Radar itself is an abbreviation for RAdio Detection and Ranging. Radar systems send out modulated waveforms using antennas in order to transmit electromagnetic energy into a specific volume of space to search for targets. Objects (i.e. targets) within a certain volume will reflect part of the energy (radar returns or echoes) back to the radar. From these radar returns, the radar reciever then extracts information such as velocity and range, angular position, and other identifying characteristics.
Assumptions made in poject for radar
In our project, we decided to keep the level of complexity of how rader is utilized down to a manageable level for a group size of two. As a result we made the following assumptions in our approach to modeling radar inside of Matlab.
The target is in direct line with our transmitted wave (i.e. not at an angle)
For velocity processing, the target has a constant velocity
For range processing, the target is not moving
We will now examine the concept of one of the most commonly used signals to do radar processing, the Linear Frequency Modulated Chirp (LFM Chirp) and its characteristics. Following that, the important concept of match filtering is discussed since it is implemented for calculating the range of a target.
Linear frequency modulated chirp (lfm chirp)
Basic definition (in continuous time)
A linear frequency modulated chirp signal for radar is defined by the equation (1)
Lfm continuous-time chirp
t = time on the range of [-T/2,T/2],
T =time duration in seconds of LFM signal pulse,
W = swept bandwitdth over the life of the pulse in Hz
Characteristics
The changing frequency of the chirp signal sweeps from (-1/2)W to +(1/2)W Hz. It is interesting to note that the phase of s(t) varies quadratically versus t while the frequency changes linearly versus time. The deriviative of phase determines the instantaneous frequency of the signal. The signal is complex valued in this case because it is the baseband form of the linear frequency modulation.
See Figure(1.1 ) below for example.
Characteristics of spectrum
Thus, it would seem like the frequency spectrum S(f) would have most of its energy in the range of | f |<(W/2). However, this is in fact only true if the frequency sweeps slowly enough or if T is large enough.
Modeling chirp with matlab
In Matlab however, the chirp signal has to be represented as a discrete time signal. A solution to this problem is to just oversample s(t) enough so that we can effectively simulate the continuous time version. Otherwise, if we just wanted to have a discrete time signal, the sampling frequency would be kept approximately equal to the swept bandwidth W. But, we will need to oversample by at least a factor of 5 at least in order to properly simulate the continous time signal.
Figure(1.1) continuous-time lfm chirp radar signal
Continuous-time LFM chirp radar signal
Since the chirp signal is compex valued and will be processed through a complex valued matched filter, all plots must be made of either the real part of equations (1), (2), or of the magnitude of the Fourier transform below. Figure 1.1 is a plot of the real part of the LFM chirp.
