Constant Modulus Waveform Design for Joint Multiuser MIMO Communication and MIMO Radar

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

We consider the problem of waveform design for Multiple-Input Multiple-Output (MIMO) radar in the presence of signal-dependent interference embedded in white Gaussian disturbance. We present two sequential optimization procedures to maximize the Signal to Interference plus Noise Ratio (SINR), accounting for a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desired properties (e.g., in terms of pulse compression and ambiguity). The presented sequential optimization algorithms, based on a relaxation method, yield solutions with good accuracy. Their computational complexity is linear in the number of iterations and trials in the randomized procedure and polynomial in the receive filter length. Finally, we evaluate the proposed techniques, by considering their SINR performance, beam pattern as well as pulse compression property, via numerical simulations.

This study investigates the problem of designing unimodular waveform with spectral compatibility for multiple-input multiple-output radar in the presence of multiple targets and the signal-dependent interferences. A new approach is proposed to optimise the spectrally compatible radar waveform subject to not only the constant modulus constraint and the similarity constraint but also the signal-to-interference-plus-noise ratio (SINR) requirements for targets, aiming at suppressing the radar energy in some space-frequency areas occupied by other cooperative communication systems. However, the formulated optimisation problem is NP-hard because of the existence of the non-convex constraints. Based on the dual ascent framework, the authors develop an iterative algorithm to solve this challenging problem. The receive filter is obtained at the beginning of each iteration with the off-the-shelf technique and an innovative method termed phase-only dual ascent method is proposed to get the desired waveform. Additionally, they analyse the performance of the waveforms designed under the global SINR constraint and the local SINR constraint, respectively. Moreover, the convergence of the proposed algorithm is discussed concretely. Finally, the numerical simulations are provided to show the validity of the proposed approach.

Beampattern synthesis with nulling for sub-arrayed MIMO radar under constant modulus constraints

In this paper, an optimal waveform design method for target recognition is proposed based on the relative entropy. Since the target recognition can be considered as a hypothesis test procedure, the detection probability could be the cost function to characterize the recognition performance. Then the cost function associated with the relative entropy is maximized to optimize the waveform for improving the recognition performance. The most proposed optimal waveform design methods just only consider the energy constraint. However, only the energy constraint is impractical. In this paper, we do not only consider the total energy limit, but also add the constant modulus constraint from the practice side to design the optimal waveform, since the radar systems commonly require constant modulus waveforms in order to utilize nonlinear power amplifiers. Finally, the simulation results show the effectiveness of the proposed algorithm.

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.

In this paper, a novel radar waveform phase function design is presented that constructs a radar waveform that spectrally manuevers around in-band co-channel interference (CCI) from active communications users that are co-channel with the radar system. The design approach treats the CCI problem as the physical interpretable problem of optical refraction where the time-frequency (TF) signature of the radar waveform is made to be analogous to a light ray propagating from a start time and position (frequency) to an end time and position (frequency) and will naturally accelerate through the CCI as if the equivalent light ray accelerated in through different mediums (with an index of refraction related to CCI power spectral density (PSD)). Using the Euler-Lagrange equations, we design the radar phase function that is used to modulate a constant modulus (CM) waveform. The radar waveform design will generally result in a nonlinear-frequency modulated (NLFM) waveform that provides improved signal-to-interference-plus-noise-ratio (SINR) on a potential target in the presence of CCI leading to improved probability of detection performance. We provide theoretical analysis and simulation results for the proposed waveform design.

In this letter, a joint communication beamforming and radar transmit waveform design method is proposed for radar and communication coexistence (RCC) systems. The optimization problem is designed to maximize the radar signal-to-interference-plus-noise ratio (SINR), under the constraints of communication constructive interference (CI), radar waveform similarity and constant modulus. A novel block fading (BF) algorithm is developed for tackling the non-convexity of the problem constructed, where the closed-form sub-optimal solutions are obtained by transforming the original problem into an element-by-element phase angle problem. Finally, the numerical simulation results verify the superiority of the proposed algorithm on the performance of radar detection and multi-user interference (MUI) elimination.

Apart from basic orthogonality, cognitive multiple-input multiple-output (MIMO) radar waveforms should have the capacity of restraining spectral interferences in complex environment. Constant-modulus waveforms are also desired for the radio frequency (RF) amplifiers. Based on above considerations, this paper proposes an optimization method to design cognitive MIMO radar waveforms with constant modulus and spectral interference constraints. The optimal waveform design problem is converted into standard semi-definite programs (SDP), which are resolved with the semi-definite relaxation (SDR) technique. Simulation results indicate that the proposed approach can effectively design the desired cognitive MIMO radar waveforms with constant modulus and restraining spectral interferences.

The sidelobes of the antenna pattern constitute a critical constraint in high-precision forward-looking radar imaging. Elevated sidelobe levels may induce false targets, while excessive sidelobe suppression risks broadening the mainlobe width, thereby degrading imaging resolution. Coherent accumulation technology enhances target detection capability and imaging resolution in low signal-to-noise ratio (SNR) environments through phase alignment and coherent superposition of multiple pulse-echo signals. Building upon coherent accumulation principles, we leverage the degrees of freedom in the slow-time dimension to establish a joint optimization model for multiple transmit sequences and their corresponding receive filters, as opposed to directly optimizing the peak-to-sidelobe ratio (PSL) or integrated sidelobe ratio (ISL) of single-pulse signals. Firstly, we adopt the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{p}$</tex>-norm of the complementary cross-correlation function under constant modulus constraints as the design metric. By judiciously selecting the p-value, flexible waveform design is achieved to simultaneously preserve mainlobe characteristics and suppress sidelobes after multi-pulse coherent integration. Secondly, to address the high-dimensional non-convex optimization problem arising from constant modulus constraints and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{p}$</tex>-norm minimization, we propose a Majorization-Minimization (MM) method under an alternating optimization framework. During single-variable optimization, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{p}$</tex>-norm is reformulated into a quadratic surrogate function to enhance computational tractability. Finally, Fast Fourier Transform (FFT) acceleration is systematically integrated into each iteration to expedite algorithm convergence, effectively reducing computational complexity by an order of magnitude. Simulation results demonstrate that the optimized transmit-receive filter pairs designed through our method maintain mainlobe width while achieving superior average ISL and PSL performance compared to conventional approaches, thereby providing an effective solution for high-precision forward-looking imaging.

In this chapter we discuss design techniques and constraints that facilitate a waveform that is useful for radar. While signal-to-noise ratio (SNR) and signal-to-interference-plus-noise ratio (SINR) have historically been the primary drivers of waveform design and are certainly discussed here, the growing need for spectral coexistence is eliciting new metrics and design approaches that address a broader set of considerations. This chapter also examines the use of performance prediction models as a means to establish relationships between waveform constraints and SINR performance, which are critical for detection in spectrally crowded environments. An empirical approach is discussed along with models that provide an intuitive way to understand the complex relationships between constraints and SINR performance in dynamic situations.

Aiming at the characteristics that the performance of millimeter wave fuze is easily affected by the natural environment, this paper studies the performance of millimeter wave fuze under rainfall conditions. By analyzing the theory of rain attenuation effect and backscattering effect, it is concluded that the rain attenuation effect reduces the received power of the signal, and the backscattering effect reduces the signal to interference plus noise ratio (SINR) of the receiving end. Based on this, the signal propagation path model under rainfall conditions is established. Finally, the variation of the maximum reliable detection range with signal wavelength and rainfall rate is simulated under different SINR requirements, and the variation of signal to noise ratio (SNR) and SINR with rainfall rate is compared under different distances. The simulation results show that both the rain attenuation effect and the backscattering effect lead to the decrease of the maximum reliable detection distance of millimeter wave fuze. With the increase of rainfall rate, the detection performance of millimeter wave fuze decreases, and the detection distance decreases by about 23.2 % under extreme conditions. The rain backscattering effect on millimeter wave fuze is higher than its attenuation effect, and the influence of rain backscattering effect on millimeter wave fuze increases with the increase of detection distance. When the detection distance increases from 15 m to 30 m, the difference between SNR and SINR at the receiving end of millimeter wave fuze increases by about 3 times. This study has important reference significance for the application of millimeter wave fuze in precision guided weapons.

In this paper, we deal with the joint design of transmit waveform and receive filter for airborne multiple-input-multiple-output (MIMO) radar in order to enhance the radar detection performance for a ground target obscured by strong ground clutter. We also assume that the priori knowledge of target including azimuth and normalized Doppler frequency is inaccurate and we use their statistical information to calculate target covariance matrix. In the design stage, we force constant modulus and similarity constraints for waveform at the same time. Moreover, we propose a new iterative procedure to solve the non-convex optimization problem. The aim is to maximize the Signal to Interference plus Noise Ratio (SINR). At the analysis stage, we assess the effectiveness of the proposed algorithm.

In this paper, the problem of blind multiuser detection based on constant modulus (CM) criterion is investigated for code division multiple access (CDMA) systems with multipath fading channel. The resultant optimization problem of blind linearly constrained CM multiuser detection is difficult to solve due to the multipath effect and fourth-order cost function. Towards this end, an approach based on contracting regularized BFGS algorithm is proposed. Specifically, the problem is firstly converted into a version of real-valued form. Then, the contracting regularized BFGS algorithm is employed to avoid solving the second derivative and ensure that the approximate Hessian matrix is non-singular. Simulation results show that the proposed method improves the system's robustness by reducing the sensitivity to the number of symbols. Moreover, it can obtain superior performance in terms of output signal-to-interference-plus-noise ratio (SINR) and bit-error rate (BER) at high signal-to-noise ratio (SNR) regime.

We consider waveform design for colocated multiple-input, multiple-output (MIMO) radar systems where the signal phase is subject to random phase perturbations during propagation. We formulate an iterative algorithm to obtain both waveform parameters and the space-time adaptive weights to maximize the signal-to-interference-plus-noise ratio (SINR). We ensure that the impact of the chosen waveforms on the interference signal is accounted for when modeling the second-order interference statistics. The waveform design technique is then extended to include peak-to-average power constraints. An example of a clutter and target model is provided to show how the optimal waveform design improves radar detection performance in the presence of the signal phase randomization.