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Symbol Detection of IDMA Systems in the Presence of Carrier Frequency Offsets

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Abstract

In this paper we investigate the detection algorithms for interleave division multiple access (IDMA) systems in the presence of carrier frequency offsets (CFOs). The existing IDMA detection algorithm is designed under the zero CFO assumption and its performance will be degraded when the CFOs are present. We first extend the existing algorithm to the nonzero CFO case by utilizing effective channel coefficients which take the CFO effects into account. Then we turn to a more practical scenario with imperfect CFO estimates. We propose an algorithm that can cope with the residual CFO effects by integrating the CFO updating into the iterative receiver. Signal-to-interference-plus-noise ratio analysis and simulations show the feasibility and superiority of our proposed algorithms.

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Authors and Affiliations

  1. National Mobile Communications Research Laboratory, Southeast University, Nanjing, 210096, China

    Jian Dang & Zaichen Zhang

  2. Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, 80523, USA

    Liuqing Yang

Authors
  1. Jian Dang
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  2. Liuqing Yang
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  3. Zaichen Zhang
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Corresponding author

Correspondence to Liuqing Yang.

Additional information

This work is in part supported by the National Science Foundation under Grant No. 1129043, the National Natural Science Foundation of China (No. 60902010 and 61172105), the Research Fund of NCRL (No. 2012A03), National Science & Technology Major projects of China (2009ZX03006-008-02 and 2010ZX03006-003-02), and the Program for New Century Excellent Talents in University (NCET-09-0299).

Appendix: Mean and Variance of \(I_{k}^{Re}(n)\)

Appendix: Mean and Variance of \(I_{k}^{Re}(n)\)

Denote \(\alpha _{k,i}=h_k^*h_i\). It can be shown that

$$\begin{aligned} I_{k}^{Re}(n) =\sum _{i=1,i\ne k}^K \left[ \mathfrak R \{\alpha _{k,i}\}\mathfrak R \{x_i(n)\}- \mathfrak I \{\alpha _{k,i}\}\mathfrak I \{x_i(n)\}\right] +\mathfrak R \{h_k^*z(n)\}, \end{aligned}$$
(20)

which is a function of the Gaussian random variable \(z(n)\) and the independent Bernoulli random variables \(\mathfrak R \{x_i(n)\}\) and \(\mathfrak I \{x_i(n)\}\), \(\forall i\). Therefore the mean and variance of \(I_{k}^{Re}(n)\) are given by

$$\begin{aligned} \mathrm{E}\{I_{k}^{Re}(n)\}&= \sum _{i=1,i\ne k}^K \left[ \mathfrak R \{{\alpha }_{k,i}\}\mathrm{E}\{\mathfrak{R }\{x_i(n)\} \} -\mathfrak I \{{\alpha }_{k,i}\}\mathrm{E}\{\mathfrak{I }\{x_i(n)\} \}\right] ,\end{aligned}$$
(21)
$$\begin{aligned} \mathrm{var}\{I_{k}^{Re}(n)\}&= \sum _{i=1,i\ne k}^K \left[ \mathfrak R ^2\{{\alpha }_{k,i}\}\mathrm{var}\{\mathfrak{R }\{x_i(n)\} \} +\mathfrak I ^2\{\alpha _{k,i}\}\mathrm{var}\{\mathfrak{I }\{x_i(n)\} \}\right] \nonumber \\&+\frac{\sigma ^2}{2}|h_k|^2, \end{aligned}$$
(22)

where

$$\begin{aligned} \mathrm{E}\left\{ \mathfrak{R }\{x_i(n)\}\right\}&= 1 \cdot P(\mathfrak{R }\{x_i(n)\}=1) +(-1)\cdot P(\mathfrak{R }\{x_i(n)\}=-1)\nonumber \\&= \tanh \left( \frac{L_a\left( \mathfrak{R }\{x_i(n)\}\right) }{2}\right) ,\end{aligned}$$
(23)
$$\begin{aligned} \mathrm{var}\{\mathfrak{R }\{x_i(n)\}\}&= 1-\mathrm{E}^2\{\mathfrak{R }\{x_i(n)\}\}. \end{aligned}$$
(24)

At the first iteration, there is no a priori information on the symbols so \(L_a\left( \mathfrak R \{x_i(n)\}\right) =0\) and \(\mathrm{E}\left\{ \mathfrak{R }\{x_i(n)\}\right\} =0\).

\(\mathrm{E}\{\mathfrak{I }\{x_k(n)\}\}\) and \(\mathrm{var}\{\mathfrak{I }\{x_k(n)\}\}\) can be obtained in a similar way.

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Dang, J., Yang, L. & Zhang, Z. Symbol Detection of IDMA Systems in the Presence of Carrier Frequency Offsets. Wireless Pers Commun 72, 1453–1466 (2013). https://doi.org/10.1007/s11277-013-1088-x

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