# Ultra-wideband antenna arrays--The basics--Part II

**Dense Wideband Antenna Arrays**

When designing an antenna array to operate over a wide bandwidth and over a large scan volume, the conventional approach is to use a lattice where the elements are placed close together in terms of electrical spacing. Because of this, the mutual coupling between the individual radiating elements becomes significant and must be factored into the design of the array. The most robust and effective way to design a dense array is to treat the radiating elements as if they were in an infinite array environment [4], [5]. Radiating elements are typically modeled using some type of full-wave computational electromagnetics software package; however, the boundary conditions of the model are assumed to be periodic. In this manner the fields on one side of the model are set to be equal to the fields on the other, plus some phase offset that is associated with the scan of the array. Effective dense UWB array designs include the connected array and the Vivaldi array [6], [7]. An illustration of a linear Vivaldi array is shown in Fig. 1-4. Note how the currents are shared between individual apertures, leading to the high levels of mutual coupling in the array.

However, there are some difficulties associated with the design of these dense arrays. First of all, since the array elements are designed to function in an infinite array environment, the elements near the edges of the constructed finite array do not function as expected. The active S-parameter match of these edge elements can be significantly degraded compared to the interior elements, which can cause issues in the performance of the array. In addition, the active S-parameter match of the radiating elements can also vary significantly with frequency and scan angle. For these reasons extra hardware is often required to protect each radiating element site. Finally, the costs of integrating the associated power, control, and protection hardware at each antenna site can be extremely high. Not only are there many elements in a dense array to fill a required aperture size, the hardware must be necessarily packaged to fit in a small area.

When deciding between using a dense array and a sparse array architecture to build an UWB system, one must consider the advantages and disadvantages of each. First, the dense array radiation pattern has many of the same properties as a periodic array, which has higher peak sidelobes along the lattice grid but also has lower average sidelobe levels overall.

On the other hand, the optimized sparse array typically has an almost uniform sidelobe level with lower peak sidelobes. In addition, the power per element must be because there are fewer elements. However, the hardware costs for a dense array can be significantly more expensive than the sparse array because there are more elements and it must accommodate the mutual coupling effects of the neighboring elements. The bandwidth achievable by these two types of arrays can be ultra-wide (>10:1) [4]; however, it is difficult to compare them since the challenges and solutions offered by each are very different. The bandwidth of a dense array is dependent on the system as a whole, because all of the elements are essentially connected; however, the bandwidth of a sparse array can theoretically be extremely large and is limited only by which antenna element is employed in the final design. This fact, along with the extra area provided per element, allows for the integration of different antenna technology and interleaving of antenna arrays [73]. Table 1-1 illustrates the trade-offs between these two array technologies. Depending on the application, one array technology may be more appropriate than the other.

**Early Aperiodic Design Methods**

Since the early 1960s, when it was first discovered that placing antenna elements in an aperiodic layout can yield radiation patterns devoid of grating lobes, many array design techniques have been proposed that attempt to provide array thinning with no grating lobes and low sidelobe levels [8]-[12]. Arrays with randomly located elements have become popular as a way to avoid grating lobes over wide bandwidths, but they are often plagued with high peak sidelobe levels [8], [17]-[20]. These arrays are usually uniformly excited when the main beam is steered to broadside since this is the easiest method for practical implementations.

Early designs using mathematically determined element locations were presented in [21], although the small number of elements considered in these arrays significantly limited their performance. Modifications to basic array layouts such as the planar ring array yielded modest bandwidths in [22], where space-tapering of uniformly excited, isotropic elements was used to emulate a specific aperture amplitude distribution. Space tapering, covered in detail in [23], was introduced as a method for enlarging an array aperture without requiring an unrealistically large number of antenna elements (which a periodic array would require), as well as reducing the sidelobe level of the arrays.

The tapering introduces aperiodicity into the array layout, which suppresses the grating lobes observed in Fig. 1-3. Increased array bandwidth was occasionally a design goal of space-tapering, but most often a byproduct of attempting to create large, thinned arrays with low sidelobe levels [24], [25].

More recently, new and potentially transformative approaches such as the fractal random array began to appear in the literature. Unlike deterministic fractal arrays, fractal random arrays are not restricted to the repetitive application of a single generator (see Section 1.2.1.1) and are therefore able to retain the beneficial aspects of both deterministic and random arrays. The random application of random generators leads to arrays with large bandwidths and moderate sidelobe levels [13]-[15]. Although the sidelobe levels associated with fractal-random arrays were too high for many practical applications, their introduction set the stage for the development of some very powerful UWB array design techniques, which will be covered in the following section. With the introduction of fractal and fractal-random arrays, the underlying concepts of array representation began to emerge. Array representation is the combination of a relatively small set of parameters with a mathematical construct (such as fractals) to define complex linear, planar, or volumetric array layouts. The following sections illustrate the usefulness of (and often prerequisite) array representation techniques for designing UWB antenna arrays.

This chapter will focus on providing an overview of new design methodologies for sparse UWB array architectures. The chapter will begin by discussing the foundations of multiband and UWB array design techniques. In addition, the mathematical foundations used to describe these complicated geometries and the optimization toolkits employed to synthesize sparse arrays are described. After that, the specific methodologies and techniques behind the construction of sparse arrays are discussed in detail. Finally, several linear and planar UWB sparse array design examples are presented, including experimental (measured) results for a sparse linear UWB array prototype.

**Next: Foundations of Multiband and UWB Array Design**

Excerpted from Frontiers in Antennas: Next Generation Design & Engineering by Frank B. Gross (McGraw-Hill Professional; 2011) with permission from McGraw-Hill.