## 1 Introduction  
### Preliminaries  
In the realm of modern technology, radar and communication stand as two pivotal pillars of innovation and progress. Radar, a sophisticated system rooted in electromagnetic waves, plays a crucial role in detecting, tracking, and identifying objects in our physical environment. Whether it is guiding aircraft safely through the skies, enabling weather forecasting, or aiding in military operations, radar's multifaceted applications have revolutionized various industries [1]. On the other hand, communication, the art of transmitting information, has undergone a remarkable transformation in recent years. From the advent of the internet to the widespread adoption of smartphones, the evolution of communication methods has significantly impacted how we interact, collaborate, and share information on a global scale [2]. Communication and radar systems share some common principles while exhibiting distinct differences. Both systems involve transmitting and receiving signals, relying on electromagnetic waves. They employ transmitters to send out signals and receivers to capture and process them. However, the primary purpose of a communication system is to convey information or data from a sender to a specific recipient. In contrast, the primary purpose of radars is to detect and track objects, such as aircraft, ships, or weather patterns. Radar systems emit signals and measure the time it takes for the signals to bounce back, enabling the determination of an object's location, speed, and direction. In contrast, communication systems focus on delivering a message or information reliably, often with error correction mechanisms in place. Despite their distinct core objectives, communication and radar systems have the potential for a shared architecture. This unique commonality lies in the design of their transmitters, which can be configured to generate a single signal capable of serving both communication and radar purposes. This dual-function capability underscores the versatility and efficiency achieved through a well-designed transmitter, offering the potential for applications that seamlessly integrate communication and radar functionalities within the same system. As technology advances, the radio frequency front-end architectures of radar and wireless communication systems increasingly resemble each other [3; 4]. This structural similarity allows communication systems to benefit from the advanced hardware of radar systems and vice versa. This paper proposes an ISAC system based on direct sequence spread spectrum (DSSS) technology. Integrating communication and sensing in DSSS-based systems primarily enhances spectral efficiency, improves sensing accuracy and communication reliability, and reduces hardware complexity [5]. These gains can be summarized as follows:  
* By using the same DSSS signal for both communication and sensing, the system can achieve better spectral efficiency. This integration avoids the need for separate frequency bands for communication and radar sensing, leading to more effective use of the available spectrum. * Since both communication and sensing functions use the same transceiver hardware, there is a reduction in hardware complexity and cost. The shared use of DSSS signals simplifies the design, leading to a more compact and energy-efficient system. * DSSS has inherent properties that enhance both communication and sensing performance. For communication, the spreading gain of DSSS improves the signal-to-noise ratio (SNR) and provides robustness against jamming and interference, which is advantageous for reliable communication. Meanwhile, the same spreading gain can enhance the resolution and accuracy in sensing tasks using radars. In any event, to realize an ISAC system, several hypotheses or assumptions are typically required.