We derive Cramer-Rao bound (CRB) expressions for the range (time delay), velocity (Doppler shift), and direction of a point target using an active radar or sonar array. First, general CRB expressions are derived for a narrowband signal and array model and a space-time separable noise model that allows both spatial and temporal correlation. We discuss the relationship between the CRB and ambiguity function for this model. Then, we specialize our CRB results to the case of temporally white noise and the practically important signal shape of a linear frequency modulated (chirp) pulse sequence. We compute the CRB for a three-dimensional (3-D) array with isotropic sensors in spatially white noise and show that it is a function of the array geometry only through the "moments of inertia" of the array. The volume of the confidence region for the target's location is proposed as a measure of accuracy. For this measure, we show that the highest (and lowest) target location accuracy is achieved if the target lies along one of the principal axes of inertia of the array. Finally, we compare the location accuracies of several array geometries.

Cramer-Rao bounds for estimating range, velocity, and direction with an active array

In this letter, we present a two-dimensional 2-bit 4 $\,\times\,$ 4 phased-array antenna on a flexible Kapton substrate fabricated using inkjet printing. Printed carbon nanotube thin-film transistors (CNT-TFTs) form the switching elements in the phase-shifting network. A multilayer interconnection scheme has been utilized to fully package the subsystem and enable convenient access of the control lines to the 64 CNT-TFTs. By appropriately controlling the on and off states of the TFT switches using a computer mainframe, beam steering of a 5-GHz RF signal at four steering angles of $\theta = 0^{\circ},$ $\varphi = 0^{\circ};$ $\theta = 14.5^{\circ},$ $\varphi = 0^{\circ};$ $\theta = 20.7^{\circ},$ $\varphi = -45^{\circ}$ ; and $\theta = 34^{\circ},$ $\varphi = -26.5^{\circ}$ are experimentally demonstrated. The insertion loss and the power consumption by the switch array are measured to be 8.17 dB and 11.2 mW, respectively .

Inkjet-Printed Two-Dimensional Phased-Array Antenna on a Flexible Substrate

This paper presents two different ultra-broadband antenna designs for mobile communications and navigation, which can be integrated conformally into the bodywork of a car. Both antennas are based on the frequency-independent spiral structure. One antenna, which is intended to be integrated into the car's window, is an externally fed spiral antenna in order to obtain a flat structure. The second spiral antenna consists of four arms which are fed by a coplanar waveguide transmission line. This enables the excitation of two different radiation patterns for terrestrial and satellite services. With a low cost feed network both radiation modes can be excited simultaneously and independently of each other. Measurement results are presented within and beyond the specifications.

Ultra-broadband car antennas for communications and navigation applications

The design of a wideband circularly polarized (CP) equiangular spiral antenna is described. Contrary to the conventional spiral antenna using the coaxial line or the vertically connected feeding structure, a tapered microstrip balun is fully integrated into one spiral arm of the proposed antenna and hence this construction can be realized completely planar. The measured results show that the return loss is better than 10 dB from 3.75 to 18.6 GHz, the axial ratio is below 3 dB from 3 to 14.5 GHz, the radiation is bidirectional with opposite polarization, and the antenna peak gain is 3.5 to 7 dBic. The time-domain characteristic of the transmitting/receiving system using the proposed ultrawideband (UWB) CP antennas is investigated by transient response. The pulse distortion is insignificant and is verified by the measured antenna performance with high signal fidelity (ges 0.89) and low variation of group delay (les 0.1 ns ). The transmitting/receiving antenna system using the proposed antennas is constructed to demonstrate the CP characterization and to detect the target position.

Ultrawideband Circularly Polarized Spiral Antenna Using Integrated Balun With Application to Time-Domain Target Detection

A novel 3-arm spiral antenna structure is presented in this paper. This antenna similar to traditional two-arm or four-arm spiral antennas exhibits wideband radiation characteristic and circular polarization. Advantages offered by the new design are two fold. Unlike the traditional spiral antennas the three-arm spiral can be fed by an unbalanced transmission line, such as a coaxial line or coplanar waveguide, and therefore an external balun is not needed at the feed point. Also by proper choice of arms' dimensions the antenna can be directly matched to any practical transmission line characteristic impedance and therefore external matching networks are not required. This is accomplished by feeding the antenna at the outer radius by a coplanar waveguide (CPW) transmission line and tapering it towards the center. The antenna can also be fed from the center using a coaxial or CPW line perpendicular to the plane of the spiral antenna. A full-wave numerical simulation tool is used to optimize the geometry of the proposed 3-arm spiral to achieve a compact size, wide bandwidth operation, and low axial ratio. The antenna is also designed over a ground plane to achieve a unidirectional radiation and center loading is examined that improves the axial ratio. Simulated results like return loss, radiation pattern, gain, and axial ratio are compared with those obtained from measurements and good agreements are shown. Because of its unique feed structure and compact size, application of the proposed 3-arm spiral antenna for wideband array applications is demonstrated

Design and Analysis of a 3-Arm Spiral Antenna

Spiral antennas are conventionally fed in the center of the spiral. For planar integration of the spiral antenna this conventional feeding structure is not possible. This contribution investigates the possibility of feeding an archimedean spiral antenna with two transmission lines connected to the outer radius of the spiral at opposite sides. Experimental results show that an operation bandwidth of 3:1 with radiation characteristics corresponding to the center-fed spiral is possible.

Spiral antenna with external feeding for planar applications

Conformal antennas on different kinds of surfaces as circular cylinders, elliptic cylinders, spheres, cones and even more complex formed surfaces like wings of aeroplanes have received more and more attention due to their extended beam scanning capabilities in comparison with planar arrays as well as their close mechanical fit to the carrying structure. This contribution discusses the advantages and drawbacks of cylindrical and spherical microstrip array antennas in terms of electrical performance and mechanical setup. It further outlines the design of these antennas and shows measured results for aperture coupled microstrip patch arrays on cylindrical and spherical surfaces.

Design and measurement of conformal antennas on cylindrical and spherical geometries

The design of conformal phased array antennas on cylindrical and spherical geometries is demonstrated, including the calculation of important system parameters, e. g. pattern, gain and G/T. Due to the SiGe-technology used in the beam steering electronics a low cost L-band conformal array demonstrator is fabricated. The combination of these technologies leads to new solutions with outstanding performance at acceptable prices.

Low cost conformal phased array antenna using high integrated SiGe-technology

A C-band conformal aperture coupled microstrip patch phased array was modelled and fabricated. The measured results show the capability of the array to form a directive sector beam as well as an omnidirectional pattern within the measured bandwidth of 19%. As the gain variation is negligible while scanning the direction of the array, it is recommended for 360/spl deg/ cover in communication systems.

https://ieeexplore.ieee.org/iel5/6373/17067/00789453.pdf

Conformal aperture coupled microstrip phased array on a cylindrical surface

This paper presents the calculated and measured space division multiple access (SDMA) performance of a conformal 16x4 element microstrip patch phased array on a cylindrical surface. The described pattern synthesis algorithm allows a fast and efficient evaluation of all the array excitation coefficients, which are necessary to generate the required beams for the SDMA operation of base stations. The array shows an excellent scanning and beam forming capability and is a very promising candidate for the SDMA operation of base stations for mobile communications and for point-to-multipoint connections.

D. Loffler

Papers

Spiral antenna with external feeding for planar applications

Design and measurement of conformal antennas on cylindrical and spherical geometries

Low cost conformal phased array antenna using high integrated SiGe-technology

Conformal aperture coupled microstrip phased array on a cylindrical surface

Conformal microstrip patch array for SDMA applications