# Analysis of Dual-Band Direction of Arrival Estimation in Multipath Scenarios
## 4 Simulation Environment: Implemented Scenario  
As previously mentioned in Section 2, the aim of this paper is to propose a simulation environment capable of correctly predicting the improvement due to the use of the aforementioned dual-band system approach. This simulation tool permits the full investigation of the effects of multi-path contributes and their impacts on the estimation results based on a simple but effective model. The basic idea is to recreate a real-life scenario making use of trustful full-wave simulations, thought to be compatible with experimental results presented in [16]. As a first step, the link between the actual anchor (\(A\)) and target (\(T\)) is simulated by means of Ansys HFSS. The 8-beam SBA and the target antenna are modeled and simulated to match those presented in [31]. The spatial configuration of the whole system is chosen in the same way as that illustrated in the aforementioned manuscript. In Figure 4 is depicted a representation of multi-path phenomena based on a two-ray reflection model. Starting from this key point, the simulation environment introduces the multipath contributes by means of a second radiating element which acts as an Image (I) antenna and removing the ground plane. This approach is depicted in Figure 5 where the Image antenna is explicitly highlighted and operates as a coherent communication interferer. The insertion of this element allows the accomplishment of a controlled multipath scenario. Consequently, the full-wave simulation requires the use of a total of \(8+2=10\) antennas. The resulting \(10\times 10\) scattering matrix describes the coupling between the involved antennas with full-wave accuracy. The goal of describing a truly realistic multi-path environment is attained running a series of full-wave simulation. In each of them, the position of \(T\) is varied to cover a different scenario. Additionally, the location of \(I\) is varied accordingly, to emulate a two-way bounce in a consistent way following an approach that is perfectly coherent with the equivalence theorem. For each position of \(T\) (and therefore \(I\)) the anchor is rotated over 360\({}^{\circ}\) with steps of 5\({}^{\circ}\), meaning 73 full-wave simulations for each relative position. This is coherent with the measurements in [16], which can therefore be used for validation. Figure 6 shows the proposed controlled multi-path scenario, based on the image-source model. The EM simulation sets representing the link data may be manipulated interconnecting a set of 73 \(10\times 10\) scattering matrices with an ideal circuital network composed by a Wilkinson Power Divider (PD), a Phase-Shifter (PS) and an Attenuator (ATT). The resulting circuital network is configured in such a way that the source signal, i.e., the broadcast message, is split between the two branches of the PD connected, respectively, to the Target and the Image antenna. The latter branch enabling the manipulation the of incoming signal by means of a PS and an ATT to create a controllable interference, both in absolute value and phase. As a result, the link between the anchor and target is described by means of a set of 73 \(9\times 9\) scattering matrices, which is in turn manipulated for the setting of ATT and PS using command lines. Thanks to this, the interferer signal may cover a wide range of possible scenario. In accordance with Figure 6, the attenuation factor on the image antenna branch is indicated with the letter \(\chi\), while the relative phase between target and image signal is indicated with \(\alpha\). Referring to Equation (2), the resulting RSSI used in the DoA estimation algorithm include an unavoidable contribution of noise. Formally, the latter consists of two main components. The first one takes into account both thermal noise as well as process errors.