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Power Adaptation for Cognitive Radio Systems Under an Average SINR Loss Constraint in the Absence of Path Loss Information

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Abstract

An upper bound is derived on the capacity of a cognitive radio system by considering the effects of path loss and log-normal shadowing simultaneously for a single-cell network. Assuming that the cognitive radio is informed only of the shadow fading between the secondary (cognitive) transmitter and primary receiver, the capacity is achieved via the water-filling power allocation strategy under an average primary signal to secondary interference plus noise ratio loss constraint. Contrary to the perfect channel state information requirement at the secondary system (SS), the transmit power control of the SS is accomplished in the absence of any path loss estimates. For this purpose, a method for estimating the instantaneous value of the shadow fading is also presented. A detailed analysis of the proposed power adaptation strategy is conducted through various numerical simulations.

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Notes

  1. Section 4 discusses the approaches on how to estimate the instantaneous value of the shadow fading.

  2. Contrary to the previous case, in this framework it is necessary that the secondary transmitter moves along the line connecting the secondary transmitter to primary receiver in order to express the total distance as \(d_0+d_i\)

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Bilkent University, 06800 , Bilkent, Ankara, Turkey

    Berkan Dulek & Sinan Gezici

  2. Sony Corporation, Gotenyama Technology Center, Tokyo, 141-0022, Japan

    Ryo Sawai & Ryota Kimura

Authors
  1. Berkan Dulek
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  2. Sinan Gezici
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  3. Ryo Sawai
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  4. Ryota Kimura
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Corresponding author

Correspondence to Sinan Gezici.

Appendix

Appendix

1.1 Derivation of Instantaneous SINR Loss at PS receiver

When no SS user is present in the PS service area, the SNR at the PS receiver can be written as

$$\begin{aligned} {\hbox {SNR}}_{p} = \frac{P_p\, G\left( r_{pp},\xi _{pp}\right) }{N_p} \end{aligned}$$
(33)

where \(P_p\) is the transmission power of the PS, \(G\left( r_{pp},\xi _{pp}\right) \) is the combined shadowing and path gain between PS transmitter and receiver, and \(N_p\) is the noise power at the PS receiver. When an SS transmitter is present and interferes with the PS receiver, the SINR at the PS receiver can be written as

$$\begin{aligned} {\hbox {SINR}}_{p} = \frac{P_p\, G\left( r_{pp},\xi _{pp}\right) }{P_s\left( \mathbf{r}, \varvec{\xi } \right) \,G\left( r_{sp},\xi _{sp}\right) +N_p} \end{aligned}$$
(34)

where \(P_s\left( \mathbf{r}, \varvec{\xi } \right) \) is the transmission power of the SS and \(G\left( r_{sp},\xi _{sp}\right) \) is the combined shadowing and path gain between SS transmitter and PS receiver. From (33) and (34), the instantaneous SINR loss at the PS receiver due to the SS transmission is given as

$$\begin{aligned} {\hbox {SINR}_{\mathrm{p,loss}}}&= \frac{{\hbox {SNR}}_{p}}{{\hbox {SINR}}_{p}} = 1 + \frac{P_s\left( \mathbf{r},\varvec{\xi } \right) \,G\left( r_{sp},\xi _{sp}\right) }{N_p}\,. \end{aligned}$$
(35)

Equation (35) indicates that \({\hbox {SINR}_{\mathrm{p,loss}}}\) depends on the interference level from the SS and the thermal noise at the PS victim, and it is independent of the PS tranmit power.

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Dulek, B., Gezici, S., Sawai, R. et al. Power Adaptation for Cognitive Radio Systems Under an Average SINR Loss Constraint in the Absence of Path Loss Information. Wireless Pers Commun 77, 151–172 (2014). https://doi.org/10.1007/s11277-013-1499-8

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