## 4 Performance of Modulation Schemes over IBC Channel  
The application of efficient digital modulation can improve power efficiency and bandwidth efficiency at a reasonable cost. From the results of the time domain and frequency domain analyses above, it is concluded that signal in passband transmission enjoys the benefit of lower attenuation and lower distortion than the baseband transmission counterpart. Therefore, we now evaluate and compare the performance of different modulation schemes with a carrier frequency of 500 kHz using the proposed IBC channel model. Moreover, the use of a carrier frequency at 500 kHz could be a balance between data rate and electromagnetic radiation. Among the commonly available digital modulation techniques, FSK, PSK and QAM, high-ary modulation would not be considered due to either its high complexity in hardware, such as 16 QAM, 16 PSK, or due to its low bandwidth efficiency, such as 8 FSK and 16 FSK. PSK is generally superior than FSK in terms of bandwidth and power efficiency in the low-ary (\(\leq\)8-ary) [33]. Therefore, we focus on the performance of the following three modulation schemes, namely, BPSK, QPSK, and 8 PSK. Moreover, the data rate of the proposed IBC channel is limited by the bandwidth of the channel. It would be practical to consider low-ary power efficient modulation schemes since high data rate transmission is not practical in this case due to relatively low carrier frequency and high complexity in hardware. The data symbols are first digitally modulated using BPSK, QPSK or 8 PSK and then are pulse-shaped by the square root raised cosine filter with roll-off factor \(\alpha=0.5\) before sending to the IBC channel. The noise within the human body mainly comes from various bioelectric signals, the environment and contact impedance between the electrodes and the human body. As the frequency ranges of bioelectric signals such as ECG, EMG and EEG signal are all lower than 10 kHz [34], therefore, noise contributed to the passband comes mainly from the contact between electrodes and human body, and other background noises. We assume that the noise is Additive White Gaussian Noise (AWGN) with power spectrum density (PSD) \(N_{0}\). From the measurements without applying input signal, the estimated value of background noise PSD \(N_{0}\) is found to be around \(-123\) dBm/Hz. The transmit power for the transmitter was set to \(-25\) dBm for a compromise between feasible calculation time and bit-error-rate (BER). The communication performance (BER) in simulation and theoretical calculation is compared. In the simulation, the channel characterized by transfer function (7) and AWGN noise with PSD \(-123\)\(dBm\)/Hz is built, then a large amount (up to \(10^{7}\) bits) of random bit stream with different bit rate and different modulation scheme is applied into this channel, and output bit-stream (with possible error bits) is obtained at the receiver after demodulation. The BER can be calculated based on the comparison between input and received data bits. In the theoretical calculation, the equivalent signal to noise ratio (_i.e._, the ratio of average signal energy per bit to noise power spectral density \(E_{b}\)/\(N_{0}\)) can be calculated before demodulation at the receiver using the transmit power, the transfer function attenuation, \(N_{0}\) and data symbol rates. The theoretical BER can be calculated by the following equation:  
\[BER= \begin{cases}Q\left(\sqrt{2E_{b}/N_{0}}\right)\\ Q\left[\sin(x/8)\times\sqrt{6E_{b}/N_{0}}\right]\end{cases} \qquad \begin{split} for\,BPSK\,and\,QPSK\\ for\,8 PSK\end{split}  \tag{12}\]  
where Q(\(x\)) is the Gaussian Q-function. At a transmission distance of 11 cm, Figure 8 shows the BER performances of BPSK, QPSK and 8 PSK for the data rates between 6 kbps and 100 kbps and the BER performances _versus_\(E_{b}\)/\(N_{0}\) are presented in Figure 9. As depicted in Figures 8 and 9, the performance of BPSK and QPSK are similar.