Orthogonal Waveforms Research Articles

Generalized Ambiguity Function Properties of Ground-Based Wideband MIMO Imaging Radar

The ability of multiple-input multiple-output (MIMO) radar to provide enhanced performance has been verified in both theoretical and practical level. Through applying orthogonal waveforms, this type of system can realize far more observation channels than the actual number of transmit and receive (T/R) elements. Generally, the azimuth one-dimensional (1-D) generalized ambiguity function (GAF) and resolution of a MIMO radar system are analyzed by pattern theory, which can only analyze the GAF along the equidistant curve to the radar's center. However, the two-dimensional (2-D) GAF of wideband MIMO radar system shows that its sidelobes are not along the equidistant curve accurately due to the coupling effect between the range-dimension and the azimuth one. Obviously, the traditional pattern theory becomes invalid in this case. To tackle this problem, the 2-D GAF and the spatial spectrum of far-field targets are derived in this paper. By analyzing the 2-D GAF, existence of three individual directions of sidelobes is revealed and it is proved that every sidelobes is along a straight line in the pseudopolar coordinate system. Furthermore, a method to calculate the 1-D GAF and resolution in the arbitrary direction is proposed. Finally, a simulation and two experiments have been carried out to validate the theoretic results.

Transmit beampattern design for coherent FDA by piecewise LFM waveform

In transmit beampattern design, it is desirable to maximize the power around locations of interest. Multiple-input multiple-output (MIMO) radar transmits orthogonal waveforms, which is hardly achievable in practical applications. Moreover, the constant modulus constraint and the computational burden limit the system performance. In this paper, we propose an effective piecewise linear frequency modulation (PLFM) waveform for coherent frequency diverse array (FDA) radar to synthesize the desired transmit beampattern. By deriving the relationship between the beam direction and the transmit signal frequency, we find that different sub-band of transmitted signal corresponds to different angular sector. With the relationship between frequency band and mainlobe of beampattern, the beampattern synthesis is transformed into the design of waveform spectrum which is realized by designing the PLFM waveform in this paper. Compared with the state-of-the-art technique, the proposed PLFM waveform in coherent FDA enjoys the advantage of the constant modulus, low sidelobe level and reduced computation complexity. In addition, the multi-dimensional ambiguity function and the transmit beampattern response are derived to examine the properties. Numerical results are presented to validate the effectiveness of the proposed method.

On the Resolution Limits for MIMO Localization

Multiple-input multiple-output (MIMO) localization systems enable high localization accuracy due to their high-spatial-resolution properties. In this letter, we investigate the resolution limits of MIMO localization with general non-orthogonal waveforms based on the Fisher information analysis. Instead of the conventional range or angular resolution, we derive the general distance resolution limit incorporating the resolvability in the time and spatial domains. We show that the correlation of signals between different transmitters degrades the resolution performance, while the correlation among signals from the same transmitter antennas results in performance improvement. The closed form of the resolution limit for the orthogonal waveforms is derived as a special case. Finally, the numerical results are given to validate the theoretical analyses.

Optimization of Orthogonal MSK Waveforms for Active Sonar Using Genetic Algorithm

In order to solve the high peak to average power ratio (PAPR) problem of pseudo random code phase modulation (PRCPM) signals, minimum shift keying (MSK) modulation waveforms with constant envelope were introduced into underwater detection. Genetic algorithm (GA) was proposed to optimize pseudo random binary codes used for MSK waveforms, in order to design sonar waveforms with various performances. After MSK complex envelope signal was obtained by theoretical analysis, the optimizing objective functions for a single waveform and a group of waveforms were presented. The optimized single waveform with low autocorrelation sidelobe values can reduce false alarm number and the difficulty of target decision. When multiple sonar systems work as a team, the optimized group of orthogonal waveforms with low autocorrelation sidelobe values and cross-correlation values can alleviate interferences between each other. In the simulation, the correlation performances of a single waveform and a group of orthogonal waveforms were presented, and ambiguity function showed that the designed waveforms had good velocity and distance resolution, which means that the optimized MSK waveforms are suitable for underwater detection.

Fast PARAFAC Algorithm for Target Localization in Bistatic MIMO Radar in the Co-Existence of Unknown Mutual Coupling and Spatially Colored Noise

Target positioning using multiple-input multiple-output (MIMO) radar system has aroused extensive attention in the past decade. However, most of the existing positioning algorithms are only suitable for ideal scenarios (e.g., well-calibrated sensors, orthogonal waveforms, Gaussian white noise). In this paper, we focus on the target localization problem in a bistatic MIMO system in the co-existence of mutual coupling and spatially colored noise, i.e., to estimate the direction-of-arrival (DOA) and direction-of-departure (DOD) in such non-ideal scenario. To tackle this issue, a parallel factor (PARAFAC) analysis algorithm is proposed. Firstly, the de-noising operation is carried out to suppress the spatially colored noise. Then a PARAFAC analysis model is constructed to explore the tensor nature of measurement. After computing PARAFAC decomposition on the new tensor, the factor matrices associate with DOD and DOA are obtained. Thereafter, the de-coupling operation is followed to eliminate the mutual coupling. Finally, the idea of least squares is utilized to recovery DOD and DOA from the factor matrices. The proposed algorithm can achieve closed-form solution for DOD and DOA estimation without pairing calculation. Moreover, it provides better estimation performance than the state-of-the-art approaches. Detailed analyses are illustrated and simulation results verify the effectiveness of the proposed algorithm.

An Adaptive Resource Allocation Model With Anti-Jamming in IoT Network

With the booming expansion of the Internet of Things (IoT), flexible and configurable resource allocation in an interference environment is a key issue. In this paper, we investigate resource allocation with anti-jamming for the IoT nodes and propose a novel automatic control allocation (ACA) model to get an adaptive allocation and anti-jamming transmission. More specifically, the spreading-time technology is utilized to satisfy the low-power and band-limited requirements of the IoT node, and by mapping into an orthogonal frequency division multiplexing waveform, the ACA mathematical model is obtained. Then in the model, a new joint stepwise extreme recursion algorithm is used to allocate resource with anti-jamming. The simulation results demonstrate the effectiveness of the proposed model and algorithm.

To the question of coordinate system choice within composition of the spatial generalized MIMO radar ambiguity function

The issue of the choice of spatial coordinate system which is suitable to physical sense of the radar concept is explored on the basis of the derivation of spatial generalized ambiguity function for MIMO antenna system and of its cross-section analysis. The comparison results of generalized ambiguity function cross-sections for two dimensional target coordinates in Cartesian, spherical and modified spherical coordinate systems are given for orthogonal LFM waveforms radiated by the elements of linear MIMO antenna system transmit. This proves the desirable choice between coordinate systems with regard of physical sense of the current task.

MVDR code receiver for code multiplexing MIMO radar

Multiple-input multiple-output (MIMO) radar recently has attracted the attention of engineers and researchers. MIMO radar performance is based on the orthogonality of the transmitted waveforms. A receiver optimisation method is proposed to suppress cross-correlation rather than finding orthogonal waveforms. The method considers two transmitters and is based on the minimum variance distorsionless response (MVDR) algorithm to minimise cross-correlation while maintaining the level of auto-correlation. Performance is evaluated by simulation using random phase code sequences. The proposed method is well suited for single target tracking, or slow moving target detection.

Sequence Set Design With Accurately Controlled Correlation Properties

The topic of designing sequence set with good correlation properties has received considerable attention due to its numerous applications in many active sensing and communication systems. For example, a multiple-input multiple-output radar system transmits orthogonal waveforms or zero correlation zone sequences to achieve a long virtual aperture, which results in enhanced parameter identifiability and improved resolution. However, it is difficult to design sequence set with accurately controlled correlation properties due to numerous nonconvex and highly nonlinear inequality constraints. In this paper, new sequence set design methods, based on the local integrated sidelobe level and the local peak sidelobe level metrics, are proposed to tackle the optimization problems under the nonconvex and nonlinear inequality constraints to meet the correlation requirements. Numerical examples are provided to show the effectiveness of the proposed methods.

분산 다중 전자전 센서를 이용한 ESPRIT 기반 비등간격 선형배열 MIMO 레이다의 암맹 직교신호 분리 기법

In this paper, we propose a blind estimation scheme for the antenna spacing of nonuniform linear array MIMO radar using distributed electronic sensors based on ESPRIT. We present a blind method to separate orthogonal waveforms of a MIMO radar based on the antenna spacing estimation. The estimated orthogonal waveforms of a MIMO radar can be used for disabling opponent MIMO radars.

A Novel Orthogonal Waveform Separation Scheme for Airborne MIMO-SAR Systems.

In recent years, multi-input multi-output (MIMO) synthetic aperture radar (SAR) systems, which can promote the performance of 3D imaging, high-resolution wide-swath remote sensing, and multi-baseline interferometry, have received considerable attention. Several papers on MIMO-SAR have been published, but the research of such systems is seriously limited. This is mainly because the superposed echoes of the multiple transmitted orthogonal waveforms cannot be separated perfectly. The imperfect separation will introduce ambiguous energy and degrade SAR images dramatically. In this paper, a novel orthogonal waveform separation scheme based on echo-compression is proposed for airborne MIMO-SAR systems. Specifically, apart from the simultaneous transmissions, the transmitters are required to radiate several times alone in a synthetic aperture to sense their private inner-aperture channels. Since the channel responses at the neighboring azimuth positions are relevant, the energy of the solely radiated orthogonal waveforms in the superposed echoes will be concentrated. To this end, the echoes of the multiple transmitted orthogonal waveforms can be separated by cancelling the peaks. In addition, the cleaned echoes, along with original superposed one, can be used to reconstruct the unambiguous echoes. The proposed scheme is validated by simulations.

A Novel MIMO⁻SAR Solution Based on Azimuth Phase Coding Waveforms and Digital Beamforming.

In multiple-input multiple-output synthetic aperture radar (MIMO–SAR) signal processing, a reliable separation of multiple transmitted waveforms is one of the most important and challenging issues, for the unseparated signal will degrade the performance of most MIMO–SAR applications. As a solution to this problem, a novel APC–MIMO–SAR system is proposed based on the azimuth phase coding (APC) technique to transmit multiple waveforms simultaneously. Although the echo aliasing occurs in the time domain and Doppler domain, the echoes can be separated well without performance degradation by implementing the azimuth digital beamforming (DBF) technique, comparing to the performance of the orthogonal waveforms. The proposed MIMO–SAR solution based on the APC waveforms indicates the feasibility and the spatial diversity of the MIMO–SAR system. It forms a longer baseline in elevation, which gives the potential to expand the application of MIMO–SAR in elevation, such as improving the performance of multibaseline InSAR and three-dimensional SAR imaging. Simulated results on both a point target and distributed targets validate the effectiveness of the echo separation and reconstruction method with the azimuth DBF. The feasibility and advantage of the proposed MIMO–SAR solution based on the APC waveforms are demonstrated by comparing with the imaging result of the up- and down-chirp waveforms.

Random phase code for automotive MIMO radars using combined frequency shift keying‐linear FMCW waveform

Automotive radar is a key component for self-driving cars and advanced driver assistant systems. The major requirements of recent automotive radars are high angular resolution and multiple target detection with the constraints of small size, low power, and low cost. With appropriate transmitter spacing, co-located multiple-input–multiple-output (MIMO) radar can emulate larger aperture arrays, producing the required high angular resolution. However, MIMO radar requires waveforms that are orthogonal in frequency, time, or code domain, and orthogonal waveforms developed for pulse radars are unsuitable for automotive frequency modulated continuous waveform (FMCW) radars. This study proposes a code division multiplexing method for automotive MIMO radars by selecting the combined frequency shift key-linear FMCW waveform. The authors show the performance through simulation and discuss constraints. The proposed method is suitable for automotive radars because not only can high angular resolution be achieved by a small number of arrays, but also multiple targets can be detected with the low sampling rate and computational power.

A Driftless Estimation of Orthogonal Magnetic Flux Linkages in Sensorless Electrical Drives

Estimations of magnetic flux linkages, either between the stationary windings of the stator for the direct torque control (DTC), or between the stationary windings and the rotor for the sensorless field-oriented control (FOC), are based on integration of corresponding voltages. Integration of voltages with offsets that come from improperly calibrated measurements as well as from transient states generally produces unwanted drifts in the resulting magnetic flux linkages, which when used within any type of control of sensorless electrical drives results in instability. This paper addresses that problem and proposes a simple self-contained solution based on orthogonal properties of waveforms of input voltages and resulting magnetic flux linkages in the frame of reference fixed to the geometry of the stator. The proposed solution requires only two periodic orthogonal input waveforms with a distinct common fundamental harmonic, which as such is independent of the type and parameters of the used machine. The idea of the proposed solution is presented analytically, its stability is proven by means of the quadratic Lyapunov theory, and its functionality is demonstrated by standalone simulations and experiments within the sensorless FOC of a permanent magnet synchronous machine (PMSM).

Multibeam radar based on linear frequency modulated waveform diversity

Multibeam radar (MBR) systems based on waveform diversity require a set of orthogonal waveforms in order to generate multiple channels in transmission and extract them efficiently at the receiver with digital signal processing. Linear frequency modulated (LFM) signals are extensively used in radar systems due to their pulse compression properties, Doppler tolerance, and ease of generation. Here, the authors investigate the level of isolation between MBR channels based on LFM chirps with rectangular and Gaussian amplitude envelopes. The orthogonal properties and the mathematical expressions of the isolation are derived as a function of the chirp design diversity, and specifically for diverse frequency slopes and frequency offsets. The analytical expressions are validated with a set of simulations as well as with experiments at C-band using a rotating target.

A dual-function MIMO radar-communication system via waveform permutation

Cooperative transmissions for radar and communication tasks have been recently studied with the goal of addressing the problem of the increasingly crowded RF spectrum. In this paper, we propose a dual-function radar communication (DFRC) system in which the radar platform and radar resources are used for simultaneous target probing and communication symbol embedding. The proposed DFRC system is based on the concept of multiple-input multiple-output (MIMO) in tandem with transmit beamforming where a number of transmit beams, which can be larger than the number of transmit antennas, are formed. We show that the transmit beamforming weight vectors may be designed to achieve transmit processing gain, embed communication symbols intended for a communication receiver, and prevent eavesdroppers from intercepting the communication message. Our proposed method for embedding communication symbols into the MIMO radar emissions is based on changing the order of the orthogonal waveforms along the transmit beams from one pulse repetition period to another. In so doing, the communication symbols are represented by different associations of the orthogonal radar waveforms and transmit beams. We show that high data rate, in the megabits per seconds, is achievable for moderate number of transmit antennas, and is proportional to the factorial of the number of transmit beams. The error probability is analyzed and the bounds on the symbol error rate are derived. We show that changing the number of transmit beams leads to a tradeoff between the data rate and target detection accuracy. Simulation examples are provided for performance evaluation and to demonstrate the effectiveness of the proposed information embedding technique.

Designing Constant Modulus Sequences with Good Correlation and Doppler Properties for Simultaneous Polarimetric Radar

Simultaneous polarimetric radar transmits a pair of orthogonal waveforms both of which must have good auto- and cross-correlation properties. Besides, high Doppler tolerance is also required in measuring the highly maneuvering targets. A new method for the design of sequences with good correlation and Doppler properties is proposed. We formulate a fourth-order polynomial, but unconstrained, minimization problem. An iterative algorithm based on the gradient method on the phases is applied to solve it. Numerical results demonstrate the superiority of the proposed algorithm compared to the previous state-of-the-art method.

Joint Design of Space-Time Transmit and Receive Weights for Colocated MIMO Radar.

Compared with single-input multiple-output (SIMO) radar, colocated multiple-input multiple-output (MIMO) radar can detect moving targets better by adopting waveform diversity. When the colocated MIMO radar transmits a set of orthogonal waveforms, the transmit weights are usually set equal to one, and the receive weights are adaptively adjusted to suppress clutter based on space-time adaptive processing technology. This paper proposes the joint design of space-time transmit and receive weights for colocated MIMO radar. The approach is based on the premise that all possible moving targets are detected by setting a lower threshold. In each direction where there may be moving targets, the space-time transmit and receive weights can be iteratively updated by using the proposed approach to improve the output signal-to-interference-plus-noise ratio (SINR), which is helpful to improve the precision of target detection. Simulation results demonstrate that the proposed method improves the output SINR by greater than 13 dB.

Single-Anchor Localization and Orientation Performance Limits Using Massive Arrays: MIMO vs. Beamforming

In the next generation of cellular networks, it is desirable to use single access points both for communication and localization. This could be made possible thanks to the combination of femtocells, mm-wave technology and massive antenna arrays, and would overcome the problem of having an over-sized infrastructure for positioning which is, nowadays, the bottleneck for the widespread diffusion of indoor localization systems. In this context, our paper aims at investigating the localization and orientation performance limits employing massive arrays both at the access point and mobile side. To this end, we first asymptotically demonstrate the tightness of the Cramer-Rao bound (CRB) in the massive array regime and that the effect of multipath can be made negligible even for practical values of SNR levels. Successively, we propose a comparison between two different transmitter configurations, namely multiple-input multiple-output (MIMO), where orthogonal waveforms are sent, and beamforming, which takes advantage of highly correlated waveforms and directive array patterns. We also consider random weighting as a trade-off between the diversity gain of MIMO and the high directivity guaranteed by the beamforming. CRB results show the interplay between diversity and beamforming gain as well as the benefits achievable by varying the number of antennas in terms of localization accuracy and multipath mitigation.

A clean signal reconstruction approach for coherently combining multiple radars

Distributed radars have the potential to combine coherently for achieving a high signal-to-noise ratio (SNR) while maintaining a moderate antenna size. The key to coherently combining multiple radars is obtaining accurate coherent parameters (CPs), which are used to adjust the transmitting/receiving time and phase of each radar. One approach for CP estimation is to transmit orthogonal waveforms. However, ideally, orthogonal waveforms occupying the same frequency band may not be found in practice. Cross-correlation energy leakage exists between non-orthogonal waveforms, which seriously impairs the accurate acquisition of CPs. To solve this problem, we propose a clean signal reconstruction approach for CP estimation. This approach reconstructs clean echoes by gradually stripping out the cross-correlation energy leakage with a reconstruction-elimination-reconstruction framework. And CPs are obtained from these reconstructed clean echoes. Since the majority of cross-correction energy leakages are eliminated, enhanced CP estimation performance can be achieved. Verified simulations are designed for a dual radar scenario. Results show that the proposed approach significantly improves the performance of CP estimation while reducing the SNR requirement for coherently combining multiple radars.