Viewing the holistic human body as a linear time-invariant (LTI) system and fusing multimodal physiological signals to understand the physical state by borrowing the idea from systems medicine (SM), we propose a multimodal autoregressive moving average with exogenous terms (MARMAX) model to characterize a human body. The model parameter matrices are calculated from the real world multimodal physiological signals using two stage least square (2SLS) method for personalization. Based on the personalized MARMAX model, one can predict the physiological signals of a certain person. Taking wrist pulse signals and tongue images as output signals for LTI human systems, experimental results are provided to evaluate the effectiveness of the proposed model.

This paper proposes to employ a multiple-input multiple-output (MIMO) radar-based quickest change detection (QCD) for non-contact sudden abnormal heart rate (HR) alerting, where the HR changes from a normal to an abnormal value at an unknown change time. By developing a signal model for the non-contact sudden abnormal HR alerting using MIMO radar, we propose a sequential generalized likelihood ratio test (GLRT) based abnormal HR detector to detect the HR change immediately and evaluate the abnormal HR alerting performance employing mean time to false alarm (MTFA) and worst case average detection delay (WADD). Numerical examples validate the correctness of the theoretical analysis and demonstrate the efficiency of the proposed method by comparing with the state-of-the-art methods.

This letter investigates the non-contact heart rate (HR) and respiratory rate (RR) joint estimation employing multiple-input multiple-output (MIMO) radar with widely separated antennas. By developing a signal model for the HR and RR estimation using the MIMO radar, where the initial phases for HR and RR, as well as the reflection coefficients, are deterministic but unknown, we propose an HR-RR joint estimator. Unlike the existing methods, the theoretical performance of the HR and RR estimation is analyzed for the first time, where the corresponding Cramer-Rao Bounds (CRBs) are derived. These bounds provide the first theoretical performance benchmark for this type of radar-based estimation and guide the system parameters design to enhance the HR and RR estimation performance, thereby avoiding the complex numerical computations involved in the joint estimator. It is shown that the proposed method outperforms traditional methods and the CRB can provide the guidance for system parameter optimization.

Consider a quickest detection problem, where a sudden change of parameters needs to be detected as quickly as possible. When unknown parameters exist in the post-change distribution, generalized likelihood ratio test (GLRT) based method is a straightforward option, which may, however, lead to huge computational complexity and storage burden due to the repeated operation of the enumerating all possible change time and estimating unknown parameters every time a new observation sample is received. In this paper, a drift-oriented GLRT (D-GLRT) algorithm is proposed to avoid the repeated enumerations and reduce the storage burden. It is shown that the D-GLRT has lower complexity compared with the conventional GLRT based method, with a little loss of performance. The upper bound of the worst case average detection delay (WADD) of the D-GLRT based method is derived. Numerical results are provided to validate our theoretical analysis.

Heart rate (HR) is one of the most important indicators to assess the health condition of a person, so obtaining an accurate HR estimate is crucial. In this paper, a multiple-input multiple-output (MIMO) radar with dispersed antennas is employed to monitor the physiological signals caused by respiration and heartbeat for non-contact HR estimation. Fourier sine series is used to model the respiration and heartbeat signals measured by the MIMO radar, which enters the return signal from their impact on the human chest movement and incorporates a delay which is time-varying. Bayesian analysis is used for the HR estimation, and the corresponding Cramer-Rao bound (CRB) is derived. Via numerical studies, we show that applying the maximum likelihood (ML) estimation to estimate the HR can lead to improved estimation performance over the existing HR estimation methods. The advantage of using MIMO radar for the HR estimation is also demonstrated.

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.

Joint direction of arrival (DOA) and Doppler frequency estimation plays an important role in radar and wireless communication systems. However, the number of antennas and snapshots could be limited in real applications, so that it is necessary to design the array structure and sampling method to improve the estimation performance. We utilize coprime array and coprime sampler at the spatial and temporal domains under a constrained number of total snapshots. We propose to allow different temporal sampling parameters for the coprime samplers at different antennas, called STCS (Spatial-Temporal Coprime Sampling with possibly different temporal sampling parameters). The spatial coprime array and temporal coprime sampler parameters are optimized to maximize the degrees of freedom (DOFs). Based on the optimized coprime array and samplers, compressed sensing theory is used to jointly estimate the DOA and Doppler frequency. Numerical examples are presented to illustrate that the proposed STCS can provide the improved DOF and better estimation performance.

Abstract Target detection is investigated for the emerging integrated radar and communication (IRC) systems. Consider the case, where multiple radar and communication stations are physically separated, possibly widely spaced, while working in a cooperative way. To utilise all available information for a final decision making, the radar stations that receive signals send their local measurements to a fusion centre (FC) through a wireless channel, say the backhaul network. For the purpose of decreasing communication traffic, the local measurements are quantised and then transferred to the FC. Three strategies for the quantisation and fusion are considered, where for the first method, local sensors quantise their test statistics, which are linearly fused at the FC (quantising test statistics and linear combination fusion), for the second method, the test statistics are quantised at the local sensors and optimally fused at the FC (quantising test statistics and optimal fusion), and for the third method, the received signals are quantizsd at the local sensors and optimally fused at the FC (quantising received signals and optimal fusion). The detection probability for each method is derived for the cooperative IRC system and compared with that of the non‐cooperative counterpart. It is proved that there is a detection performance gain through cooperation between the radar and communication systems and the cooperative IRC system can achieve the same performance as the non‐cooperative system with a fewer number of quantisation bits. The correctness of theoretical analysis is verified by simulations.

Abstract Target parameter estimation is considered for the cooperative multiple‐input multiple‐output (MIMO) radar and MIMO communications system. To address the hardware limitation of the radar system, a joint transmitter selection and receiver placement (JTSRP) problem is formulated to minimise the estimation performance benchmarked by the Cramer–Rao bound (CRB), where the transmitters can be selected from a discrete set and the receivers can be deployed over a continuous region. To efficiently solve this mix‐integer non‐linear programming problem approximately, a genetic algorithm (GA)‐based method is proposed. It is shown that the result obtained by the proposed algorithm is close enough to the optimum solution of the JTSRP problem. Numerical examples are presented to analyse the performance of the cooperative system designed by the GA‐based JTSRP.

When the radar antennas are properly placed so that each antenna falls within the same target beamwidth, the coherent processing can be employed. This paper studies the problem of joint target position and velocity estimation for a coherent passive radar system. The received observation model with direct path influence is developed in frequency domain. Due to the nature of passive processing, the samples of transmitted signals from the illuminators of opportunity are assumed deterministic unknown. The maximum likelihood estimator is presented and the Cramer-Rao bound (CRB) is derived. We show that the direct path signals can help improve the estimation performance. Then, we extend the discussion to the case where the transmitted signals are known to have constant modulus. Again, we show that incorporating the direct path signals in the received observations can have a positive influence on estimating target parameters. Compared with the case of not knowing the constant modulus constraint, the knowledge of constant modulus constraint brings extra performance gain.

In this paper, we derive the distribution of the product of a complex Gaussian matrix and a complex Gaussian vector. Further, we calculate the distribution of the sum of this product and a complex Gaussian vector, which generalizes the recent results where a complex Gaussian scalar is considered instead of a complex Gaussian matrix. The exact probability density functions (pdf) are derived for both the product and the sum. The pdf and cumulative distribution function (cdf) of the square norm of the sum are also provided. Then, we apply the derived results to analyze the performance of the energy detector for a multiple-input-multiple-output (MIMO) communication system. Our analytical results are verified via numerical examples.

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.

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.

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 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.

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.

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.

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.

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.

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.