## 2 Materials and Methods  
### Experimental Setup  
Because of the high signal loss during propagation within biological tissues, the multi-static radar architecture was adopted for all measurements. With this approach, it is possible to improve the final signal-to-noise ratio of the system, since the signal backscattered by the geometry is collected M (M \(-\) 1) times, where M is the number of antennas within the array. In particular, each antenna in turn transmits, and all other (M \(-\) 1) antennas receive the signal backscattered from the target. This procedure is repeated M times, each time using a different transmitting antenna. The complete experimental setup consisted of:  
* Two truncated double-ridge waveguides (PNR180) with cut-off frequency for the fundamental mode, TE10, of 15.12 GHz and mono-modal bandwidth of [18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. A two-port PNA Network Analyzer (Keysight E8361C, [28]), working in the frequency range from 10 MHz to 67 GHz, used to generate the signals and to store the scattering parameters for each transmitting/receiving configuration;
* Two flexible coaxial cables with high performance, to connect the PNA to the two antennas;
* Four micro-step actuators (Zaber T-LSM200A) used both to support the antennas and to allow their movement in the intended positions for the generation of the synthetic linear array;
* A laptop to drive both the actuators and signal acquisition. A picture of the complete experimental setup is shown in Figure 1. In all tests presented in this paper, only two actuators were moved, allowing for the creation of a synthetic linear array for 2-D imaging. The antennas were oriented toward the floor and several anechoic panels were used to mitigate external interferences; a polystyrene layer was used as air-like phantom support. In all phantoms used for the test of our prototype, the skin layer was not included, being out of the main scope of this paper, which is the experimental validation of the possibility to achieve significant penetration depths, even at mm-wave frequencies within realistic phantoms, allowing for the formation of a suitable image. This is a simplifying hypothesis for what concerns the overall power budget, and the creation of multiple reflections within the propagation medium. However, on the one hand, the possibility of accounting for the skin losses as well, when adopting dedicated mm-wave transmit/receive modules, was already demonstrated [24]. On the other hand, possible strong multiple reflections (certainly increased by the skin, but at any rate created even by the sole presence of the air-fat interface of the phantoms used in this work, which intentionally does not use any coupling medium) can be largely addressed adopting image-formation algorithms more sophisticated than the DAS algorithm [29]. Therefore, this simplifying hypothesis is included to focus the attention on the main aspect (penetration depth at mm-wave frequencies), compensating for the sub-optimum power budget provided by a standard Vector Network Analyzer (VNA), and not confusing the results with more complex image-formation techniques, DAS being sufficient for the aim of this work, to compensate for the multiple reflections created by the air-fat interface. However, although due to the limitations of the standard VNA we used (especially its Noise Figure, NF), it was not possible to insert the skin layer or reduce the scanning time (about one hour, as explained below), the contribution of the skin was included in the theoretical calculation [24]. In addition, it should be noted that the final system, of which this prototype aims only to demonstrate the feasibility, will be composted both by dedicated transmit/receive  
Figure 1: Experimental setup used for signal acquisition. modules, with much lower NF (adding margin to consider the contribution of the skin too), as well as by a switch matrix connected to the physical antennas, which will significantly reduce scanning times. In Figure 2, a sketch of the measurement scenario is represented.