonal waveforms.

The vulnerability of smart grid systems is a growing concern. Signal detection theory is employed here to detect a change in the system. We employ a discrete-time linear state space model to capture the dynamic time behavior of the system. Since small changes are often difficult to detect, we develop new locally optimum tests for changes in matrices or vectors and apply them to smart grid intrusion and fault detection problems. The proposed tests are shown to have superior performance when compared to traditional methods.

This paper introduces a novel method to score how well proposed fused image quality measures (FIQMs) indicate the effectiveness of humans to detect targets in fused imagery. The human detection performance is measured via human perception experiments. A good FIQM should relate to perception results in a monotonic fashion. The method computes a new diffuse prior monotonic likelihood ratio (DPMLR) to facilitate the comparison of the H(1) hypothesis that the intrinsic human detection performance is related to the FIQM via a monotonic function against the null hypothesis that the detection and image quality relationship is random. The paper discusses many interesting properties of the DPMLR and demonstrates the effectiveness of the DPMLR test via Monte Carlo simulations. Finally, the DPMLR is used to score FIQMs with test cases considering over 35 scenes and various image fusion algorithms.

To address the challenges inherent to a problem of practical interest - of Neyman-Pearson detection of fluctuating radar signals using wireless sensor networks, we propose in this paper a distributed and energy-efficient framework. Such framework is scalable with respect to the network size, and is able to greatly reduce the dependence on the central fusion center. It assumes a clustering infrastructure, and addresses signal processing and communications related issues arising from different layers. This framework includes a distributed scheduling protocol and a distributed routing protocol, which enable sensor nodes to make their own decisions about information transmissions, without requiring the knowledge of the network global information. In this framework, energy efficiency manifests itself at different network layers in a distributed fashion, and a balance between the detection performance and the energy efficiency is also attained.

Recent research indicates the potential of MIMO radar with dispersed antennas to achieve high target localization accuracy via coherent processing. Coherent processing requires phase synchronization. Usually, perfect phase synchronization is difficult to realize. Assuming frequency synchronization, possibly through reception of a beacon, and white noise, possibly due to estimating the covariance matrix and whitening the observations, we consider the impact of static phase errors at the transmitters and receivers for cases with sufficiently high SNR such that the Cramer-Rao bound (CRB) provides accurate performance estimates. We model the phase errors as random variables and discuss the impact of these errors on target localization performance. In a few example cases the CRB is computed and compared with those in the ideal coherent and noncoherent processing cases. For these examples, using numerical results, we will show that at high enough signal-to-noise ratio (SNR), phase errors degrade performance only by a relatively small amount.

This paper presents an analysis of target localization accuracy, attainable by the use of multiple-input multiple-output (MIMO) radar systems, configured with multiple transmit and receive sensors, widely distributed over an area. The Cramer–Rao lower bound (CRLB) for target localization accuracy is developed for both coherent and noncoherent processing. Coherent processing requires a common phase reference for all transmit and receive sensors. The CRLB is shown to be inversely proportional to the signal effective bandwidth in the noncoherent case, but is approximately inversely proportional to the carrier frequency in the coherent case. We further prove that optimization over the sensors' positions lowers the CRLB by a factor equal to the product of the number of transmitting and receiving sensors. The best linear unbiased estimator (BLUE) is derived for the MIMO target localization problem. The BLUE's utility is in providing a closed-form localization estimate that facilitates the analysis of the relations between sensors locations, target location, and localization accuracy. Geometric dilution of precision (GDOP) contours are used to map the relative performance accuracy for a given layout of radars over a given geographic area.

We investigate the achievable rate of receive antenna selection MIMO systems in the presence of mutual coupling and spatial correlation. For that, we assume the antenna array to consist of dipole antennas placed side-by-side in a linear pattern and in a very limited physical space. In a first step, we will assume perfect channel state information at the receiver side only and a negligible training overhead compared with the payload. We will demonstrate that in contrast to what might be expected based on results for cases without mutual coupling, MIMO receive antenna selection can achieve higher data rates than the system using all antennas provided that the total number of receive antennas is larger than a critical value that we will further discuss. We then propose an optimal antenna selection processing that ensures rate maximization regardless of the number of antennas used. In a later step, we will address the impact of training overhead on the system achievable rate when the training overhead is considerable. We will show that such a rate is reduced dramatically due to the large amount of training overhead arising from the presence of mutual coupling. To overcome this problem, we will thus propose a novel channel estimation method, which reduces the training overhead greatly and improves the system achievable rate performance.

A radar system with M transmit and N receive antennas which are widely separated is employed to detect the presence of a target at a given point in space. This target is assumed to be composed of Q point scatterers which are closely spaced with respect to the waveforms transmitted by the radar system. The diversity gain for radar systems employing optimum processing (likelihood ratio tests) for detecting the presence of these targets is shown to be less than or equal to min(Q,MN).

Classification employing sensors connected by wireless networks is of great interest. As the sensor nodes are usually powered by batteries, saving transmissions is important. We demonstrate transmissions can be saved, without degradation in error probability, using an ordering approach. The average number of transmissions saved (ANTS) is lower bounded by a quantity proportional to the number of sensors employed provided a well-behaved distance measure between the sensor distributions is sufficiently large. For such cases, the ANTS over the optimum unconstrained energy approach is shown to be larger than half the number of sensors employed.

This letter addresses the sensor placement problem for monitoring spatial phenomena by employing an estimation/prediction metric, i.e., noisy observations from a limited number of sensors are used to estimate the phenomena over the whole region. To solve the formulated problem, we propose a random search-based simulation optimization algorithm to iteratively select the sensor locations out of a possibly countably infinite subset of candidates. We further consider the sensor placement problem given a constraint on the energy consumption, and we propose a scheme which superimposes the Lagrange multiplier method for nonlinear programming upon our proposed discrete simulation optimization algorithm. We present numerical examples to demonstrate the fast convergence as well as the effectiveness of this simulation based algorithm.

We consider the design of a sensor network for detecting an emitter who if present is known to be located in an interval but whose exact position is unknown. We seek to minimize the total system power consumption subject to detection performance constrains by carefully choosing the thresholds and positions of the sensors. Toward this goal, we propose an iterative algorithm for the optimization problem. Numerical results are given to provide insights into the design of such networks. We show that random sensor placement can perform poorly, in contrast to what many currently believe.

In this paper, we consider energy-efficient routing for detection in wireless sensor networks (WSNs). Energy-efficient routing for WSNs has been intensely studied recently, but routing for signal detection in WSNs has not attracted much attention. Moreover, we are not aware of any previous work on routing for detection in WSNs that specifically considers the Neyman-Pearson criterion which is the most accepted metric for radar, sonar and related signal detection problems. By deploying a simple but illustrative model for target detection in WSNs, we formulate a problem of energy-efficient routing for signal detection under the Neyman-Pearson criterion. We propose a routing metric which aims for a route with the maximum mean detection-probability-to-energy ratio, and describe methods for solving the resulting optimization problem. This proposed metric, striving for a balance between the consumed energy and detection performance, is effective for finding the optimal routing that values such an energy-detection tradeoff.

Most user cooperation protocols work in a timesharing manner, where each user transmits its own message and relays for the other at different segments of a time slot. We develop a new scheme to send these messages simultaneously using network coding. We show that network coding is more tolerant to poor inter-user channels than time-sharing, and achieves a better overall performance. We generalize the scheme to a multi-user, multi-slot cooperation framework. Under this framework, we show that the network coding scheme reaps a better diversity order and provides a better effective inter-user channel than time-sharing schemes.

Energy-efficient routing for wireless sensor networks (WSNs) has been a topic of great interest for the last few years, but thus far routing for signal detection in WSNs has not attracted much attention. In particular, little research has focused on the Neyman-Pearson criterion which is the most well accepted metric for radar, sonar and related signal detection problems. In this paper, we formulate the problem of energy-efficient routing for signal detection under the Neyman-Pearson criterion, apparently for the first time. We hereby propose two different routing metrics that aim at a tradeoff between the detection performance and the energy consumption. In particular, the first one leads to a combinatorial problem of identifying a path which achieves the largest possible mean detection-probability-to-energy ratio, while the second one reduces to finding a route which minimizes the consumed energy while maintaining a predeter-mined detection probability. We further provide efficient algorithms for solving these problems based on state-of-the-art research from operations research. We also present simulation results which indicate the distinctive energy-performance balance achieved by each proposed routing metric.

We consider a receive antenna selection MIMO system, where only one receive antenna is selected out of Nrantennas. Spatial channel correlation will be considered at the receiver side only. We investigate here the capacity performance of such a system. In particular, we derive a closed-form expression of its outage probability expressed in an infinite series representation. To do so, we derive the joint cumulative distribution function and joint probability density function of the squared row norms of the channel matrix by using the statistical properties of multivariate chi-square random variables. Our simulation results will be shown to validate our analytical findings.

We study power allocation for the decode-and-forward cooperative diversity protocol in a wireless network under the assumption that only mean channel gains are available at the transmitters. In a Rayleigh fading channel with uniformly distributed node locations, we aim to find the power allocation that minimizes the outage probability under a short-term power constraint, wherein the total power for all nodes is less than a prescribed value during each two-stage transmission. Due to the computational and implementation complexity of the optimal solution, we derived a simple near-optimal solution. In this near-optimal scheme, a fixed fraction of the total power is allocated to the source node in stage I. In stage II, the remaining power is split equally among a set of selected nodes if the selected set is not empty, and otherwise is allocated to the source node. A node is selected if it can decode the message from the source and its mean channel gain to the destination is above a threshold. In this scheme, each node only needs to know its own mean channel gain to the destination and the number of selected nodes. Simulation results show that the proposed scheme achieves an outage probability close to that for the optimal scheme obtained by numerical search, and achieves significant performance gain over other schemes in the literature

We present a novel feature-based non-rigid image registration algorithm using a small number of automatically extracted points and their associated local salient region features. Our automatic registration is a hybrid approach co-optimizing point-based and image-based terms. Motivated by the paradigm of the TPS-RPM algorithm [6], we develop the RHDM (Robust Hybrid Deformable Matching) algorithm by alternatively optimizing correspondences and transformations for registration. The local salient region features and the geometric features, together with the softassign and deterministic annealing techniques, are used for solving correspondences. Thin-plate splines are used for generating a smooth non-rigid spatial transformation. Our algorithm is built to be extremely robust to feature extraction errors. A new dynamic outlier rejection mechanism is described for rejecting outliers and generating accurate spatial mappings. A local refinement technique is used for correcting non-exactly matched correspondences arising from image noise and irregular deformations. In contrast with the TPS-RPM algorithm, which can handle only outliers in one point set, our algorithm is able to handle a considerable number of outliers in both point sets. The experimental results demonstrate the robustness and accuracy of our algorithm.

Design of space-time codes that scale with the number of transmit antennas is a difficult problem. In this paper, we introduce a new family of space-time trellis codes (STTC) that can be applied to any arbitrary number of transmit antennas. This family is constructed by utilizing QPSK STTCs as component codes to construct STTCs with larger constellation size. Unlike the design of existing STTC, the search space in our design does not grow exponentially with the constellation size or the number of transmit antennas. Additionally, we propose a practical approach to reduce the computational complexity of our proposed scheme using interference mitigation techniques. Simulation results compare the performance of our approach with that of space-time block codes for the case of two transmit antennas and several different number of receive antennas, a spectral efficiency of 4 bits/s/Hz, and slow Rayleigh fading channels.

Space time convolutional codes (STCCs) are an effective way to combine transmit diversity with coding. The computational complexity of designing STCCs generally increases exponentially with the constellation size of the transmitted symbols. In this paper, we first present an innovative approach to design STCCs with high spectral efficiencies by utilizing QPSK STCCs as component codes and consequently. Unlike existing techniques, the search space does not grow exponentially with the constellation size. Then, we present two approaches to reduce the computational complexity of our proposed scheme. This scheme is applicable to cases with any number of transmit antennas without any requirement to change the encoder design. Simulation results evaluate the performance of our approach for the case of two transmit antennas and several different number of receive antennas, a spectral efficiency of 4 bits/s/Hz, and slow Rayleigh fading channels.

We study the capacity of a large clustered wireless ad hoc network in which clusters of nodes are scattered in a sea of relatively low-density nodes. We fix the density of nodes and clusters and study behavior as we increase the total network area (or, equivalently, the total number of nodes), which we call the network size. The main result is that the capacity switches behavior at a critical network size, which depends on the cluster size and the density of clusters within the network. Thus, the clustering parameters of the network allow us to quantify the meaning of a "large" network, i.e., such that further size increase entails degradation of throughput capacity

We analyze wireless ad hoc networks that use cooperative diversity from two complementary perspectives. The network we consider uses the amplify-and-forward (AF) cooperation protocol. We first determine the capacity region and rate matrices for these networks. Numerical results indicate that cooperation is beneficial when optimal multi-hop routing is not used, but can be ineffective when optimal multi-hop routing is employed. Secondly, we develop an analytical expression for the transmission blocking probability (TBP). The TBP allows us to draw insight into the possible benefits of cooperation. We determine that the TBP for networks that use cooperation is not noticeably larger than that for networks that employ only point-to-point communications. Taken together, these two results leads us to conclude that although the blocking probability does not significantly increase when cooperation is used, the capacity is only increased in certain scenarios, i.e. when optimal multi-hop routing is not used

Adaptive modulation has been shown to have significant benefits for high-speed wireless data transmission when orthogonal frequency division multiplexing (OFDM) is employed. However, accurate channel state information (CSI) is required at the transmitter to achieve the benefits. Imperfect CSI arises from noisy channel estimates, which may also be outdated due to a delay in getting the CSI to the transmitter. In this paper, we study adaptive OFDM with imperfect CSI for the uncoded variable bit rate case, where a target bit error rate is set. A loading algorithm based on the statistics of the real channel is proposed. Performance results in terms of the average spectral efficiency are provided for adaptive OFDM systems when there is noisy channel estimation or CSI delay. The use of multiple estimates is then proposed to improve the performance. It is shown that multiple estimates from different frequencies or times can enhance the performance significantly, which enables the system to tolerate larger errors in channel estimation or longer delay in CSI

We study power allocation for the space-time-coded decode-and-forward cooperative diversity protocol in a wireless network under the assumption that only mean channel gains are available at the transmitters. In a Rayleigh fading channel with uniformly random node locations, a near-optimal power allocation that minimizes the outage probability is derived under a short-term power constraint, wherein the total power is fixed for each two-stage transmission. This near-optimal scheme allocates one half of the total power to the source node and splits the remaining half equally among selected relay nodes; a node is selected for relay if it is able to decode the signal from the source and its mean channel gain to the destination is above a threshold. Numerical results show that this scheme significantly outperforms the constant-power scheme, wherein all nodes use the same power at all times, and the best-select scheme, which employs one relay node with the largest mean relay-destination gain

Throughput capacity of large ad hoc networks has been shown to scale adversely with the size of network n. However the need for the nodes to find or repair routes has not been analyzed in this context. In this paper, we explicitly take route discovery into account and obtain the scaling law for the throughput capacity under general assumptions on the network environment, node behavior, and the quality of route discovery algorithms. We also discuss a number of possible scenarios and show that the need for route discovery may change the scaling for the throughput capacity dramatically.

The performance of an ad hoc network that contains many nodes within circular clusters with fixed node density is studied. These clusters lie within a finite square area, and the space between clusters is filled with nodes such that the density of nodes is much smaller than the density of nodes in the clusters. We obtain an upper bound on the throughput and investigate the achievability of the upper bound. Through these studies, the effect of clustering on throughput is uncovered. The impact of changing the finite square area, in which the system resides, called the system size, becomes evident. In particular, we show that in clustered networks, the size of the network is important, and in particular, the behavior of the network changes greatly for small and large networks

We consider, in this paper, the design of a cooperative relay strategy by exploiting the finite-alphabet property of the source. Assuming a single source-sink pair with L relay nodes all communicating in orthogonal channels, we derive necessary conditions for optimal relay signaling that minimizes the error probability at the sink node. The derived conditions allow us to construct an iterative algorithm to find the distributed relay signaling that is at least locally optimal. As a byproduct, one can show that the so-called decode-and-forward (DF) relay scheme does not satisfy the necessary condition hence is not optimal in its error probability performance. Indeed, numerical examples show that the proposed scheme provides substantial performance improvement over both DF and the amplify-and-forward approach.

The mutual information of a multiple-input multiple-output (MIMO) system with co-channel interference is considered. Perfect channel information is assumed to be available to the receiver, but the transmitter has no channel information. It is theoretically proved that the worst interference condition is when the total power is equally distributed among all available interfering antennas. Moreover, equal-power interferers give worse performance than unequal-power interferers, and a smaller number of interferers each with larger power degrades performance less than a larger number of interferers each with lower power. Finally, it is shown that, for asymptotically large interference, when the number of interfering antennas, N/sub I/, is smaller than the number of receive antennas, N/sub R/, the system is equivalent to a reduced MIMO system with N/sub R/-N/sub I/ receive antennas. When N/sub I//spl ges/N/sub R/, the mutual information approaches zero as interference becomes asymptotically large.

In this paper, we first develop the system model for a wireless ad hoc network employing cooperative diversity. A simple fading relay channel is considered where the relay terminals apply the amplify-and-forward protocol. An equivalent multiple input multiple-output (MIMO) channel with multiple users is developed. Based on this model, basic rate matrix theory is applied to study the average rate regions under various transmission strategies. In particular whether relaying is beneficial is studied for cases with single hop and multi-hop routing where spatial reuse may be employed. The results indicate that cooperative diversity can provide substantial gains for cases with single hop routing. However, if optimum multi-hop routing is employed, cooperative diversity gains are small.

We obtain an upper bound on the throughput of an ad hoc network which contains a square-shaped cluster with n nodes acting as sources communicating with another square-shaped cluster with n destination nodes. We consider the cases where the two clusters have no overlap, partial overlap, and complete overlap. We also investigate the achievability of the upper bound in the no overlap case and show that it can be achieved up to a typically small additive term.

The recently proposed turbo-binning scheme is shown to be both efficient and optimal for uniform source Slepian-Wolf coding problem (Z. Tu et al., 2003). This paper studies the case when sources are i.i.d. but nonuniformly distributed. It is firstly shown that any algebraic binning scheme based on linear codes is optimal for nonuniform sources only asymptotically. Next two modifications are proposed to improve the performance of the turbo-binning scheme for nonuniform sources. The first is to carefully design the constituent encoder structures to maximally match the turbo code to the nonuniform source distribution, and the second is to use variable-length syndrome sequences to index the bins. Simulations show that the combination of both strategies can lead to an improvement of as much as 0.22 bit/symbol in overall compression rate for highly nonuniform sources.

This work presents an efficient structured binning scheme for solving the noiseless distributed source coding problem with parallel concatenated convolutional codes, or turbo codes. The novelty in the proposed scheme is the introduction of a syndrome former and an inverse syndrome former to efficiently and optimally exploit an existing turbo code without the need to redesign or modify the code structure and/or decoding algorithms. Extension of the proposed approach to serially concatenated codes is also briefed and examples including conventional turbo codes and asymmetric turbo codes are given to show the efficiency and the general applicability of the approach. Simulation results reveal good performance which is close to the theoretic limit.

Polarization Mode Dispersion (PMD) imposes a new challenge for high speed optical transmission. This paper proposes a novel Single-Input Multiple-Output (SIMO) Decision Feedback Equalizer (DFE) technique to combat all orders of PMD-induced distortion. The scheme is based on a new SIMO PMD channel model, which utilizes information embedded in both polarization states. Explicit expressions for the filter coefficients are provided. The simulation results show that the new scheme provides improvement over first order optical compensator and conventional DFE.

The delay-limited throughput of an ad hoc wireless network confined to a finite region is investigated. An approximate expression for the achievable throughput as a function of the maximum allowable delay is obtained. It is found that: 1) for moderate values of the delay d, the throughput that can be achieved by taking advantage of the motion increases as d/sup 2/3/ and 2) for a fixed value of d, the dependence of the achievable throughput on the number of nodes n is n/sup -1/3/. A transmission and relaying strategy ensuring continuous information flow is constructed. It is shown that there exists a critical value of the delay such that: 1) for values of the delay d below the critical delay, the throughput does not benefit appreciably from the motion and 2) the dependence of the critical delay on the number of nodes is a very slowly increasing function (n/sup 1/14/). Finally, asymptotic optimality of the proposed strategy in a certain class is shown.

Signaling for optimum mutual information with limited feedback of channel state information is studied for the case when multiple transmit and receive antenna arrays are used to form multiple input multiple output channels. A simple mean square error based approach for finding near optimum signaling is suggested and its performance studied. Prior to limiting, the channel estimates are assumed perfect and delay in obtaining these estimates is ignored to focus on the effects of limited feedback.

System capacity is considered for a group of interfering users employing single user detection and antenna selection of multiple transmit and receive antennas for flat Rayleigh fading channels with independent fading coefficients for each path. The case considered is that where there is very limited channel state information (only the selected antennas) at the transmitter, but channel state information is assumed at the receiver. The focus is on extreme cases with very weak interference or very strong interference. It is shown that the optimum signaling covariance matrix is sometimes different from the standard scaled identity matrix. In fact this is true even for cases without interference if SNR is sufficiently weak. Further the scaled identity matrix is actually that covariance matrix that yields worst performance if the interference is sufficiently strong.

System capacity is considered for a group of interfering users employing single-user detection and multiple transmit and receive antennas for flat Rayleigh fading channels with independent fading coefficients for each path. The focus is on the case where there is no channel state information at the transmitter, but channel state information is assumed at the receiver. It is shown that the optimum signaling is sometimes different from cases where the users do not interfere with each other. In particular, the optimum signaling sometimes put all power into a single transmitting antenna, rather than divide power equally between the different antennas. We show that either the optimum interference-free approach, which puts equal power into each antenna, or the approach that puts all power into a single antenna are optimum for the majority of signal and interference powers and we show how to find the regions where each approach is best.

This paper derives some properties of the diversity gain and the coding gain of space-time codes (STCs) for frequency selective channels. It is shown that additional diversity order can be obtained by STCs when they are employed in frequency selective channels rather than in flat fading channels. It is demonstrated that spatial dependence, correlated taps and non-uniform power delay profile will cause coding gain penalty. The optimum codes designed for spatial independence with uncorrelated taps and uniform power distribution are shown to be the optimum codes for the other channels scenarios with the same number of taps. A systematic design procedure is applied to search for the best space-time trellis code (STTC) for frequency selective channels. At an FER of 0.01, our example 16-state BPSK STTC outperforms the delay diversity code by 3.4 dB for a channel with 3 uncorrelated uniform taps. It is demonstrated that a STC designed for a channels with the maximum expected memory, will guarantee good performance if a channel with less memory is encountered.

The delay limited capacity of an ad hoc wireless network confined to a finite region is investigated. A transmission and relaying strategy making use of the nodes' motion to maximize the throughput is constructed. An approximate expression for the capacity as a function of the maximum allowable delay is obtained. It is found that there exists a critical value of the delay such that: (1) for values of the delay d below critical, the capacity does not benefit appreciably from the motion, (2) for moderate values of the delay d above critical, the capacity that can be achieved by taking advantage of the motion increases as d2/3, (3) the dependence of the critical delay on the number of nodes is a very slowly increasing function (n1/14). Finally, asymptotic optimality of the proposed strategy in a certain class is shown.

System capacity is considered for a group of interfering users employing single-user detection and multiple transmit and receive antennas for flat Rayleigh-fading channels with independent fading coefficients for each path. The focus is on the case where there is no channel state information at the transmitter, but channel state information is assumed at the receiver. It is shown that the optimum signaling is sometimes different from cases where the users do not interfere with each other. In particular, the optimum signaling will sometimes put all power into a single transmitting antenna, rather than divide power equally between independent streams from the different antennas. If the interference is either sufficiently weak or sufficiently strong, we show that either the optimum interference-free approach, which puts equal power into each antenna, or the approach that puts all power into a single antenna is optimum and we show how to find the regions where each approach is best.

The problem of capacity of a wireless ad hoc network in the presence of a uniform end-to-end delay constraint is explored. A general model for the random motion of the nodes is used. An approximate expression for the capacity as a function of the maximum allowable delay is obtained, and the asymptotic optimality of the proposed transmission strategy in a certain class is shown.

Wireless communication systems with transmit and receive antenna arrays are studied when antenna selection is used. A case with very limited feedback of information from the receiver to the transmitter is considered, where the only information fed back is the selected subset of transmit antennas to be employed. It is shown that the optimum signaling, for the largest ergodic capacity of a single isolated link with given interference and antenna selection, is generally different from that which is optimum without antenna selection for some range of signal-to-noise ratios (SNRs). In cases with interference, the improvement obtained from using the true optimum signaling approach tends to increase for this range of SNRs. Further, the optimum approach for cases without antenna selection tends to be optimum in fewer cases as interference power is increased.

A statistical signal processing approach to multisensor image fusion is presented for concealed weapon detection (CWD). This approach is based on an image formation model in which the sensor images are described as the true scene corrupted by additive non-Gaussian distortion. The expectation-maximization (EM) algorithm is used to estimate the model parameters and the fused image. We demonstrate the efficiency of this approach by applying this method to fusion of visual and non-visual images with emphasis on CWD applications.

We investigate the performance of adaptive modulation in OFDM under a constant-bit-rate requirement When the transmitter knows the channel state information perfectly, a large gain over a non-adaptive system is possible. However, channel estimation errors and delay in feedback may cause channel mismatch, which diminishes the gain of adaptive modulation. The mechanism of how channel mismatch leads to performance degradation is also investigated. Based on the insights we obtain, two approaches are proposed to mitigate the adverse effect: a coding technique assisted by differential channel information, and a robust loading scheme.

Adaptive modulation has been shown to have significant benefits for high-speed wireless data transmission when orthogonal frequency division multiplexing (OFDM) is employed. However, accurate channel state information (CSI) is required at the transmitter to achieve the benefits. Imperfect CSI arises from noisy channel estimates, which may also be outdated due to a delay in getting the CSI to the transmitter. We study adaptive OFDM with both perfect and imperfect CSI for the variable bit rate case, where a target bit error rate is set. Performance results are provided for adaptive OFDM with imperfect CSI. The use of multiple estimates is shown to mitigate the effect of CSI delay. In addition, the fundamental error mechanisms which result in performance degradation are studied. Robust approaches are then proposed that are less sensitive to CSI errors.

Space-time convolutional codes have shown considerable promise for providing improved performance for wireless communication through combined diversity and coding gain. An efficient design procedure is presented for optimizing the coding and diversity gain measures proposed in the first papers on space-time codes. The procedure is based on some simple lower and upper bounds on coding gain. The same calculations needed to compute these bounds can be used to check either necessary or sufficient conditions on space-time codes which achieve maximum diversity gain. A new simple, but useful, measure of code performance is also suggested which augments existing measures. The use of the design procedure is illustrated and new codes are provided. These codes are shown to outperform the space-time convolutional codes provided in the initial papers introducing space-time codes.

The design of space-time (ST) codes employing multiple trellis coded modulation (MTCM) is considered. This structure is shown to be necessary for achieving maximum transmit diversity gain when using trellis codes with parallel paths. Systematic code search procedures with low complexity are described based on the properties of ST-MTCM codes. It is illustrated that, if the trellis branches are properly labeled, the overall coding gain can be made larger than that achieved by conventional ST codes with the same transmission rate and the same number of states.

Space-time convolutional codes, that provide maximum diversity and coding gain, are produced for cases with PSK modulation and various numbers of states and antennas. The codes are found using a new approach introduced previously in a companion paper. The new approach provides an efficient method that allows a search for optimum codes for many practical problems. The new approach also provides a simple method for augmenting the criteria of maximum diversity and coding gain with a new measure which is shown to be extremely useful for evaluating code performance without extensive simulations. To validate the approach, an extensive set of simulation results are presented comparing the codes designed here to many other previously proposed space-time convolutional codes. The comparisons, given in terms of frame error rate (FER), indicate that our new method provides codes which yield excellent performance. The approach is especially useful for finding a handful of good codes. Selection among these codes can be made with a limited number of simulations for FER.

The study of space-time block coding has mainly focused on cases with quasi-static flat fading channels. We discuss robust space-time block code design for rapid flat fading channels. Trade-offs between rate, diversity gain and constellation size are presented. A design methodology is proposed which considers the performance metrics for both small signal-to-noise ratio (SNR) and large SNR cases. Our approach suggests incorporating traditional single antenna block codes in a particular way to simplify code design. Some example codes are presented which provide improvement over existing space-time block codes.

We study multiuser detection for a synchronous DS-CDMA system in a flat Rayleigh fading channel. An approximate MMSE detector which is independent of the magnitude of the received signal is proposed. This detector is not only easier to implement but also easier to analyze than the exact MMSE detector. This is especially true for the case employing ML sequences. We have developed a closed form expression for its performance. Numerical simulations for CDMA systems employing ML and random sequences are provided. These results demonstrate that the performance difference between the exact and approximate MMSE algorithms is very small which makes the latter a very good approximation.

Space-time coding is a highly effective approach for combating fading in wireless communications and improving the capacity of wireless networks. However, Catreux et al. (2000) showed that cochannel interference can degrade performance significantly in cellular systems. Here we design and demonstrate the interference suppression capability of low rate space-time codes. Optimal 1 b/s/Hz 2-space-time trellis codes with various numbers of states over Z/sub 4/ and GF(4) are obtained through search. We also propose rate adaptive space-time modulation which can increase the overall throughput. The effectiveness of this proposed method is demonstrated by using 2-space-time codes in an orthogonal frequency division multiplexing (OFDM) system with 2 transmit and 2 receive antennas.

It is shown that the capacity of a single, isolated, multiple transmit and receive antenna array link, with given interference, is maximized by transmitting an independent data stream from each antenna for a quasistatic and flat Rayleigh fading channel with independent fading coefficients for each path. However, if such links mutually interfere, in some cases the overall system capacity can be increased by transmitting fewer streams.

Improved space-time coding for multiple-input multiple-output orthogonal frequency division multiplexing is studied for wireless systems using QPSK modulation for four transmit and four receive antennas. A 256-state code is shown to perform within 3 dB of outage capacity (and within 2 dB with perfect channel estimation), which is better than any other published result without using iterative decoding.

We develop an iterative multiuser receiver for decoding turbo-coded synchronous code-division multiple-access signals in both Gaussian and non-Gaussian noise. A soft-input soft-output nonlinear multiuser detector is combined with a set of single-user channel decoders in an iterative detection/decoding structure. The nonlinear multiuser detector utilizes the prior probabilities of each user's bits to form soft estimates used for multiple-access interference cancellation. The channel decoders perform turbo-code decoding and produce posterior probabilities which are fed back to the multiuser detector for use as prior probabilities. Simulation results show that the proposed multiuser receiver performs well in both Gaussian and non-Gaussian noise. In particular, single-user turbo-code performance can be approached within a few iterations with medium to low cross correlation (/spl rho//spl les/0.5).

Distributed multiple sensor detection problems with quantized observations are investigated for cases of nonbinary hypothesis and possibly statistically dependent observations from sensor to sensor conditioned on the hypothesis. The observations available at each sensor are quantized to produce a multiple digit sensor decision which is sent to a fusion center. At the fusion center, the sensor decisions are combined to form a final decision using a predetermined fusion rule. First, it is demonstrated that there is a maximum number of digits that should be used to communicate the sensor decision from a given sensor to the fusion center. This maximum is based on the number of digits used to communicate the decisions from all the other sensors to the fusion center. If more than this maximum number of digits is used, the performance of the optimum scheme will not be improved. In some special cases of great interest, the upper bound on the number of digits that should be used can be made significantly smaller. Secondly, the optimum way to allocate a fixed overall number of digits across sensors is investigated. Illustrative numerical results are also presented in this correspondence.

A procedure for finding the Neyman-Pearson optimum distributed sensor detectors for cases with statistically dependent observations is described. This is the first valid procedure we have seen for this case. This procedure is based on a theorem proven in this paper. These results clarify and correct a number of possibly misleading discussions in the existing literature. Cases with networks of sensors in fairly general configurations are considered along with cases where the sensor detectors make multiple bit sensor decisions.

Optimum space-time convolutional codes, that provide maximum diversity and coding gain, are produced for cases with PSK modulation and various numbers of states and antennas. The codes are found using a new approach introduced recently in a companion paper. The new approach provides an efficient method that allows a search for optimum codes for many practical problems, while previous research was only able to find optimum codes for a single case. The new approach also provides a simple method for augmenting the criteria of maximum diversity and coding gain with a new measure which is shown to be extremely useful for evaluating code performance without extensive simulations.

Sequence detection is studied for communication channels with intersymbol interference and non-Gaussian noise using a novel adaptive receiver structure. The receiver adapts itself to the noise environment using an algorithm which employs a Gaussian mixture distribution model and the expectation maximization algorithm. Two alternate procedures are studied for sequence detection. These are a procedure based on the Viterbi algorithm and a symbol-by-symbol detection procedure. The Viterbi algorithm minimizes the probability the sequence is in error and the symbol-by-symbol detector minimizes symbol error rate, which are different.

In practical radar applications of the adaptive matched filter algorithm, the covariance matrix for the clutter-plus-noise is typically estimated using data taken from range cells surrounding the cell under test. In a nonhomogeneous environment, this can lead to a mismatch between the mean of the estimated covariance matrix and the true covariance matrix for the range cell under test. Closed form expressions are provided, which give the performance for such cases. These equations are exact in some cases and provide useful approximate results in others. Performance depends on a small number of important parameters. These parameters describe which types of mismatches are important and which are not. Numerical examples illustrate how the performance varies with each of the important parameters. Monte Carlo simulations are included which closely match the predictions of our equations.

The objective of image fusion is to combine information from multiple images of the same scene. The result of image fusion is a single image which is more suitable for human and machine perception or further image-processing tasks. In this paper, a generic image fusion framework based on multiscale decomposition is studied. This framework provides freedom to choose different multiscale decomposition methods and different fusion rules. The framework includes all of the existing multiscale-decomposition-based fusion approaches we found in the literature which did not assume a statistical model for the source images. Different image fusion approaches are investigated based on this framework. Some evaluation measures are suggested and applied to compare the performance of these fusion schemes for a digital camera application. The comparisons indicate that our framework includes some new approaches which outperform the existing approaches for the cases we consider.

A multiple-antenna diversity scheme is investigated for digital communications. Antenna observations are immediately quantized and sent to a fusion center. At the fusion center, the quantized observations are combined to form a final decision on which symbol was transmitted. The optimum reception scheme is described for the case where frequency-shift keying is employed and where slow Rayleigh fading and Gaussian additive noise are present. Two cases are studied. In the first case, an accurate estimate of the signal-to-noise ratio is available at each receiver. In the second case, estimates are not available. Results indicate that two- or three-bit quantizations may be most appropriate. Further, if binary decisions are made at each antenna, the performance may not improve if an estimate of the signal-to-noise ratio is available at each antenna or if two antennas are used instead of one.

A central problem in sensor array processing is the localization of multiple sources and the reception of the signals emitted by those sources. Many approaches have been studied for this problem when the additive noise in the sensor array data is modeled with a Gaussian distribution. However, the schemes designed for Gaussian noise typically perform very poorly when the noise is non-Gaussian. An algorithm is presented for array processing in non-Gaussian noise. The algorithm is based on modeling the noise with a Gaussian mixture distribution. The expectation-maximization (EM) algorithm is then used to derive an iterative processing structure that estimates the source locations, estimates the source waveforms, and adapts the processing to match the characteristics of the noise. Simulation examples are presented to illustrate the performance of the algorithm.

Some new techniques are proposed for estimating the quality of a noisy image of a natural scene. Analytical justifications are given which explain why these techniques work. Experimental results are provided which indicate that the techniques work well in practice. These techniques need only the images to be evaluated and do not use detailed information about the formation of the image. The focus is on the case where the image is only corrupted by additive Gaussian noise, which is independent from pixel to pixel, but some cases with blurring are also considered. These results should be useful in the process of fusing several images to obtain a higher quality image. Quality measures of this type are needed for fusion, but they have not received much attention to date. In this research, a mixture model is used in conjugation with the expectation-maximization (EM) algorithm to model edge images. This approach yields an accurate representation which should also be useful in other image processing research.

Distributed detection of weak random signals in additive, possibly non-Gaussian, noise is considered for cases with multibit sensor decisions. Signal-to-noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent. Analytical expressions are provided that describe the best way to fuse the quantized observations for cases with any given number of sensors. The best schemes for originally quantizing the observations at each sensor are also studied for the case of an asymptotically large number of sensors. These schemes are shown to minimize the mean-squared error between the best weak-signal test statistic based on unquantized observations and the best weak-signal test statistic based on quantized observations. Analytical expressions describing optimum sensor quantizers are provided. The approach used to obtain these expressions insures these sensor quantizers give good performance for cases with a finite number of sensors. A novel iterative technique to search for optimum sensor quantizers efficiently is described. Numerical solutions are presented, some of which involve cases where the best schemes for independent signal observations are shown to be suboptimum.

Following the foundational work that established basic ideas for optimum distributed defection schemes using multiple sensors (as reviewed in Part I of this two-part review), further work on distributed detection has developed many useful and interesting extensions of the basic concepts. These more recent developments parallel those that arose from the early work on centralized, classical signal detection, resulting in new ideas of asymptotically optimum nonparametric, robust, and sequential centralized detection. Recent developments on these topics in the setting of distributed signal detection are reviewed in the present paper. Results in these directions are important in practice because they allow cases of modeling uncertainty to be addressed, and they provide more efficient detection schemes by optimizing more general performance criteria.

Simulations of continuous-time systems are frequently used by designers of signal processing and communication systems. Windowed finite-impulse response models are often used in these simulations to model continuous-time linear filters. We investigate the performance of some common windows with respect to waveform fidelity, which is a primary goal in waveform simulation, and we also obtain the form of optimum windows for this criterion. Our results indicate that the rectangular window is generally a practical and reasonably good choice for waveform simulation.

Distributed signal detection schemes have received significant attention, but most research has focused on cases where the observations at the different sensors are independent and the statistical model for the observations is completely known. If the observations at the different sensors consist of noisy versions of random signals which were produced by the same source, then these observations may not be independent. It is also possible that the noise distribution may not be completely known. Cases where weak random signals are observed in possibly non-Gaussian additive noise are considered. The focus is on cases where the sensor tests are based only on the ranks and signs of the observations. Numerical results are provided which indicate that distributed schemes based on ranks and signs are less sensitive to the exact noise statistics when compared to optimum schemes based directly on the observations. This is especially true for some cases where the actual noise distribution has heavy tails, which can cause the optimum schemes based directly on the observations to perform poorly. Analytical forms are given for the locally optimum sensor test statistics based on the ranks and signs of the observations, and we use these to find the best distributed detection schemes for some cases. In the course of obtaining our results, a general set of necessary conditions is given which provide the analytical forms of the locally optimum distributed sensor tests for cases where the observations are discrete random variables. Conditions of this type have not been given previously.

Distributed signal detection schemes that are optimum under the Neyman-Pearson criterion continue to be of interest. The functional forms of these schemes can be difficult to specify, especially for cases with dependent observations from sensor to sensor. For cases with dependent observations from sensor to sensor, the optimum sensor test statistics are generally not the likelihood ratios of the sensor observations. Equations expressing the forms of the optimum sensor test statistics in terms of the other optimum test statistics and the optimum fusion rule are given. Detailed proofs of these results are given in this correspondence and have not been given previously. In some communication, radar, and sonar system problems the amplitude of the received signal may be unknown, but the signal may be known to be weak. Equations expressing the forms of the optimum sensor test statistics for such cases are given. These expressions have already been shown to be useful for interpreting and finding optimum distributed detection schemes, but detailed proofs of the type given here have not yet been given.

Optimum detection schemes based on quantized data are of great interest in radar and sonar applications. The design and properties of multisensor schemes are considered here for detection of weak random signals in additive, possibly non-Gaussian, noise. Signal-to-noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent. Analytical expressions describing the best way to fuse the quantized observations for cases with any given observation sample size are provided. The best schemes for originally quantizing the observations are also studied for the case of asymptotically large observation sample sizes. These schemes are shown to minimize the mean-squared error between the best weak-signal test statistic based on unquantized observations and the best weak-signal test statistic based on quantized observations (under signal absent). Numerical results indicate it is sometimes best for each quantizer to use different size alphabets when a quantizer is located at each sensor.>

Distributed signal detection schemes have received significant attention, but most research has focused on cases with independent observations at the different sensors. Cases with dependent narrowband signals, which are of practical interest in communication, radar, and sonar problems, are studied. The focus is on applications where the observations consist of a weak common signal in possibly non-Gaussian additive noise which is independent from sensor to sensor. The author finds that the best (locally optimum) sensor test statistics for such cases are often different from the best test statistics for cases with isolated sensors and that these sensor test statistics may be nonsymmetric for highly symmetric problems. The possible difference between the best weak-signal distributed sensor test statistic and the best weak-signal test statistic for an isolated sensor can be shown to be due to the distributed sensors attempting to approximate the correlation terms found in the corresponding centralized tests.>

Constant false alarm rate detection is considered in a decentralized, two-sensor context. Cases with observations which are dependent from sensor to sensor are investigated, for which results have been lacking. The in-phase and quadrature components of the received narrowband observation at each sensor consist of a common weak random signal in additive Gaussian combined clutter and noise. The sensors use cell-averaging CFAR tests to each generate binary decisions which are sent to a fusion center. Optimal sensor thresholds are found and the performance of the best schemes using AND and OR fusion rules are compared. The ability of these schemes to maintain constant false alarm probability in the presence of clutter edges is also studied.>

The asymptotic relative efficiency (ARE) of two centralized detection schemes has proved useful in large-sample-size and weak-signal performance analysis. In the present paper ARE is applied to some distributed detection cases which use counting fusion rules. In such cases one finds that ARE generally depends on the power of the tests which can make its application difficult. This dependence turns out to be relatively weak in the cases considered and the ARE is reasonably well approximated by the limit of the ARE as the detection probability approaches the false alarm probability. This approximation should be useful for distributed cases. Some specific results provide the best counting (k-out-of-N) fusion rules for cases with identical sensor detectors if one uses asymptotically large observation sample sizes at each sensor. These results indicate that for false alarm probabilities of less than 0.5, OR rules are generally never optimum.>

Robust detection of known weak signals of unknown amplitude is considered for a class of combined additive and nonadditive noise models and an asymptotically large set of independent observations. This class includes observation models that may have combinations of multiplicative and signal-dependent noise terms. Sufficient conditions are given for robust detection schemes for cases where the general form of the observation model is known but the additive noise distribution is known only to be a member of a general convex uncertainty class. Robust schemes satisfying these conditions are found for some example cases where additive signals and noise have been processed by memoryless nonlinearities. Some interesting example cases of combined multiplicative and signal-dependent noise are shown to use redescending nonlinearities, instead of the limiter nonlinearities typically found for similar additive noise cases.>

Locally optimum (LO) distributed detection is considered for observations that are dependent from sensor to sensor. The necessary conditions are presented for LO distributed sensor detector designs. and a locally optimum fusion rule for an N-sensor parallel distributed detection system with dependent sensor observations is given. Specific solutions are obtained for a random signal additive noise detection problem with two sensors. These solutions indicate that the LO sensor detector nonlinearities, in general, contain a term proportional to f'/f, where f is the noise probability density function (pdf). For some non-Gaussian pdf's, the new term is significant and causes the LO sensor detector nonlinearities to be nonsymmetric even for symmetric pdfs. LO solutions are presented for finite sample sizes, and the solutions for the asymptotic case are discussed. These results are extended to yield the form of the solutions for the N-sensor LO random signal distributed detection problem that generalize the two-sensor results.>

The limitations of the asymptotic relative efficiency (ARE) in predicting finite sample size detector performance have been noted in several previous studies. It has been observed that the finite-sample-size relative efficiency (RE) may converge very slowly to its asymptotic limit. In addition, in some cases the RE approaches the ARE from below, while in other cases the RE either starts above or overshoots the ARE and approaches it from above. Results indicate that both of these effects can be predicted for a useful class of detectors for known signals in additive noise. The prediction formula is developed for the generalized correlation detector structure. The result is then used to analyze some specific detectors. Among these are the sign detector, the dead-zone detector, the soft-limiter and the noise blanker. Calculations and simulations giving the relative efficiency as a function of sample size have been used to verify predictions.>

The nonlinear equations whose solution determines the locally optimum detection quantizer design are derived for a general parametric detection problem where the breakpoints are constrained to be time invariant. These quantizers maximize the efficacy of a test based on quantized data. Some specific optimum detection quantizer problems for the case of time-invariant breakpoints have been solved in the past, but only for the special case when the locally optimum nonlinearity factors in a certain way. Examples of observation models that do not satisfy these conditions are given. It is demonstrated that the locally optimum quantizer design for the time-invariant breakpoint constraint is the same as that quantizer design that minimizes the time-average mean-square difference between the quantizer and the locally optimum time-varying nonlinearity. A specific result shows that the optimum quantizer is not symmetric for the quadratic detector for random signals in Gaussian noise.>