# Scalp-Implanted Ultra-Wideband Circularly Polarized MIMO Antenna for Biotelemetry Systems
## 3 Results and Discussion
### Channel Parameters  
1. Envelope Correlation Coefficient (\(ECC\)): The \(ECC\) is a crucial metric that indicates the diversity and coupling performance of a multiple-antenna configuration in a MIMO system. It is used to verify the system's independence regarding separation performance. In the ideal case, the value of \(ECC\) is 0, and the channel of MIMO does not want to be turned off at all, but in practical applications, \(ECC<0.5\) is usually considered acceptable. \(ECC\) can be calculated using either S-parameters or far-field radiated directional maps, and the S-parameter method of Equation (8) was used for \(ECC\) calculations in this work [29]: \[ECC=\frac{|\iint_{\mathcal{A}\pi}(\overset{\rightarrow}{A}n_{i}(\theta,\phi)) \times(\overset{\rightarrow}{A}n_{ij}(\theta,\phi))d\Omega|^{2}}{\iint_{ \mathcal{A}\pi}|(\overset{\rightarrow}{A}n_{i}(\theta,\phi))\,|^{2}d\Omega \iint_{\mathcal{A}\pi}|(\overset{\rightarrow}{A}n_{j}(\theta,\phi))\,|^{2}d \Omega}\] (8) where \(\overset{\rightarrow}{A}n_{i}(\theta,\phi)\) is the 3D radiation pattern of antenna-1 and \(\overset{\rightarrow}{A}n_{j}(\theta,\phi)\) is the 3D radiation pattern of antenna-2; \(\Omega\) is the solid angle. Figure 9 illustrates the plot of the \(ECC\) value against frequency. It should be noted that the antenna system's overall \(ECC\) remains below 0.03, with a specific measurement of 0.02 at the 2.45 GHz frequency point. The sufficiently low \(ECC\) value confirms the excellent diversity performance, making the antenna system suitable for implantable devices with high data rates, such as scalp IMDs. 2. Diversity Gain (\(DG\)): Moreover, the \(DG\) reflects how the diversity scheme influences the transmission power. A \(DG\) value of 10 dB is considered optimal, indicating a perfectly uncorrelated channel. The \(DG\) for a MIMO antenna can be calculated as follows [30]: \[DG=10\sqrt{1-(ECC)^{2}}\] (9) From the above equation, it is evident that the \(ECC\) value determines the \(DG\) value. Specifically, as the \(ECC\) increases, the \(DG\) decreases, and vice versa. Figure 9 shows the \(ECC\) and \(DG\) of the antenna across various frequencies. The results show that the simulated and measured \(ECC\) of this antenna system is less than 0.03 over the entire range of the target operating band, that the measured \(DG\) is greater than 9.995 dB over the entire operating band, and that this MIMO antenna system is more independent. (3) Channel Capacity (\(CC\)): The primary goal of MIMO antenna systems is to enhance capacity without requiring extra spectral or power resources. The bit error rate (BER) of the antenna system increases as the number of both transmitting and receiving antennas rises, provided that the channels are uncorrelated. However, in practical applications, achieving completely uncorrelated channels is not feasible. The \(CC\) is affected by both the number of antennas and the degree of channel correlation. Figure 9: MIMO channel parameters: ECC and DG. Achieving high \(CC\) requires an increased number of antennas and high isolation. The \(CC\) for an \(N\times N\) MIMO antenna system can be described by the following formula [31]:  
\[CC=\log_{2}\left(\det\left[I_{N}+\frac{SNR}{N}HH^{*}\right]\right) \tag{10}\]  
where \(I_{N}\) represents the identity matrix, \(H\) includes the amplitude-phase information of the antenna in the form of a channel matrix, and \(H^{*}\) is the covariance matrix of \(H\). In this study, the channel matrix was derived from the radiation direction map of the antenna [32]. Figure 10 shows the \(CC\) in bps/Hz plotted against the signal-to-noise ratio (SNR) in decibels for ideal SISO, ideal \(2\times 2\), and the proposed \(2\times 2\) antennas. When the SNR hits 20 dB, the capacity of an ideal MIMO antenna system significantly outperforms that of an ideal SISO system. As can be seen from the figure, the channel capacity of the designed MIMO antenna system exceeds that of the ideal SISO antenna in the overall range.