Transmit Beam Pattern Research Articles

A stochastic approach to delays optimization for narrowband transmit beam pattern in medical ultrasound

In ultrasound imaging, state-of-the-art methods for transmit beam pattern (TBP) optimization have well-known drawbacks like non-uniform beam width over depth, significant side lobes, and quick energy drop-out beyond the focal region. To overcome these limitations, we develop a TBP optimization approach by focusing on its narrowband approximation and considering transmit delays as free variables instead of linked to specific focal depths. We formulate a non-linear Least Squares problem to minimize the difference between the TBP corresponding to a set of delays and the desired one, modeled as a 2D rectangle elongated along the beam axis. Three metrics are defined to quantitatively evaluate the results. Results obtained by synthetic simulations show that the main lobe width is considerably more intense (+31.5%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$+31.5\\%$$\\end{document} on average) and uniform (+28.7%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$+28.7\\%$$\\end{document} on average) over the whole depth range compared to classical focalized Beam Patterns. The application of the method to elastography shows improvements in the ultrasound energy concentration along a desired axis.

Wideband MIMO Radar Transmit Beampattern Synthesis in a Spectrally Crowded Environment

Wideband MIMO Radar Transmit Beampattern Synthesis in a Spectrally Crowded Environment

Transmit Beampattern Synthesis for Active RIS-Aided MIMO Radar via Waveform and Beamforming Optimization

Transmit Beampattern Synthesis for Active RIS-Aided MIMO Radar via Waveform and Beamforming Optimization

Design and realization of directivity adjustable ring transducer

In this paper, a directional segmented ring transmitting transducer, which can radiate sound waves in any horizontal region, has been developed. First, we introduce the structure of the segmented ring transducer and the characteristics of its radiation sound field, investigate the transmitting beam pattern control method based on the modal synthesis, and propose orthogonal beam pattern functions to adjust steering angles. Then, the three-dimensional finite element model of the segmented ring transducer is established, and the amplitude and phase of sound pressure excited by the first three modes, respectively, are calculated as a function of the frequency. We can combine each mode to obtain the desired beam patterns, and simulate the transmitting beam patterns steering to different directions. Finally, we manufacture the segmented ring transducer and measure its transmitting directivity in an anechoic water tank, and the first three modes are also calibrated according to the measured sound pressure. The experimental results show that the beam pattern synthesized by the first two modes has a 3 dB down beam width of about 156◦ at 15 kHz after calibration, and the maximum source level is approximately 24 dB higher than the minimum. The −3 dB beam width synthesized by the first three modes is about 84◦ at 17 kHz after calibration. In addition, we also carry out the experimental test on the proposed beam control method, and the driving-voltage weighting vectors are designed to obtain good transmitting beam patterns steering to different angles.

Robust beamforming for dual‐function radar‐communication with imperfect channel state information

AbstractDual‐function radar and communication (DFRC) have recently received significant attention as an effective way to alleviate spectrum congestion and reduce system costs. Joint transmit beamforming plays a critical role in DFRC systems, as it can effectively reduce mutual interference and improve the performance of both the radar and communication systems. This paper investigates the problem of robust beamforming design with imperfect channel state information (CSI) to ensure communication performance while optimizing radar performance. Considering elliptically bounded CSI errors, the objective function is designed to minimize the radar loss function, which is related to the radar transmit beam pattern, subject to worst‐case signal‐to‐interference‐plus‐noise ratio constraints at each user, which ensure fairness between users. An efficient algorithm based on semidefinite relaxation and the S‐procedure is proposed to solve the non‐convex problem. Simulation results are presented to illustrate the effectiveness of the proposed robust beamforming scheme, which can reduce the impact of channel errors.

Transmit Beampattern Design for Distributed Satellite Constellation Based on Space–Time–Frequency DoFs

For distributed satellite constellations, detection performance can be equivalently regarded as a single large satellite by the cooperative operation of multiple small satellites, which is a promising research topic of the Next-Generation Radar (NGR) system. However, dense grating lobes inevitably occur in the synthetic transmit pattern due to its distributed configuration, as a result of which the detection performance of dynamic coherent radar is seriously weakened. In this paper, a novel transmit beampattern optimization method for dynamic coherent radar based on a distributed satellite constellation is presented. Firstly, the effective coherent detection range interval is determined by several influence factors, i.e., coherent detection, far-field, and system link constraints. Then, we discuss the quantitative evaluation method for coherent integration in terms of synchronization error, beam pointing error, and high-speed motion characteristics and we allocate the corresponding terms in a reasonable way from the perspective of engineering. Finally, the space–time–frequency degrees of freedom (DOFs), which can be collected from satellite spacing, carrier frequencies, and platform motion characteristics, are utilized to realize a robust transmit beampattern with low sidelobe by invoking a genetic algorithm (GA). Simulation results validate the effectiveness of our theoretic analysis, and unambiguous coherent transmit beamforming with a satellite constellation of limited scale is accomplished.

Transmit beampattern design for joint radar-communications system with circulating code array

A new transmit beampattern design method is proposed for the joint radar-communications (JRC) systems with circulating code array. Each array element of the designed JRC system transmits the same basic waveform with different starting time, multiple beams towards the radar targets and the communication receivers are formed. For circulating code array, there is a certain relationship between the spectrum band of the transmitted signal and the coverage of the synthesized beampattern. By implementing spectrum planning according to the desired beampattern, flexible beampattern synthesis can be realized. Phase modulation term is attached to the phase of the transmitted signal in the corresponding communication spectrum band, and it is used to carry communication information. Unlike previous works, benefiting from the use of circulating coed array, multiple wide beams and narrow beams can be synthesized simultaneously in this paper without solving optimization problems. The effectiveness of the designed method is validated by numerical results.

Eavesdropping area for evaluating the security of wireless communications

Compared with wired communication, the wireless communication link is more vulnerable to be attacked or eavesdropped because of its broadcast nature. To prevent eavesdropping, many researches on transmission techniques or cryptographic methods are carried out. This paper proposes a new index parameter named as eavesdropping area, to evaluate the anti-eavesdropping performance of wireless system. Given the locations of legitimate transmitter and receiver, eavesdropping area index describes the total area of eavesdropping regions where messages can be wiretapped in the whole evaluating region. This paper gives detailed explanations about its concept and deduces mathematical formulas about performance curves based on region classification. Corresponding key system parameters are analyzed, including the characteristics of eavesdropping region, transmitted beam pattern, beam direction, receiver sensitivity, eavesdropping sensitivity, path loss exponent and so on. The proposed index can give an insight on the confirmation of high-risk eavesdropping region and formulating optimal transmitting scheme for the confidential communications to decrease the eavesdropping probability.

Joint Design of the Transmit Beampattern and Angular Waveform for Colocated MIMO Radar under a Constant Modulus Constraint

In this paper, we investigate the joint design of a transmit beampattern and angular waveform (AW) for colocated multiple-input multiple-output (MIMO) radars. The importance of the AW in the proposed signal processing strategy is first clarified, and then, two optimization models are established, which are aimed at either the power spectral density (PSD) design or the spectral compatibility and similarity design of the AW. There are two main differences between the proposed models and existing models. First, instead of matching a desired template or maximizing the transmit power on specific regions, the transmit beampattern in this paper is optimized to approach several key points, which guarantees the high transmit gain and the flexible adjustment of each beam gain. Second, instead of optimizing the performance of the transmit waveform, only the characteristics of the AW are examined, and they can be constrained quantitatively according to their relationship with the transmit gain. The two models can be unified into the same framework, and an efficient algorithm is proposed to solve the problem under a constant modulus constraint. The convergence of the proposed algorithm is demonstrated, and some improvements to reduce the computational complexity are proposed. Numerical simulations showed that compared to the existing methods, the proposed approach can be used to obtain a higher transmit gain, flexibly adjust each beam gain, and more accurately control the PSD, spectral compatibility, and similarity of the AW. Moreover, numerical simulations showed that, compared to the use of existing methods, the proposed algorithm has higher computational efficiency.

Transmit beampattern synthesis for MIMO radar with one-bit digital-to-analog converters

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.

Wideband MIMO Radar Transmit Beampattern Synthesis via Majorization–Minimization

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.

Parameter estimation and CRB analysis of 1‐bit colocated MIMO radar

The increasing demand for low-cost and low-power radars has led to the emergence of 1-bit sampling technology. 1-bit sampling technology is introduced in a multiple-input and multiple-output (MIMO) radar that has many advantages such as a high degree of freedom and flexible transmit beam pattern. The authors’ theoretical derivation shows that after 1-bit quantisation, the received signal can be expressed as a linear combination of infinite components, which include the original component and high-order components that can be regarded as interference terms. On this basis, the signal-to-noise-ratio (SNR) loss after 1-bit sampling at a low SNR is 1.96 dB. Furthermore, the Cramér-Rao bound (CRB) of a MIMO radar with 1-bit sampling is derived. In the derivation, the concept of 1-bit equivalent noise is proposed. At low SNRs, the equivalent noise power is π/2 (1.96 dB) times the original noise power, which is consistent with a previous derivation. Numerical simulations showed the feasibility of traditional algorithms for a MIMO radar with 1-bit sampling and the correctness of the authors’ derivation.

Spatial Modulation for Joint Radar-Communications Systems: Design, Analysis, and Hardware Prototype

Dual-function radar-communications (DFRC) systems implement radar and communication functionalities on a single platform. Jointly designing these subsystems can lead to substantial gains in performance as well as size, cost, and power consumption. In this paper, we propose a DFRC system, which utilizes generalized spatial modulation (GSM) to realize coexisting radar and communications waveforms. Our proposed GSM-based scheme, referred to as spatial modulation based communication-radar (SpaCoR) system, allocates antenna elements among the subsystems based on the transmitted message, thus achieving increased communication rates by embedding additional data bits in the antenna selection. We formulate the resulting signal models, and present a dedicated radar processing scheme. To evaluate the radar performance, we characterize the statistical properties of the transmit beam pattern. Then, we present a hardware prototype of the proposed DFRC system, demonstrating the feasibility of the scheme. Our results show that the proposed GSM system achieves improved communication performance compared to techniques utilizing fixed allocations operating at the same data rate. For the radar subsystem, our experiments show that the spatial agility induced by the GSM transmission improves the angular resolution and reduces the sidelobe level in the transmit beam pattern compared to using fixed antenna allocations.

Transmit beampattern synthesis for chirp space-time coding array by time delay design

In a multiple-input multiple-output (MIMO) radar, it is desired to maximize the power radiation in an angular region of interest, which, however, is hardly achievable because a set of orthogonal waveforms is employed at the engineering. Different from traditional colocated MIMO radar, space-time coding array (STCA) transmits an identical waveform with a tiny time delay circulating across array elements. It can provide a simple way to achieve the full angular coverage with a stable gain. In this paper, a new scheme referred to as chirp-STCA is proposed to synthesize the desired beampattern flexibly. With the quantitative relationship between the time delay and the span of beam spreading, the transmit beampattern synthesis issue is converted to the design of time delay value which can be readily realized based on the framework of chirp-STCA. As a result, the desired angular sector coverage of the radiation power can be realized by setting a proper time delay. The proposed chirp-STCA can provide many desired features including low range sidelobe level, low computational complexity, and constant modulus. In addition, the range-angle properties are examined by analyzing the transmit beampattern response and the ambiguity function. Numerical results are presented to demonstrate the effectiveness and simplicity of the chirp-STCA scheme for the transmit beampattern synthesis.

The digital beam forming technique in AgileDARN high-frequency radar

An all-digital agile dual auroral radar network (AgileDARN) was developed by the National Space Science Center, Chinese Academic of Sciences (NSSC, CAS). AgileDARN can achieve higher performance and greater flexibility based on highly digitized hardware and its distributed digital signal processing system. Multiple receiving beams can be created within the transmitting beam pattern better to determine the direction of arrival (DOA). In each beam, seven real-time azimuthal sub-beams are synthesized simultaneously with 16 main digital receiver channels. Each sub-beam detects the echo around the transmitting boresight with an angular separation of 0.46°. Comparing the echoes from different sub-beams, the azimuthal geolocation of the irregularities can be improved when their volume is smaller than the beamwidth. Furthermore, the Chebyshev window enables the control of the sidelobes and antenna pattern, effectively suppressing interference. To implement multi-beam forming, extra processing resources of the field-programmable gate array (FGPA) are required. This paper introduces the signal processing procedure and analyzes the requirements on the FPGA resources，and the technique is validated with meteor echoes received by the AgileDARN radar. The azimuthal geolocation of echoes increases by seven times compared with the single beamforming SuperDARN radar.

Co-Design of Waveform Correlation Matrix and Antenna Positions for MIMO Radar Transmit Beampattern Formation

In this paper, we investigate the problems of co-design of the waveform correlation matrix (WCM) and antenna positions (AP) for multiple-input multiple-output (MIMO) radar transmit beampattern formation. To design beampattern with good behaviors, we propose two co-design methods. In the first method, the co-design problem of WCM and AP is formulated by minimizing the mean square error (MSE) between the designed beampattern and a desired one. The second method optimizes the WCM and AP to control the mainlobe ripples and the peak sidelobe level. Moreover, the lower- and upper-bound constraints are also considered within some predefined regions, for both two optimization problems. The co-design schemes provide an extra degree of freedom (DoF) to enhance the transmit beampattern behaviors but also make optimization problems very difficult to solve. To cope with the resultant optimization problems, a successive convex approximation (SCA) algorithm is devised. Finally, simulation results are presented to demonstrate the superiorities of the co-design schemes over state-of-the-art methods in terms of the beampattern behaviors.

Application of LFM-CPM signal into a DFRC system based on circulating code array

A dual-function radar-communications (DFRC) system based on circulating code array is designed in this paper. The communication symbols are firstly embedded into the continuous phase modulation (CPM) term and then attached to the transmitted basic waveform. The particular configuration of the circulating code array provides a possibility to recover the spectrum of the transmitted basic waveform. According to the relationship between the spectrum of the synthesized signal and the spectrum of the basic waveform, a modified spatial-frequency modulation coefficient (SFMC) is proposed in the demodulation procedure. The proposed technique requires only one waveform to implement a DFRC system with an omnidirectional transmitted beam pattern. The communication function can be realized no matter that the communication direction is within the mainlobe or sidelobe of radar. It is verified that the designed DFRC system can make a balance between radar coherent processing performance and communication bit error rate (BER) performance. The communication information is secure from directions other than the intended ones. Simulation results are presented to validate the performance of the designed DFRC system.

ADMM-based transmit beampattern synthesis for antenna arrays under a constant modulus constraint

Transmit beampattern synthesis for antenna arrays is addressed in this paper. In pursuit of high radiation efficiency, most phased array radar systems utilize nonlinear power amplifiers, which leads to a constant modulus constraint for transmit weight vector optimization. Existing methods to solve this hard nonconvex problem (unit-modulus quadratic program) generally have high computational cost and large memory burden, which may increase dramatically as the array size increases. To that end, we propose a low-complexity algorithm based on the alternating direction method of multipliers (ADMM) framework. By introducing auxiliary variables, the original problem is decomposed into several subproblems with closed-form solutions. The transmit weight vector and the phase response of the desired beampattern is updated alternately so that the cost function value can be monotonically reduced. With bounded penalty parameters, the proposed ADMM-based algorithm can guarantee to converge. We further prove that the converged solution satisfies the Karush-Kuhn-Tucker conditions of the nonconvex optimization problem. Numerical simulation results confirm the effectiveness of the proposed method.

Constrained Transmit Beampattern Design Using a Correlated LFM-PC Waveform Set in MIMO Radar.

This paper considers the design of a desired transmit beampattern under the good ambiguity function constraint using a correlated linear frequency modulation-phase coded (LFM-PC) waveform set in multiple-input-multiple-output (MIMO) radar. Different from most existing beampattern design approaches, we propose using the LFM-PC waveform set to conquer the challenging problem of synthesizing waveforms with constant-envelope and easy-generation properties, and, meanwhile, solve the hard constraint of a good ambiguity behaviour. First, the ambiguity function of the LFM-PC waveform set is derived, and the superiority of LFM-PC waveforms over LFM and PC waveforms is verified. The temporal and spatial characteristic analysis of the LFM-PC waveform set demonstrates that both the transmit beampattern and sidelobe level are mainly affected by the frequency intervals, bandwidths, and phase-coded sequences of the LFM-PC waveform set. Finally, the constrained beampattern design problem is formulated by optimizing these parameters for desired beampatterns and low sidelobes at different doppler frequencies, which is a bi-objective optimization problem. To solve this, we propose a joint optimization strategy followed by a mandatory optimization, where the sequence quadratic programming (SQP) algorithm and adaptive clonal selection (ACS) algorithm are exploited iteratively. The simulation results demonstrate the efficiency of our proposed method.

Joint Transmit Beamforming for Multiuser MIMO Communications and MIMO Radar

Future wireless communication systems are expected to explore spectral bands typically used by radar systems, in order to overcome spectrum congestion of traditional communication bands. Since in many applications radar and communication share the same platform, spectrum sharing can be facilitated by joint design as dual function radar-communications system. In this paper, we propose a joint transmit beamforming model for a dual-function multiple-input-multiple-output (MIMO) radar and multiuser MIMO communication transmitter sharing the spectrum and an antenna array. The proposed dual-function system transmits the weighted sum of independent radar waveform and communication symbols, forming multiple beams towards the radar targets and the communication receivers, respectively. The design of the weighting coefficients is formulated as an optimization problem whose objective is the performance of the MIMO radar transmit beamforming, while guaranteeing that the signal-to-interference-plus-noise ratio (SINR) at each communication user is higher than a given threshold. Despite the non-convexity of the proposed optimization problem, it can be relaxed into a convex one, which can be solved in polynomial time, and we prove that the relaxation is tight. Then, we propose a reduced complexity design based on zero-forcing the inter-user interference and radar interference. Unlike previous works, which focused on the transmission of communication symbols to synthesize a radar transmit beam pattern, our method provides more degrees of freedom for MIMO radar and is thus able to obtain improved radar performance, as demonstrated in our simulation study. Furthermore, the proposed dual-function scheme approaches the radar performance of the radar-only scheme, i.e., without spectrum sharing, under reasonable communication quality constraints.