Energy efficient communication in body area networks using collaborative communication in Rayleigh fading channel

Abstract

Due to resource limited nature of nodes in body area networks (BAN), it is often very difficult to replace or recharge its power source. To prolong the network’s life, only way out is energy efficient communication system. In this article an energy efficient communication system based on collaborative communication is proposed for BAN. Signals from the implanted nodes are received out-of-phase at the base station with no line-of-sight through an AWGN channel. Mathematical model derived here is based on three figures of merit i.e, received power, bit error rate and energy consumption. Analysis of the proposed model and Monte Carlo simulation show that the gain in received power increases as the number of collaborative nodes increase whereas BER is directly related to SNR $(E_b/N_0)$. To evaluate energy consumption of the proposed system, it is compared with single-input-single-output (SISO) system. In this comparison it has been found that SISO performs well at short distances but collaborative communication outperforms SISO in case of long distances. It is also found that collaborative communication requires “N $\times$ Transmitted power”, less transmission power in comparison to SISO systems. It is observed that collaborative communication achieve energy saving very close to 99 %. On the basis of these results it is safe to recommend collaborative communication for resource limited BAN.

Appendix

1.1 Mean values of trigonometric functions

1.1.1 Mean value of $\cos (\theta _f)$

$$\begin{aligned} E\left[ \cos (\theta _f)\right]= & {} \int \limits _{-\infty }^{\infty }\cos (\theta _f)P(\theta _f)d(\theta _f) \nonumber \\= & {} \int \limits _{-\phi }^{\phi }\cos (\theta _f)\frac{1}{2\phi }d(\theta _f) \nonumber \\= & {} \frac{1}{2\phi } \int \limits _{-\phi }^{\phi }\cos (\theta _f)d(\theta _f) \nonumber \\= & {} \frac{\sin (\phi )}{\phi } \end{aligned}$$

(32)

1.1.2 Mean value of $\cos ^2(\theta _f)$

$$\begin{aligned} E\left[ \cos ^2(\theta _f)\right]= & {} \int \limits _{-\infty }^{\infty } \cos ^2(\theta _f)P(\theta _f)d(\theta _f) \nonumber \\= & {} \int \limits _{-\phi }^{\phi }\cos ^2(\theta _f)\frac{1}{2\phi }d(\theta _f) \nonumber \\= & {} \frac{1}{2\phi }\int \limits _{-\phi }^{\phi }\cos ^2(\theta _f)d(\theta _f) \nonumber \\= & {} \frac{1}{2\phi }\left( \phi +\frac{\sin (2\phi )}{2}\right) \nonumber \\= & {} \frac{1}{2}+\frac{\sin (2\phi )}{4\phi } \end{aligned}$$

(33)

1.1.3 Variance of $\cos (\theta _f)$

$$\begin{aligned} Var\left( \cos (\theta _f)\right) = E\left[ \cos ^2(\theta _f)\right] - \left( E\left[ \cos (\theta _f)\right] \right) ^2 \end{aligned}$$

Using Eqs. (32) and (33) in the above equation we get

$$\begin{aligned} Var\left( \cos (\theta _f)\right)= & {} \frac{\sin (\phi )}{\phi } - \left( \frac{1}{2}+\frac{\sin (2\phi )}{4\phi }\right) \end{aligned}$$

(34)

1.1.4 Variance of $hS\cos (\theta _f)$

Since all of these are independent random variables, therefore the multiplication can be calculated as

$$\begin{aligned}&Var\left[ hS\cos (\theta _f)\right] \nonumber \\&\quad = S^2( Var[h]\left( E\left[ \cos (\theta _f)\right] \right) ^2 + (E\left[ h\right] )^2\nonumber \\&\quad \times \, Var\left[ \cos (\theta _f)\right] + Var\left[ h\right] Var\left[ \cos (\theta _f)\right] ) \nonumber \\ \end{aligned}$$

(35)

Since we know from Eqs. (32) and (34) that, $Var(h) = \sigma _h^2 = (2-\frac{\pi }{2})b^2$ and $E\left[ h\right] = \mu _h = \left( \sqrt{\frac{\pi }{2}}\right) b$

by putting these values in Eq. (35), we get

$$\begin{aligned} Var\left[ hS\cos (\theta _f)\right]= & {} b^2S^2\left[ 1 - \frac{pi}{2}\left( \frac{\sin (\phi _f)}{\phi }\right) ^2 + \frac{\sin (\phi _f)}{2\phi }\right] \nonumber \\ \end{aligned}$$

(36)