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Impact of Channel Estimation Error on the Performance of Relay Selection in Cognitive Radio Networks

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Abstract

Channel estimation error, which adversely affects the performance of any wireless communication system, is inevitably available in receivers. However, its impact on the bit error rate (BER) performance of relay selection in underlay cognitive networks has not been investigated analytically. This paper fills in this literature gap by firstly proposing an exact single-integral form BER formula for general network topology. Based on this proposal, we further analyze the diversity gain to have insights into asymptotic performance and system design. Secondly, we derive a closed-form approximate BER formula, which has been shown highly accurate, for a typical network topology where relays are closely positioned for reduced simulation time. Various results demonstrate that the channel estimation error significantly degrades the performance of the relay selection in underlay cognitive networks and completely destroys its diversity gain. In addition, increasing the number of involved relays drastically remedies its impact.

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Notes

  1. The effect of channel estimation error on relay selection in underlay cognitive networks was studied for the AF relays in [16, 17]. The literature related to the AF relays should not be further surveyed since this paper concentrates the DF relays in underlay cognitive networks.

  2. It is worth emphasizing that multiple works investigate the impact of the channel estimation error on the BER performance of underlay cognitive networks (e.g., [25–27]). Nevertheless, the issue of the relay selection which makes the theoretical analysis complicated has not been discussed in any work.

  3. \({h}\sim {{\mathcal {CN}}}\left( a,p \right) \) stands for a circular symmetric complex Gaussian random variable with mean a and variance p.

  4. The BER of other modulation schemes such as M-ary Phase Shift Keying (M-PSK) can be analyzed in the same manner.

  5. For notation simplicity without any confusion, we also denote \({\vartheta }_{X,L} = {\vartheta }_{3}\). Generally, \({{\vartheta }_{1}}\ne {{\vartheta }_{2}}\ne {{\vartheta }_{3}}\ne {{\vartheta }_{4}}\) and so, this case is considered in the current paper.

  6. The computer program shows that the high-SNR approximate BER matches with the single-integral form BER at very low values, which are not convenient to be displayed together with high BERs (i.e., the BERs for W = 1) on the same graph. Therefore, we limit to plot BERs up to \({{10}^{-10}}\).

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Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.04-2014.42.

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Authors and Affiliations

  1. Telecommunications Engineering Department, HoChiMinh City University of Technology, 268 Ly Thuong Kiet Str., District 10, HoChiMinh City, Vietnam

    Khuong Ho-Van, Khai Doan-Nguyen & Huynh Ho-Ngoc

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  1. Khuong Ho-Van
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Correspondence to Khuong Ho-Van.

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Ho-Van, K., Doan-Nguyen, K. & Ho-Ngoc, H. Impact of Channel Estimation Error on the Performance of Relay Selection in Cognitive Radio Networks. Wireless Pers Commun 84, 2513–2536 (2015). https://doi.org/10.1007/s11277-015-2717-3

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