Optimum Co-Design for Spectrum Sharing between Matrix Completion Based MIMO Radars and a MIMO Communication System

Non-orthogonal multiple access based cooperative spectrum sharing between MIMO radar and MIMO communication systems

The paper proposes a cooperative scheme for the coexistence of a multiple-input-multiple-output (MIMO) communication system and a matrix completion (MC) based, collocated MIMO (MIMO-MC) radar. To facilitate the coexistence, and also deal with clutter, both the radar and the communication systems use transmit precoding. For waveform flexibility, the radar uses a random unitary waveform matrix. We prove that for such waveforms and any precoding matrix, the error performance of MC is guaranteed. The radar transmit precoder, the radar subsampling scheme, and the communication transmit covariance matrix are jointly designed in order to maximize the radar SINR, while meeting certain communication rate and power constraints. The joint design is implemented at a control center, which is a node with whom both systems share physical layer information, and which also performs data fusion for the radar. We provide efficient algorithms for the proposed optimization problem, along with insight on the feasibility and properties of the proposed design. Simulation results show that the proposed scheme significantly improves the spectrum sharing performance in various scenarios.

PREFACE. CONTRIBUTORS. 1 MIMO Radar - Diversity Means Superiority (Jian Li and Petre Stoica). 1.1 Introduction. 1.2 Problem Formulation. 1.3 Parameter Identifiability. 1.4 Nonparametric Adaptive Techniques for Parameter Estimation. 1.5 Parametric Techniques for Parameter Estimation. 1.6 Transmit Beampattern Designs. 1.7 Conclusions. Appendix IA Generalized Likelihood Ratio Test. Appendix 1B Lemma and Proof. Acknowledgments. References. 2 MIMO Radar: Concepts, Performance Enhancements, and Applications (Keith W. Forsythe and Daniel W. Bliss). 2.1 Introduction. 2.2 Notation. 2.3 MIMO Radar Virtual Aperture. 2.4 MIMO Radar in Clutter-Free Environments. 2.5 Optimality of MIMO Radar for Detection. 2.6 MIMO Radar with Moving Targets in Clutter: GMTI Radars. 2.7 Summary. Appendix 2A A Localization Principle. Appendix 2B Bounds on R(N). Appendix 2C An Operator Norm Inequality. Appendix 2D Negligible Terms. Appendix 2E Bound on Eigenvalues. Appendix 2F Some Inner Products. Appendix 2G An Invariant Inner Product. Appendix 2H Kronecker and Tensor Products. Acknowledgments. References. 3 Generalized MIMO Radar Ambiguity Functions (Geoffrey San Antonio, Daniel R. Fuhrmann, and Frank C. Robey). 3.1 Introduction. 3.2 Background. 3.3 MIMO Signal Model. 3.4 MIMO Parametric Channel Model. 3.5 MIMO Ambiguity Function. 3.6 Results and Examples. 3.7 Conclusion. References. 4 Performance Bounds and Techniques for Target Localization Using MIMO Radars (Joseph Tabrikian). 4.1 Introduction. 4.2 Problem Formulation. 4.3 Properties. 4.4 Target Localization. 4.5 Performance Lower Bound for Target Localization. 4.6 Simulation Results. 4.7 Discussion and Conclusions. Appendix 4A Log-Likelihood Derivation. Appendix 4B Transmit-Receive Pattern Derivation. Appendix 4C Fisher Information Matrix Derivation. References. 5 Adaptive Signal Design For MIMO Radars (Benjamin Friedlander). 5.1 Introduction. 5.2 Problem Formulation. 5.3 Estimation. 5.4 Detection. 5.5 MIMO Radar and Phased Arrays. Appendix 5A Theoretical SINR Calculation. References. 6 MIMO Radar Spacetime Adaptive Processing and Signal Design (Chun-Yang Chen and P. P. Vaidyanathan). 6.1 Introduction. 6.2 The Virtual Array Concept. 6.3 Spacetime Adaptive Processing in MIMO Radar. 6.4 Clutter Subspace in MIMO Radar. 6.5 New STAP Method for MIMO Radar. 6.6 Numerical Examples. 6.7 Signal Design of the STAP Radar System. 6.8 Conclusions. Acknowledgments. References. 7 Slow-Time MIMO SpaceTime Adaptive Processing (Vito F. Mecca, Dinesh Ramakrishnan, Frank C. Robey, and Jeffrey L. Krolik). 7.1 Introduction. 7.2 SIMO Radar Modeling and Processing. 7.3 Slow-Time MIMO Radar Modeling. 7.4 Slow-Time MIMO Radar Processing. 7.5 OTHr Propagation and Clutter Model. 7.6 Simulations Examples. 7.7 Conclusion. Acknowledgment. References. 8 MIMO as a Distributed Radar System (H. D. Griffiths, C. J. Baker, P. F. Sammartino, and M. Rangaswamy). 8.1 Introduction. 8.2 Systems. 8.3 Performance. 8.4 Conclusions. Acknowledgment. References. 9 Concepts and Applications of A MIMO Radar System with Widely Separated Antennas (Hana Godrich, Alexander M. Haimovich, and Rick S. Blum). 9.1 Background. 9.2 MIMO Radar Concept. 9.3 NonCoherent MIMO Radar Applications. 9.4 Coherent MIMO Radar Applications. 9.5 Chapter Summary. Appendix 9A Deriving the FIM. Appendix 9B Deriving the CRLB on the Location Estimate Error. Appendix 9C MLE of Time Delays - Error Statistics. Appendix 9D Deriving the Lowest GDOP for Special Cases. Acknowledgments. References. 10 SpaceTime Coding for MIMO Radar (Antonio De Maio and Marco Lops). 10.1 Introduction. 10.2 System Model. 10.3 Detection In MIMO Radars. 10.4 Spacetime Code Design. 10.5 The Interplay Between STC and Detection Performance. 10.6 Numerical Results. 10.7 Adaptive Implementation. 10.8 Conclusions. Acknowledgment. References. INDEX.

In this thesis we study the problem of exact completion for 𝑚 × 𝑛 sized matrix of rank 𝑟 and the problem of low-rank estimation with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces. Using this relation, wepropose matrix completion algorithms that exactly recovers the target matrix. These algorithms are superior to previous works in two important ways. First, our algorithms exactly recovers 𝜇0-coherent column space matrices byprobability at least 1 − 𝜖 using much smaller observations complexity than - 𝒪(𝜇0𝑟𝑛log𝑟 𝜖 )—the state of art. Specifically, many of the previous adaptive sampling methods require to observe the entire matrix when the column space is highly coherent. However, we show that our method is still able to recover this type of matrices by observing a small fraction of entries under many scenarios. Second, we propose an exact completion algorithm, whichrequires minimal pre-information as either row or column space is not being highly coherent. We provide an extension of these algorithms that is robust to sparse random noise. Besides, we propose an additional low-rank estimationalgorithm that is robust to any small noise by adaptively studying the shape of column space. At the end of the thesis, we provide experimental results that illustrate the strength of the algorithms proposed here. This thesis have been written mainly based on the paper [12].

This paper investigates the problem of low probability of intercept-based optimal power allocation (LPI-OPA) for an integrated multistatic radar and communication system, which consists of multiple transmitters operating at different frequencies, a radar receiver, and a communication receiver (CR). The integrated multistatic radar and communication system is capable of fulfilling the requirements of both radar and communication subsystems. The key tenet of the integrated system is to minimize the total power consumption by optimizing the transmit power allocation at each transmitter for radar waveforms and information signals, which is constrained by a predetermined target detection performance for the RR and a desired information rate for the CR. Since the analytical closed-form expression of the probability of detection is not tractable, its upper bound is derived. We analytically show that the resulting optimization problem can be reformulated as two subproblems, which can be solved by an efficient solution procedure based on the approach of linear programming and the Karush–Kuhn–Tuckers optimality conditions. Simulation results are provided to show that the LPI performance of the integrated multistatic radar and communication system can significantly be enhanced by employing our proposed LPI-OPA scheme.

In this paper, we investigate the physical layer security of multiuser multi-input single-output (MU-MISO) communication and colocated multi-input multi-output (MIMO) radar coexistence systems, in which the strong radar signals are exploited as inherent jamming signals to disrupt mali-cious receptions. The transmit beamformers of communication and radar systems are jointly designed to ensure the secure transmission by minimizing the maximum eavesdropping signal-to-interference-plus-noise ratio (SINR) on multiple legitimate users, while satisfying the quality-of-service (QoS) of legitimate transmission, the requirement of radar target detection, and the transmit power constraints of radar and communication systems. An efficient fractional programming (FP) and semi-definite relaxation (SDR) based algorithm is proposed to solve the non-convex optimization problem. Simulation results verify the advancement of the proposed joint transmit beamforming on secure transmission for radar and communication coexistence systems and the effectiveness of the associate design algorithm.

It was recently shown that MIMO radars with sparse sensing and matrix completion (MC) can significantly reduce the volume of data required by MIMO radars for accurate target detection and estimation. In MIMO-MC radars, the subsampled target returns are forwarded by the receive antennas to a fusion center, partially filling a matrix, referred to as the data matrix. The data matrix is first completed via MC techniques and then used to estimate the target parameters via standard array processing methods. This paper studies the applicability of MC theory on the data matrix arising in colocated MIMO radars using uniform linear arrays. It is shown that the data matrix coherence, and consequently the performance of MC, is directly related to the transmit waveforms. Among orthogonal waveforms, the optimum choices are those for which, any snapshot across the transmit array has a flat spectrum. The problem of waveform design is formulated as an optimization problem on the complex Stiefel manifold, and is solved via the modified steepest descent method, or the modified Newton algorithm with nonmonotone line search. Although the optimal waveforms are designed for the case of targets falling in the same range bin, sensitivity analysis is conducted to assess the performance degradation when those waveforms are used in scenarios in which the targets fall in different range bins.

The paper proposes a matrix completion based colocated MIMO radar (MIMO-MC) approach that employs transmit beamforming. The transmit antennas transmit correlated waveforms to illuminate certain directions. Each receive antenna performs sub-Nyquist sampling of the target returns at uniformly random times, and forwards the samples to a fusion center along with information on the sampling times. Based on the forwarded samples, the fusion center partially fills a matrix, recovers the Nyquist rate samples via matrix completion, and subsequently proceeds with target estimation via standard techniques. The performance of matrix completion depends on the matrix coherence. The paper derives the relations between transmit waveforms and matrix coherence. Specifically, it is shown that, for a rank-1 beamformer, the coherence is optimal, i.e., 1, if and only if the waveforms are unimodular. For a multi-rank beamformer, the coherence of the row space of the data matrix is optimal if the waveform power is constant across each snapshot. Simulation results show that the proposed scheme achieves high resolution with a significantly reduced number of samples.

Spectrum sharing in cognitive radio communication system using power constraints: A technical review

Electromagnetic spectrum congestion is a serious problem. The majority of the desirable spectrum lie below 6 GHz, and is consumed by communication and RADAR systems. DARPA's Shared Spectrum Access for Radar and Communications (SSPARC) program seeks to improve efficient use of spectrum by allowing RADAR and communication systems to share spectrum in the 3.5 GHz S-band. In this paper, we present some results on the MAC layer performance of the IEEE 802.11 protocol in the presence of RADAR interference. We propose a simple model for the carrier sense multiple access mechanism and use it to gain insight into some important performance metrics such as MAC layer throughput, and packet service time. Finally, we provide some numerical examples to demonstrate the usefulness of the results in designing spectrum sharing strategies in real systems.

This work considers the joint transmit design of multiuser MIMO communications and MIMO radar. In particular, we propose to maximize the sum-rate capacity of multiuser MIMO communications under certain transmit correlation mismatch level for MIMO radar, and solve the maximization via convex optimization. Then, a practical transmit design scheme based on Tomlinson-Harashima precoding is proposed to approach the sum-rate capacity. The numerical results on the sum-rate capacity indicate that the average capacity under Rayleigh fading channel is the highest when radar intends to form a omnidirectional transmit beam. The bit error rate simulation shows that the proposed transmit design scheme is about 7dB from the theoretic capacity.

It was recently shown that MIMO radars with matrix completion (MIMO-MC radars) can achieve the performance of MIMO radars but with significantly fewer samples. The matrix completion performance depends on the coherence of the matrix. In MIMO-MC radars and for the scenario in which the targets fall in the same range bin, the coherence of the received data matrix is asymptotically optimal, i.e., 1, when the transmit waveforms have flat spatial spectrum. In this paper, we study the performance of such waveforms when used to estimate targets that fall in different range bins. We show that, if such optimal waveforms are additionally designed to have good correlation properties, the matrix coherence is slightly larger than 1 but bounded by 2 as long as the maximal range delay is of the order of the pulse duration. Thus, in such cases the MC performance degrades only slightly.

Coexisting radar and communication (CRC) systems on the same spectrum band have been recently recognized as a promising approach to solve the spectrum scarcity problem. Additionally, with the new requirements of achieving higher energy efficiency and restoring the consumed power, an initiative has been exploited to embed both information and energy within the same signal. Motivated by that, this paper presents a unified model to implement the concept of simultaneous wireless information and power transfer (SWIPT) in the coexistence environment between radar and communication systems. Specifically, we propose a novel energy harvesting based CRC model (CRCEH), in which the signals transmitted from both the communication and radar transmitters are precoded towards their conventional targets, communication receiver and radar targets respectively, as well as to an energy harvesting receiver. This system is capable of solving the spectrum scarcity problem as well as supporting low power devices with their energy requirements from the energy harvested at the energy harvesting receiver. The design problem is formulated as maximizing the radar detection probability subject to communication capacity and energy harvesting constraints. However, directly processing the data from the radar receiver requires high computational complexity and hardware costs. In order to circumvent this issue, this paper also proposes to deploy lens antenna array (LNA) to CRCEH system to sharply direct the signals to the energy harvesting receiver together with their respective destinations. Since LNA is able to focus the signal power on a subset of antennas, we may only deal with the data from the selective antenna subset associated with the maximal power. Numerical results show that the proposed method is able to achieve improved performance in terms of radar detection under communication capacity constraints compared to the conventional approaches besides the great benefit of harvesting the energy to feed some limited energy devices.

Spectrum sharing is proposed as one of the solutions to help the commercial cellular industry meet the 1000x mobile data challenge they are facing. Most of the valuable spectrum lies below 6 GHz and is currently being occupied by commercial communication and RADAR systems. Commercial communication systems of the future are expected to be based on 3GPP Long Term Evolution (LTE) standards. In this paper, we present an overview of some of the techniques that can be used for enabling efficient co-existence of commercial LTE and RADAR systems. The solutions outlined in this paper do not require any changes to the existing standards nor are they specific to any regional regulatory requirements.

Based on recent advances in passive radar, we propose a unified multi-static passive radar and communication system that is capable of fulfilling the requirements of both radar and communication sub-systems. More specifically, we provide a performance tradeoff analysis for a system consisting of multiple transmitters, a passive radar receiver (RR), and a communication receiver (CR). The total power at each transmitter is allocated for transmitting the radar waveforms and information signals in such a way that the probability of detection (PD) is maximized, while satisfying the information rate requirement of the CR. The exact optimization is not tractable since the probability of detection is not analytically tractable. By exploiting its bound, the approximated optimization problem is solved to optimize the power allocation between the transmissions of the radar waveforms and information signals. The performance tradeoff between the two sub-systems is then characterized by the boundaries of the PD-rate regions for a given false alarm requirement. Simulation results show the improved performance of the proposed power allocation method over a sub-optimal one.