This paper considers observer-based detection of sensor bias injection attacks (BIAs) on linear cyber-physical systems with single output driven by white Gaussian noise. Despite their simplicity, BIAs pose a severe risk to systems with integrators, which we refer to as integrator vulnerability. Specifically, the residual generated by any linear observer is indistinguishable under attack and normal operation at steady state, making BIAs detectable only during transients. To address this, we propose a principled method based on Kullback-Leibler divergence to design a residual generator that significantly increases the signal-to-noise ratio against BIAs. For systems without integrator vulnerability, our method also enables a trade-off between transient and steady-state detectability. The effectiveness of the proposed method is demonstrated through numerical comparisons with three state-of-the-art residual generators.

In this paper, we address the problem of covert communication under the presence of multiple wardens with a finite blocklength. The system consists of Alice, who aims to covertly transmit to Bob with the help of a jammer. The system also consists of a Fusion Center (FC), which combines all the wardens' information and decides on the presence or absence of Alice. Both Alice and jammer vary their signal power randomly to confuse the FC. In contrast, the FC randomly changes its threshold to confuse Alice. The main focus of the paper is to study the impact of employing multiple wardens on the trade-off between the probability of error at the FC and the outage probability at Bob. Hence, we formulate the probability of error and the outage probability under the assumption that the channels from Alice and jammer to Bob are subject to Rayleigh fading, while we assume that the channels from Alice and jammer to the wardens are not subject to fading. Then, we utilize a two-player zero-sum game approach to model the interaction between joint Alice and jammer as one player and the FC as the second player. We derive the pay-off function that can be efficiently computed using linear programming to find the optimal distributions of transmitting and jamming powers as well as thresholds used by the FC. The benefit of using a cooperative jammer is shown by means of analytical results and numerical simulations to neutralize the advantage of using multiple wardens at the FC.

This paper focuses on the analysis of an optimal sensing and quantization strategy in a multi-sensor network where each individual sensor sends its quantized log-likelihood information to the fusion center (FC) for non-Bayesian quickest change detection. It is assumed that the sensors are equipped with a battery/energy storage device of finite capacity, capable of harvesting energy from the environment. The FC is assumed to have access to either non-causal or causal channel state information (CSI) and energy state information (ESI) from all the sensors while performing the quickest change detection. The primary observations are assumed to be generated from a sequence of random variables whose probability distribution function changes at an unknown time point. The objective of the detection problem is to minimize the average detection delay of the change point with respect to a lower bound on the rate of false alarm. In this framework, the optimal sensing decision and number of quantization bits for information transmission can be determined with the constraint of limited available energy due to finite battery capacity. This optimization is formulated as a stochastic control problem and is solved using dynamic programming algorithms for both non-causal and causal CSI and ESI scenario. A set of non-linear equations is also derived to determine the optimal quantization thresholds for the sensor log-likelihood ratios, by maximizing an appropriate Kullback-Leibler (KL) divergence measure between the distributions before and after the change. A uniform threshold quantization strategy is also proposed as a simple sub-optimal policy. The simulation results indicate that the optimal quantization is preferable when the number of quantization bits is low as its performance is significantly better compared to its uniform counterpart in terms of average detection delay. For the case of a large number of quantization bits, the performance benefits of using the optimal quantization as compared to its uniform counterpart diminish, as expected.

The problem of evaluating compound probability distributions where one of the involved distributions is normal, frequently occurring when modelling communication channels in indoor industrial environments, is considered. Three different methods are investigated. They will here be named Gauss Newton Raphson (GNR), based on the Laplace approximation, Gauss- Hermite Quadratures (GHQ), and a Discrete Convolutional Sum (DCS). These three methods are investigated and compared for a one point problem assuming data that are continuous in amplitude, and a problem where data are assumed to be received in quantized bins. The relative integral approximation error, resulting from computing the compound distribution, is evaluated for the different methods and their complexities are compared. Simulations are provided to illustrate the advantages and disadvantages of the different methods.

A shortcoming of multichannel sound reproduction standards, such as stereo or 5.1 surround, is their incompatibility with multiple off-axis listening positions. Accurate reproduction of virtual sound sources can only be experienced in the sweet spot, which is located equidistant to the loudspeakers. We here present a novel methodology to compensate audio systems such that the channel similarity is optimized in several listening positions simultaneously. To that end we propose a novel MIMO personal audio filter design framework based on feed-forward control. By proper design choices, filters that successfully compensate for multiple off-axis positions and irregularities in the frequency sum responses are obtained. The design choices include allpass filters with appropriate phase shifts as target for each listening position in addition to a weighted similarity requirement. Evaluations based on measurements of two four-channel car audio systems show that the proposed method significantly improves timbral sound reproduction and phantom center reproduction in several listening positions simultaneously.

This paper investigates an optimal energy allocation problem for multi sensor estimation of a random source where sensors communicate their measurements to a remote fusion centre (FC) over orthogonal fading wireless channels using uncoded analog transmissions. The FC reconstructs the source using the best linear unbiased estimator (BLUE). The sensors have limited batteries but can harvest energy and also transfer energy to other sensors in the network. A distortion minimization problem over a finite-time horizon with causal and non-causal information is studied and the optimal energy allocation policy for transmission and sharing is derived. Several structural necessary conditions for optimality are presented for the two sensor problem with non-causal information and a horizon of two time steps. Numerical simulations are included to illustrate the theoretical results.

This paper presents a design methodology for optimal energy allocation to estimate a random source using multiple wireless sensors equipped with energy harvesting technology. In this framework, multiple sensors observe a random process and then transmit an amplified uncoded analog version of the observed signal through Markovian fading wireless channels to a remote station. The sensors have access to an energy harvesting source, which is an everlasting but unreliable random energy source compared to conventional batteries with fixed energy storage. The remote station or so-called fusion centre estimates the realization of the random process by using a best linear unbiased estimator. The objective is to design optimal energy allocation policies at the sensor transmitters for minimizing total distortion over a finite-time horizon or a long term average distortion over an infinite-time horizon subject to energy harvesting constraints. This problem is formulated as a Markov decision process (MDP) based stochastic control problem and the optimal energy allocation policies are obtained by the use of dynamic programming techniques. Using the concept of submodularity, the structure of the optimal energy allocation policies is studied, which leads to an optimal threshold policy for binary energy allocation levels. Motivated by the excessive communication burden for the optimal control solutions where each sensor needs to know the channel gains and harvested energies of all other sensors, suboptimal decentralized strategies are developed where only statistical information about all other sensors' channel gains and harvested energies is required. Numerical simulation results are presented illustrating the performance of the optimal and suboptimal algorithms.

Wireless sensor networks (WSNs) are being increasingly used for monitoring and control in modern process industries, which until a few years ago were almost exclusively done by cables. In order to successfully integrate WSNs in process industries, proper understanding of the radio channel characteristics is necessary. Predominantly, in control applications, the sensors are static, and variations in the channel are caused by the objects in the region, which move to different locations every now and then. Hence, over a period of several hours, the radio channel will have completely different properties, which will have a significant impact on network performance. In this paper, we conduct and analyze channel measurements in a fully functional factory over a much longer time horizon of 20 hours, which, to the best of our knowledge, have not been undertaken before. A key observation from our analysis is that the radio channel, over a longer time scale, shows a more complicated behavior than over a relatively shorter time period. We also show that if the long-term channel variations are not effectively characterized, then we run the risk of transmitting at a rate, as low as, 94% less than what the channel could actually support.

One of the challenges for a successful use of wireless sensor networks in process industries is to design networks with energy efficient transmission, to increase the lifetime of the deployed network while maintaining the required latency and bit-error rate. The design of such transmission schemes depend on the radio channel characteristics of the region. This paper presents an investigation of the statistical properties of the radio channel in a typical process industry, particularly when the network is meant to be deployed for a long time duration, e.g., days, weeks, and even months. Using 17-20-h-long extensive measurement campaigns in a rolling mill and a paper mill, we highlight the non-stationarity in the environment and quantify the ability of various distributions, given in the literature, to describe the variations on the links. Finally, we analyze the design of an optimal received signal-to-noise ratio (SNR) for the deployed nodes and show that improper selection of the distribution for modeling of the variations in the channel can lead to an overuse of energy by a factor of four or even higher.

A new multichannel approach to robust broadband loudspeaker-room equalization is presented. Traditionally, the equalization (or room correction) problem has been treated primarily by single-channel methods, where loudspeaker input signals are prefiltered individually by separate scalar filters. Single-channel methods are generally able to improve the average spectral flatness of the acoustic transfer functions in a listening region, but they cannot reduce the variability of the transfer functions within the region. Most modern audio reproduction systems, however, contain two or more loudspeakers, and in this paper we aim at improving the equalization performance by using all available loudspeakers jointly. To this end we propose a polynomial based MIMO formulation of the equalization problem. The new approach, which is a generalization of an earlier single-channel approach by the authors, is found to reduce the average reproduction error and the transfer function variability over a region in space. Moreover, pre-ringing artifacts are avoided, and the reproduction error below 1000 Hz is significantly reduced with an amount that scales with the number of loudspeakers used.

In this paper, a new multichannel approach to robust loudspeaker-room equalization is presented. Traditionally, the equalization (or room correction) problem has been treated mostly by single-channel methods, with loudspeaker signals being prefiltered individually by separate scalar filters. Single-channel methods can generally improve the average spectral flatness of the acoustic transfer functions in a listening region, but the variability of the transfer functions within the region cannot be affected. Most modern audio reproduction systems, however, contain two or more loudspeakers, and in this paper we aim at improving the equalization performance by using all available loudspeakers jointly. To this end we propose a general MIMO formulation of the problem, which is a multichannel generalization of an earlier single-channel approach by the authors. The new approach is found to reduce the average reproduction error and the spatial variability of the acoustic transfer functions. Moreover, pre-ringing artifacts are avoided, and the reproduction error below 1000 Hz is significantly reduced with an amount that scales with the number of loudspeakers used.

We study state estimation via wireless sensor networks over fading channels affected by random packet loss. In the configuration examined, the sensors send their measurements to a single gateway, which decides upon the source coding scheme and the sensor transmitter power levels. The decision process is carried out on-line and adapts to changing channel conditions to achieve an optimal trade-off between estimation quality and sensor energy expenditure. In particular, if some channel conditions are poor, then the gateway commands the corresponding sensors to increase power levels and use multiple-description coding. Simulations based on measured channel data illustrate that the proposed scheme gives excellent results.

A well known problem in loudspeaker equalization is that mixed phase design of the inverse filter causes residual "pre-ringings" in the equalized system, due to the spatial variability of loudspeaker- room transfer functions. A common strategy for robust and perceptually acceptable equalization is therefore to use minimum phase filters only. In this paper, a method for cautious mixed phase equalization is proposed. By analysis of a set of room transfer functions, it is concluded that some non-minimum phase zeros are insensitive to receiver position, and can therefore be robustly inverted. The method improves upon a minimum phase equalization by extending the minimum phase model with a robustly invertible all pass link. Validation measurements show that the time-domain aspect of equalization is improved throughout the spatial region of interest, while pre-ringings are kept at a very low and prespecified level.

A common technique in wireless sensor networks (WSN) is to use multihopping, that is, relaying messages via intermediate nodes. In this work we compare the energy efficiency of single-hop and multihop taking into account circuit energy consumption as well as transmission energy. We consider a simple two-hop case as well as a multihop case for a uniform two-dimensional network of arbitrary size. Contrary to common beliefs, we find that single-hop is superior for all realistic cases covered by our model. Even in comparison to the simple two-hop case single-hop is preferable. Only at very large path losses would multihop be a serious alternative. At present there are however very few WSN radios available that can operate under such conditions. In spite of the relatively simple networks considered we argue that our findings have quite general applicability with strong implications for the choice of routing protocols.

We investigate whether adapting the transmit power optimally to the time-varying channel compares favorably, in terms of total energy consumption, to using a fixed link margin in wireless networks over short transmission distances. Over short distances, the circuit energy consumption dominates the transmission energy. For that reason, feeding back channel state information a requirement for power control - may not be a power efficient strategy. We investigate both slow and fast power control and conclude, somewhat surprisingly, that using a fixed margin is typically more power-efficient than using power control.

High data rates, high spectral efficiency, flexibility, and low delays over the air interface will be important features in next-generation wireless systems. The overall challenge will be packet scheduling and adaptive radio transmission for multiple users, via multiple antennas and over frequency-selective wideband channels. This problem needs to be structured to obtain feasible solutions. The basic simplifying assumptions used here are clustering of antennas into cells, orthogonal transmission by use of cyclic-prefix orthogonal frequency-division multiplexing (OFDM) and a time-scale separation view of the total link adaptation, scheduling and intercell coordination problem. Based on these assumptions, we survey techniques that adapt the transmission to the temporal, frequency, and spatial channel properties. We provide a systematic overview of the design problems, such as the dimensioning of the allocated time-frequency resources, the influence of duplexing schemes, adaptation control issues for downlinks and uplinks, timing issues, and their relation to the required performance of channel predictors. Specific design choices are illustrated by recent research within the Swedish Wireless IP program and the EU IST-WINNER project. The presented results indicate that high-performance adaptive OFDM transmission systems are indeed feasible, also for challenging scenarios that involve vehicular velocities, high carrier frequencies, and high bandwidths.

Adaptation laws with constant gains, that adjust parameters of linear regression models, are investigated. The class of algorithms includes LMS as its simplest member, while other algorithms such as Wiener LMS may improve performance by including linear filters. Expressions in closed form for the tracking MSE are obtained for rapidly varying parameters of FIR systems with white inputs. This situation may occur in e.g. the tracking of fading communication channels. Stability and convergence in MSE are ascertained by the stability of a transfer function, without assuming independent regressor vectors. A key technique for obtaining these results is a transformation of these adaptation algorithms into linear time-invariant filters, called learning filters, that operate in open loop for slow parameter variations.

This paper investigates the estimation and tracking of time varying propagation channels in the uplink of a time slotted CDMA system. An antenna array is adopted at the base station. Both the estimation and tracking are performed by exploiting the low-rank nature of the channel matrix. The accuracy of the estimate is improved by using a multi-slot approach: the slowly varying component of the low-rank channel is estimated from the observation of successive midambles (inter-slot tracking), while the fast varying component is updated over the burst interval in decision-directed mode (intra-slot tracking).

For pt.I see ibid., vol.49, p.2207-17 (2001). Low-complexity Wiener LMS (WLMS) adaptation algorithms, of use for channel estimation, have been derived in Lindbom et al. (2001). They are here evaluated on the fast fading radio channels encountered in IS-136 TDMA systems, with the aim of clarifying several issues: How much can channel estimation performance be improved with these tools, as compared to LMS adaptation? When can an improved tracking MSE be expected to result in a meaningful reduction of the bit error rate? Will optimal prediction of future channel estimates significantly improve the equalization? Can one single tracker with fixed gain be used for all encountered Doppler frequencies and SNRs, or must a more elaborate scheme be adopted? These questions are here investigated both analytically and by simulation. An exact analytical expression for the tracking MSE on two-tap FIR channels is presented and utilized. With this tool, the MSE performance and robustness of WLMS algorithms based on different statistical models can be investigated. A simulation study then compares the uncoded bit error rate of detectors, where channel trackers are used in decision directed mode in conjunction with Viterbi algorithms. A Viterbi detector combined with WLMS, based on second order autoregressive fading models possibly combined with integration, provides good performance and robustness at a reasonable complexity.

We present a method for optimizing adaptation laws that are generalizations of the LMS algorithm. Time-varying parameters of linear regression models are estimated in situations where the regressors are stationary or have slowly time-varying properties. The parameter variations are modeled as ARIMA processes and the aim is to use such prior information to provide high-performance filtering, prediction or fixed lag smoothing estimates for arbitrary lags. The method is based on a novel signal transformation that recasts the algorithm design problem into a Wiener design.

Adaptation laws with constant gains, that adjust parameters of linear regression models, are investigated. The class of algorithms includes LMS as its simplest member. Closed-form expressions for the tracking MSE are obtained for parameters described by ARIMA processes. A key element of the analysis is that adaptation algorithms are expressed as linear time-invariant filters, here called learning filters, that work in open loop for slow parameter variations. Performance analysis can then easily be performed for slow variations, and stability is assured by stability of these learning filters.

Adaptation algorithms with constant gains are designed for tracking smoothly time-varying parameters of linear regression models, in particular channel models occurring in mobile radio communications. In a companion paper, an application to channel tracking in the IS-136 TDMA system is discussed. The proposed algorithms are based on two key concepts. First, the design is transformed into a Wiener filtering problem. Second, the parameters are modeled as correlated ARIMA processes with known dynamics. This leads to a new framework for systematic and optimal design of simple adaptation laws based on prior information. The algorithms can be realized as Wiener filters, called learning filters, or as "LMS/Newton" updates complemented by filters that provide predictions or smoothing estimates. The simplest algorithm, named the Wiener LMS, is presented. All parameters are here assumed governed by the same dynamics and the covariance matrix of the regressors is assumed known. The computational complexity is of the same order of magnitude as that of LMS for regressors which are either white or have autoregressive statistics. The tracking performance is, however, substantially improved.

A general MMSE decision feedback equalizer (DFE) for multiple input-multiple output channels is presented. It is derived under the constraint of realizability, requiring finite smoothing lag and causal filters both in the forward and feedback link. The proposed DFE, which provides an optimal structure as well as optimal filter degrees, is obtained as an explicit solution in terms of the channel and noise description. A generalization of the scalar zero-forcing DFE is also presented. Conditions for the existence of such an equalizer are discussed. We argue that when no zero-forcing equalizer exists, poor near-far resistance of the corresponding optimal minimum mean square error DFE can be expected. A numerical example indicates the potential advantages of using a decision feedback equalizer with appropriate structure. The main improvements are obtained at moderate to high signal-to-noise ratios.

We investigate the use of an antenna array at the receiver in frequency-division multiple-access/time-division multiple-access systems to let several users share one communication channel within a cell. A decision-feedback equalizer (DFE) which simultaneously detects all incoming signals is compared to a set of DFEs, each detecting one signal and rejecting the remaining as interference. We also introduce the existence of a zero-forcing solution to the equalization problem as an indicator of near-far resistance of different detector structures. Near-far resistance guarantees good performance if the noise level is low. Simulations show that with an increased number of users in the cell, the incremental performance degradation is small for the multiuser detector. We have also applied the proposed algorithms to experimental measurements from a DCS-1800 antenna array testbed. The results from these confirm that reuse within a cell is indeed possible using either an eight-element array antenna or a two-branch diversity sector antenna. Multiuser detection will, in general, provide better performance than interference rejection, especially when the power levels of the users differ substantially. The difference in performance is of crucial importance when the available training sequences are short.

The purpose of this paper is to investigate the use of combined spatial and temporal equalization, in particular for short training sequences. The motivation for combining spatial and temporal equalization is the existence of multipath propagation and co-channel interference. Our main concern is to obtain good performance yet low complexity. We will suggest a low complexity algorithm utilizing a circular antenna array. Although it has inferior performance in an asymptotic sense, it turns out to be superior to the general solution for short training sequences. This conclusion is supported by simulations where a number of algorithms are evaluated for different scenarios involving co-channel interference.

During the last few years, the second generation mobile cellular telephone systems have become operational. One can foresee a dramatic increase in traffic demands, both concerning transmission quality and system capacity. We present a multivariable minimum mean square error (MMSE) DFE, which has the ability to operate on channels with different number of inputs and outputs. It is derived under the constraint of realizability and is calculated by solving a system of linear equations. The suggested DFE can be used for combined temporal and spatial equalization, as well as for narrowband, multiuser detection in systems with multiple antenna elements. The DFE may also serve as a multiuser detector in DS-CDMA systems. Simulations indicate that the DFE performs well as a multiuser detector. In a system with multiple antennas, it outperforms a corresponding detector for a single user in terms of the BER while doubling the capacity. If utilized for multiuser detection in CDMA, its performance is comparable to the best achievable performance of the decorrelating detector, and is attained at a substantially lower computational cost.

A simple algorithm for optimizing decision feedback equalizers (DFEs) by minimizing the mean-square error (MSE) is presented. A complex baseband channel and correct past decisions are assumed. The dispersive channel may have infinite impulse response, and the noise may be colored. Consideration is given to optimal realizable (stable and finite-lag smoothing) forward and feedback filters in discrete time. They are parameterized as recursive filters. In the special case of transmission channels with finite impulse response and autoregressive noise, the minimum MSE can be attained with transversal feedback and forward filters. In general, the forward part should include a noise-whitening filter (the inverse noise model). The finite realizations of the filters are calculated using a polynomial equation approach to the linear quadratic optimization problem. The equalizer is optimized essentially by solving a system of linear equations Ax=B, where A contains transfer function coefficients from the channel and noise model. No calculation of correlations is required with this method. A simple expression for the minimal MSE is presented. The DFE is compared to MSE-optimal linear recursive equalizers. Expressions for the equalizer in the limiting case of infinite smoothing lags are also discussed.>