**2. The General Radar Process Model**

The radar process model formulation first introduced in [16] is ideally suited for our purpose as it makes explicit the temporal sequence of the signal trajectory and of this in mind, and noting that multizone scattering in the course of signal propagation (see below) has been observed to be significant for both skywave and surface wave HF radars [17,18], the formulation of the radar process is expressed as a concatenation of operators,

$$s = \sum\_{n\_B=1}^{N} \overline{\mathcal{R}} \left[ \prod\_{j=1}^{n\_B} \overline{\mathcal{M}}\_{\mathcal{S}(j)}^{\mathbb{S}[j+1]} \widetilde{\mathcal{S}}(j) \right] \overline{\mathcal{M}}\_T^{\mathbb{S}(1)} \overline{T} \overline{w} + \sum\_{l=1}^{N\_l} \sum\_{m\_B=1}^{M} \overline{\mathcal{R}} \left[ \prod\_{k=1}^{n\_B} \widetilde{\mathcal{M}}\_{\mathcal{S}(k)}^{\mathbb{S}[k+1]} \widetilde{\mathcal{S}}(k) \right] \overline{\mathcal{M}}\_N^{\mathbb{S}(1)} n\_l + m \tag{1}$$

where

*w* represents the selected waveform,

*T* represents the transmitting complex, including amplifiers and antennas,

*<sup>M</sup>S*(1) *<sup>T</sup>* represents propagation from transmitter to the first scattering zone,

*S*(*j*) represents all scattering processes in the j-th scattering zone,

*<sup>M</sup>Sj*+1 *<sup>S</sup>*(*j*) represents propagation from the j-th scattering zone to the (j+1)-th zone,

*nB* denotes the number of scattering zones that the signal visits on a specific route from the transmitter to the receiver,

*NJ* denotes the number of external noise sources or jammers,

*<sup>M</sup>S*(1) *<sup>N</sup>* represents propagation from the i-th noise source to its first scattering zone,

*mB* denotes the number of scattering zones that the i-th noise emission visits on a specific route from its source to the receiver,

*N*, *M* denote the maximum number of zones visited by signal and external noise, respectively,

*R* represents the receiving complex, including antennas and receivers,

*m* represents internal noise,

*s* represents the signal delivered to the processing stage.

If the transmitter and/or receiver are in motion, as with shipborne radars, for example, a slight generalization is in order. Adopting the frame-hopping paradigm, we insert Lorenz transformation operators:

$$
\overline{T} \to \overline{L}\_T \overline{T} \tag{2}
$$

and

$$
\overline{\mathcal{R}} \to \, \overline{\mathcal{R}} \, \overline{L}\_{\mathcal{R}} \, \tag{3}
$$

to take kinematic effects into account.

The effective design of bistatic HF radar systems requires decisions that involve all the terms in the process model, singly, pairwise, or collectively. Ultimately, the design problem is one of optimization; that is, finding the best combination of siting and radar parameters as measured by performance over the set of missions to be addressed. In general, this is a multi-objective problem as radars may be designed to perform air and surface surveillance as well as remote sensing of one or more geophysical variables. Later in this paper, we will describe tools for achieving this optimization, but first we examine some of the most important considerations associated with the individual operators.
