5.1.1 The Radar Range Equation
Radar stands for radio detection and ranging, is meant to detect objects and determine their range, angle or velocity. The basic concept of a radar system using the electromagnetic spectrum to transmit a waveform and receive a backscatter from the target is depicted in Fig. 5.1.
The transmitter generates a waveform of power 𝑃 , which is sent through the transmit antenna of gain 𝐺 into free space, where it propagates at the speed of light 𝑐. The main objective of the antenna is to concentrate the waveform energy in a specific direction, namely the area of interest, where a target should be detected. The waveform beam broadens as it propagates through free space from the radar, and loses strength with
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increasing distance (path loss), the power density 𝑝 at a specific distance 𝑟 from the antenna is given by [61]
𝑝 = 𝑃 𝐺
4𝜋𝑟 (5.1)
Once the waveform reaches the target, some of the incident energy is absorbed and another amount is backscattered according to the target specific RCS. The backscattered waveform attenuates again as it propagates through free space toward the direction of the transceiver and is incident upon the receiving antenna of effective aperture 𝑎 , then the power received can be expressed by [61]
𝑃 = 𝑃 𝐺 𝑎
(4𝜋𝑟 ) 𝑅𝐶𝑆 (5.2)
the effective aperture of any antenna can also be written as [61] 𝑎 = 𝜆 𝐺
4𝜋 (5.3)
and the received power becomes [61]
𝑃 = 𝑃 𝐺 𝐺 𝜆
(4𝜋) 𝑟 𝑅𝐶𝑆 (5.4)
Equation (5.4) is known as the radar equation. It provides the relation between the free space losses, antenna gains, wavelength, received and transmit power of a radar system.
As shown in Fig. 5.1, the radar waveform must make a two-way journey to the target and back, the distance or range to the target is given by 𝑟, so the waveform travels a total distance of 2𝑟 at a speed of 𝑐. If time 𝑡 that it takes the waveform to travel from the radar to the target and back is known, then the range can also be calculated as [61]
Fig. 5.1: Radar system basic principle, Tx: transmit waveform, Rx: receive waveform
Transmitter Target Tx Rx Receiver Antenna Transceiver 𝑅𝐶𝑆 𝐺 /𝐺 𝑃 𝑃 𝑟
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2 (5.5)
5.1.2 Range Resolution
The resolution is the UWB readers’ ability, like in a radar system, to distinguish between two or more UWB chipless RFID transponders that are closely spaced, whether in angle or space. Fig. 5.2a illustrates the concept. The UWB reader transmits a single pulse of duration 𝜏, which is backscattered by two UWB chipless RFID transponders located at 𝑟 and 𝑟 distances from the RFID reader antennas, separated a distance ∆𝑟 from each other. In the case ∆𝑟 is large enough, the RFID reader should receive two distinctive signals as shown in Fig. 5.2b, and the chipless RFID transponders are resolved in range. In Fig. 5.2c, the chipless RFID transponders are located so close together that the received signals overlap, producing a composite signal, which means that the chipless RFID transponders are not resolved in range, and since they both carry embedded
Fig. 5.2: Range resolution: a) concept, b) resolved signals, c) unresolved signals, d) limit
RFID reader
𝜏
UWB chipless RFID transponders
∆𝑟 𝑟 𝑟 ∆𝑟 >𝑐𝜏 2 ∆𝑟 <𝑐𝜏 2 ∆𝑟 =𝑐𝜏 2 a) b) c) d)
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information, they combine destructively, which means, no identification code could be retrieved from neither of them [62].
Fig. 5.2d shows the limit, when the pulses arrive exactly one after the other, and this specific distance value can be found replacing 𝑡 by 𝜏 and 𝑟 by ∆𝑟 in equation (5.5)
∆𝑟 = 𝑐𝜏
2 (5.6)
where ∆𝑟 is named the range resolution, two UWB chipless RFID transponders spaced a distance greater than ∆𝑟 will be resolved in range (Fig. 5.2b), while transponders spaced by less than ∆𝑟 will not (Fig. 5.2c) for a pulse of duration 𝜏 [62]. A pulse duration of 1 ns result in a range resolution of 15 cm, which could make the simultaneous detection of multiple chipless RFID transponders quite difficult, when separated at distances smaller than that. Furthermore, to achieve finer resolutions, shorter pulses are required, nevertheless, they will have less energy and therefore make the detection more challenging [62].
5.1.3 Frequency Band Selection
The selection of the frequency band of the RFID system with chipless transponders is based on several requirements. As discussed in chapter 4, the design of chipless RFID transponders based on scattering structures require larger bandwidths, as well as, to implement additional features like the simultaneous detection of multiple chipless RFID transponders, a high range resolution is needed, as discussed in section 5.1.2.
The UWB technology spreads the signal over a very wide frequency range allowing the transmission of information at very low power levels. Because the targeted RFID system with chipless transponders range is low, it may be classified as a short-range device (SRD), having low capability to interfere with other radio equipment. The European Telecommunications Standard Institute (ETSI) has issued a standardization allocating the unlicensed UWB frequencies between 3.1 GHz and 10.6 GHz with a signal width no less than 500 MHz and with a radiated power density of -41 dBm/MHz for the frequency bands: 3.1 to 4.8 GHz and 6 to 9 GHz, -70 dBm from 4.8 to 6 GHz and -65 dBm from 9 to 10.6 GHz [63], [64].
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The previous UWB spectrum specifications should serve as a baseline for the design and implementation of the RFID Systems with chipless transponders. Provided that the transponder is merely a passive device and can’t generate power by itself, the supply of the required power relies completely in the reader part and need to be optimized to guarantee the achievement of the target reading range. Moreover, the influence of the path loss increases with the frequency, thereby limiting the chipless RFID transponder reading range for its higher frequency components due to a decrease in the received signal-to-noise ratio (SNR). Therefore, two different sections of the UWB frequency band are chosen to guarantee maximum reading capabilities: 3.8 – 5.7 GHz, and 4 – 9 GHz for the frequency domain and time domain readers respectively.