Abstract time t that is needed by the
Posted On May 18, 2019
Radar is an electromagnetic system that is used for detecting locations and distances of objects. The most common digital signal processing technique that is used by radar is Pulse compression technique, for increasing the range resolution and the signal to noise ratio (SNR). Pulse compression lets us to attain the large transmitted power of a long pulse while attaining the range resolution consistent in a short pulse. This can be achieved by modulation of the transmitted pulse in the transmitter and matching the received signal with the transmitted pulse in the receiver. For the pulse compression, matched filter is used. The impulse response of the matched filter is determined by a known signal, so that when the signal that is accompanied by white noise is passed through the filter, it will be able to attain the maximum signal to noise ratio (SNR) at the output. Several methods for pulse compression exist, Linear Frequency Modulation (LFM) or chirp signal is the most popular technique. In this paper, the application of pulse compression radar for object detection in military radar is discussed, and developing and simulating pulse compression and matched filter algorithm in MATLAB is proposed to study the pulse compression technique for a chirp (LFM) signal.
1.1 implementation of matched filter in pulse compression radar
The word RADAR is came from Radio Detection and Ranging. It is mainly an electromagnetic system used for discovering positions and distances of objects from the place where the RADAR is placed by using radio signals. Radar radiates energy to the space and monitors the reflected echo from the objects. It operates in the first range of microwave spectrum which is ultra-high frequency range. We can denote the space between the object and the radar as (R). The time t that is needed by the signal to travel from the radar to reach the object and then back to the radar is:
… … … … 1
(c) represents the speed of light. (Athley, 2003)
Equation (1) gives only information about the range of the object. According to the theories of antenna the antenna size D and the carrier wavelength are both affecting the 3dB beam width of the antenna
… … … … 2
the antenna has a pointing direction which gives us the direction of the object. Augmenting the antenna dimensions results in increasing the accuracy of the direction estimation.
Figure 1: typical radar system
The radar transmission equation is :
… … … … 3
Where the received power at the receiving antenna, represents the power transmitted by antenna, G represents the gain of the antenna because in many cases both the transmitter antenna and the receiver antenna the same, and represents radar cross section .
The radar range equation is:
… … … … 4
Radar has applications in five areas which are:
· Military applications: for air and marine navigation, detection and tracking of objects and aircrafts, weapon fuses, missile guidance, fire control for missiles and artillery, and reconnaissance.
· Air traffic applications: it is used in the airports for the purpose of air traffic, for guiding the aircraft to land in bad weather, and for scanning the surface of the airport.
· Remote Sensing applications: radar is used for the weather observations, and for detecting ice in the sea for safe routing of ships.
· Ground Traffic Control applications: radar is used for determining the speed of the vehicles by traffic police.
· Space: To guide the space vehicle, to observe the planetary systems, and for detecting and tracking satellites. (Agarwal, 2006.)
For these applications of radar; bigger ranges of detection, higher resolution ranges, righter visibility in clutter, and better reliability are the requirements for modern radar systems. All these requirements are fulfilled by using pulse compression technique.
Pulse compression is concerned with transmitting a long coded pulse and the process of compressing the received signal to get a narrow pulse. Pulse compression lets us to attain the large transmitted power of a long pulse while attaining the range resolution consistent in a short pulse. Short pulses have better range resolutions. The problem is that short pulses require higher peak power. When the pulse becomes shorter, more energy is required for packing the pulse by increasing the peak power. This high power requirement makes the system design complicated because the system components that are used in the entire system must be able to tolerate this peak power. The way for fixing this problem is by converting the short duration pulse into a longer pulse. When the pulse length is increased, the pulse’s peak power will decrease, and this will lead to decreasing in the range resolution. To preserve the range resolution; modulation is to be incorporated for increasing the transmitted pulse’s bandwidth.
This technique that is used is the pulse compression technique, it is widely used in Radar applications that the high peak powers are undesirable.(Farnett & Stevens, 2009)
Pulse compression radar makes the use of signal processing technique to provide the most of the advantage of narrow pulse width whilst remaining with the peak power limitation of the transmitter.
Pulse-compression radar is a practice implementation of a matched-filter system.
The matched filter is an LTI system linear time invariant system that maximizes the signal to noise ratio (SNR) in the attendants of noise.
The reasons for using matched filter are that by increasing SNR the probability of detection increases. For a deterministic signal in white Gaussian noise, by using a filter whose transfer function is matched to the signal, the SNR can be increased at the receiver. The matched filter is a conjugated and time-reversed version of the signal.
The generated signal can be represented as a frequency response H(?) or it can be represented as an impulse time response h(t) of a generating filter. Figure ( 1 ) shows pulse compression radar using filters that are conjugate to each other. After the generation of the coding signal by stimulating the coding filter with unit impulse, the transmitter sends the generated signal. At the receiver, the signal that is received will be the input of the matched filter, the frequency response of the matched filter is the coding filter’s complex conjugate H*(?). The compressed pulse will be the output of the matched-filter, the compressed pulse is the which is the inverse Fourier transform of the product of the signal spectrum H(?) and the matched-filter response H*(?):
… … … … 5
Figure 2: pulse compression radar using conjugate filters
The implementation of Figure (2) is by using filters that are conjugates of each other, which are the expansion filter and the compression filter.(Farnett & Stevens, 2009.)
Another way for matching the filter to a signal is that the signal must be the complex conjugate of the time inverse of the impulse response of the filter. This can be achieved by applying the time-inverse of the signal that is received to the matched filter, as shown in Figure (3). The filters that is used for the expansion can be the same as the filter that is used for the compression, or one filter can be used for the expansion and for the compression but appropriate switching must be done between the transmitting and the receiving functions. The matched filter output will be is the convolution process between the signal h(t) and the matched filter impulse response’s conjugate h*(- t):
… … … … 6
Figure 3 : pulse compression radar using time inversion
Matched filtering can also be achieved by a correlation process between the received signal and the transmitted signal. for covering the whole range interval of interest, multiple delays and correlators must be used. (Farnett & Stevens, 2009)
Figure 4: pulse compression radar using correlation
The compressed pulse which is the matched filter’s output is with some responses at other ranges, which are side lobes. For decreasing these side lobes we must employ frequency weighting for the output signal.
The pulse compression system’ choice is depending on the waveform type that was selected and both the generation and processing methods. The reasons for choosing a particular waveform are generally the radar demands of range coverage, side lobe levels of range and Doppler, Doppler coverage, interference refusal, waveform elasticity, and SNR. Implementation methods are categorized to two classes, active and passive. Active generation involves in phase and frequency modulation of the carrier without time expansion, but passive generation is involved in time expansion SAW surface-acoustic-wave is an example of passive generation. Active processing is the correlation process by mixing delayed replicas of the receiving signal and the transmitting signals. Passive processing is concerned with using filters for expansion and compression that are conjugate version of each other. Most systems employ the same type of generation and processing. If the generation is active the processing is active too.
Different methods, different coding techniques are used for pulse compression including binary phase coding, frequency modulation, poly phase coding, and frequency stepping. The most popular method is the one which was invented by R.H. Dickie and is called linear frequency modulation (LFM) or chirp waveform.
In this paper, by using the MATLAB tool we are designing to implement the matched filter algorithm for pulse compression radar which uses LFM for detecting an object in military applications.