# ISAC towards 6G Satellite-Terrestrial Communications: Principles, Status, and Prospects
## 2 The Development Status and Key Technology Of ISAC
### Evaluation Indicators  
With the development of existing ISAC technologies, several evaluation metrics have been commonly used as a basis for measuring the performance of ISAC, and in this subsection, we present the commonly used existing metrics. (1) MSE  
Mean squared error (MSE) is a statistical measure that quantifies the average squared difference between predicted and actual values. It is often used as an evaluation metric to measure the consistency between the optimized radar beam and the desired beam in ISAC. In [23], MSE is used as the radar beam objective function at time 0, to accurately align the target direction with the known position. \[MSE=\frac{1}{n}\sum_{i=1}^{n}{(\theta_{i}-\hat{\theta}_{i})^{2}}, \tag{1}\]  
where \(\theta_{i}\) and \(\hat{\theta}_{i}\) denote the ideal and estimated value in direction \(i\), and \(n\) denotes the number of directions. (2) CRB  
The Cramer-Rao bound (CRB) stands for the lowest possible variance attainable for any unbiased estimator of the parameter \(\theta\) that is unbiased and calculated by inverting the Fisher information. The accuracy of ISAC parameter estimation is usually measured by the CRB. The authors of [24] use the CRB as the target estimation, and the CRB is denoted as  
\[\text{CRB}(\theta)=\frac{\sigma_{\text{F}}^{2}\text{tr}(A^{H}(\theta)A(\theta )R_{\text{x}})}{2|\alpha|^{2}L(\text{tr}(A^{H}(\theta)A(\theta)R_{\text{x}}) \text{tr}(A^{H}(\theta)A(\theta)R_{\text{x}})-|\text{tr}(A^{H}(\theta)A( \theta)R_{\text{x}})|^{2}}, \tag{2}\] \begin{table}
\begin{tabular}{c c} \hline
**Institutions** & **Related Work** \\ \hline ITU & ITU considers ISAC as an emerging technology trend for the future [11]. \\ \hline Hexa-X & Hexa-X considers ISAC as one of the main architectures of 6G and emphasizes its role in sensing services [12]. \\ \hline IEEE & In IEEE 802.11 bf, it focuses on enhancing wireless local area network sensing [13]. \\ \hline
3 GPP & 3 GPP summarized and proposed the future use cases and service requirements of ISAC [14]. \\ \hline \end{tabular}
\end{table} 
Table 1: The work of institutes participating in ISAC research. where \(L\) represents the length of frame, \(\sigma_{R}^{2}\) is the variance of Gaussian noise, \(\theta\) is the azimuth angle of the target relative to the BS, \(\alpha\) is the reflection coefficient, \(R_{X}\) denotes the sample covariance matrix of \(X\), and \(\dot{A}(\theta)=\frac{\partial A(\theta)}{\partial\theta}\). (3) SCNR  
Signal-to-clutter-noise ratio (SCNR) represents the ratio of radar sensing signal to clutter plus noise signal, which can effectively measure the quality of radar signal in an ISAC system. In [25], the problem of maximizing the sensing SCNR was formulated to optimize the performance of the system. SCNR can be expressed as  
\[\omega^{*}=arg\max\frac{|\omega^{H}A(\theta_{0})x|^{2}}{\omega^{H}(R_{c}+I) \omega}, \tag{3}\]  
where \(\omega\) denotes the received beamforming vector, \(R_{c}\) is a corresponding covariance matrix, \(\theta_{0}\) is the location of radar target, \(x\in\mathcal{C}^{1\times N_{i}}\) is composed of the data signal for all users, and \(A\) is a matrix representing the product of the transmit and receive array steering vectors. (4) SINR  
Signal-to-interference-plus-noise ratio (SINR) is a crucial performance metric that measures the quality of the received signal. It can effectively measure the quality of communication signal in an ISAC system. In [26], it is used as a condition to constrain the optimal solution of the target function. SINR can be mathematically expressed as  
\[\text{SINR}=\frac{P_{s}}{P_{i}+P_{n}}, \tag{4}\]  
where \(P_{s}\), \(P_{i}\), and \(P_{n}\) denote the power of signals, interference, and noise. (5) Achievable rate  
The achievable rate refers to the transmission throughput that can be realized under the given communication channel conditions and is an important indicator for communication performance evaluation.