## 3 Near-Space Passive Radar Remote Sensing
### Power Budget Analysis  
Using opportunistic illuminator, particularly GPS satellite as the transmitter for near-space passive radar imaging brings a problem of signal detection because the received signal will be very weak. Thus, power budget analysis is necessary. The power of the target reflection available at the near-space receiver antenna is determined by  
\[P_{r}=\frac{P_{t}G_{t}}{4\pi R_{t}^{2}}\cdot\frac{\sigma_{0}}{4\pi R_{r}^{2}} \cdot\frac{\lambda^{2}G_{r}}{4\pi} \tag{1}\]  
where \(P_{t}\) is the transmit power, \(G_{t}\) is the transmit antenna gain, \(R_{t}\) is the transmitter-to-target distance, \(R_{r}\) is the target-to-receiver distance, \(\sigma_{0}\) is the target RCS per unit area, \(\lambda\) is the wavelength and \(G_{r}\) is the receive antenna gain, respectively. In radar imaging applications, the total data samples are processed coherently to produce a single image resolution cell. The thermal noise samples can be taken as independent from sample to sample within each pulse, and from pulse to pulse.  
After coherent range and azimuth compression, the image signal-to-noise ratio (SNR) can be represented by [23]  
\[SNR_{image}=\frac{P_{t}G_{t}}{4\pi R_{t}^{2}}\cdot\frac{A_{r}\sigma_{0}}{4\pi R _{r}^{2}}\cdot\frac{1}{KT_{0}\beta F_{n}}\cdot\frac{\tau_{i}}{\tau_{0}}\cdot \frac{PRF\cdot R\cdot\lambda}{v_{a}\cdot\rho_{a}}\cdot\eta \tag{2}\]  
where \(PRF\) is the pulsed repeated frequency (PRF), \(A_{r}\) is the antenna area, \(R_{s}\) is the distance from the moving carrier that provides the synthetic aperture to the target, the power flux density near the Earth's surface produced by GPS satellite is assumed to be \((P_{t}G_{t})/(4\pi R_{t}^{2})=\Pi_{0}\approx 3\times 10^{-14}Wt/m^{2}\)[43]. The ratio of the compressed signal duration \(\tau_{0}\) and uncompressed signal duration \(\tau_{i}\) is equivalent to the SNR gain after range compression, which is the correlation between the reflected signal and reference signal. \((PRF\cdot R_{s}\cdot\lambda)/(v_{a}\cdot\rho_{a})\) is the processing gain during the time of the aperture synthesis with \(PRF\), \(v_{a}\) and \(\rho_{a}\) are the pulse repeated frequency, relative velocity and azimuth resolution cell, respectively. Assuming the receiver bandwidth and transmitting signal bandwidth are matched and \(\eta=0.5\), then there is \(\beta\tau_{0}\approx 1\). The receiver noise coefficient \(F_{n}\) is considered to be \(2 dB\). Additionally, \(K\) and \(T_{0}\) denote the Boltzmann constant, and system noise temperature, respectively.  
As the potential azimuth resolution can be rewritten as  
\[\rho_{a}=\frac{\lambda R_{s}}{v_{a}T_{s}} \tag{3}\]  
where \(T_{s}\) is the integration time, we can get [54]  
\[SNR_{image}=\frac{\Pi_{0}A_{r}\lambda\eta}{4\pi F_{n}KT_{0}\rho_{a}}\frac{ \sigma_{0}}{R_{s}v_{a}} \tag{4}\]  
A quantity directly related to radar imaging performance is noise equivalent sigma zero (NESZ), which is the mean RCS necessary to produce a \(SNR_{image}\) of unity. NESZ can be interpreted as the smallest target cross section which is detectable by the SAR system against thermal noise. Setting \(SNR_{image}=1\) Equation (4) gives  
\[NESZ=\frac{4\pi F_{n}KT_{0}\rho_{a}R_{s}v_{a}}{\Pi_{0}A_{r}\lambda\eta}. \tag{5}\]In a like manner as [43], assuming a typical system with the following parameters: \(\sigma_{0}=20^{2}\), \(T_{s}=1,000s\), \(T_{0}=300\), \(\eta=0.5\), and \(F_{n}=2 dB\), the calculated SNR can be illustrated as in Figure 5. Here the SNR is favorable owing to an essentially long integration time. Although this SNR can be further improved by using non-coherent integration of the signals from more than one receiver channel, weak signal detection and processing is a technical challenge for near-space passive radars.