Table 1 Non-coherent case of the identical signaling scheme: closed-form BER expressions for the N × L RFID channel (Equation 17)

N = 1

$e^{\frac{1}{g\bar{\gamma }}}\frac{E_1(\frac{1}{g\bar{\gamma }})}{2g\bar{\gamma }}$

$e^{\frac{1}{g\bar{\gamma }}}\frac{E_2(\frac{1}{g\bar{\gamma }})}{2g\bar{\gamma }}$

N = 2

$\frac{2e^{\frac{1}{g\bar{\gamma }}}{E}_2(\frac{1}{g\bar{\gamma }})}{g\bar{\gamma }}+$

$\frac{2(-g\bar{\gamma }+e^{\frac{1}{g\bar{\gamma }}}{E}_1(\frac{1}{g\bar{\gamma }})+g\bar{\gamma })}{g\bar{\gamma }}+$

$\frac{{(g\bar{\gamma })}^2-2g\bar{\gamma }{e}^{\frac{1}{g\bar{\gamma }}}{E}_1(\frac{1}{g\bar{\gamma }})+g\bar{\gamma }-e^{\frac{1}{g\bar{\gamma }}}{E}_1(\frac{1}{g\bar{\gamma }})}{4{\left(g\bar{\gamma }\right)}^3}$

$\frac{e^{\frac{1}{g\bar{\gamma }}}{E}_1(\frac{1}{g\bar{\gamma }})-3{(g\bar{\gamma })}^2+2{(g\bar{\gamma })}^2{e}^{\frac{1}{g\bar{\gamma }}}{E}_1(\frac{1}{g\bar{\gamma }})-g\bar{\gamma }+4g\bar{\gamma }{e}^{\frac{1}{g\bar{\gamma }}}{E}_1(\frac{1}{g\bar{\gamma }})}{4{\left(g\bar{\gamma }\right)}^3}$