Hybrid beamforming involves digital beamforming of the data streams from digital receivers attached to analog subarrays. This paper examines the special signal weighting required to perform hybrid beamforming when the analog subarrays have unequal sizes. The need arises because signals from the antenna elements in each analog subarray are summed in power with RF power combiners while the digital beamformer sums voltages, thus adding quantities with different units. We show that the signal from the $r$ th analog subarray with $M_{r}$ elements must be weighted by a correction factor of sqrt( $M_{r}$ ) prior to summation in the digital beamforming processor if the proper array output is to be obtained. Array SNR and dynamic range are then computed using these correction factors. Patterns for a quasi-circular phased array with and without taper are provided as examples.

This paper derives the bandwidth that signals should be limited to, by filtration or frequency binning, to ensure that they are narrowband and are processed correctly by array processing algorithms for, e.g., interference nulling and angle of arrival estimation. The narrowband condition is defined as the maximum bandwidth signal that can be fully described by a single significant eigenvalue of the array covariance matrix. A simple closed-form expression for this bandwidth is derived that applies to arrays of arbitrary geometry and that clearly indicates how the maximum bandwidth scales with signal SNR and with array geometry.

Program status for the Airborne Phased Array Radar (APAR) currently being developed by Ball Aerospace for the University Corporation for Atmospheric Research (UCAR) will be discussed. Trade studies balancing mission performance, manufacturing, maintainability and cost were performed to drive design decisions for the phased array radar system. This presentation outlines these analyses, our results given the system constraints, and design decisions made that best balance the goals of affordability, robustness, maintainability and engineering performance in an AP AR antenna system. This paper focuses on two of the more critical requirements for APAR mission success: integrated cross-polarization and integrated sidelobe level performances.

According to a widely used rule of thumb, an MVDR adaptive beamformer achieves output SINR within 3 dB of the theoretical optimum value, on average, when the number of data snapshots K is approximately twice the number of array elements, 2M. Real applications depend on the performance of individual updates rather than averages, however, and we show that an omni-directional quiescent array pattern is particularly poorly matched to a desired incoming plane wave signal. This results in unstable performance with a small number of snapshots. Many more than 2M snapshots are needed to achieve stable operation and good SINR in this case.

Arrays used for direction finding (DF) are often plagued by ambiguities that can increase RMS error levels as well as generate occasional angle estimates that are totally wrong-these latter are often called “wild bearings.” A new analysis framework is introduced to understand how wild bearings are generated and where they are likely to occur. The analysis utilizes the squared correlation between array manifold vectors, leveraging prior work on the spatial distinguishability of cellphone users at an adaptive “smart antenna” basestation. It is shown that this metric, which was derived originally for adaptive beamforming, is also appropriate for DF algorithms such as Beamforming, Capon's method and MUSIC. Examples and simulation results are included that show the location and density of wild bearings for a simple linear array.

Ourline of First Half I.Introduction to Adaptive Antennas II.Array Analysis and Synthesis III.Array Beams IV.Direction Finding V.Adaptive Nulling without Digital Beamforming.

This paper recommends a consistent and efficient approach to computing the integrated sidelobe ratio (ISLR) and the rms or mean sidelobe level of an antenna. In the proposed method, radiated power (electric field amplitude squared) is integrated on the surface of a hemisphere using spherical polar coordinates. The fields are measured at positions, however, that lie on a square grid in the u-v plane. The former ensures proper integration in physical beam space, while the latter provides uniform sampling of the main lobe and all sidelobes, since these all have the same size in the u-v plane. Compared to uniform sampling in spherical coordinates, u-v plane sampling requires fewer measurements for the same accuracy and has integration boundaries that do not change shape or size with scan. Expressions are presented in both one- and two-dimensional versions, together with an example of their use.

The University Corporation for Atmospheric Research (UCAR) is exploring options for an airborne weather observation radar system, called Airborne Phased Array Radar (APAR), that would employ four large C-band phased arrays. This study examines a notional array design that addresses key performance goals of: small transmit beam width, a provision for transmitting with a beam that is broadened or "spoiled" in elevation, and low two-way integrated sidelobe ratio. The specific techniques used-array tapering and thinning, with phase weight beam spoiling-are described in detail, and results are provided.

This paper revisits a method of synthesizing array beam patterns using phase weights. The original paper by Kinsey suggested the technique but omitted implementation details. The present paper provides mathematical justification for the technique as well as a step-by-step process for designing a shaped beam using phase weights. The validity and flexibility of the technique is illustrated with examples of broadened and scanned beams, both with and without amplitude tapers. We believe that this "rediscovered" method is a useful addition to the phased-array designer's toolbox.

Our team has performed trade and design studies for the FAA and NOAA of multifunction phased array radar (MPAR) concepts that would combine the functionalities of air traffic control, air surveillance, precision weather observation, and detection of clear air turbulence in a single radar unit. Such a system requires multiple independently operating sectors to perform all functions within the required timeline. Our study identified a pyramidal building with four phased array faces as an attractive geometry, in part because faces are isolated from each other by the structure and corners, permitting reception on one face while simultaneously transmitting on its neighbors. We report here on an initial risk-reduction investigation involving simulations that characterized the achievable face-to-face isolation. We conclude that an MPAR design based on a four-faced pyramidal structure should provide sufficient isolation to allow simultaneous and independent operation and tasking of adjacent faces.

This paper examines the effects of time-domain pulse droop on linear FM chirp signals used in pulse compression radar. The radar literature is oddly quiet on how to specify power amplifier droop for a desired level of radar performance, with the result that overly stringent droop specifications (-0.5 dB maximum droop, e.g.) are sometimes imposed on modern phased array radar antennas. Since this drives array cost, mass, and power consumption, it is worthwhile asking how much droop can be tolerated. The present paper analyzes the effects of droop on compressed linear FM chirp waveforms and derives criteria that maintain the fidelity of the matched filter output. The application of a spectral window to control time sidelobes is included in the analysis. We show the perhaps surprising result that chirps are robust to as much as 3 dB of droop. In fact, loss of sensitivity due to reduced energy on the target becomes an issue before significant distortion of the compressed chirp waveform occurs. This work should point the way to sensible droop specifications resulting in more cost effective phased array antennas.

A concept for a Multi-Function Phased Array Radar (MPAR) to provide next generation simultaneous aircraft and weather surveillance has been developed. This paper discusses a number of system design considerations that are needed to address the multi-mission challenges of MPAR, especially with respect to its stringent timeline objectives.

The National Oceanic and Atmospheric Administration’s (NOAA) National Weather Service (NWS) and the Federal Aviation Agency (FAA) operate national networks of radar systems that are used for weather monitoring/observation and aircraft surveillance. These radar systems are aging and costly to maintain. The networks could benefit from the advances in multi-functional performance, capabilities, and scalability afforded by modern phased array radar technologies. The scalability and multi-mission functionality of modern phased array radar systems offers the ability to replace several different types of aging legacy radars that had been designed around different weather monitoring/measurement and air traffic surveillance missions with a common, phased array radar system implementation that is easily scaled to the mission needs of the installation location. Nationally, approximately 350 S-band radars could replace the existing NWS and FAA radar installations. This paper summarizes findings from a 2012 study commissioned by the NOAA and the FAA into certain engineering analyses and cost/performance trades dealing with dual polarization implementation strategies for a new Multifunction Phased Array Radar (MPAR) that might address the nation’s future weather and air traffic surveillance needs. The radar functionality and mission considerations for the following radars were addressed in our study:  ARSR-4 en route  ASR-11 terminal air surveillance radars  Terminal Doppler Weather Radar (TDWR)  Doppler and polarimetric WSR-88DP weather observation radars Particular attention is paid to comparing and contrasting various dual-pol implementation approaches, including Simultaneous, Alternating, and Simultaneous-with-Waveform-Diversity (SWD) modes. Three major classes of array geometry—a single rotating face, a four faced truncated pyramid, and a cylindrical commutating array—are also studied, leading to a comprehensive matrix of dual-polarization approaches and geometry options. The outcome represents a scalable system that ranges from a basic configuration intended to perform the core air surveillance mission of the ASR-11 and the TDWR weather observation mission, up to a MPAR system that can also perform the precision weather observations of the Doppler/polarimetric WSR88DP weather radars and the en route air surveillance mission of the ARSR-4. Some representative key requirements for the MPAR study are listed in Table 1.

An initial study performed for the FAA and NOAA explores dual-polarization implementation options for a multifunction phased array radar (MPAR) that could replace the nation's air and weather surveillance radars. The study focuses on approaches to acquiring polarimetric data and on array geometries, both of which drive phased array costs of an MPAR design. Two dual-polarized approaches are found to result in reasonable phased array polarization purity requirements and costs. One of them (simultaneous collection of Hand V data using orthogonal waveforms) additionally makes efficient use of the radar timeline available for weather observation and hard target search and track missions. Three array geometries-a flat rotating array, a four-faced pyramid, and a commutating cylinder-meet mission requirements, with varying degrees of cost and complexity. A key study finding is that dual-polarized capabilities can be added to MPAR with modest increase in complexity and cost.

Why do square antennas produce circular main beams? An intuitive answer to this question comes from applying a series expansion to the expression for the far-field radiation pattern, which, in turn, is the Fourier transform of the aperture fields. This paper explains how filtering properties of the resulting Bessel functions cause rounding of the pattern corners near the beam center. The same expansion and filtering explain rounding of the beams of planar apertures of arbitrary shape.

It is well known that the area of a synthetic aperture radar (SAR) antenna must exceed a minimum value to avoid image ambiguities. The classic minimum ambiguity-free area criterion was derived for rectangular antennas that are aligned with the direction of travel and are rolled to the look angle. This paper derives an analogous criterion that is valid for nadir-facing, yawed, and non-rectangular antenna geometries. The resulting maximum beam area criterion (MAXBAC) includes the classic result as a special case for rectangular antennas of conventional orientation. It is shown theoretically, and verified numerically for representative examples, that using an unconventional antenna geometry does not improve main beam ambiguity performance.