## 3 Signal-to-Noise Ratio (SNR) and Noise-Equivalent Sigma Zero (NESZ)  
SNR is a measure of the signal strength relative to the background noise. In the context of SAR, it is the ratio of the power of the reflected radar signal (signal) to the power of the noise signal (noise) at the receiver. A higher SNR usually translates to better image quality. This is because a stronger signal relative to noise enables clearer and more distinguishable features in the SAR imagery. In SAR, detecting various features or targets on the Earth's surface is crucial. A good SNR ensures that these features are not lost in the noise, making detection more accurate and reliable. A higher SNR can contribute to better resolution and accuracy in SAR images. It helps in distinguishing between closely spaced targets and in providing detailed surface information. NESZ is the metric that quantifies the minimum radar cross-section (\(\sigma\)0) of a target that can be detected by a SAR system with an SNR of 1. It represents the radar cross-section value at which the signal power from the target equals the noise power in the system. NESZ is a parameter in SAR system design, as it indicates the system's sensitivity and its ability to detect weak radar reflections. In practice, NESZ is used to assess the noise performance of the SAR system and helps to determine the system's ability to detect and distinguish radar reflections from various targets, especially in challenging or noisy environments. By calculating NESZ, system designers can ensure that the SAR system meets minimum sensitivity requirements for its intended applications. Calculating NESZ for SNR = 1 is a standard approach and provides a baseline reference for system performance. If NESZ is lower, it means that the system can detect even smaller radar cross-sections, which is favorable. If NESZ is higher, it indicates that the system's sensitivity is lower, and it may struggle to detect smaller targets. NESZ is a fundamental parameter for optimizing SAR system design and ensuring its capability to fulfill mission objectives. The references used in explaining the effect of SNR and NESZ are [33; 37; 38; 45; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64]. NESZ and SNR are two metrics used in the design of space-based SAR systems, each playing a distinct role depending on the mission's specific goals, the design stage of theSAR system, and the aspects under analysis. While both NESZ and SNR are essential in SAR system design, they serve different purposes and are emphasized at different stages of the system's development. NESZ is predominantly utilized during the early design and system specification phase. It is instrumental in determining the system's sensitivity, enabling the detection and differentiation of radar reflections from diverse targets. NESZ is centered around the noise performance of the system, critical for assessing the minimum detectable target signal against noise. This parameter incorporates factors like antenna area, bandwidth, PRF resolution, and system losses, thereby shaping the fundamental design of the SAR system. Conversely, SNR is pivotal in assessing the quality of radar images, particularly during the image formation and interpretation phase. SNR quantifies the strength of the signal relative to the background noise and is indispensable for evaluating image quality, enhancing target detection, and distinguishing fine details. It involves considering the power of the received signal in comparison to the noise power inherent in the radar data. The emphasis on NESZ or SNR varies according to specific objectives and the developmental phase of the SAR system. In the initial design and specification phase, a focus on NESZ is critical. It helps to determine whether the system can meet minimum sensitivity requirements and sets fundamental parameters to ensure effective operation in the intended environment. As the system development progresses towards image processing and data analysis, the importance of SNR grows.