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Rate and Power Optimization Under Received-Power Constraints for Opportunistic Spectrum-Sharing Communication

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Abstract

In this paper, the channel capacity of secondary user is investigated for opportunistic spectrum sharing with primary user in a Rayleigh fading environment. In the proposed communication scenario, on finding transmission opportunities in licensed band, secondary user utilizes the band as long as the interference power inflicted on primary receiver is below the predefined threshold, and adjusts its transmission power and data rate based on the sensing information available from spectrum sensor. In this context, two different adaptation schemes namely adaptive transmission power scheme and adaptive rate and transmission power scheme are investigated under joint peak and average received power constraints at primary receiver for multilevel quadrature amplitude modulation format. The closed form expressions are derived for the ergodic channel capacities of these schemes and numerical results are presented to validate the theoretical results. Moreover, a comparison between channel capacities is given to illustrate the benefit of using soft sensing information under said constraints.

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Author information

Authors and Affiliations

  1. ECE Department, Punjabi University, Patiala, Punjab, India

    Indu Bala & Manjit Singh Bhamrah

  2. ECE Department, JUIT Waknaghat, Solan, Himachal Pradesh, India

    Ghanshyam Singh

Authors
  1. Indu Bala
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  2. Manjit Singh Bhamrah
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  3. Ghanshyam Singh
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Corresponding author

Correspondence to Indu Bala.

Appendix

Appendix

To compute inner integration in (25), we need integration limit on soft sensing metric \(\xi\). From (19), we have

$$\alpha + \bar{\alpha }\frac{{f_{off} \left( \xi \right)}}{{f_{on} \left( \xi \right)}} = \gamma_{u} \left( \xi \right)$$

Using (3) and (4), it becomes

$$\frac{{\left( {\xi - \mu_{off} } \right)^{2} }}{{2 \delta_{off}^{2} }} - \frac{{\left( {\xi - \mu_{on} } \right)^{2} }}{{2 \delta_{on}^{2} }} + \log \left( {\frac{{\delta_{off} }}{{\delta_{on} }}\left( {\frac{{\gamma_{u} \left( \xi \right) - \alpha }}{{\bar{\alpha }}} } \right) } \right) = 0$$
(41)
$$\xi^{2} \left( {\frac{1}{{2 \delta_{off}^{2} }} - \frac{1}{{2 \delta_{on}^{2} }}} \right) + \xi \left( {\frac{{\mu_{on} }}{{\delta_{on}^{2} }} - \frac{{\mu_{off} }}{{\delta_{off}^{2} }}} \right) + \frac{{\mu_{off}^{2} }}{{2\delta_{off}^{2} }} - \frac{{\mu_{on}^{2} }}{{2\delta_{on}^{2} }} + \left( {\frac{{\delta_{off} }}{{\delta_{on} }}\left( {\frac{{\gamma_{u} \left( \xi \right) - \alpha }}{{\bar{\alpha }}} } \right) } \right) = 0$$
(42)

\(P_{1} \left( {\gamma_{u} \left( \xi \right)} \right)\) and \(P_{2} \left( {\gamma_{u} \left( \xi \right)} \right)\) are the roots of quadratic equation in (42), and given by

$$P_{1} \left( {\gamma_{u} \left( \xi \right)} \right), P_{2} \left( {\gamma_{u} \left( \xi \right)} \right) = \frac{1}{2a}\left( { - b \pm \sqrt {b^{2} - 4ac} } \right)$$
(43)

where

$$a = \left( {\frac{1}{{2 \delta_{off}^{2} }} - \frac{1}{{2 \delta_{on}^{2} }}} \right)$$
(44)
$$b = \left( {\frac{{\mu_{on} }}{{\delta_{on}^{2} }} - \frac{{\mu_{off} }}{{\delta_{off}^{2} }}} \right)$$
(45)
$$c = \frac{{\mu_{off}^{2} }}{{2\delta_{off}^{2} }} - \frac{{\mu_{on}^{2} }}{{2\delta_{on}^{2} }} + \left( {\frac{{\delta_{off} }}{{\delta_{on} }}\left( {\frac{{\gamma_{u} \left( \xi \right) - \alpha }}{{\bar{\alpha }}} } \right) } \right)$$
(46)

Using \(P_{1} \left( {\gamma_{u} \left( \xi \right)} \right)\) and \(P_{2} \left( {\gamma_{u} \left( \xi \right)} \right)\) as inner integration limit in (25), we get (27), thus completing the proof.

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Bala, I., Bhamrah, M.S. & Singh, G. Rate and Power Optimization Under Received-Power Constraints for Opportunistic Spectrum-Sharing Communication. Wireless Pers Commun 96, 5667–5685 (2017). https://doi.org/10.1007/s11277-017-4440-8

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