# An Efficient Dynamic Engineering Implementation Architecture for MIMO Radar System
## 2 MIMO FMCW Radar Principle and System Analysis  
### Fundamentals of FMCW Radar  
FMCW radar has become the most widely used system in MIMO radar applications due to its ability to simultaneously measure target distance and velocity, its high resolution and measurement accuracy, and its relatively simple and cost-effective hardware implementation with high energy efficiency. Moreover, the continuous wave signal characteristics of FMCW radar align seamlessly with the multi-channel transmission and reception framework of MIMO technology, enabling significant improvements in spatial resolution and multi-target detection capabilities. Accordingly, this paper introduces the fundamental principles of radar using FMCW as a representative example. The following sections provide a detailed explanation of the working principles of FMCW radar, including the methodologies for measuring target distance, velocity, and angle. FMCW radars acquire target information by transmitting FMCW signals and capturing the reflected signals from the target. The radar system exhibits a time delay, denoted as \(\tau\), between the transmitted and received signals, and this delay represents the time required for the signal to propagate between the radar and the target. In the radar system, the mixer combines the received signal with the contemporaneously transmitted signal to generate an intermediate frequency (IF) signal, commonly called a beat frequency signal [14]. The frequency of this beat frequency signal serves as a basis for calculating the distance between the radar and the target. The correlation between the distance to the target and the IF signal can be mathematically represented as follows:  
\[R=\frac{cf_{b}T_{c}}{2B}, \tag{1}\]  
where \(R\) denotes the distance between the radar and the target, \(c\) is the speed of light, \(T_{c}\) represents the chirp cycle, \(B\) refers to the bandwidth, and \(f_{b}\) signifies the frequency of the beat frequency signal. To measure the velocity of a target, the radar system must transmit at least two chirp pulses separated by a time interval \(T_{c}\)[15; 16]. Given that the signal frequency substantially exceeds the bandwidth, the phase change \(\Delta\phi\) induced by the target velocity can be articulated as  
\[\Delta\phi=2\pi f_{0}t=\frac{4\pi f_{0}\Delta R}{c}=\frac{4\pi vT_{c}}{\lambda}, \tag{2}\]where \(\lambda\) represents the wavelength of the signal, and \(v\) is the velocity of the target. The relationship between the phase difference and the Doppler shift within the chirp period \(T_{c}\) is formulated as  
\[\Delta\varphi=2\pi f_{d}T_{c}, \tag{3}\]  
where \(f_{d}\) corresponds to the Doppler shift resulting from the target velocity \(v\). The relationship between the velocity and the Doppler shift is described by  
\[f_{d}=\frac{2v}{\lambda}, \tag{4}\]  
To estimate the azimuth of a target, the radar system must be equipped with at least two receiving antennas [17]. It is assumed that these antennas are uniformly spaced, with a separation distance \(d\) between neighboring antennas, and that the angle between the target and the radar is \(\theta\). Geometrically, the difference in the propagation distance of the signal between the receiving antennas is \(d\sin(\theta)\), resulting in a phase difference \(\Delta\omega\) between the signals received at neighboring antennas, expressed as  
\[\Delta\omega=\frac{2\pi}{\lambda}d\sin(\theta), \tag{5}\]  
Therefore, the angle of arrival \(\theta\) of the target can be calculated using the following formula [18]:  
\[\theta=\arcsin\biggl{(}\frac{\Delta\omega\lambda}{2\pi d}\biggr{)}, \tag{6}\]  
In practical applications, critical parameters such as the beat signal frequency \(f_{b}\), Doppler shift \(f_{d}\), and phase difference \(\Delta\omega\) can be accurately extracted through the implementation of the FFT and signal detection techniques. Angular resolution is the ability of a radar system to distinguish between two targets with the same distance and velocity but different azimuths [19].