# Exploring ISAC: Information-Theoretic Insights
## 2 Pre-ISAC: Sensing (Radar) vs. Communication  
### Radar Systems  
Radar is a system that utilizes radio waves to learn about positions, motions, or the mere presence of target objects in an environment through the analysis of backscattered signals. In fact, a radar terminal radiates a waveform that propagates through space until it reaches a target, where it is reflected in a way that depends on the properties of the target. The radar terminal collects and analyzes the backscattered signals so as to gain information about these properties. In the radar system, if the presence and position of a target are already known, the transmitter tries to steer all the energy of the transmitted waveform towards the target, so as to obtain more information through the backscattered waveform. Radar thus uses line-of-sight (LoS) techniques. Traditional radar systems mainly operate within the 24-79 GHz frequency band. Sensing tasks can be roughly classified into three categories, detection, estimation, and recognition, which are all based on collecting signals/data concerning the sensed objects. Detection refers to making decisions on an object's _state_ given some observations, such as the presence/absence of the target or other events related to the target. The detection problem can be modeled as a binary or multi-hypothesis testing problem. In the binary hypothesis testing problem, as an example, one selects from two hypotheses: the alternative hypothesis \begin{table}
\begin{tabular}{l l l} \hline \hline
**Category** & **Result Description** & **Reference(s)** \\ \hline \multirow{8}{*}{Sensing as Monostatic Radar} & Lemma 1: Optimal estimator for P2P and BC & [56] \\ \cline{2-3}  & Theorem 1: Exact Capacity–Distortion for Memoryless P2P, & [56] \\ \cline{2-3}  & asymptotic analysis & [57] \\ \cline{2-3}  & Strong converse Remark 1 & [58] \\ \cline{2-3}  & Log-Loss Distortion Theorem 2 & [59] \\ \cline{2-3}  & Nonasymptotic P2P, Theorem 3 & [59] \\ \cline{2-3}  & Channel with memory, RL approach Theorem 3 & [60] \\ \hline \multirow{4}{*}{Sensing as Bi-Static Radar (P2P)} & C-D with No CSI at Tx Theorem 4 & [21] \\ \cline{2-3}  & C-D with Strictly Causal CSI at Tx Theorem 5 & [61] \\ \cline{2-3}  & C-D Non-Causal CSI, Gaussian Channel at Tx Theorem 6 & [62] \\ \hline \multirow{4}{*}{Network-ISAC} & General BC Outer Theorem 7 and inner Proposition 1 bounds & [63; 64] \\ \cline{2-3}  & Optimal symbolwise estimator & – \\ \cline{2-3}  & Outerbounds for MAC Theorem 8 & [65; 66] \\ \cline{2-3}  & Innerbound MAC Theorem 9 & [65; 66; 67; 68] \\ \cline{2-3}  & Innerbound D2D Theorem 10 & [68] \\ \hline \multirow{3}{*}{Secrecy-ISAC} & Secrecy–Capacity–Distortion Inner Theorem 11 and Outer Theorem 12 Bounds & [69] \\ \cline{2-3}  & Secrecy of the Message and the State Theorem 13 & [70] \\ \hline \multirow{4}{*}{ISAC Exponents} & Non-adaptive Rate–Detection-Exponent Theorem 14 & [57; 71; 72; 73; 74] \\ \cline{2-3}  & Adaptive Rate–Detection-Exponent Theorem 15 & [73] \\ \cline{2-3}  & Sequential (Variable Length) Rate–Detection-Exponent Theorem 16 & [73] \\ \cline{2-3}  & Sequential (Variable Length) ISAC with Change Point & [75] \\ \cline{2-3}  & Detection Theorem 17 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A Comprehensive Overview of this Survey. \(\mathcal{H}_{1}\) and the null hypothesis \(\mathcal{H}_{0}\). Detection metrics are the probability that \(\mathcal{H}_{1}\) holds but the detector chooses \(\mathcal{H}_{0}\) (often denoted miss-detection probability), and the probability that \(\mathcal{H}_{0}\) holds but the detector chooses \(\mathcal{H}_{1}\) (often denoted false-alarm probability). Estimation refers to extracting valuable parameters, typically with continuous alphabets, of the sensed object from observations. For example, distance/velocity/angle/quantity/size of targets are possible parameters that a radar system desires to estimate. Various interesting performance metrics exist for estimation, whose suitability depends on the application.