## 1 Introduction  
The characterization of materials using a free-space method is based on the reflection and/or transmission of electromagnetic waves by/through a sample of the material placed in the air at some distance from the transmitting/receiving antennas [1]. This technique is contactless, non-destructive, and can be used over a wide frequency range [1; 2; 3; 4; 5]. The possibility of performing non-invasive and contactless in situ measurements is useful in many fields of application, including the characterization of building materials in propagation modeling [6], remote sensing of structural health and through-the-wall imaging [7; 8] and the characterization of materials at high temperatures [9]. Despite these advantages, there are issues regarding free-space wave propagation that need to be addressed to correctly formulate our problem. First of all, when these measurements are performed in an ordinary non-anechoic environment, care should be taken to avoid results being affected by noise and unwanted reflections [1]. Furthermore, sample size dictates the choice of the propagation model, where geometrical optics applies to cases of high frequency (small wavelength), whereas full wave or numerical models should be adopted in cases where the dimensions are comparable with the wavelength. Another issue with free-space wave propagation is the hardware, because microwave equipment and fixtures such as vector network analyzers [10], antennas [11], phase-stable cables [2] and precision positioning systems are quite expensive. Regarding the electronics of the measurement setup, software-defined radios (SDR) are becoming an interesting and flexible alternative for projects in microwave frequencies [12], such as the measurement of antennas [13] and radar systems [14; 15], including ground-penetrating radar (GPR) for soil characterization [16] and landmine detection [17]. SDR can also be used for materials characterization, as shown in [18], though not in free space in this case. Most of the abovementioned references use a single radio platform containing both a transmitter (Tx) and a receiver (Rx). This configuration is favorable because it ensures synchronization between the Tx and Rx, thus providing coherent measurements [19]. In this work, we investigate a setup with two separate Tx and Rx radios in the 0.85-1.55 GHz range, which costs considerably less than the most commonly adopted solutions. In particular, we focus on the comparison between our measurements and simulated data, with the aim of understanding the impact of the different parameters on the measurements, and, ultimately, assessing the possibility of recovering unknown material parameters from data measured in realistic conditions. Indeed, the frequency was low and its range was narrow compared with the recent literature [5; 20; 21]. The working frequencies are limited by low-cost devices. However, we intentionally kept the setup as simple as possible, as an alternative to complex, expensive free-space-based measurement setups. For the sake of simplicity and due to the narrow bandwidth, we assumed that the material was not dispersive. It should be noted that the type of device (software-defined radio) used in this work is not commonly used for materials characterization. Indeed, the main contribution of this paper is to provide free-space materials characterization based on software-defined radios. Moreover, a transmission-only configuration was considered. This entailed having less information than in other contexts, such as ones mentioned in previous papers where all four S parameters [5] or two different incident angles [20] are exploited. In this context, the role of the computational electromagnetics model was crucial [22].