Abstract
We analyze the bit error rate (BER) performance of a multiple-input multiple-output (MIMO) radio-frequency-identification (RFID) system employing orthogonal space-time block codes when the forward and backward channels exhibit independent but not necessarily identically distributed Nakagami-m fading. A closed-form upper bound on the BER performance is derived, and the corresponding diversity order is quantified. Numerical results provide some insight into the impact of several different parameters on the system performance.
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Acknowledgments
This work has been supported by DFG project “MIMO Backscatter-Übertragung auf Basis von Mehrantennen-Transpondern in RFID-basierten Funksystemen” with grant no. KA 1154/30-1.
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Appendix
Appendix
Let us define \(\eta _{j}={\sum }_{i=1}^{L}\big {|}g_{i,j}\big {|}^{2}\) and \(\varphi _{j}=\big {|}{\sum }_{l=1}^{L}h_{j,l}\nu _{l}\big {|}^{2}\). Hence, the variable β j defined in Section 4 can be rewritten as β j = η j φ j . For notational simplicity, the subscript j in these three variables is omitted hereafter. One can show that η follows a Gamma distribution whose probability density function (PDF) is
Using [16, Eq. (8)] and with the help of [17, p. 62], the PDF of φ can be obtained as
With the aid of [17, p. 140], the PDF of β can be derived as follows:
where the last equality is obtained by using [10, Eq. (3.471.9)]. Since the MGF of β, denoted by \(\mathcal {M}_{\beta }(s)={\int }_{0}^{\infty }\exp (sz)\,f_{\beta }(z)\,\text {d}z\), is the Laplace transform of f β (z) with the exponent reversed in sign [13, p. 100], we have
where the third, fourth, and last equalities are obtained by using the change of variable \(r=\sqrt {z}\), the identity in [10, Eq. (9.232.1)], and the transformation in [11, Eq. (13.1.33)], respectively. Changing the sign of s in Eq. 16 yields (8).
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Maichalernnukul, K., Zheng, F. & Kaiser, T. Performance analysis of a MIMO-RFID system in Nakagami-m fading channels. Ann. Telecommun. 71, 151–156 (2016). https://doi.org/10.1007/s12243-015-0481-8
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DOI: https://doi.org/10.1007/s12243-015-0481-8