[1] processing, as we have seen throughout

 

 

 

 

 

 

1 F. Athley. Space-Time Parameter Estimation in Radar Array
Processing.PhD thesis, Chalmers University of Technology, Department of Signals
and Systems, G¨oteborg, Sweden, 2003.

References

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In this paper the concept of pulse compression was presented using
the linear FM (or chirp) pulse modulation. In this method, the received echo
signal is compared to matched filter impulse by correlation. The compressed
pulse width of the received pulse provides advantages in range as well as
resolution. The selection of signal processing techniques according to the
radar performance requirements is one of the most important step in military
radar design. Signal processing, as we have seen throughout this paper,
provides figures that tactical leaders take into account when looking for
performances and capabilities. Nowadays, digital processing allows fast and
efficient computation. The basic example is the use of FFT and IFFT to perform
time-convolution (filtering).Here by using the Matlab tool we are designing to
implement the matched filter algorithm for pulse compression radar which uses
LFM. In this paper, the moving target path is identified to check whether it is
following the predetermined path or not. As an extension of this we can
implement it in hardware.

Conclusion

 

Table 1:
specifications of simulation

                                   

parameters

Pulse
width,  T

60

Bandwidth,    BW

5MHz

Center
frequency,    fc

20KHz

Sampling
frequency,    f

10MHz

 (b) Output of pulse
compression filter

Fig 8: (a) The received echo signal

                                                            
(b) Output of pulse compression filter

Fig 7: (a) The received stationary target
echo signal

 In the receiver section the path followed is
traced by analyzing the result gained from the graphical model. The strength of
the Signal decreases as the range increases. So the amplitude decrease
corresponds to that.

 

(b) Frequency response of the transmitted LFM signal.

Fig 6: (a) LFM signal transmitted

The experimental results are the given below in graphical model.
Here in the graph the pulse compression filter is used for the compression of
pulse. Pulse-compression radar is the practical implementation of a
matched-filter system.

Simulation results

 

 

In
radar signal theory, the matched filter output is affected by the Doppler
Effect. The apriori unknown frequency shift introduced by the Doppler effect
can also be seen in the time domain as an additional def, say tD. Therefore,
since both target range and target Doppler shift are unknown to the system, a
bank of matched filters is used to determine the overall delay. Doppler
filtering output, i.e. a frequency shift, helps to best estimate the target
range by subtracting the delay tD to the total delay.

Where
z(t) represents the noise-free output from the matched filter and w(t)
represents the filtered noise. Note that since the transmitted signal spans a
wide frequency range, the matched filter cuts out some signal as well as some
background noise since it has a limited bandwidth.7

 

 

 

The
output of the matched-filter is expressed as the convolution in the time domain
of the received signal with the matched-filter impulse response:

 

20

 

The
impulse response of the matched filter is simply the image of the received
signal; that is, it is the same as the received signal but run backward in time
starting from instant t0.However, since the noise n(t) is an unknown signal,
the filter is matched to the transmitted signal x(t):

 

That        

(White
noise). It does not need to be Gaussian. In the time domain, using inverse
Fourier transform, the matched filter impulse response can be expressed as
follow using the fact

The
noise that accompanies the signal is assumed to be stationary and to have a
uniform spectrum

 


Ga: filter gain (generally set to unity)


t0: fixed value of time at which the signal is oberved to be maximum (equals
the round trip delay of the transmitted signal)


Y(f) is the Fourier transform of y(t):

where:

 

  …………….19

 

peak-signal-to-mean-noise (power) ratio for a given input
signal-to-noise ratio is given by:

The frequency response function of the linear, time-in variant
filter which maximize the output

18

the transmitted antenna to the target and back to the antenna. In
order to maximize the signal-to noise ratio at the receiving stage, the matched
filter is the optimal solution Here we give a summarized overview. For a
received signal y(t) which is a time-shifted (delayed) replica of the transmitted
signal with additive noise n(t)

The above diagram represents the block diagram of Matched Filter.
As any signal transmitted over the air, the chirp signal encounters noise in
its two way trip from

                                            
Fig 5: block diagram of matched filter

 

 

 

 

 

 

 

       Input signal                                                                        
                            Matched filter output                   

 

 Matched filtering is a process for detecting a known piece of
signal that is corrupted by noise. A correlation operation at indicates the
presence of a received echo at the radar receiver by compressing the received
signal in time using its time-correlation properties. Matched Filter performs
the correlation operation. Correlation of signals in time domain, the
well-known DSP technique has been a popular method to implement a pulsed
matched filter in DSP. This can be achieved by performing multiplying their
frequency responses in frequency domain. The two time domain correlated signals
are to be transformed to frequency domain by applying Fourier Transforms. The
portion of the transformed signal with matching patterns will have identical
frequency domain signatures. When two frequency domain vectors are multiplied,
the product obtained will be a match which is independent of time alignment
between the two signals. The matched filter always responds for each target
reflected energy irrespective of the received radar signals. When converting
back the product vector to the time domain, each target will produce a narrow
pulse whose delay and amplitude correspond to target distance and size
respectively. The FFT converts time domain signals to frequency domain signals
and the inverse FFT (IFFT) performs the reverse conversion, these two
algorithms are key blocks in the pulse compression system. The Fig.5 shows
block diagram of matched filtering core.

Model of Matched Filter

 

=  ……………….17

Hence,
the transmitted pulse train signal, composed of Np pulses, is written as

 –   ………………. 16

In a
realistic scenario, it is necessary to consider a complex  signal as the noise is modeled as complex. It
affects both amplitude and phase.

   ,    …………………15

It is
possible to show that for  , the
envelope module is approximately constant within the considered bandwidth

 =        ………….. 14

Integrals
C(x) and S(x) are called Fresnel integrals. Using the fact that the signal is
composed of successive pulses transmitted every TR=1/FR, the signal spectrum is
a discontinuous spectrum composed of regularly spaced narrow rays (every FR in
the frequency domain). The spectrum envelope module is given by

 ……………. 13

 

 …………….. 12

= ……………. 11

=  ……………….  10

Where

 

 =     ( (     ……………  9

After
calculations we obtain

 

 =   …………… 8

 = FT {

 

Fourier
Transform

Where is the carrier frequency of the transmitted
signal. Its spectrum is computed using the

=(+),    –      ………….  7

The chirp signal is a signal where the instantaneous frequency
linearly varies within the duration T of the transmitted pulse. We define the
phase variation rate in rad/s as ?=2f/T
and we build the signal x(t) as follow

 

Chirp
Signal: Mathematical Approach

 

Fig 5: pulse 
burst diagram

 

                

 

Where is
the pulse duration, Ppis the peak power. The duty cycle, defined as  ,
provides information on radar average operation, one thousand is a common value.

=  …………….. 6

This parameter is
involved in the calculation of the radar average transmitted power Pa

=  ………….. 5

With
a pulsed radar, the signal to be transmitted is composed with a train of
individual pulses, each pulse is shifted in time by TR seconds. The pulse
repetition frequency FR is defined as

                    

be passive or active. It can also be digital or
analog. An LFM signal (Fig 4.) is a frequency modulated
waveform in which carrier frequency varies linearly with time, over a specific
period.

Several techniques exist when it comes to
generate the transmitted signal. Signal generation can

 Generation of signal:

Methodology

 

 In this paper we are
discussing the application of pulse compression radar to track launch vehicles,
the stationary target as well as moving vehicle so as to check whether it had
followed the predetermined path or not. Here in this project, we propose to develop
and simulate pulse compression and matched filter algorithm in MATLAB to study
the LFM pulse compression  technique with
chirp diversity and the hardware implementation of the same in FPGA platform.

 

The aim of this paper is to design the implementation of matched
filter in pulse compression radar which uses LFM. Matched filter has a better
performance. In the de-chirping processing we can track the path followed by
the launch vehicle.

Objective

There are several methods of pulse compression linear FM, non-liner
FM, phase coded wave forms, and etc … (7) they have implemented pulse
compression using three different methods instead of a single frequency signal
in normal radar “Linear frequency modulation”, “Barker Codes” and “Compound
Barker Codes”.

(6) Describes
the implementation of a full-digital system for radar pulse
compression and the use of a high-speed FFT processor that allows the matched
filter to operate in the frequency domain at a throughput rate of some MHz .
Significant experimental results are reported, and compared with those yielded
by equivalent SAW compressors.

      Major advances are
continually being made in the devices used in pulse compression radars.
Significant advances are evident in the digital and SAW techniques.

And there are many other researches for different applications of
radar by using matched filter.

(2)also uses matched filter in pulse compression radar for
defferent application of radar which is tracking  launch vehicles, the stationary target as well
as moving vehicle so as to check whether it had followed the predetermined path
or not.  In this project, they
propose to develop and simulate pulse compression and matched filter algorithm
in MATLAB to study the LFM pulse compression technique with chirp diversity and
the hardware implementation of the same in FPGA platform.

Detecting a target in a noisy environment is a many folds
sequential process. The signal processing chain only provides to the overall
system boolean indicators stating the presence (or not) of targets inside the
coverage area. It is part of the strategical operation of the radar. The  paper mainly focuses on Design of Matched
filter and generation of chirp Signal.

(3)uses matched filter in military RADARS.

(1)Implemented cross correlation and  matched filter in radar to detect small
targets (like small icebergs) in an oceanic environment. These small targets
are difficult to detect for a marine radar system since they protrude only
about a meter or so above the sea surface level. Unfortunately these small
targets can cause severe damage to ships traveling in ice-ridden waters. Results
give the exact result even when the received signal is attenuated more than
90%.

The applications of matched filter in radar is a topic of great
interest over past few decades. A lot of research work has been carried out by
using matched filter for different applications of radar.

Literature review:

 Here by using the MATLAB
tool we are designing to implement the matched filter algorithm for pulse compression
radar which uses LFM

Different methods, different 
coding techniques are used for pulse compression including binary phase
coding, polyphase coding, frequency modulation, and frequency stepping.  The most popular method is linear frequency
modulation (LFM) or chirp waveform which was invented by R.H. Dickie.

Passive generation involves exciting a device or network with a
short pulse to produce a time-expanded coded waveform. An example is an
expansion network composed of a surface-acoustic wave (SAW) delay structure. Active processing
involves mixing delayed replicas of the transmitted signal with the received
signal and is a correlation-processing approach. Passive processing involves
the use of a compression network that is the conjugate of the expansion network
and is a matched-filtering approach. Most systems employ the same type for
generation and processing.

Active generation involves generating the waveform by phase or
frequency modulation of a carrier without the occurrence of an actual time
expansion.

The choice of a pulse compression system is dependent upon the type
of waveform selected and the method of generation and processing. The primary factors
influencing the selection of a particular waveform are usually the radar
requirements of range coverage, Doppler coverage, range and Doppler side lobe
levels, waveform flexibility, interference rejection, and signal-to-noise ratio
(SNR). The methods of implementation are divided into two general
classes, active and passive.

The output of the matched filter consists of the compressed pulse
accompanied by responses at other ranges, called time or range side lobes.
Frequency weighting of the output signal is usually employed to reduce these
side lobes.

 

Fig. 3 pulse
compression radar using correlation

The matched filter results in a correlation of the received signal
with the transmitted signal. Hence, correlation processing as shown in Fig.
10.Ic is equivalent to matched filtering. In practice, multiple delays and
correlators are used to cover the total range interval of interest.

 

Fig.2 pulse compression radar using time inversion

 ……………… 4

 A filter is also matched to
a signal if the signal is the complex conjugate of the time inverse of the
filter’s response to a unit impulse. This is achieved by applying the time
inverse of the received signal to the compression filter, as shown in Fig. 2.  Identical filters may be used for both
expansion and compression, or the same filter may be used for both expansion
and compression with appropriate switching between the transmitting and
receiving functions. The output of this matched filter is given by the
convolution of the signal h(t) with the conjugate impulse response h*(- t) of
the matched filter:

The implementation of Fig. 1. Uses filters which are conjugates of
each other for the expansion and compression filters.

 

                                        Fig. 1 pulse compression radar using conjugate
filters

 3

complex conjugate H*(?) of the coding filter. The output of
the matched-filter section is the compressed pulse, which is given by the
inverse Fourier transform of the product of the signal spectrum H(?) and
the matched-filter response H*(?):

The coded signal may be represented either as a frequency response H(?)
or as an impulse time response h(t) of a coding filter. In Fig. 1
the coded signal is obtained by exciting the coding filter H(?) with
a unit impulse. The received signal is fed to the matched filter, whose
frequency response is the

The reasons for Using Matched Filter the probability of
detection increases with increasing SNR. For a deterministic signal in white
Gaussian noise, you can maximize the SNR at the receiver by using a filter
matched to the signal. The matched filter is a time-reversed and conjugated version
of the signal.2

The matched filter is the optimal linear filter for maximizing the
signal to noise ratio (SNR) in the presence of additive stochastic noise.

 Pulse-compression radar is the practical
implementation of a matched-filter system.

Pulse compression radar make 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 .

 This used
technique is called the Pulse Compression Technique (PCT) and is used widely in
Radar applications where high peak power is undesirable.3

 Good range
resolution can be achieved with a shorter pulse. But on the other hand, shorter
pulses require more peak power. The shorter the pulse gets, more energy is
required to pack the pulse by increasing the peak power.  Introduction
of high peak power makes the design of transmitters and receivers difficult
since the components used in the entire system must be able to withstand the
peak power. In order to overcome this problem, convert the short duration pulse
into a longer pulse. Increasing the length of the pulse results in reduction in
the peak power of it, but it reduces range resolution To preserve the range
resolution, modulation is to be incorporated to increase the bandwidth of the
long pulse (transmitting pulse).

Pulse
compression involves the transmission of a long coded pulse and the processing
of the received echo to obtain a relatively narrow pulse. The increased
detection capability of a long pulse radar system is achieved while retaining
the range resolution capability of a narrow pulse system.4

For these
applications of radar; modern radar systems require greater detection ranges,
finer range resolution, better visibility in clutter, and high reliability. Pulse
compression in one form or another is the only technique which meets the
present needs.

·        
Space: To guide the space
vehicle, to observe the planetary systems, and to detect and track satellites. 1

·        
Ground Traffic Control:  RADAR can also be used by traffic police to
determine speed of the vehicle.

·        
Remote Sensing: RADAR can be used for observing
weather or observing planetary positions and monitoring sea ice to ensure
smooth route for ships.

·        
air traffic control: to control air traffic
near airports, to guide the aircraft to land in bad weather, and to scan the
airport surface for aircraft and ground vehicle positions.

·        
military applications: for target detection and
target recognition in air defense, and identifying enemy locations in map.

Radar  has applications in five areas which are:

 

The direction of the
target is directly given by the antenna pointing direction. The accuracy of the
direction estimation is increased by augmenting the antenna dimensions.

… 2

Equation (1) only
gives information on the target range. Antenna theory states that the
3dBbeamwidth of an antenna is related to the carrier wavelength _ and the size of the Antenna D in
the given plane.

 …………… 1

RADAR stands for Radio Detection and Ranging System. It is basically an
electromagnetic system used to detect the location and distance of an object
from the point where the RADAR is placed. It works by radiating energy into
space and monitoring the echo or reflected signal from the objects. It operates
in the UHF and microwave range. Radars can also be used to measure the range, direction
and velocity of the target. According to optic/electromagnetic
fundamental rules, this time denoted t0 is directly proportional to the light
velocity C.  1

Introduction: