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Design principles of MIMO radar detectors
Abstract
This paper considers the problem of multiple-input multiple-output (MIMO) radars employing space-time coding (STC) to achieve diversity. To this end, after briefly outlining the model of the received echo, a suitable detection structure is derived, and its performance is expressed in closed form as a function of the clutter statistical properties and of the space-time code matrix. Interestingly, this receiver requires prior knowledge of the clutter covariance, but the detection threshold is functionally independent thereof. At the transmitter design stage, we give two criteria for code construction: the first is based on the classical Chernoff bound, the second is an information-theoretic criterion. Interestingly, the two criteria lead to the same condition for code optimality, which in turn specializes, under the assumption of uncorrelated clutter and square code matrix, in some well-known full-rate space-time codes. A thorough performance assessment is also given, so as to establish the optimum achievable performance for MIMO radar systems.
... The authors of [12] have shown that under the same transmit power constraint, the performance of MIMO radar waveforms obtained by optimizing the mutual information or the minimum mean squared error (MMSE) are the same when the target impulse vector follows the Gaussian distribution. In the space-time coding design of MIMO radar, code construction based on the MI conincides with code construction based on the Chernoff bound under the assumption of uncorrelated sensing targets [13]. In the RCC system, designing waveforms by maximizing the MI is beneficial to the co-existence of the MIMO radar and the communication in spectrally crowded environments [14]. ...
... Here, (16b) is the power constraint for the BS with P 0 being the maximum transmit power, and (16c) follows from (13). ...
... Furthermore, maximizing (24) is equivalent to maximize the following expression 13 The problem of maximizing (25) is still difficult to address, so by means of the Schur complement and an auxiliary variable, maximizing (25) can be reformulated as the following ...
Integrated sensing and communication (ISAC) unifies sensing and communication, and improves the efficiency of the spectrum, energy, and hardware. In this work, we investigate the ISAC beamforming design to maximize the mutual information between the target response matrix of a point radar target and the echo signals, while ensuring the data rate requirements of communication users. In order to study the impact of the echo interference caused by communication users on sensing performance, we consider three types of echo interference problems caused by a single communication user, including no interference, a point interference, and an extended interference, as well as the problem of an extended interference caused by multiple communication users. To address these problems, we provide a closed-form solution with low complexiy, a semidefinite relaxation (SDR) method, a low-complexity algorithm based on the Majorization-Minimization (MM) method and the successive convex approximation (SCA) method, and an algorithm based on MM method and SCA method, respectively. Numerical results demonstrate that, compared to the ISAC beamforming schemes based on the Cram\'er-Rao bound (CRB) metric and the beampattern metric, the proposed maximizing mutual information metric can bring better beampattern and root mean square error (RMSE) of angle estimation. Apart from this, our proposed schemes based on the mutual information can suppress the echo interference from the communication users effectively.
... In Ref. [36], the authors obtained the optimal waveforms based on minimising the mean-square error (MSE), which is closely related to the estimation accuracy of parameters. In Ref. [37,38], the authors utilised the lower Chernoff bound as the metric to design waveforms. Moreover, waveform optimisation based on maximising the mutual information between the receive signals and the target response was also considered. ...
... Moreover, waveform optimisation based on maximising the mutual information between the receive signals and the target response was also considered. The results in Ref. [37,38] revealed the connection between the waveforms designed based on the two metrics. In Ref. [39][40][41][42][43], the authors proposed to design waveforms based on maximising the relative entropy between the distributions of the observations under two hypotheses (viz., the target is present/absent). ...
... The problem in (37) can be tackled by the method presented in Ref. [41]. Precisely, we tackle the optimisation problem min x kx − t k;n k 2 2 ; s:t: ...
In this paper, the waveform design for Rician target detection with multiple‐input‐multiple‐output radar is addressed. The relative entropy between the distributions of the observations under two hypotheses is employed as the design metric. Due to the difficulty of tackling the non‐convex waveform design problem, a novel algorithm based on minorisation‐maximisation is developed. Since a simple quadratic function is established to minorise the objective function, the presented algorithm has lower computational complexity than its counterparts. Moreover, it can be extended to design waveforms under many practical constraints, including the constant‐envelope constraint, the similarity constraint, and the constant‐envelope and similarity constraints. Numerical results are provided to show the effectiveness of the proposed algorithm for detecting Rician targets. Moreover, the designed waveforms can be used to enhance the detection performance of a Swerling 0 target in the presence of angle mismatch.
... Reference [322] derived the GLRT for distributed MIMO radar with arbitrary transmitted waveforms and arbitrary time-correlation of the noise, and it was shown that there is an inherent trade-off between diversity and integration, and that no uniformly optimum waveform design strategy exists. In [323], the GLRT was derived for distributed MIMO radar, with arbitrary transmit waveform and adopting Doppler processing. It was assumed that all transmitreceive pairs share the same known covariance matrix, then the expressions for the PD of the GLRT was given [323], according to which the optimum transmit waveform was given. ...
... In [323], the GLRT was derived for distributed MIMO radar, with arbitrary transmit waveform and adopting Doppler processing. It was assumed that all transmitreceive pairs share the same known covariance matrix, then the expressions for the PD of the GLRT was given [323], according to which the optimum transmit waveform was given. Reference [324] generalized the data model in [323] to the case that different transmit-receive pairs have different but known covariance matrices. ...
... It was assumed that all transmitreceive pairs share the same known covariance matrix, then the expressions for the PD of the GLRT was given [323], according to which the optimum transmit waveform was given. Reference [324] generalized the data model in [323] to the case that different transmit-receive pairs have different but known covariance matrices. Then the statistical performance of the corresponding GLRT was given for Swerling I target. ...
Multichannel adaptive signal detection jointly uses the test and training data to form an adaptive detector, and then make a decision on whether a target exists or not. Remarkably, the resulting adaptive detectors usually possess the constant false alarm rate (CFAR) properties, and hence no additional CFAR processing is needed. Filtering is not needed as a processing procedure either, since the function of filtering is embedded in the adaptive detector. Moreover, adaptive detection usually exhibits better detection performance than the filtering-then-CFAR detection technique. Multichannel adaptive signal detection has been more than 30 years since the first multichannel adaptive detector was proposed by Kelly in 1986. However, there are fewer overview articles on this topic. In this paper we give a tutorial overview of multichannel adaptive signal detection, with emphasis on Gaussian background. We present the main deign criteria for adaptive detectors, investigate the relationship between adaptive detection and filtering-then-CFAR detection, relationship between adaptive detectors and adaptive filters, summarize typical adaptive detectors, show numerical examples, give comprehensive literature review, and discuss some possible further research tracks.
... Reference [324] derived the GLRT for distributed MIMO radar with arbitrary transmitted waveforms and arbitrary time-correlation of the noise, and it was shown that there is an inherent trade-off between diversity and integration, and that no uniformly optimum waveform design strategy exists. In [325], the GLRT was derived for distributed MIMO radar, with arbitrary transmit waveform and adopting Doppler processing. It was assumed that all transmitreceive pairs share the same known covariance matrix, then the expressions for the PD of the GLRT was given [325], according to which the optimum transmit waveform was given. ...
... In [325], the GLRT was derived for distributed MIMO radar, with arbitrary transmit waveform and adopting Doppler processing. It was assumed that all transmitreceive pairs share the same known covariance matrix, then the expressions for the PD of the GLRT was given [325], according to which the optimum transmit waveform was given. Reference [326] generalized the data model in [325] to the case that different transmit-receive pairs have different but known covariance matrices. ...
... It was assumed that all transmitreceive pairs share the same known covariance matrix, then the expressions for the PD of the GLRT was given [325], according to which the optimum transmit waveform was given. Reference [326] generalized the data model in [325] to the case that different transmit-receive pairs have different but known covariance matrices. Then the statistical performance of the corresponding GLRT was given for Swerling I target. ...
Multichannel adaptive signal detection jointly uses the test and training data to form an adap-tive detector, and then make a decision on whether a target exists or not. Remarkably, the resulting adaptive detectors usually possess the constant false alarm rate (CFAR) properties, and hence no additional CFAR processing is needed. Filtering is not needed as a processing procedure either, since the function of filtering is embedded in the adaptive detector. Moreover, adaptive detection usually exhibits better detection performance than the filtering-then-CFAR detection technique. Multichannel adaptive signal detection has been more than 30 years since the first multichannel adaptive detector was proposed by Kelly in 1986. However, there are fewer overview articles on this topic. In this paper we give a tutorial overview of multichannel adaptive signal detection, with emphasis on Gaussian background. We present the main deign criteria for adaptive detectors, investigate the relationship between adaptive detection and filtering-then-CFAR detection , relationship between adaptive detectors and adaptive filters, summarize typical adaptive detectors, show numerical examples, give comprehensive literature review, and discuss some possible further research tracks.
... Following is the comprehensive set of publications resulting from the Ph.D. research. MI has been widely used as a performance metric for radar and communication systems [49,[58][59][60][61][62]. This is because MI maximization is related to the maximization of the probability of detection in radar systems for a fixed probability of false alarm [58]. ...
... MI has been widely used as a performance metric for radar and communication systems [49,[58][59][60][61][62]. This is because MI maximization is related to the maximization of the probability of detection in radar systems for a fixed probability of false alarm [58]. ...
Spectrum sharing has become increasingly important since the past decade due
to the ongoing congestion of spectral resources. Higher data rates in wireless communications require expansion of existing frequency allocations. Significant research
efforts have been made in the direction of cognitive radio to effectively manage the
existing frequency usage. Recently, coexistence of multiple platforms within the same
frequency bands is considered effective to mitigate spectral congestion. This requires
both systems to work collaboratively to mitigate their mutual interference. This challenging problem can be significantly simplified if both systems are controlled by the
same entity. Joint radar-communication (JRC) system is such an example where radar
and communication system objectives are achieved by the same physical platform.
In this dissertation, we consider three different types of JRC systems. These
JRC systems respectively exploit a single transmit antenna, an antenna array for
beamforming, and a distributed JRC network, and develop novel signal processing
techniques to optimize the performance of these systems. Special attention is given
to the resource optimization objectives and numerous resource allocation schemes are
developed and investigated.
First, we consider a single transmit antenna-based JRC system which exploits
dual-purpose transmit orthogonal frequency division multiplexing (OFDM) waveforms to perform radar and communication objectives simultaneously. We optimize
the power allocation of the OFDM subcarriers based on the frequency-sensitive target response and communication channel characteristics. For this purpose, we employ
mutual information as the optimization metric. In the simulation examples considered
for this system, we observed that the JRC system enjoys approximately 20% improvement in the performance of communication subsystem with a mere 5% reduction in
radar subsystem performance.
Second, we propose a quadratic amplitude modulation (QAM) based sidelobe
modulation scheme for beamforming-based JRC systems which enhances the communication data rate by enabling a novel multiple access strategy. The main principle of this proposed strategy lies in enabling the beamformer to transmit signals
with distinct amplitudes and phases in different directions. We also investigate optimal power allocation for such a spectrum sharing approach by employing a spatial
power control-based beamforming approach. Furthermore, the robustness of these
beamforming-based JRC systems is improved using chance constrained programming.
In this context, we observe that the chance constrained optimization can be relaxed
to form a deterministic and convex problem by employing the statistical profile of the
communication channels. When dealing with JRC systems that are equipped with
more antennas than the number of radio frequency chains, we perform the resource
optimization in terms of minimized power usage and optimal selection of antennas
resulting in an efficient utilization of hardware up-conversion chains. In the simulation examples considered for these schemes, we observe that, even with a reduction
of nearly 30% of the transmit antennas, the beamforming-based JRC system is able
to perform the required radar and communication tasks without any disadvantage.
Our last contribution is on a distributed JRC system, which is the first effort in
this research direction, enabling spectrum sharing for networked radar systems coexisting with the communication systems. We devise a power allocation strategy for
such a system by employing convex optimization techniques. In this strategy, the
target localization error and the Shannon capacity are respectively considered as the
optimization criteria for radar and communication systems. For the simulation example considered in this case, we observe that the proposed resource allocation strategy
achieves a communication performance that was approximately 5 times greater than
that achieved by the radar-only counterpart. Moreover, the target localization performance achieved by the JRC system using the proposed approach was approximately
4 times better than the performance achieved by the communication-only approach.
... Mutual information between radar and communication plays vital role in terms of channel capacity and radar performance [199][200][201][202]. In this technique, mutual information (MI) between the communication user and radar target is used as optimization objective for radar at transmitter side [203]. Radar MI is used to evaluate the radar performance, while channel capacity calculation is used as performance measure of the communication system. ...
... Therefore, we present some of the latest waveform that can also be used in DFRC to accommodate the requirements of 5G and beyond. [170][171][172][173][174][175][176][177][178][179][180][181][182][183] Communication waveform-based approach OFDM-based mutual information [67,[199][200][201][202][203][204][205][206][207][208] OFDM-based index modulation [151,[209][210][211][212][213][214] Beampattern-based approach Subbeam approach [219][220][221] 17 Wireless Communications and Mobile Computing potential candidate known as orthogonal time frequency space modulation (OTFS). This is a two-dimensional technique, which exploits the full diversity in time and frequency. ...
Wireless spectrum is a limited resource, and the rapid increase in demand for wireless communication-based services is increasing day by day. Hence, maintaining a good quality of service, high data rate, and reliability is the need of the day. Thus, we need to apportion the available spectrum in an efficient manner. Dual-Function Radar and Communication (DFRC) is an emerging field and bears vital importance for both civil and military applications for the last few years. Since hybridization of wireless communication and radar designs provoke diverse challenges, e.g., interference mitigation, secure mobile communication, improved bit error rate (BER), and data rate enhancement without compromising the radar performance, this paper reviews the state-of-the-art developments in the spectrum shared between mobile communication and radars in terms of coexistence, collaboration, cognition, and cooperation. Compared to the existing surveys, we explore an open research issue on radar and mobile communication operating with mutual benefits based on collaboration in terms of spectrum sharing. Additionally, this paper provides important perspectives for future research of DFRC technology.
... However, waveform optimization still remains a challenge 48 in such systems especially if the waveforms have to be designed in real-time. 49 To perform optimized waveform design, mutual information (MI) has been ex-50 tensively used in the literature as a quantitative performance measure for both radar 51 and communication systems [18,[33][34][35][36]. For radar systems, MI maximization is directly 52 linked to maximizing the probability of detection while maintaining a constant false 53 alarm rate [33]. ...
... 49 To perform optimized waveform design, mutual information (MI) has been ex-50 tensively used in the literature as a quantitative performance measure for both radar 51 and communication systems [18,[33][34][35][36]. For radar systems, MI maximization is directly 52 linked to maximizing the probability of detection while maintaining a constant false 53 alarm rate [33]. On the other hand, for communication systems, MI maximization is 54 also analogous to maximizing the channel capacity for the systems [35]. ...
We propose novel joint radar-communication spectrum sharing strategies exploiting orthogonal frequency-division multiplexing (OFDM) waveforms that concurrently achieve the objectives of both radar and communication systems. An OFDM transmitter is considered that transmits dual-purpose OFDM sub-carriers such that all the sub-carriers are exploited for the primary radar function and further exclusively allocated to the secondary communication function serving multiple users. The waveform optimization is performed by employing mutual information (MI) as the optimization criterion for both radar and communication operations. For the purpose of radar performance optimization, we consider MI between the frequency-dependent target response and the transmit OFDM waveforms. On the other hand, communication system performance is evaluated in terms of MI between the frequency-dependent communication channels of communication users with the transmit OFDM sub-carriers. These optimization objectives not only enable the transmit power allocation of the OFDM sub-carriers but also govern the sub-carrier distribution among the communication users. Two resource optimization scenarios are considered, resulting in radar-centric and cooperative resource allocation strategies that exploit convex and mixed-integer linear programming optimization problems for power allocation and sub-carrier distribution, respectively. We further present a chunk sub-carrier allocation approach that applies to both optimization strategies to reduce the computational complexity with a trivial performance loss. Simulation results are presented to illustrate the effectiveness of the proposed strategies.
... Remark 1: Note that, the SNR (INR) mentioned above is not the input SNR (INR) for a single observation. Here, the SNR for a single observation, i.e., the SNR per sample, is about 1/N r L of that defined in (13), which is defined as ...
... 7: Computet (n) by (34), then update t (n) = Pt (n) . 13: until ||s (n) − t (n) || 2 ≤ and ||s (n) − r (n) || 2 ≤ , or the maximal number of iterations is achieved. Output:s =s (n) , t = t (n) , and r = r (n) . ...
Adopting extremely low-resolution (e.g. one-bit) analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) is able to bring a remarkable saving of low-cost and circuit power for multiple-input multiple-output (MIMO) radar.In this paper, the problem of joint design of transmit waveform and receive filter for collocated MIMO radar with a architecture of one-bit ADCs and DACs is investigated. Under this architecture, we derive the output quantized signal-to-interference-plus-noise ratio (QSINR), which is relative to the detection performance of target, in the presence of signal-dependent interference. The optimization problem is formulated by maximizing the QSINR with a binary waveform constraint. Due to the nonconvex objective and binary constraint, the resulting problem is hard to be directly solved. To this end, we propose an alternating minimization algorithm. More concretely, at each iteration, the closed-form solution of the receive filter is attained by exploiting the minimum variance distortionless response (MVDR) method, and then the one-bit waveform is optimized with the aid of the alternating direction method of multipliers (ADMM) algorithm. In addition, the performance gap between the one-bit MIMO radar and infinite-bit MIMO radar is theoretically analyzed under the noise-only case. Several numerical simulations are provided to demonstrate the effectiveness of the proposed methods.
... In [14,18,46,47], the authors considered the optimization of quasi-orthogonal waveforms with low auto-correlation sidelobes and cross-correlations. In [6,15,16,31,37,39,40,42], the authors considered information theoretic waveform design methods for MIMO radar. In [13,21,41,44], joint design of transmit waveforms and receive filters is considered to maximize the output signalto-interference-plus-noise-ratio (SINR) of MIMO radar. ...
... where the first inequality and the third equality hold with the results in (14) and (15). The second inequality holds because of the optimality of x (q+1) (given x (q) ). ...
We consider the design of constant-modulus waveforms for wideband multiple-input multiple-output radar. The aim is to match a desired transmit beampattern. To tackle the non-convex design problem, we develop an iterative algorithm, which is based on cyclic optimization and majorization–minimization. We prove that the sequence of the objective values of the proposed algorithm has guaranteed convergence. Moreover, we can obtain closed-form solutions for the associated optimization problems at every iteration. Furthermore, the proposed method can be implemented without matrix inversion and hence is computationally efficient. Simulation results demonstrate that the performance of the proposed algorithm is better than existing methods.
... I N THE last decade, the research on multiple-input multipleoutput (MIMO) radar systems has drawn significant attention. Compared to conventional radar systems, MIMO radar may offer in principle increased probability of detection and improved angular resolution [1]- [5]. ...
... We have four antennas, each of which can take different angles and distances. Due to the limitation [1,5] m, respectively, is depicted in Fig. 4. The greater the distance of the transmitter antenna from the target, the lower the determinant due to the reduction of the equivalent single radar gain. In fact, the best distance is the minimum distance, i.e. 1 m, and this confirms the statement expressed in Remark 1. Also, the optimal angle θ * 2 confirms (30). ...
In this paper, we analyze the accuracy of target localization in multiple-input multiple-output (MIMO) radars with widely-separated antennas. The relative target-antennas geometry plays an important role in target localization. We investigate the optimal placement of transmit and receive antennas for coherent and non-coherent processing, based on maximizing the determinant of the Fisher information matrix (FIM), which is equivalent to minimizing the error ellipse area. The square root of the average determinant of the FIM can be expressed as a product of three parameters, namely the equivalent single radar gain, coherency gain and geometry gain. It is shown that the coherency gain of coherent MIMO radar is greater than the non-coherent one, while the geometry gain of coherent MIMO radar is always smaller than or equal to the non-coherent case. The maximum value of the geometry gain for a MIMO radar system with
$N$
transmit and
$M$
receive antennas is proportional to
$MN$
for coherent while it is
$\sqrt{2}MN$
for the non-coherent case.
... In the past decade, MIMO and cognitive radar developed rapidly by exploiting waveform diversity [14][15][16][17][18][19][20][21][22], and the waveform design methods under the MTIC were further investigated. In [14], the MI criterion and the mean square error criterion were employed for MIMO radar waveform design with Gaussian assumption, and it was shown that the two different criteria lead to the same result eventually. ...
... where e(δ 1 ) denotes the error term related to δ 1 . Applying discrete Fourier transform (DFT) column-wise to (15) leads to ...
Although the transmit radar waveform design problem for maximizing target information has been studied widely in the past, the resolution requirement is normally ignored in such designs. Using maximizing target information as a criterion, a new radar waveform design method meeting the high resolution requirement is proposed in this paper, which makes no assumptions on the statistical distribution of target scattering. The objective function is proposed by maximizing the Pearson correlation coefficient (PCC) and the design is then transformed into an optimization problem, which is solved in two steps. Firstly, a closed-form expression for the discretized waveform with constant power constraint is derived in the time domain. Secondly, based on the bandwidth analysis of the optimal solution, a resolution improvement method considering information distortion is introduced and a suboptimal waveform is proposed while satisfying the constant power and resolution requirements. Finally, performance of the proposed radar waveform in terms of information acquisition, classification and resolution is analyzed and compared with the classic high-resolution linear frequency modulated waveform (LFMW). Simulation results show that the resolution of the suboptimal waveform is slightly lower than the LFMW, but more desirable in terms of peak sidelobe ratio (PSLR), information acquisition and classification.
... The MI criterion (19) for sensing is widely used for waveform optimization in radar systems [38], and especially in the multicarrier ISAC waveform optimization [7]- [10]. It can be used for target recognition tasks [38], as a surrogate for the probability of detection at a fixed false alarm rate [39], as well as for multi-target target tracking [40], for example. There is also a direct connection between the mean square error (MSE) and the MI, as established in [41]. ...
This paper proposes a Model-Based Online Learning (MBOL) framework for waveform optimization in integrated sensing and communications (ISAC) systems. In particular, the MBOL framework is proposed to enhance the ISAC performance under dynamic environmental conditions. Unlike Model-Free Online Learning (MFOL) methods, our approach leverages a rich structural knowledge of sensing, communications, and radio environments, offering better explainability and sample efficiency. This paper establishes a theoretical analysis of the proposed class of MBOL methods, showing essential performance conditions and convergence rates. This theoretical analysis is critical for understanding the potential of MBOL in active waveform optimization tasks. We demonstrate the proposed MBOL framework in multicarrier ISAC systems, focusing on the sub-carrier selection and power allocation problem. Via numerical experiments, we show that the proposed MBOL method outperforms the MFOL method in terms of sample efficiency. The results underline the potential of MBOL for improving the active waveform optimization performance in ISAC systems, particularly when sample efficiency and explainability are critical.
... It has already received attention from experts and scholars in the radar community. For example, De et al. considered the problem of implementing MIMO radar with diversity using space-time coding (STC) and performed a comprehensive performance evaluation to determine the best achievable performance for MIMO radar systems [5]. Jajamovich et al. elucidated the optimal firing strategy of a radar when detecting a target at an unknown location [6]. ...
Realization and enhancement of detection techniques for multiple-input–multiple-output (MIMO) radar systems require polyphase code sequences with excellent orthogonality characteristics. Therefore, orthogonal waveform design is the key to realizing MIMO radar. Conventional orthogonal waveform design methods fail to ensure acceptable orthogonal characteristics by individually optimizing the autocorrelation sidelobe peak level and the cross-correlation sidelobe peak level. In this basis, the multi-objective Archimedes optimization algorithm (MOIAOA) is proposed for orthogonal waveform optimization while simultaneously minimizing the total autocorrelation sidelobe peak energy and total cross-correlation peak energy. A novel optimal individual selection method is proposed to select those individuals that best match the weight vectors and lead the evolution of these individuals to their respective neighborhoods. Then, new exploration and development phases are introduced to improve the algorithm’s ability to increase its convergence speed and accuracy. Subsequently, novel incentive functions are formulated based on distinct evolutionary phases, followed by the introduction of a novel environmental selection method aimed at comprehensively enhancing the algorithm’s convergence and distribution. Finally, a weight updating method based on the shape of the frontier surface is proposed to dynamically correct the shape of the overall frontier, further enhancing the overall distribution. The results of experiments on the orthogonal waveform design show that the multi-objective improved Archimedes optimization algorithm (MOIAOA) achieves superior orthogonality, yielding lower total autocorrelation sidelobe peak energy and total cross-correlation peak energy than three established methods.
... The authors in [32] showed that for the linear-Gaussian channel, mutual information maximization and MMSE minimization have the same optimal MIMO waveforms. Moreover, for the uncorrelated targets in the MIMO radar, the authors in [33] proved that maximization of mutual information can obtain the Chernoff bound. Also, from the communication perspective, providing the minimum quality of service (QoS) requested by the users is a promising communication performance metric, which has been widely used in different communication system problems [35]. ...
This paper proposes beamforming designs for net-zero energy multi-input multi-output (MIMO) dual-functional radar-communication (DFRC) systems that are powered through energy harvesting (EH) resources and aim to operate autonomously without access to the power grid. We propose a weighted optimization problem to jointly maximize the radar mutual information and minimum quality of service (QoS) requested by communication users subject to energy balancing constraints. The proposed problem is not convex, hence it is tough to solve. We exploit semidefinite relaxation (SDR) and first-order Taylor expansion techniques to relax its non-convexity issues. We then propose an iterative algorithm to obtain the beamforming matrices for the reference scenario when full channel state information (CSI) and energy arrival information (EAI) are available. For the single-target scenario, we show that the proposed optimization contains rank-one solutions. For the multiple targets scenario, by adding auxiliary optimization variables, we show that rank-one matrices can be achieved from the optimal solutions of the proposed optimization. We then propose a robust optimization for the case where only imperfect CSI and EAI are assumed to be known. Finally, numerical simulations show that the proposed DFRC designs are convergent and obtain a graceful trade-off between the radar and communication performances.
... Note that in the sequel, we assume that round-trip channel coefficients g i,j 's are independent by assuming that the transmit antennas and receive antennas at the BS are sufficiently spaced so that the angle diversity can be explored. In addition, we consider a Swerling-I target model, where the channel coefficient follows identically distributed CSCG with mean 0 and variance δ 2 g , i.e., g i,j ∼ CN 0, δ 2 g [27]. Upon collecting L symbols at the ith BS receive antenna and defining y I r,i = [y r,i [1] , . . . ...
This paper studies a communication-centric integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) simultaneously performs downlink communication and target detection. A novel target detection and information transmission protocol is proposed, where the BS executes the channel estimation and beamforming successively and meanwhile jointly exploits the pilot sequences in the channel estimation stage and user information in the transmission stage to assist target detection. We investigate the joint design of pilot matrix, training duration, and transmit beamforming to maximize the probability of target detection, subject to the minimum achievable rate required by the user. However, designing the optimal pilot matrix is rather challenging since there is no closed-form expression of the detection probability with respect to the pilot matrix. To tackle this difficulty, we resort to designing the pilot matrix based on the information-theoretic criterion to maximize the mutual information (MI) between the received observations and BS-target channel coefficients for target detection. We first derive the optimal pilot matrix for both channel estimation and target detection, and then propose an unified pilot matrix structure to balance minimizing the channel estimation error (MSE) and maximizing MI. Based on the proposed structure, a low-complexity successive refinement algorithm is proposed. Simulation results demonstrate that the proposed pilot matrix structure can well balance the MSE-MI and the Rate-MI tradeoffs, and show the significant region improvement of our proposed design as compared to other benchmark schemes. Furthermore, it is unveiled that as the communication channel is more correlated, the Rate-MI region can be further enlarged.
... For both types of MIMO radar, it is important to design the waveforms appropriately. In the past years, many criteria have been adopted to design MIMO radar waveforms, including minimizing the auto-correlations and cross-correlations of the waveforms (see, e.g., [4], [5] and the references therein), maximizing the signal-to-interference-plus-noise ratio (SINR) [6]- [9], maximizing the mutual information between the receive signals and the target response [10]- [12], to name just a few. ...
This paper addresses robust waveform design for multiple-input-multiple-output (MIMO) radar detection. A probabilistic model is proposed to describe the target uncertainty. Considering that waveform design based on maximizing the probability of detection is intractable, the relative entropy between the distributions of the observations under two hypotheses (viz., the target is present/absent) is employed as the design metric. To tackle the resulting non-convex optimization problem, an efficient algorithm based on minorization-maximization (MM) is derived. Numerical results demonstrate that the waveform synthesized by the proposed algorithm is more robust to model mismatches.
... Many methods have been proposed to design waveforms for MIMO radar. In [6][7][8][9][10], the authors developed several information-theoretic approaches for the MIMO radar waveform design. In [3,[11][12][13], the joint design of transmit waveforms and receive filters is considered to maximise the output signal-to-interference-plus-noise-ratio (SINR) to enhance the detection performance of MIMO radar. ...
Abstract Unimodular waveforms with good correlation properties are desired for multiple‐input‐multiple‐output radar to achieve an increased transmitting/receiving virtual aperture. In this study, a new optimisation framework is introduced to design waveforms with good correlations. It is shown that many existing waveform design problems can be incorporated into this framework. Since the considered problem is in general highly non‐linear and non‐convex, an iterative optimisation method based on majorisation‐minimisation is developed. By carefully devising the surrogate function, the only requirement is to deal with a series of simple problems, which have closed‐form solutions. The proposed algorithm can be implemented via fast Fourier transform and hence is computationally efficient. In addition, the proposed algorithm is extended to deal with spectral constraints. Numerical results demonstrate the efficiency of the proposed algorithm compared with the state‐of‐the‐art techniques.
... Different from the traditional phased-array radar systems, multiple-input multiple-output (MIMO) radar radiates multiple different waveforms to improve the radar abilities [1][2][3][4][5][6] . It is known that, for completely orthogonal waveforms, the radiated energy will be uniformly distributed within the whole spatial domain. ...
This paper considers the problem of transmit beampattern synthesis (i.e., transmit beamforming) in multiple-input multiple-output (MIMO) radar which deploys one-bit digital-to-analog converts (DACs). By appropriately designing the transmitted signal waveforms quantized by one-bit DACs, the majority of radiated energy can be focused into the mainlobe(s) region to enhance the intensity of backscattered signals from targets. Meanwhile, the amount of energy inevitably leaked into the sidelobe region is minimized to suppress the interferences. More specifically, the essence of the proposed design can be regarded as optimizing the one-bit signal waveforms such that the synthesized transmit beampattern has a minimum integrated-sidelobe-to-mainlobe ratio (ISMR). In order to tackle the nonconvex discrete constraint in the resulting optimization problem, we propose to introduce auxiliary variables to reformulate the discrete constraint into continuous constraints. On this basis, the alternating direction multiplier method (ADMM) framework is applied to deal with the reformulated problem. The proposed method can approximately solve the sub-problems with closed-form solutions in each iteration, and hence, it is computationally efficient. Simulation results indicate that the proposed method is able to provide promising performance.
... The authors in [6] gave a comprehensive introduction to multi-channel adaptive signal detection. A multiple input multiple output (MIMO) radar detector utilising space-time coding under Gaussian background was proposed in [7]. MIMO detectors suitable for non-Gaussian clutter were addressed in [8,9]. ...
Abstract Multistatic radar has the advantage of spatial diversity, but its detection performance is decreased in dense multipath scattering environments. This problem can be solved by using the time reversal (TR) technique to take advantage of the multipath effect to improve target detection; however, this usually requires a stationary channel response that is difficult to achieve in practice. This article studies a TR detection algorithm for a multistatic radar system in a varying multipath channel environment. We establish a varying channel response model and derive a time reversal likelihood ratio test (TR–LRT) detector to utilise the characteristics of multiple paths when the multipath environment is changing during the detection process. We use Monte Carlo simulations and theoretical analysis to show the superior performance of the proposed TR detector compared with a conventional detector. Our proposed TR–LRT detector shows good robustness to environmental variations. Simulation results show that better detection results are achieved in a more severe multipath scattering environment.
... Target identification and parameter estimation are the main application fields of MIMO radar. Since the target scattering matrix is composed of target related parameters, retrieving target scattering matrix will contribute to target identification and parameter estimation [21], [22]. Recently, radar waveform design has been proved to be an effective way VOLUME 4, 2016 for retrieving target scattering matrix [23], [24]. ...
In this paper, we investigate a novel framework on the waveform optimization for multiple-input multiple-output (MIMO) radar systems under assumptions of statistical information of scattering matrices and colored noise. Different from most of traditional designs under total power constraint, in our framework, a general power constraint named as multiple weighted power constraints is provided, which includes total power constraint, per-antenna power constraints as its special cases. In the framework, the transmit and receive correlations of parameter matrix to estimate and the spatial and time correlations of noise matrix are all taken into account. Moreover, the signal-dependent interference is also taken into account, which can be considered as a self-interference noise. Based on the available statistics of scattering matrices and colored noise, two kinds of estimation schemes are proposed in this paper, which can realize different trade-offs between complexity and performance. Finally, some numerical results are given to demonstrate the performance advantages of the proposed radar waveform designs.
This work investigates a new concept to finely resolve the vertical structure of natural media, like snow, ice, vegetation, by using a formation of spaceborne Synthetic Aperture Radars (SAR) mounted onboard different satellites. The formation is assumed to operate in Multiple Input Multiple Output (MIMO) mode by implementing a Frequency Division Multiplexing (FDM) access scheme, where all satellites transmit simultaneously on different frequency bands and receive the echoes scattered by the Earth’s surface in all transmitted bands. In so-doing, a formation on
N
satellites is used to produce
N
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>
SAR images. By the principle of Diffraction Tomography, each of these images represents a distinct set of wavenumbers, i.e. a distinct region of the spatial spectrum of the observed scene. The vertical separation between any two sets of wavenumbers defines the interferometric differential wavenumber, which determines the sensitivity of that particular pair to the vertial structure of the observed scene. Fine vertical resolution is achieved by developing a novel approach to set the satellite positions in such a way that the resulting interferometric differential wavenumbers form an almost uniformly-spaced array of maximum length under the constraint of a given height of ambiguity and interferometric coherence magnitude. As a result, we show two examples where formations of 4 or 5 satellites are deployed to provide the equivalent of 17 and 26 monostatic acquisitions, respectively. Such figures are comparable to the best airborne and ground-based systems available as of today, and indicate the concrete possibility to image the vertical structure of natural targets from space at fine resolution. The concept here developed to deploy the formation is referred to as Minimum Redundancy Wavenumber Illumination (MRWI), as it is shown to be a generalization to distributed targets of the principle of Minimum Redundancy Virtual Array (MRVA) used in array theory. The analysis is supported by results from synthetic data generated by numerical simulations.
Integrated sensing and communication (ISAC) unifies sensing and communication, and improves the efficiency of the spectrum, energy, and hardware. In this work, we investigate the ISAC beamforming design to maximize the mutual information between the target response matrix of a point radar target and the echo signals, while ensuring the data rate requirements of the communication users. The scenarios in this paper are considered from two perspectives: one is from the perspective of the number of communication users, and the other is from the perspective of the type of echo interference caused by other interfering scatterers. For the case of a single communication user, in order to reduce the complexity of the algorithm, we consider three types of echo interference, no interference, a point interference, and an extended interference. For the case of multiple communication users, the interference is also an extended one, and furthermore, each user's communication rate requirement needs to be satisfied. To find the optimal beamforming design in these problems, we provide a closed-form solution with low complexity, a semidefinite relaxation (SDR) method, a low-complexity algorithm based on the Majorization-Minimization (MM) method and the successive convex approximation (SCA) method, and an algorithm based on MM method and SCA method, respectively. Numerical results demonstrate that, compared to the ISAC beamforming schemes based on the Cramér-Rao bound (CRB) metric, the beampattern metric and the MSE metric, the proposed mutual information metric can bring better beampattern and root mean square error (RMSE) of angle estimation. Furthermore, our proposed schemes designed based on the mutual information metric can suppress the echo interference from interfering scatterers in the environment effectively.
This paper studies the orthogonal frequency-division multiplexing (OFDM) waveform design for dual-function radar-communication (DFRC) systems in an information-theoretic framework. Mutual information (MI) is used as the performance metrics for both functions. MI defines the information rate in communications and has attracted interest in extended target estimation. A cognitive framework assumes knowledge of the communication channel state and the second-order statistics of the stochastic extended target. Compared to state-of-the-art designs, the transmitted waveform is regarded as a
random
variable to derive not only the communication MI
but also
the radar MI. The so-called
conditional
MI (CMI) is thus considered between the stochastic target’s impulse response and the received signal while averaging over the distribution of all waveform realizations. Accordingly, a power allocation problem is formulated to maximize the weighted sum of radar and communication MIs with a power constraint. Jensen’s and Hadamard’s inequalities are successively applied to the radar CMI to formulate two suboptimal yet tractable problems. The two proposed waveforms are studied in various scenarios, demonstrating their ability to trade off MIs between radar and communication functions.
Assuming the stochastic model of Target Impulse Response (TIR), we address the radar waveform-filter design for extended targets with the recently proposed probabilistically robust detection criterion. The waveform-filter design is formulated as a non-convex fractional programming problem. We devise the Block Coordinate Descent (BCD) based algorithm to tackle this problem, where the waveform codes and filter are optimized alternately. It is shown that the waveforms can be optimized by sequentially checking the feasibility of a polynomial system based on the bisection method. The filter can be designed based on Semi-Definite Relaxation (SDR) and the Dinkelbach’s transform. The proposed algorithm has guaranteed convergence. Numerical experiments are conducted to verify the effectiveness of the proposed algorithm. Results highlight that the designed waveform-filter is able to behave adaptively according to the ambient and more robust than that designed by the competing algorithm.
This paper addresses the detection and estimation problems of a distributed multiple-input and multiple-output (MIMO) radar system with synchronization errors. In such cases, the outputs of all waveform-specific matched filters contain errors in the resulting time delay estimates, which will cause biases in the corresponding estimation of the active range cells. To overcome the impact resulting from the presence of such errors, a joint robust detection and estimation framework is introduced. We first propose an extended generalized likelihood ratio test (GLRT) detector exhibiting the constant false alarm rate property to robustly detect multi-channel misaligned data by extending the matching range cells among multiple channels, on which a Radon-Fourier transform is employed to coherently accumulate the response of potentially moving targets. Then, a clustering algorithm is employed to obtain the unique time delays and Doppler shifts for each channel from the redundant results generated by the detector. Finally, we estimate the target locations and their velocities using the estimated multi-channel time delays and Doppler shifts using a weighted least squares formulation, which is reformulated as a convex optimization problem in order to allow for an efficient solution. Both Numerical and experimental results demonstrate the performance and the robustness of the proposed framework as compared to other recent approaches.
This paper addresses the hybrid quantized signal detection problem in a distributed radar system, where widely separated antennas transmit low-bit quantized data with varying quantization levels depending on the different bandwidth constraint for each channel to a fusion center. To enable a high detection performance with such hybrid quantized data, we formulate the generalized likelihood ratio, Rao, Wald, Gradient, and Durbin tests based on the derived likelihood functions, with the batch gradient descent algorithm (BGDA) being introduced to efficiently form an estimate of the unknown parameters. Furthermore, the theoretical distributions of all designed detectors are also presented, ensuring the constant false alarm rate property. Finally, the unimodality of the derived detection probability with respect to the quantization thresholds is proved, yielding the optimal quantizer to improve the detection performance, which may be efficiently solved using the BGDA. Numerical and experimental results demonstrate the performance of the detectors using the optimal quantizers, illustrating that 2-bit quantization can achieve excellent detection performance while significantly reducing the resulting data size.
The airborne coherent multi-input multi-output (MIMO) radar benefiting from coherent integration (including intra-channel integration and inter-channel integration) of multi-channel echoes can obtain superior detection performance for high-speed maneuvering targets. However, due to the coupling motion characteristic between multiple airborne platforms and high-speed targets, the range walk (RW) and Doppler walk (DW) will occur within the intra-channel integration. Besides, the inter-channel signals also exist envelope and phase differences, which will lead to the difficulty in multi-channel integration. We make contributions towards addressing these limitations. On the one hand, we establish a three-dimensional (3-D) geometrical model for high-speed maneuvering target detection with airborne coherent MIMO radar and derive the mathematical expression of radar echoes, while the generalized Radon-Fourier transform (GRFT) is utilized to simultaneously correct the RW and DW for acquiring intra-channel integration. On the other hand, we analyze the properties of GRFT outputs and propose a GRFT-domain integration method to achieve the multi-channel coherent integration. More specifically, the proposed method first constructs a set of coupling equations for the estimation of target motion parameters (i.e., position, velocity and acceleration), then, the target's motion parameters can be estimated by Newton-Raphson method and solving the linear equations. Second, in order to settle the envelope and phase differences between multi-channel echoes, the envelope alignment and phase compensation functions of inter-channel echoes are constituted based on the estimated parameters. Finally, the coherent accumulation of multi-channel echoes can be implemented. Numerical simulations demonstrate the effectiveness of the proposed method.
This paper addresses the weak signal detection problem in a massive colocated multiple-input multiple-output (MIMO) radar. To cope with the sheer amount of data produced by the large-scale antennas, a low-bit quantizer is introduced in the sampling process to enable both for hardware limitations and a high detection performance. The generalized likelihood ratio test (GLRT) detector is proposed for the quantized data, with the batch gradient descent algorithm being introduced to form an estimate of the unknown parameters. Furthermore, as a low-complexity alternative to the GLRT detector, we propose a multi-bit Rao detector, yielding a closed-form test statistic, whose theoretical distribution is also presented. Finally, we refine the design of the quantizer by optimizing the quantization thresholds, which are obtained using the particle swarm optimization algorithm. Results from simulation and experimental data demonstrate the performance of the detectors using both unquantized and quantized data. They corroborate the theoretical analyses and show that the performance with 3-bit quantization yields a performance that approaches the cases without quantization, while reducing the overall complexity of the system substantially.
Target localization is one of the most important research topics in the field of radar signal processing. In this article, the problem of multitarget enumeration and localization in the distributed multiple-input multiple-output radar with noncoherent processing mode is investigated. We first analyze the theoretical bound of the multitarget localization accuracy under the discrete time signal model and the Swerling 1 target model. It is determined by the Cram
$\acute{\text{e}}$
r–Rao lower bound at a low signal-to-noise ratio (SNR) and the sampling lower bound when the SNR is high. Furthermore, an innovative multitarget enumeration and localization scheme is developed, which is based on the energy modeling of the multiple transmitter–receiver paths and the compressive sensing theory. To solve the sparse vector recovery issue, we design a lightweight iterative greedy pursuit algorithm including the similarity evaluation strategy. In addition, an iterative-based target position refinement process is designed to alleviate the off-grid problem caused by the spatial discretization. The proposal utilizes the samples of the raw signals and belongs to the category of the direct localization. Nevertheless, it has significantly higher computational efficiency and lower data communication burden than the conventional direct localization methods, while avoiding the complex data association encountered by the indirect localization methods. Finally, the simulation results validate the effectiveness and robustness of the proposed method.
Extremely low-resolution (e.g. one-bit) analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) can substantially reduce hardware cost and power consumption for MIMO radar especially with large scale antennas. In this paper, we focus on the detection performance analysis and joint design for the MIMO radar with one-bit ADCs and DACs. Specifically, under the assumption of low signal-to-noise ratio (SNR) and interference-to-noise ratio (INR), we derive the expressions of probability of detection (
$\mathcal {P}_{d}$
) and probability of false alarm (
$\mathcal {P}_{f}$
) for one-bit MIMO radar and also the theoretical performance gap to infinite-bit MIMO radars for the noise-only case. We further find that for a fixed
$\mathcal {P}_{f}$
,
$\mathcal {P}_{d}$
depends on the defined quantized signal-to-interference-plus-noise ratio (QSINR), which is a function of the transmit waveform and receive filter. Thus, an optimization problem arises naturally to maximize the QSINR by joint designing the waveform and filter. For the formulated problem, we propose an alternatin
g
wavefo
r
m and filt
e
r d
e
sign for QSINR maximiza
t
ion (GREET). At each iteration of GREET, the optimal receive filter is updated via the minimum variance distortionless response (MVDR) method, and due to the difficulty in global optimality, an alternating direction method of multipliers (ADMM) based algorithm is devised to efficiently find a high-quality suboptimal one-bit waveform. Numerical simulations are consistent to the theoretical performance analysis and demonstrate the effectiveness of the proposed design algorithm.
In this article, we propose a novel solution to detect multiple targets using a distributed multiple-input multiple-output (MIMO) radar under the so-called “defocused transmit-defocused receive” operating mode. The proposed method employs a grid-based data matching algorithm, aiming to associate the target responses to potential target locations, solving the resulting data puzzle that evaluates the various cells under test (CUTs) in the surveillance area resulting from the intertwined range cells across all transmit-receive channels. Sketchily, the approach divides the surveillance area into identically interlocking and analytically expressible grid cells and then selects the grid cells with the best fitting multichannel data to be equivalently regarded as the CUTs. Next, the generalized likelihood ratio test (GLRT) detector is derived to test for target presence in each of the selected grid cells. A separate procedure is introduced to eliminate the spurious “shadow targets,” false alarms occurring in the grid cells without a target while sharing range cells with the targets. The essence of this procedure is to find the source of the observed contributions to the grid cells whose test statistics exceed their thresholds, and simultaneously obtain the positions of the targets. The proposed method is evaluated using both numerical simulations and experimental data recorded by five small radars, demonstrating the effectiveness of the proposed technique.
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Target localization is one of the most important research topics in the field of radar signal processing. In this paper, the problem of multi-target counting and localization in the distributed multiple-input multiple-output (MIMO) radar is investigated. We first analyze the theoretical bound of the multi-target localization accuracy in the discrete time signal model. It is determined by the Cramer-Rao lower bound (CRLB) at low signal-to-noise ratio (SNR) and the sampling lower bound (SLB) when the SNR is high. Furthermore, an innovative multi-target counting and localization scheme is developed, which is based on the energy modeling of the multiple transmitter-receiver paths and the compressive sensing theory. To solve the sparse vector recovery issue, we design a lightweight iterative greedy pursuit algorithm including the similarity evaluation strategy. The proposal utilizes the samples of the raw signals and belongs to the category of the direct localization. Nevertheless, it has significantly higher computational efficiency and lower communication burden than the conventional direct localization methods, while avoids the complex data association that encountered by the indirect localization methods. Finally, the simulation results validate the effectiveness and robustness of the proposed method.
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div>
Target localization is one of the most important research topics in the field of radar signal processing. In this paper, the problem of multi-target counting and localization in the distributed multiple-input multiple-output (MIMO) radar is investigated. We first analyze the theoretical bound of the multi-target localization accuracy in the discrete time signal model. It is determined by the Cramer-Rao lower bound (CRLB) at low signal-to-noise ratio (SNR) and the sampling lower bound (SLB) when the SNR is high. Furthermore, an innovative multi-target counting and localization scheme is developed, which is based on the energy modeling of the multiple transmitter-receiver paths and the compressive sensing theory. To solve the sparse vector recovery issue, we design a lightweight iterative greedy pursuit algorithm including the similarity evaluation strategy. The proposal utilizes the samples of the raw signals and belongs to the category of the direct localization. Nevertheless, it has significantly higher computational efficiency and lower communication burden than the conventional direct localization methods, while avoids the complex data association that encountered by the indirect localization methods. Finally, the simulation results validate the effectiveness and robustness of the proposed method.
</div
In this paper, an additional degree of freedom in phased multi‐input multi‐output (phased‐MIMO) radar with any arbitrary desired covariance matrix is proposed using space‐time codes. By using the proposed method, any desired transmit covariance matrix in MIMO radar (phased‐MIMO radars) can be realized by employing fully correlated base waveforms such as phased‐array radars and simply extending them to different time slots with predesigned phases and amplitudes. In the proposed method, the transmit covariance matrix depends on the base waveform and space‐time codes. For simplicity, a base waveform can be selected arbitrarily (ie, all base waveforms can be fully correlated, similar to phased‐array radars). Therefore, any desired covariance matrix can be achieved by using a very simple phased‐array structure and space‐time code in the transmitter. The main advantage of the proposed scheme is that it does not require diverse uncorrelated waveforms. This considerably reduces transmitter hardware and software complexity and cost. One the receiver side, multiple signals can be analyzed jointly in the time and space domains to improve the signal‐to‐interference‐plus‐noise ratio.
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 paper, 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.
In this paper, we study the joint design of a transmit sequence and a receive filter for an airborne multiple-input multiple-output (MIMO) radar system to improve its moving target detection performance in the presence of signal-dependent interference. The optimization problem is formulated to maximize the output signal-to-noise-plus-interference ratio (SINR), subject to the waveform constant-envelope (CE) constraint. To address the challenge of this non-convex problem, we propose a novel optimization framework for solving the problem over a Riemannian manifold which is the product of complex circles and a Euclidean space. Manifold optimization views the constrained optimization problem as an unconstrained one over a restricted search space. The Riemannian gradient descent algorithms and the Riemannian trust-region algorithm are then developed to solve the reformulated problem efficiently with low iteration complexity. In addition, the proposed manifold-based algorithms provably converge to an approximate local optimum from an arbitrary initialization point. Numerical experiments demonstrate the algorithmic advantages and performance gains of the proposed algorithms.
The problem of target detection in colocated multiple-input multiple-output radar with unknown disturbance covariance matrix is considered. According to the generalized likelihood ratio test, we design an adaptive detector by exploiting the persymmetric structure of the covariance matrix. In particular, training data are not required in the proposed adaptive detector. Analytical expressions for the probability of false alarm and detection probability are derived, which are confirmed by Monte Carlo simulations. The expression for the probability of false alarm shows that the proposed detector exhibits a constant false alarm rate property against the disturbance covariance matrix. Numerical examples based on both simulated and experimental data confirm that the proposed detector has better detection performance than its counterparts.
For a statistical multiple-input multiple-output (MIMO) radar, we investigate the maximum achievable diversity gain and the minimum possible probability of miss detection and the conditions of achieving those at sufficiently high signal-to-noise ratio (SNR) when the matched subspace detector is employed in the presence of signal-dependent interference. In addition to linear dependence between target returns at each receiver, we show that linear dependence between target and interference subspaces reduces the diversity gain when the matched subspace detector is employed. We derive the approximated form of the probability of miss and introduce the signaling loss concept based on it. We show that the probability of miss is minimized at high SNR when not only is the diversity gain maximized, but the signaling loss is also minimized. Then, we use the signaling loss corresponding to the maximum diversity gain as a novel design metric for designing signals and minimizing the probability of miss at sufficiently high SNR in statistical MIMO radar. Due to the fact that designing the optimal signals is challenging, we derive analytically the detection performance loss of quasi-optimal signals by employing the signaling loss concept.
The conventional concept of radar is based on stand-alone and independent apparatuses. Superior performance is possible, exploiting distributed points of view (i.e., distributed radars) and centralized data fusion, but systems based only on radio-frequency technology are not able to guarantee the requested degree of coherence and high capacity links among radars. In the current distributed systems, radars act almost independently from each other. Thus, data fusion, which must be performed on locally pre-processed information, can only exploit partial information content, harming the imaging capability of the distributed system. Here we present, to the best of our knowledge, the first extended analysis and experiment of a distributed coherent multiple input-multiple output radar system, enabled by photonics, which maximizes the information content extracted by a centralized data fusion, providing unprecedented resolution capabilities. Stepping from previous achievements, where photonics has been demonstrated in single radars, here photonics is used also for providing coherence and high capacity links among radars. The numerical analysis also demonstrated the benefits of coherent multi-band operation for sidelobe reduction, i.e., false alarms reduction.
A compilation is presented of probability density functions, distribution functions, and characteristic functions for several arithmetic combinations of Gaussian random variables. These functions, the distribution functions in particular, need to be known for the evaluation of the error probabilities of many communication systems. These functions are expressed in closed form in terms of well known (and tabulated) transcendental functions. The purpose is to have a convenient list of canonical forms which will be useful when working with arithmetic combinations of Gaussian random variables.
It has recently been shown that multiple-input multiple-output (MIMO) antenna systems have the potential to improve dramatically the performance of communication systems over single antenna systems. Unlike beamforming, which presumes a high correlation between signals either transmitted or received by an array, the MIMO concept exploits the independence between signals at the array elements. In conventional radar, target scintillations are regarded as a nuisance parameter that degrades radar performance. The novelty of MIMO radar is that it takes the opposite view; namely, it capitalizes on target scintillations to improve the radar's performance. We introduce the MIMO concept for radar. The MIMO radar system under consideration consists of a transmit array with widely-spaced elements such that each views a different aspect of the target. The array at the receiver is a conventional array used for direction finding (DF). The system performance analysis is carried out in terms of the Cramer-Rao bound of the mean-square error in estimating the target direction. It is shown that MIMO radar leads to significant performance improvement in DF accuracy.
The paper presents a new method for allowing radar digital
beamforming (DBF) with only one receiver channel. The key point is the
use of a particular spatio-temporal waveform transmitted by an active
phased array antenna. By properly choosing the temporal modulation
applied on each of the transmission elements, one can transmit different
signals in different directions, allowing (under certain hypotheses)
angular localisation with only one receiver channel. The major advantage
is the design of a low cost system providing DBF capabilities
We consider the design of channel codes for improving the data
rate and/or the reliability of communications over fading channels using
multiple transmit antennas. Data is encoded by a channel code and the
encoded data is split into n streams that are simultaneously transmitted
using n transmit antennas. The received signal at each receive antenna
is a linear superposition of the n transmitted signals perturbed by
noise. We derive performance criteria for designing such codes under the
assumption that the fading is slow and frequency nonselective.
Performance is shown to be determined by matrices constructed from pairs
of distinct code sequences. The minimum rank among these matrices
quantifies the diversity gain, while the minimum determinant of these
matrices quantifies the coding gain. The results are then extended to
fast fading channels. The design criteria are used to design trellis
codes for high data rate wireless communication. The encoding/decoding
complexity of these codes is comparable to trellis codes employed in
practice over Gaussian channels. The codes constructed here provide the
best tradeoff between data rate, diversity advantage, and trellis
complexity. Simulation results are provided for 4 and 8 PSK signal sets
with data rates of 2 and 3 bits/symbol, demonstrating excellent
performance that is within 2-3 dB of the outage capacity for these
channels using only 64 state encoders
Motivated by information-theoretic considerations, we propose a
signaling scheme, unitary space-time modulation, for multiple-antenna
communication links. This modulation is ideally suited for Rayleigh
fast-fading environments, since it does not require the receiver to know
or learn the propagation coefficients. Unitary space-time modulation
uses constellations of T×M space-time signals (Φ<sub>i</sub>,
l=1, ..., L), where T represents the coherence interval during which the
fading is approximately constant, and M<T is the number of
transmitter antennas. The columns of each Φ<sub>i</sub> are
orthonormal. When the receiver does not know the propagation
coefficients, which between pairs of transmitter and receiver antennas
are modeled as statistically independent, this modulation performs very
well either when the signal-to-noise ratio (SNR) is high or when T≫M.
We design some multiple-antenna signal constellations and simulate their
effectiveness as measured by bit-error probability with
maximum-likelihood decoding. We demonstrate that two antennas have a
6-dB diversity gain over one antenna at 15-dB SNR
The problem of target detection and signal parameter estimation in a background of unknown interference is studied, using a multidimensional generalization of the signal models usually employed for radar, sonar, and similar applications. The required techniques of multivariate statistical analysis are developed and extensively used throughout the study, and the necessary mathematical background is provided in Appendices. Target detection performance is shown to be governed by a form of the Wilks' Lambda statistic, and a new method for its numerical evaluation is given which applies to the probability of false alarm of the detector. Signal parameter estimation is shown to be directly related to known techniques of adaptive nulling, and several new results relevant to adaptive nulling performance are obtained.
This paper addresses digital communication in a Rayleigh fading environment when the channel characteristic is unknown at the transmitter but is known (tracked) at the receiver. Inventing a codec architecture that can realize a significant portion of the great capacity promised by information theory is essential to a standout long-term position in highly competitive arenas like fixed and indoor wireless. Use (nT, nR) to express the number of antenna elements at the transmitter and receiver. An (n, n) analysis shows that despite the n received waves interfering randomly, capacity grows linearly with n and is enormous. With n = 8 at 1% outage and 21-dB average SNR at each receiving element, 42 b/s/Hz is achieved. The capacity is more than 40 times that of a (1, 1) system at the same total radiated transmitter power and bandwidth. Moreover, in some applications, n could be much larger than 8. In striving for significant fractions of such huge capacities, the question arises: Can one construct an (n, n) system whose capacity scales linearly with n, using as building blocks n separately coded one-dimensional (1-D) subsystems of equal capacity? With the aim of leveraging the already highly developed 1-D codec technology, this paper reports just such an invention. In this new architecture, signals are layered in space and time as suggested by a tight capacity bound.
To achieve high signal-to-noise ratios (SNR) while maintaining moderate sensor size, an architecture is proposed to combine several independent radar apertures into a coherently functioning unit. The proposed system utilizes several distinct apertures which are to be adaptively cohered based on observed target returns. Two operating modes are presented (in addition to each aperture operating as an independent radar). In the first, a Multiple Input Multiple Output (MIMO) mode, each aperture transmits a distinct waveform. The independent, multi-static returns allow the estimation of several coherence parameters. These estimates may then be used to produce a fully coherent transmit/receive mode, wherein all of the apertures cooperatively transmit a waveform which allows the system to perform as a fully coherent, sparse array. The success of each of these modes, particularly the coherent transmit/receive mode, is dependant upon accurate estimates of several coherence parameters. In particular, the one-way travel times between each aperture and the target and the local oscillator phases of each aperture must be precisely estimated from observed returns. This paper examines the estimation problem in the context of the Cramer-Rao lower bound. Based upon this theoretical bound on the estimate accuracy, the desired performance gain lies within the theoretically achievable realm using the adaptive coherence process.
Half-title pageSeries pageTitle pageCopyright pageDedicationPrefaceAcknowledgementsContentsList of figuresHalf-title pageIndex
Information theory answers two fundamental questions in communication theory: what is the ultimate data compression (answer: the entropy H), and what is the ultimate transmission rate of communication (answer: the channel capacity C). For this reason some consider information theory to be a subset of communication theory. We will argue that it is much more. Indeed, it has fundamental contributions to make in statistical physics (thermodynamics), computer science (Kolmogorov complexity or algorithmic complexity), statistical inference (Occam's Razor: “The simplest explanation is best”) and to probability and statistics (error rates for optimal hypothesis testing and estimation). The relationship of information theory to other fields is discussed. Information theory intersects physics (statistical mechanics), mathematics (probability theory), electrical engineering (communication theory) and computer science (algorithmic complexity). We describe these areas of intersection in detail.
Radar equipment specifications are often driven by the need to detect small targets in clutter. Relevant specifications include dynamic range, phase noise, system stability, isolation and spurs. Furthermore, the desire for low probability of intercept radar operation also influences the radar hardware design. This paper describes how digital array radars can be used to manage radar time and energy, thereby simplifying radar equipment design. Digital arrays enable both highly focused transmit beams (e.g., for track) and broad transmit illumination (e.g., for search). Regarding the latter, multi-input multi-output (MIMO) techniques, which allow wide angular coverage, are described.
Inspired by recent advances in multiple-input multiple-output (MIMO) communications, this paper introduces the statistical MIMO radar concept. The fundamental difference between statistical MIMO and other radar array systems is that the latter seek to maximize the coherent processing gain, while statistical MIMO radar capitalizes on the diversity of target scattering to improve radar performance. Coherent processing is made possible by highly correlated signals at the receiver array, whereas in statistical MIMO radar, the signals received by the array elements are uncorrelated. It is well known that in conventional radar, slow fluctuations of the target radar cross-section (RCS) result in target fades that degrade radar performance. By spacing the antenna elements at the transmitter and at the receiver such that the target angular spread is manifested, the MIMO radar can exploit the spatial diversity of target scatterers opening the way to a variety of new techniques that can improve radar performance. In this paper, we focus on the application of the target spatial diversity to improve detection performance. The optimal detector in the Neyman-Pearson sense is developed and analyzed for the statistical MIMO radar. An optimal detector invariant to the signal and noise levels is also developed and analyzed. In this case as well, statistical MIMO radar provides great improvements over other types of array radars.
Proposed next-generation radar systems have multiple transmit apertures with complete flexibility in the choice of the signals transmitted at each aperture. Here we propose the use of multiple signals with arbitrary cross-correlation matrix R and show that R can be chosen to achieve or approximate a desired spatial transmit beampattern. This leads to the constrained optimization problem of the finding the value of the R, which causes the true transmit beampattern to be close in some sense to a desired beam-pattern. This is approached using a gradient search in the space of Cholesky factors of R.
The continuing progress of Moore's law has enabled the development of radar systems that simultaneously transmit and receive multiple coded waveforms from multiple phase centers and to process them in ways that have been unavailable in the past. The signals available for processing from these multiple-input multiple-output (MIMO) radar systems appear as spatial samples corresponding to the convolution of the transmit and receive aperture phase centers. The samples provide the ability to excite and measure the channel that consists of the transmit/receive propagation paths, the target and incidental scattering or clutter. These signals may be processed and combined to form an adaptive coherent transmit beam, or to search an extended area with high resolution in a single dwell. Adaptively combining the received data provides the effect of adaptively controlling the transmit beamshape and the spatial extent provides improved track-while-scan accuracy. This paper describes the theory behind the improved surveillance radar performance and illustrates this with measurements from experimental MIMO radars.
In this paper, radar is discussed in the context of a multiple-input multiple-output (MIMO) system model. A comparison is made between MIMO wireless communication and MIMO radar. Examples are given showing that many traditional radar approaches can be interpreted within a MIMO context. Furthermore, exploiting this MIMO perspective, useful extensions to traditional radar can be constructed. Performance advantages in terms of degrees of freedom and resolution are discussed. Finally, a MlMO extension to space-time adaptive processing (STAP) is introduced as applied to ground moving-target indication (GMTI).
Inspired by recent advances in multiple-input multiple-output (MIMO) communications, this proposal introduces the statistical MIMO radar concept. To the authors' knowledge, this is the first time that the statistical MIMO is being proposed for radar. The fundamental difference between statistical MIMO and other radar array systems is that the latter seek to maximize the coherent processing gain, while statistical MIMO radar capitalizes on the diversity of target scattering to improve radar performance. Coherent processing is made possible by highly correlated signals at the receiver array, whereas in statistical MIMO radar, the signals received by the array elements are uncorrelated. Radar targets generally consist of many small elemental scatterers that are fused by the radar waveform and the processing at the receiver, to result in echoes with fluctuating amplitude and phase. It is well known that in conventional radar, slow fluctuations of the target radar cross section (RCS) result in target fades that degrade radar performance. By spacing the antenna elements at the transmitter and at the receiver such that the target angular spread is manifested, the MIMO radar can exploit the spatial diversity of target scatterers opening the way to a variety of new techniques that can improve radar performance. This paper focuses on the application of the target spatial diversity to improve detection performance. The optimal detector in the Neyman-Pearson sense is developed and analyzed for the statistical MIMO radar. It is shown that the optimal detector consists of noncoherent processing of the receiver sensors' outputs and that for cases of practical interest, detection performance is superior to that obtained through coherent processing. An optimal detector invariant to the signal and noise levels is also developed and analyzed. In this case as well, statistical MIMO radar provides great improvements over other types of array radars.
This paper presents a simple two-branch transmit diversity scheme.
Using two transmit antennas and one receive antenna the scheme provides
the same diversity order as maximal-ratio receiver combining (MRRC) with
one transmit antenna, and two receive antennas. It is also shown that
the scheme may easily be generalized to two transmit antennas and M
receive antennas to provide a diversity order of 2M. The new scheme does
not require any bandwidth expansion or any feedback from the receiver to
the transmitter and its computation complexity is similar to MRRC
We introduce space-time block coding, a new paradigm for
communication over Rayleigh fading channels using multiple transmit
antennas. Data is encoded using a space-time block code and the encoded
data is split into n streams which are simultaneously transmitted using
n transmit antennas. The received signal at each receive antenna is a
linear superposition of the n transmitted signals perturbed by noise.
Maximum-likelihood decoding is achieved in a simple way through
decoupling of the signals transmitted from different antennas rather
than joint detection. This uses the orthogonal structure of the
space-time block code and gives a maximum-likelihood decoding algorithm
which is based only on linear processing at the receiver. Space-time
block codes are designed to achieve the maximum diversity order for a
given number of transmit and receive antennas subject to the constraint
of having a simple decoding algorithm. The classical mathematical
framework of orthogonal designs is applied to construct space-time block
codes. It is shown that space-time block codes constructed in this way
only exist for few sporadic values of n. Subsequently, a generalization
of orthogonal designs is shown to provide space-time block codes for
both real and complex constellations for any number of transmit
antennas. These codes achieve the maximum possible transmission rate for
any number of transmit antennas using any arbitrary real constellation
such as PAM. For an arbitrary complex constellation such as PSK and QAM,
space-time block codes are designed that achieve 1/2 of the maximum
possible transmission rate for any number of transmit antennas. For the
specific cases of two, three, and four transmit antennas, space-time
block codes are designed that achieve, respectively, all, 3/4, and 3/4
of maximum possible transmission rate using arbitrary complex
constellations. The best tradeoff between the decoding delay and the
number of transmit antennas is also computed and it is shown that many
of the codes presented here are optimal in this sense as well
MIMO radar theory and experimental results Performance of MIMO radar systems: Advantages of angular diversity Spatial diversity in radars–Models and detection performance
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- omura