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Frequency Reuse Techniques with a Distributed Antenna System

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Abstract

The performance of cellular networks is strongly limited by inter-cell interference. In order to reduce this interference, several techniques have been proposed, e.g., the frequency reuse techniques and distributed antenna system (DAS). This paper investigates the combinations of hard frequency reuse (HFR) and soft frequency reuse (SFR) techniques with DAS in a unique cell architecture, which are called DAS–HFR and DAS–SFR, respectively. This paper analytically quantifies the performance of the downlink multi-cell for DAS–HFR and DAS–SFR in terms of the average spectral efficiency. This also shows, the most appropriate frequency reuse technique depends not only on the average achievable data rate inside the cell, but also on the guaranteed achievable data rate (the minimum achievable data rate which is necessary to be obtained regardless of geographic location). The results show that DAS–SFR improves the achievable data rate of cell edges in a multi-cell environment as compared to a DAS–HFR when frequency reuse factor 1 is utilized. The results also show that DAS–SFR significantly increases the system capacity as compared to the DAS–HFR when frequency reuse factor 3 is utilized.

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Notes

  1. \(\mu _{N}= \sum _{n \in {SoS}} \left[ {D_n^{(0)}} \right] ^{ - \delta }{P_n^{(0)}} \text {exp} \left( { {\lambda } \mu _n^{(0)} + \lambda ^2 \frac{ \left[ {\sigma _n^{(0)}} \right] ^2 }{2} }\right) \)

  2. \(\sigma _{N}^2 =\sum _{n \in {SoS}} \left[ {D_n^{(0)}} \right] ^{ - 2\delta } \left[ {P_n^{(0)}} \right] ^2 \text {exp} \left( { {2 \lambda }{ \mu _n^{(0)}} + \lambda ^2 \left[ {\sigma _n^{(0)}} \right] ^2 }\right) \left( { \text {exp} \left( \lambda ^2 \left[ {\sigma _n^{(0)}} \right] ^2 \right) -1 }\right) \)

  3. \(\mu _{D}= \sum _{i = 1}^{18} \sum _{n \in {SoS}} \left[ {D_n^{(i)}} \right] ^{ - \delta } {P_n^{(i)}} \text {exp} \left( { {\lambda } \mu _n^{(i)} + \lambda ^2 \frac{\left[ {\sigma _n^{(i)}} \right] ^2}{2} }\right) \)

  4. \(\sigma _{D}^2 = \sum _{i = 1}^{18} \sum _{n \in {SoS}} \left[ {D_n^{(i)}} \right] ^{ - 2\delta } \left[ {P_n^{(i)}} \right] ^2 \text {exp} \left( { {2 \lambda } \mu _n^{(i)} + \lambda ^2 \left[ {\sigma _n^{(i)}} \right] ^2 }\right) \left( { \text {exp} \left( \lambda ^2 \left[ {\sigma _n^{(i)}} \right] ^2 \right) -1 }\right) \)

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Authors and Affiliations

  1. School of Engineering Science, Simon Fraser University, Burnaby , V5A 1S6, Canada

    Seyed Amin Hejazi & Shawn P. Stapleton

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  1. Seyed Amin Hejazi
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  2. Shawn P. Stapleton
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Correspondence to Seyed Amin Hejazi.

Appendix

Appendix

Let’s assume the \(\psi _i\) is the a lognormal random variable with probability density function, \((f_{\psi }(\psi ))\), where \(\sigma _{\psi }\) and \(\mu _{\psi }\) are the shadowing standard deviation and mean respectively, and \(\lambda = {\frac{\ln 10}{10}}\).

$$\begin{aligned} {f_\psi }(\psi ) = \frac{1}{{\sqrt{2\pi } \lambda {\sigma _\psi }\psi }}\exp \left( { - \frac{{{{(\ln \psi - \mu _{\psi })}^2}}}{{2{\lambda ^2}\sigma _\psi ^2}}} \right) ,\quad \psi > 0, \end{aligned}$$
(21)

Therefore, the summation, multiplication and ratio of lognormal random variables can be approximated as a lognormal variable [30]. The summation of lognormal random variables \(\left( \sum \limits _{i=1}^{m} d(i) \psi _i\right) \) is expressed as a lognormal variable with mean \(\mu _{sum}\) and variance \(\sigma _{sum}\) as,

$$\begin{aligned} \mu _{sum}&= \sum \limits _{i=1}^{m}d(i)\text {exp} \left( {{\lambda }{\mu _{\psi _i}}+\lambda ^2 \frac{\left[ {\sigma _{\psi _i}}\right] ^2}{2}}\right) \end{aligned}$$
(22)
$$\begin{aligned} \sigma _{sum}^2&= \sum \limits _{i=1}^{m}d(i)\text {exp} \left( {{2\lambda }{\mu _{\psi _i}}+\lambda ^2\left[ {\sigma _{\psi _i}}\right] ^2}\right) \left( {\text {exp}\left( \lambda ^2\left[ {\sigma _{\psi _i}}\right] ^2\right) -1}\right) \end{aligned}$$
(23)

where \(d(i) \in \left\{ {-1,1} \right\} \). The multiplication of lognormal random variables \((\prod \nolimits _{i=1}^{m} \psi _i^{d(i)})\) is expressed as a lognormal variable with mean \(\mu _{mul}\) and variance \(\sigma _{mul}\) as,

$$\begin{aligned} \mu _{mul}&= \sum \limits _{i=1}^{3} d(i) \left( \lambda ^ {-1} \ln {( \mu _{\psi _i})} - \frac{\lambda ^{-1}}{2} \ln {\left( {\frac{ \sigma _{\psi _i} ^2}{ \mu _{\psi _i} ^2}}+1 \right) } \right) \end{aligned}$$
(24)
$$\begin{aligned} \sigma _ {mul} ^2&= \sum \limits _{i=1}^{3} d(i) \lambda ^ {-2} \ln {\left( {\frac{\sigma _{\psi _i} ^2}{ \mu _{\psi _i}^2}}+1 \right) } \end{aligned}$$
(25)

where \(d(i) \in \left\{ {-1,1} \right\} \).

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Hejazi, S.A., Stapleton, S.P. Frequency Reuse Techniques with a Distributed Antenna System. Wireless Pers Commun 78, 171–192 (2014). https://doi.org/10.1007/s11277-014-1742-y

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