Abstract
In this manuscript, an exact symbol error rate analysis of orthogonal frequency division multiplexing system is presented in the presence of carrier frequency offset over two wave with diffuse power (TWDP) fading channel. Both Binary Phase Shift Keying and Quadrature Phase Shift Keying modulation techniques are considered in this study over TWDP channel which contains Rayleigh, Rician and two ray fading as its special cases. The results are validated by means of Monte Carlo simulations and also verified from the benchmark results available in the literature.
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Appendices
Appendix 1: Analytical Expression for BPSK
The integral (5) can be simplified by using the definition of Q function given in [13] and expressed as a sum of four similar terms-
Here, the computation of \(I_1\) is considered as an example where, \(I_1\) is defined as-
After some mathematical adjustments and using the identity [12, (6.61)], the above expression can be rewritten as
By using Maclaurin series for \(\exp (x) = \sum _{n=0}^{\infty } \frac{x^n}{n!}\) and by using [12], the integral in (11) can be solved as
Similarly, the integrals \(I_2\), \(I_3\) and \(I_4\) can be solved and combined to form the complete SER expression given in (6).
Appendix 2: Analytical Expression for QPSK
The unconditional SER for QPSK is determined as
where \(A_1=\frac{(S_A +\mu _{k,n}[1,m])}{\sqrt{\gamma C_{\tau _1\tau _1}/2} \sqrt{1+\frac{V_{k,n}[m]}{\gamma C_{\tau _1\tau _1}}}}, A_2=\frac{(S_B +\mu _{k,n}[2,m])}{\sqrt{\gamma C_{\tau _1\tau _1}/2} \sqrt{1+\frac{V_{k,n}[m]}{\gamma C_{\tau _1\tau _1}}}}\). By using the identity of product of two Q functions [7], and substituting the value of Q function from [13], \(f_\tau (\tau )\) from (3); the above expression (13) can be simplified as sum of four different integral terms-
where \(I_A\) is defined as
The outer integral in (15) can be solved by using [13] can be written as
Finally, using the identity from [13, App. A.5], the integral in (16) can be solved. Similarly, the integrals \(I_2\), \(I_3\) and \(I_4\) can be solved and combined to form the complete SER expression is given in (8).
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Singh, D., Kumar, A., Joshi, H.D. et al. Symbol Error Rate Analysis of OFDM System with CFO Over TWDP Fading Channel. Wireless Pers Commun 109, 2187–2198 (2019). https://doi.org/10.1007/s11277-019-06674-7
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DOI: https://doi.org/10.1007/s11277-019-06674-7