Implementation of a flexible frequency-invariant broadband beamformer based on fourier properties

Aperture and operating frequency of a beamformer are generally proportional to its resolution, and inversely proportional to its beamwidth. This paper addresses the design and implementation of a beamformer with a frequency-dependent limitation of its aperture such that the frequency-dependence of its resolution is eliminated. Operating across a number of octaves, firstly an octave-invariance design is achieved by means of a nested array structure. Secondly, within each octave, a frequency-dependent aperture control then removes the remaining frequency-dependency. By exploiting Fourier properties and correspondences between coefficient and beamspace, we show that this design is exact, and can accommodate the inclusion of arbitrary shading and different look directions

Reducing the number of elements in the synthesis of a broadband linear array with multiple simultaneous frequency-invariant beam patterns

© 2018 IEEE. The problem of reducing the number of elements in a broadband linear array with multiple simultaneous crossover frequency-invariant (FI) patterns is considered. Different from the single FI pattern array case, every element channel in the multiple FI pattern array is divided and followed by multiple finite-impulse-response (FIR) filters, and each of the multiple FIR filters has a set of coefficients. In this situation, a collective filter coefficient vector and its energy bound are introduced for each element, and then the problem of reducing the number of elements is transformed as minimizing the number of active collective filter coefficient vectors. In addition, the radiation characteristics including beam pointing direction, mainlobe FI property, sidelobe level, and space-frequency notching requirement for each of the multiple patterns can be formulated as multiple convex constraints. The whole synthesis method is implemented by performing an iterative second-order cone programming (SOCP). This method can be considered as a significant extension of the original SOCP for synthesizing broadband sparse array with single FI pattern. Numerical synthesis results show that the proposed method by synthesizing multiple discretized crossover FI patterns can save more elements than the original iterative SOCP by using a single continuously scannable FI pattern for covering the same space range. Moreover, even for multiple FI-patterns case with complicated space-frequency notching, the proposed method is still effective in the reduction of the number of elements

The Statistics of Superdirective Beam Patterns

Superdirective arrays have been extensively studied because of their considerable potential accompanied, unfortunately, by a high sensitivity to random errors that affect the responses and positions of array elements. However, the statistics of their actual beam pattern (BP) has never been systematically investigated. This paper shows that the Rician probability density function (PDF), sometimes adopted to study the impact of errors in conventional arrays, is a valid approximation for superdirective BP statistics only where some mathematical terms are negligible. The paper also shows that this is the case for all linear end-fire arrays considered. A similar study is proposed concerning the correlation between BP lobes, showing that for the superdirective arrays considered the lobes, especially non-adjacent ones, are almost independent. Furthermore, knowledge of the PDF of the actual BP allows one to define quantile BP functions, whose probability of being exceeded, at any point, is fixed. Combining the lobes' independence with quantile BP functions, an empirical equation for the probability that the entire actual BP will not exceed a quantile function over an interval larger than a given size is obtained. This new knowledge and these tools make it possible to devise new methods to design robust superdirective arrays via optimization goals with clearer and more relevant statistical meaning

Investigation on maneuverability improvement of a four-wheel drive and rear-wheel steering system : numerical simulation analysis

X-by-wire technology is an advancement in the automotive industry and is recognized by many countries in recent years. It includes drive-by-wire (DBW) and steer-by-wire (SBW). DBW is available in two-wheel drive (2WD) and four-wheel drive (4WD) forms. 4WD has two forms: centralized motor drive and distributed motor drive. A centralized motor drive is to use the motor to replace the engine to provide power for the vehicle. The distributed motor drive is mainly based on the in-wheel motor, and the wheel is driven by the in-wheel motor to provide power for the vehicle. SBW has two forms: two-wheel steering (2WS) and four-wheel steering (4WS). It not only dramatically reduces the operating burden of the driver but also solves the problem that ordinary vehicles cannot perform 4WS. Usually, the lower maneuverability is easy to show on 2WS vehicles during vehicle turning. No matter when driving a vehicle on a narrow city road or parking, it is required to turn the steering wheel several times when the vehicle needs to steer. Moreover, the vehicle can be prone to understeer (US) or oversteer (OS) phenomena that occur when steering. The main purpose of this research is to simulate the steering performance of the vehicle by constructing a model of modern conventional vehicles and to solve the problems that may occur during vehicle cornering by applying an active 4WS control system to control the yaw rate. In this research, experiments of 2WS cornering at several constant speeds and steer angles were conducted using an actual experimental vehicle. A simulation model of the test car was constructed in MATLAB Simulink using nonlinear vehicle dynamics equations with the specification of the vehicle as the parameters. A PID control system was used in this simulation to control the rear-wheel steering angle in order to achieve 4WS. By comparing the simulation and the experimental result, it can be concluded that the nonlinear vehicle dynamics equation can be used to do the simulation of the vehicle motion. After verifying the vehicle dynamics equation, in order to verify whether the time of rotating the steering wheel will affect the motion of the vehicle, this study simulated two different times to complete the rotation of the wheel which is 2 seconds and 25 seconds with the front steering angle is 10 degrees. The results show that no matter whether the time of steering wheel rotation is fast or slow, it does not affect the speed of the vehicle's US and OS phenomenon. By simulating the cornering situation of the vehicle speeds from 10km/h to 80 km/h in the 10km/h increment. It is concluded that the vehicle will occur US phenomenon when the vehicle turning speed is lower around 20km/h; when the vehicle corners with a speed higher than 50km/h, the vehicle will have an OS phenomenon happen. After applying the 4WS system, the OS and US problems are solved efficiently. Although the vehicle is turning at a speed of 80km/h, steady-state cornering (SSC) can still be achieved. After applying the PID control system, most of the cornering can be controlled. except when the wheels rotate to 10° in only two seconds and the vehicle speed is greater than 60km/h which is the vehicle is out of control in a very short time, the PID control system cannot make the rear wheels have an appropriate steering angle to make the vehicle have an SSC. In short, this study solved almost all US and OS phenomena that can occur in 2WS vehicles by applying the 4WS system

Design of Frequency-Invariant Robust Beam Patterns by the Oversteering of End-Fire Arrays

none3F. Traverso; M. Crocco; A. TruccoTraverso, Federico; M., Crocco; Trucco, Andre