# Exploring ISAC: Information-Theoretic Insights
## 2 Pre-ISAC: Sensing (Radar) vs. Communication
### Coexisting Communication and Radar Systems  
Early approaches [76] modulated the communication bits on a missile range radar pulse interval. Interference rejection and robustness in multipath fading environments, inherent properties of spread spectrum systems, also made chirp signaling (used in the radar application) very active in the expanding wireless communications market. Another approach in [77] proposed as early as 1962 is based on chirp signals, which were originally proposed for both analog and digital communication [78] but are also commonly used in radar applications. These works can be categorized as the first steps towards _untegrated sensing and communication (ISAC)_. \begin{table}
\begin{tabular}{c c} \hline \hline
**Communication** & **Sensing** \\ \hline
2.4 GHz & 24–79 GHz \\ \hline Data/Source Transmission & Estimation/Detection \\ \hline Bit/Signal/Frame Error Rate & Minimum Mean Squared Error (MMSE), \\  & Cramer–Rao Bound (CRB) \\ \hline Distortion & Detection/False Alarm Probability \\ \hline All Propagation Paths & Line of Sight (LoS) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between Communication and Sensing Systems. Since then, significant evolution has lead to an entire set of pre-ISAC systems, see [32] where a category of solutions is revisited. Some straightforward solutions are called _non-overlapped resource allocation_. In subsequent information-theoretic models, as we will see later, such a system corresponds to time- or resource-sharing between communication and sensing; we shall call this _basic time-sharing (TS)_, and with a minor modification, we will introduce _improved time-sharing_. A common but naive approach to address sensing and communication is to separate the two tasks into independent systems and split the available resources, such as bandwidth and power, between them so that they do not interfere. Time-division ISAC can be conveniently implemented into existing commercial systems by splitting the transmission duration into radar and radio cycles, for example [79]. For radar sensing, frequency-modulated continuous waveform (FMCW) with up-and-down-chirp modulations is used, while various different modulation schemes (e.g., BPSK, PPM) can be used for communication. In an orthogonal frequency division multiplexing (OFDM) system, frequency-division ISAC can be implemented by allocating different communication and sensing tasks to specific subcarriers, depending on the channel conditions and power budget of the Tx [80]. Similarly, the 3 GPP/5G-NR standards were originally designed primarily for communication but have evolved to accommodate additional functionalities, such as positioning and sensing. The 5G-NR standard primarily uses OFDM due to its flexibility and efficiency, and its inherent structure can also be exploited for sensing tasks such as radar-like functions and localization. In practice, enhancements (e.g., pilot designs and advanced signal processing techniques) are introduced to extract sensing information from these communication signals. Meanwhile, orthogonal time frequency space (OTFS) modulation [81; 82] has attracted increasing interest as an alternative to OFDM, placing symbols in the delay-Doppler domain to handle high-mobility channels more robustly. By directly leveraging delay and Doppler features, OTFS can inherently support sensing-like operations, making it appealing for ISAC in future releases of 5G and beyond. In information-theoretic studies, these models are often incorporated into resource-splitting approaches. The ideal goal of ISAC is to further serve both tasks, as discussed in this work. For details on the evolution of 3 GPP, see [83]. ISAC with non-overlapped resources can also be implemented over orthogonal spatial resources, e.g., different antenna groups [84].