# Performance Aspects of Retrodirective RFID Tags +
## 3 Results
So, to assist the forthcoming outcomes,we assume \(|\Delta\Gamma|=1\), meaning the reflection coefficient varies from perfect reflection to perfect absorption. Note that the h variables are random variables of Rayleigh, Rician or other channel coefficient. Also, the random variable \(\theta\) is a uniform one over the full angular sector. Since ASK is used, the error probability obeys:  
\[P=Q\bigg{(}\frac{|V|}{\sqrt{2N_{o}}}\bigg{)}. \tag{12}\]  
We aim to compute the average BER with respect to the SNR. This is computed as follows [17]:  
\[\text{average BER}=\int_{0}^{+\infty}P(|V|;N_{o})f_{|V|}(|V|)d|V|. \tag{13}\]  
Thus, we need to compute \(f_{|V|}(|V|)\). For the cases listed in (11), the respective PDFs are calculated numerically through a Monte Carlo simulation, and using (13), we compute the results, which are shown in Figure 4. In the results, the average fading power of the Rayleigh channels is set to be equal to one. Note that for BER = 10\({}^{-2}\), the retrodirective array provides a \(\sim\)6 dB gain compared to the one-antenna case. The respective gain for the spatial diversity case is theoretically higher but cannot be attained since the incident signals to the different antenna elements are correlated. The broadside array performs badly. The stated results indicate that the retrodirective array has an increased operation range compared with that of the conventional tag. Indeed, to quantify and intuitively present the attained results, let us adopt the easily understood and widely accepted backscatter communication radio link budget formula from [18], which is as follows:  
\[P=A-B\cdot log_{10}(R). \tag{14}\]  
where A and B are constants relative to the channel and adopted system, and R is the tag-reader distance. Equation (14) indicates that there is a distance at which the signal power is such that the SNR is not adequate for the desired or needed BER. Now, as shown in (14), we can understand that B is mainly dependent on the propagation conditions (it can be easily identified as being the path loss exponent), which are the same for the one-antenna tag and for the retrodirective two-element array tag. This is not the case for A. A is dependent on the specific system used. As Figure 4 shows, the A parameter for the  
Figure 4: Average BER versus SNR. retrodirective two-element array tag should be 6 dBs greater than that of a one-antenna conventional tag. Thus, in the retrodirective case, the critical distance is clearly greater, with the ultimate limit determined by the chip sensitivity [19]. By examining (11) and the 6 dB gain that exhibit the used Tag compared to the one antenna case, useful conclusions can be drawn. The use of the retrodirective mechanism allows for linear, (with the number of the antenna elements used), scaling of the attained gain with respect to the single element, conventional, Tag. Furthermore, this gain seams not to depend on the BER target used. Those characteristics are extremely important indicating that retrodirective RFID Tags are extremely robust and potent. Another point that should be addressed is that to the counterpoint that multielement Tags are not low profile radiators anymore, the author refers the reader to [20] where a four element array fits into the area that hosts one element.