# Performance Aspects of Retrodirective RFID Tags +
## 1 Introduction  
The concept behind the use of simple electromagnetic systems to assist in radio frequency identification is to utilize numerous tags (with at least one placed at each desired identification point, product, asset, device, etc. ), ideally at little to no cost (and thus extremely easy to build, transfer, place, handle, and configure) and accessible effortlessly (this means mainly wirelessly) from acceptable distances. In the author's opinion, RFID's greatest constraints are not the lack of mass production or its level of complexity; they are its operational coverage and the amount of space around the tag in which it can communicate. Of course, the channel is wireless, and (assuming that far-field testing is conducted) the limit is set by the Friis formula. But usually, the performance of passive tags is far worse than this. And it is not just the possible obstacles between the tag and the reader that can be blamed. The main reason is that the wave that reaches the tag is scattered in all directions in an uncontrolled manner, which, after a critical distance, makes the tag invisible to the reader. Here, we focus on this very mechanism of scattering and in a way modulate the tag's radar cross-section to present a main beam scattered towards the incoming wave's direction. Although, at first, such an endeavor would seem to require signal processing to estimate the direction of its arrival and subsequent active signal response, this is not necessary, in addition to being complicated and expensive. The stated claim is presented in detail and validated in the following text. It can be easily deduced from the preceding paragraph that there is an urgent need to increase the reliable communication distance from the tag while maintaining minimal levels of complexity and minimal costs [1]. In order to improve its performance and achieve this goal, the employment of a small array antenna, not only on the reader but also on the tag, was proposed by [PERSON] et al [2]. In this case, while the reader can be designed effectively [3; 4; 5; 6] without very strict constraints on its complexity, this is not the case for the RFID tag array. Tag arrays should be extremely inexpensive but at the same time extremely effective. Furthermore, their analysis and design, when they are embedded in complex environments and must conform to the host surface, are challenging [7; 8; 9], as can be seen from Figure 1.  
Here, we propose the design of retrodirective tag arrays, i.e., those that passively scatter the incident power back in the direction of the incoming wave. This retrodirective response can be achieved by the utilization of a lossless passive feeding network [10; 11] attached to the tag array antenna. To assess the merits of such a proposal, we need to study the respective channel. In [2], the resulting channel was investigated, employing spatial multiplexing and transmit diversity for active tags. Thus, it was based only on the temporal characteristics and the stochastic properties of the exchanged information. Here, a backscatter channel model incorporating the spatial signature of the incident and backscattered signals is contributed to RF tag application, (see Equation (3)). Up to now, related works on pinhole channels on RF tags with multiple antennas have neglected the spatial aspects of incident and backscattered signals. Taking into account the directions of arrivals (DoAs) and the directions of departures (DoDs) of the propagating signals, beamforming gains can be attained. This can be achieved with minimal extra costs, since we propose the exploitation of the spatial signature of the channel to be performed in the RF domain (not in the digital domain). This is accomplished by employing \(90^{\circ}\) hybrids to achieve proper retrodirective backscattering. Various cases are examined, and the relative results are given to present the performance aspects of the retrodirective tags.