Feasibility of Green Network Deployment for Heterogeneous Networks

Abstract

Green technology is a new term which is used to describe the energy efficient technologies. In the context of mobile communications industry, complying with the green technology strategy is a challenge. This is because of the tradeoff between the Quality of Service (QoS) provided and the total energy used in the transmission. Reducing the transmission energy may cause degradation in the QoS, more distinctively, in highly populated areas. This paper explores the possibility of achieving the green technology goal in planning and deployment of the HetNet mobile network with efficient network QoS. A decoupled two stage multi-objective genetic algorithm is developed to provide the network base station distribution that would satisfy both the network QoS and green network demands. In the first stage the algorithm estimates the base station parameters for more energy efficient HetNet deployment for optimum network coverage. The initial base station candidate locations are provided by a network operator in Kuala Lumpu, Malaysia. The second stage of the developed algorithm selects the number and location of RS associated with each base station optimized in the first stage to improve the network capacity. To optimize the network power, a novel arrival rate based HetNet total power consumption model is derived to investigate the parameters that affect the network power expenditure. Results show that a remarkable energy saving of about 40 % of the operator transmission power could be achieved with full network coverage. The addition of RS associated with each base station would greatly improve network capacity on the expense of its power expenditure. The relative RS to base station capacity plays major rule in reducing HetNet power expenditure.

Appendix

The shadow fading is modeled as a normal distribution with zero mean and $\sigma$ standard deviation as follows:

$$\begin{aligned} {X}=\frac{1}{\sqrt{{2} \pi \sigma }} {e}^ {x^2/2\sigma ^2} \end{aligned}$$

(45)

Thus the total pathloss can be written as the summation of the mean pathloss and the shadow fading component:

$$\begin{aligned} {Pl}=\overline{Pl} + X \end{aligned}$$

(46)

where $\overline{Pl}$ is the local mean pathloss defined as:

$$\begin{aligned} {Pl}=A + Blog_{10} \left( r\right) \end{aligned}$$

(47)

where A is the intercept point, $B=10n$, n is the pathloss exponent, and r is the distance from the base station in meter.

By defining the Shadow Fading Margin (SFM), the probability of cell coverage can be defined by requiring the sum of the signal received and the SFM at distance r from the receiver to be greater than the mean pathloss, thus:

$$\begin{aligned} P_{cov}=Pr\left( Pl+SFM >\overline{Pl}\right) \end{aligned}$$

(48)

Substituting Eq. (46) in (48) and calculating at distance r, yields:

$$\begin{aligned} P_{cov} &= Pr\left( \overline{Pl}(r)+X+SFM >\overline{Pl}(R)\right) \end{aligned}$$

(49)

$$\begin{aligned} P_{cov} &= Pr\left( X > \overline{Pl}(R) - \overline{PL}(r) - SFM \right) \end{aligned}$$

(50)

where r is the user distance from the base station and R is the radius of the base station.

Using Eq. (47)

$$\begin{aligned} P_{cov} &= Pr(X>A-Blog_{10}(R)- (A+Blog_{10} (r)) - SFM) \end{aligned}$$

(51)

$$\begin{aligned} P_{cov} &= Pr\left( X>Blog_{10}\left( \frac{R}{r} \right) - SFM \right) \end{aligned}$$

(52)

From Eq. (45), the coverage probability can be written as:

$$\begin{aligned} P_{cov}=\frac{1}{\sqrt{2\pi \sigma }} \int ^{\infty }_{Blog_{10}(R/r)-SFM} {\mathrm {e}}^{\frac{x^2}{2\sigma ^2}}\,\mathrm {d}x \end{aligned}$$

(53)

Defining $t=x/\sigma$ and substituting in Eq. (53)

$$\begin{aligned} P_{cov} &= \frac{1}{\sqrt{2\pi }} \int ^{\infty }_{\frac{Blog_{10}(R/r)-SFM}{\sigma }} {\mathrm {e}}^{\frac{t^2}{2}}\,{\mathrm {d}}t \end{aligned}$$

(54)

$$\begin{aligned} P_{cov} &= erf\left( \left( Blog_{10}\left( R/r\right) -SFM\right) /\sigma \right) \end{aligned}$$

(55)

Equation (55) defines the coverage probability at a distance r from the base station. For cell coverage probability (Pcell), it is defined as the average of the coverage probability at all possible locations covered by the cell. Mathematically Pcell can be written as:

$$\begin{aligned} P_{cell}=\int ^{2\pi }_{0} \int ^{R}_{0} {\mathrm P}{_{cov}(r)}P(r,\varphi )\,{\mathrm {d}}r {\mathrm (d)}\varphi \end{aligned}$$

(56)

where $P(r,\varphi )$ is the distribution function of the mobile users.

For uniform users distribution, the probability of a user to be at distance r with angle $\varphi$ from the base station can be defined as follows:

$$\begin{aligned} P(r,\varphi )=\frac{r}{\pi R^2}, 0<r<R, and\,0<\varphi <2\pi \end{aligned}$$

(57)

From Eqs. (53), (56) and (57), the cell probability can be written as:

$$\begin{aligned} P_{cell}=\frac{2}{R^2}\int ^{R}_{0}{\mathrm r}(erf((B log_{10} (R/r) -SFM)/\sigma )){\mathrm {d}}r \end{aligned}$$

(58)

where the erf is defined as:

$$\begin{aligned} erf(t)=\int ^{\infty }_{\frac{Blog_{10}(R/r)-SFM}{\sigma }} {\mathrm e}^{{-t^2}/2} {\mathrm {d}}t \end{aligned}$$

(59)

Let define

$$\begin{aligned} x= \frac{\left( Blog_{10}\left( \frac{R}{r}\right) -SFM\right) }{\sigma } \end{aligned}$$

(60)

Calculating for r, yields

$$\begin{aligned} \sigma x &= \left( Blog_{10}\frac{R}{r}-SFM\right) \end{aligned}$$

(61)

$$\begin{aligned} \frac{(\sigma x + SFM)}{B} & = log_{10}\left( \frac{R}{r}\right) =\frac{ln\left( \frac{R}{r}\right) }{2.303} \end{aligned}$$

(62)

where

$$\begin{aligned}&ln(10)= 2.303 \end{aligned}$$

(63)

$$\begin{aligned}&\frac{(2.303(\sigma x + SFM))}{B}=ln\left( \frac{R}{r}\right) \end{aligned}$$

(64)

$$\begin{aligned}&\frac{R}{r}=e\left(\frac{2.303 \sigma x}{B}\right) \times e\left(\frac{2.303 SFM}{B}\right) \end{aligned}$$

(65)

let

$$\begin{aligned} c= \left( \frac{2.303 \sigma }{B}\right) , {\text { and }} \ b= e\left(\frac{2.303 SFM}{B}\right) \end{aligned}$$

(66)

Equation (66) will be:

$$\begin{aligned} \left( \frac{R}{r}\right) =be^{cx} \end{aligned}$$

(67)

Changing the limits of the integration and substitute in Eq. (58), yields:

$$\begin{aligned} r= \left( \frac{R}{b}\right) e^{cx} \longrightarrow dr =\left( \frac{-cR}{b}\right) e^{cx} dx = -crdx \end{aligned}$$

(68)

$r\longrightarrow 0 \longrightarrow x \longrightarrow \infty$

$r\longrightarrow R= e^{cx} \longrightarrow (\frac{-ln(b)}{c})=x$

$$\begin{aligned} P_{cell}= & {} \left( \frac{2}{R^2}\right) \int ^{\left( \frac{-ln(b)}{c}\right) }_{\infty }\nonumber \\&\left( \left( \frac{R}{b}\right) e^{-cx} erf(x) \left( -c\left( \frac{R}{b}\right) e^{-cx}\right) \right) {\mathrm {d}}x \end{aligned}$$

(69)

$$\begin{aligned} P_{cell}= & {} \left( \frac{-2c}{b^2}\right) \int ^{\left( \frac{-ln(b)}{c}\right) }_{\infty } {\mathrm e}(^{-2cx} erf(x)) {\mathrm {d}}x \end{aligned}$$

(70)

$$\begin{aligned} P_{cell}= & {} \left( \frac{2c}{b^2}\right) \int ^{\infty }_{\left( \frac{-lb(b)}{c}\right) } {\mathrm e}(^{-2cx} erf(x)) {\mathrm {d}}x \end{aligned}$$

(71)

By integration Eq. (71) by parts, the cell coverage probability is represented as:

$$\begin{aligned} P_{cell}=\frac{b^2 erf\left( \frac{-ln((b)}{c}\right) }{2c} - \frac{e^{-c^2}}{2c\sqrt{2\pi }} erf\left( \frac{-ln(b)}{c\sqrt{2}} + \frac{c}{\sqrt{2}}\right) \end{aligned}$$

(72)