## 3 Analysis of I2O WBAN Systems
### I2O Channel Model  
Energy efficient modulation schemes are beneficial in reducing the hardware structure, lowering the noise interference and prolonging the communication network lifetime, due to the shortage of implanted device battery capacity. Moreover, low error probabilities are required in the modulation methods to ensure the reliability of the communication transmission. In [18], M-ary PSK (M-PSK) is reported to achieve significant energy saving and high system outage probability. In addition, 16 QAM is the most spectral efficient modulation technique, which can meet higher data rates than QPSK and 8 PSK when operating under the same bandwidth [10; 26; 27]. An I2O communication channel shares the property with all fading RF channels that the instantaneous SNR, \(\gamma\), at the receiver side, can be regarded as a random variable due to the fading effect. Since this means that the bit errors in demodulation are therefore not fixed since the SNR varies randomly, we investigate the expected bit error rate (BER) for channel performance evaluation, where the expectation is with respect to the probability distribution of the SNR. Figure 4: Path loss model versus distance between Tx and Rx antennas. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value (Unit)** & **Description** \\ \hline \(n\) & 3.6 & PL exponent \\ \(\sigma_{dB}\) & 2.93 & average deviation \\ \(d_{ref}\) & 0.5 cm & reference distance \\ \(P_{LdB}\left(ref\right)\) & 23.49 dB & PL at the reference distance \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation Results of the Path Loss Model. The average BER of the I2O shadow fading communication channel can be evaluated by the following integral [5;28]:  
\[P_{e}\left(\overline{\gamma}\right)=\int_{0}^{\infty}P_{b,AWGN}\left(\gamma \right)P_{0}\left(\gamma\right)d\gamma \tag{3}\]  
where \(P_{b,AWGN}\left(\gamma\right)\) represents the BER performance of the additive white Gaussian noise (AWGN) channel for an SNR, \(\gamma\), and assuming a mean SNR, \(\overline{\gamma}\). The function \(P_{0}\left(\gamma\right)\) denotes the probability density function of the \(\gamma\), which is lognormal distributed with the same standard deviation \(\sigma_{\mathrm{s}}\) as the BER performance for the I2O shadow fading channel when employing the four selected modulation techniques. The received power can be obtained simply from the transmitted power \(P_{t}\) and PL via:  
\[P_{r}=\frac{P_{t}}{PL} \tag{4}\]  
The received energy per bit \(E_{b}\) can be related to the data rate \(R_{b}\) and the received power and it then can be expressed as:  
\[\frac{E_{b}}{N_{o}}=\frac{P_{r}}{N_{0}R_{b}}=\frac{P_{t}}{R_{b}N_{0}PL} \tag{5}\]  
where \(N_{0}\) is the noise power. Expressing (6) in dB:  
\[\ln\left(\frac{E_{b}}{N_{o}}\right)=\ln\left(\frac{P_{t}}{R_{b}N_{0}PL}\right) =\ln\left(\frac{P_{t}}{R_{b}N_{0}}\right)-\ln\,PL \tag{6}\]  
The first term in the Expression (6) for \(\ln\left(E_{b}/N_{o}\right)\) is fixed for a given data rate \(R_{b}\) and transmitter power \(P_{t}\). Thus, since the PL model presented earlier follows a lognormal distribution, \(\ln\left(E_{b}/N_{o}\right)\) is normally distributed, i.e., \(E_{b}/N_{0}\) follows a lognormal distribution:  
\[P_{0}\left(\gamma\right)=\frac{1}{\sqrt{2\pi}\sigma\gamma}e^{-\frac{\left(\ln \gamma-\mu\right)^{2}}{2\sigma^{2}}} \tag{7}\]  
where \(\mu=\ln\overline{\gamma}-\frac{1}{2}\left(\frac{\ln 10}{10}\right)^{2} \sigma_{dB}^{2}\), and \(\sigma=\frac{\ln 10}{10}\sigma_{dB}\). Detailed information on the four selected modulation techniques can be found in [5; 18; 26; 27]. We use coherent BPSK modulation as a concrete example, where [5]:  
\[P_{b,AWGN}\left(\gamma\right)=\frac{1}{2}\mathrm{erfc}\left(\sqrt{\gamma}\right) \tag{8}\]  
where \(\mathrm{erfc}(.