*5.1. The Orthogonality Criterion*

Intuitively, one might suspect that the benefits of bistatic configurations should be maximized when the bistatic angle is close to 90◦, just as it is for stereoscopic radar configurations measuring currents or tracking targets—minimizing the well-known geometric dilution of precision (GDOP). This reasoning does not lead to practical or even good solutions for many applications. First, there is the obvious limitation of site availability—suitable locations offering near-orthogonality over the priority part of the coverage criterion may not be exist, or if they do, may be inaccessible for some reason. Second, near-orthogonality is no guarantee of increased radar cross section. Indeed, it is often the case that the bistatic RCS of targets of interest is consistently low for such scattering geometries; examining the trailing diagonal offset by 90◦ in either row or column space in Figure 9 makes this very clear.

Even for stereoscopic configurations, the issue of optimum radar disposition is nontrivial. As an example, in the case of ship detection against the sea clutter background, the signal-to-clutter ratio is not a monotonic function of bistatic angle, as shown schematically in Figure 23. While stereoscopic viewing clearly unmasks air targets, where the clutter may be taken as a narrow band centered on zero Doppler, the case for ship detection in clutter is complicated by the existence of Bragg line pairs and the associated second-order clutter. As shown in the figure, for some course-speed combinations, the ship can remain close to Bragg lines for both radars simultaneously.

**Figure 23.** Blind speed diagrams for a bistatic radar system: (**a**) Aircraft detection, (**b**) ship detection. The blue arrows show the projection of the target velocity vector (black) onto the axis of Radar 1; the red arrows show the projection onto the axis of Radar 2. The blind speeds are shaded in the velocity annulus: Blue for Radar 1, red for Radar 2, yellow for doubly blind azimuths that can arise in the case of sea clutter.

Thus, an appreciation of the spatial distribution of the geometric attributes of a radar configuration plays a significant role in system design, and it has been found helpful to present this information in a graphical format. For the case of stereoscopic radar system operation, where the bistatic signal path may not be exploited, and focusing on current vector measurement and aircraft detection, where GDOP is important, it suffices to map the degree of orthogonality at each cell in the surveillance zone, as illustrated in Figure 24. It presents the information in two ways. Figure 24a plots the sine of the included angle in areas of common illumination, while Figure 24b converts this to yield the minimum radial speed that a target can present to one or other radar in its monostatic mode, expressed as a percentage of the target's actual speed. This kind of display facilitates site selection that optimizes performance over priority areas for the specified missions. It is a straightforward matter to generate equivalent displays for the case where bistatic modes of operation are available.

One must also bear in mind that potentially damaging crosstalk can occur when multiple radars in a network, perhaps stereoscopic, are obliged to share a common frequency band. In this circumstance, special signal processing is required to cancel the interfering transmissions [10].

**Figure 24.** Trigonometric properties of overlapped radar coverage from the viewpoint of stereoscopic modes of operation. Figure 24a shows the degree of orthogonality as measured by the sine of the bistatic angle, while Figure 24b expresses it in terms of the minimum component of radial velocity that a target can present. The figure is for illustrative purposes only: The radar sites shown do not correspond to existing radars.

## *5.2. Site Selection via Multi-Objective Optimization*

In order to take account of a multiplicity of mission types, each with its own performance criteria and dependence on prevailing environmental parameters, a far more rigorous approach to radar siting is needed. One methodology that has been used with success [58] is based on the concept of Pareto dominance. In this approach, a number of figures of merit are defined and then the site parameter space is searched to locate those solutions that possess the following property: That they are at least as good as their competitors against every FOM and better than any competitor in at least one FOM. The set of solutions that emerge from this search define the so-called Pareto front, and site selection can be carried out far more easily when one need only deal with this greatly reduced number of possibilities. Attributes such as clustering can be exploited to assess robustness of the solutions, and additional factors may then be taken into account, including less quantifiable criteria such as visual impact or even personal taste.

An important practical aspect of this methodology is its numerical implementation when the search space is large, as happens when one is designing a network of radars. Typically, one is confronted with need to select m sites out of n possibilities, where m is modest, but n may be large. One study of the South China Sea [59] encountered a sample space of ~10<sup>23</sup> solutions. To handle realistic cases successfully, an efficient nonlinear optimization algorithm is essential. One such technique has been reported in [60]; it employs a genetic algorithm fitted with a special acceleration routine that enables it to address highly demanding radar network design problems.

#### **6. Conclusions**

It may seem surprising that we have not partitioned this paper into distinct sections dealing with individual radar configurations, such as skywave and surface wave radars. Our decision was based on two considerations. First, bistatic configurations such as the hybrid sky–surface mode obviously straddle the disciplines that may be relevant to either skywave or surface wave monostatic radars, but not both. Second, and just as importantly, during half a century of first-hand experience with several forms of HF radar, we frequently encountered circumstances where cross-fertilization of ideas provided significant benefits.

Accordingly, in this paper, we have set out with four goals:


The taxonomy speaks for itself; it may serve to provoke thought on the possible merits of alternative bistatic configurations in particular applications. The consequences of bistatism for waveforms, propagation, scattering, and so on extend beyond the brief treatment we have provided here, but hopefully the underlying message is clear: Some of the basic radar principles that we take for granted and seldom bother to reflect upon need careful re-examination when we leave the monostatic domain. We have described several radar missions where clear benefits of bistatic configurations are evident; some of these missions are familiar ones that have long been addressed with monostatic configurations, but others, such as ice monitoring and characterization, ship wake detection and analysis, and space-borne interception of HFSWR clutter for global scale radio oceanography are only now entering the HF radar user's lexicon. The list is hardly exhaustive, and no doubt there are surprises in store for us all. Finally, the practical techniques that are mentioned in the text have all been used successfully in serious applications.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The author declares no conflict of interest.
