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

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: