DOI : 10.17577/IJERTV3IS100764
- Open Access
- Total Downloads : 835
- Authors : Muralidhara. N, Vinod. V, Santhoshkumar. D, Kiran. V
- Paper ID : IJERTV3IS100764
- Volume & Issue : Volume 03, Issue 10 (October 2014)
- Published (First Online): 27-10-2014
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Comparative Analysis of Polyphase Codes for Digital Pulse Compression Applications
N. Muralidhara
Bharat Electronics Limited, Bangalore
Santhoshkumar D
Bharat Electronics Limited, Bangalore
Vinod V
Bharat Electronics Limited, Bangalore
Kiran V
Bharat Electronics Limited, Bangalore
Abstract -Pulse compression permits us to trade-off between the average transmitted power of a reasonably long pulse and the range resolution corresponding to a short pulse. Polyphase codes viz., Frank, P1, P2, P3 and P4 have the ability to achieve low side lobes without amplitude weighting. Polyphase wave forms have the advantages of low main lobe width, high peak side lobe ratio and good Doppler tolerance.
In this paper Digital Pulse Compression technique is analyzed using Polyphase codes and a comparison between different Polyphase codes (Frank, P1, P2, P3 and P4) is analyzed with respect to main lobe width, side lobe reduction, Doppler tolerance and pre-compression band-limiting effects.
IndexTerms – Pulse Compression, Barker sequence, Frank codes, Polyphase codes, side lobe reduction, auto-correlation, Doppler tolerance.
-
INTRODUCTION
Range resolution for Radar can be considerably improved by means of very short pulses. Utilizing short pulses reduces the average transmitted power, which can hamper the Radars regular modes of operation. Because the average transmitted power is connected to the receiver SNR, it is often advantageous to increase the pulse width (thereby increasing the average transmitted power) while at the same time
-
POLYPHASE CODES
Polyphase codes [2, 3] uses harmonically related phases based on a certain fundamental phase increment. In Polyphase codes, a particular pulse of time support is split into P equal parts; each part is subsequently partitioned into additional P sub-pulses each of chip width . As a result, the total number of sub-pulses insideeach pulse is P2, and the Pulse Compression Ratio (PCR) is P2. The phase within each sub- pulse is maintained constant with regard to some continuous wave reference signal.
The phase coding methods of Frank, P1, P2, P3 and P4 are explained in the next section. The phase codes are selected so that the auto-correlation function of the coded waveform has the largest Peak signal to Side Lobe Ratio (PSLR) for a fixed code length.
-
Phase relationships in Polyphase codes
Polyphase codes are usually obtained from the phase variation of linear frequency modulated pulse. The Frank code, P1 and P2 codes are derived from the frequency stepped pulses. These threecodes are only appropriate for perfect square length of pulse compression ratio and can be stated as
preserving adequate range resolution. Pulse compression [1]
Frank:
2
. . . (1)
permits us to attain the average transmitted power of a
, =
1
1
P1:
1 + 1 . . . (2)
reasonably long pulse, while acquiring the range resolution
, =
2( 1)
corresponding to a short pulse.
P2:
+1
+1
LFM signals are also often the waveform of choice for
, =
2
(3)
2
wideband systems, where the required bandwidth may be hundreds of megahertz. The ambiguity function of the LFM signal suffers from significant sidelobes, both in delay (range) and in Doppler. It is known, for example, that the first range sidelobe is approximately 13 dB below the main peak of the ambiguity function. Such sidelobes may be unacceptable in
Two other Polyphase codes are P3 and P4 codes obtained from the linear frequency-modulated pulse. The length of P3 and P4 codes can be arbitrary. P3 and P4 codes can be expressed as
1 2
many applications due to system performance degradation
P3: =
(4)
caused by high sidelobes. To suppress the sidelobes some form of weighting can be applied to the matched filter
P4:
= 1 1
(5)
response. The main drawbacks associated with conventional weighting functions (e.g., Hamming, Kaiser Windows) are the broadening of the main lobe of the ambiguity function cut along the time axis and an inevitable attenuation in the peak response which decreases the signal-to-noise ratio.
-
-
AUTO-CORRELATION FUNCTIONS OF
POLYPHASE CODES
The matched filter response of Polyphase waveforms can be studied using auto-correlation functions of Polyphase
0
-10
-20
-30
-40
-50
-60
0 10 20
Autocorrelation function of P3 code (PCR = 100)
codes. The peak side lobe ratio and 6-dB time width (or compressed pulse width) can be calculated from the auto- correlation functions of the Polyphase codes.
Amplitude in dB
For Polyphase Barker sequences, very good Integrated Sidelobe Levels (ISL), defined as
2
= 10 10 2
0
(6)
30
time in s
where the Ri are the elements of the auto-correlation
sequence, i = 1 to N-1, and R0 is the auto-correlation peak. This is done because long codes cannot have Barker-level sidelobes without also having good ISL. With this in mind good ISL codes are found, and then used as starting points for local searches for low-PSL codes [4].
The following Polyphase auto-correlation functions simulations are carried out with Matlab© for Pulse-Doppler radar with Pulse Repetition Frequency (PRF) = 1000Hz, PCR
Amplitude in dB
= 100, and range resolution of 50m (chip width of 33 ns).
Autocorrelation function of Frank code (PCR = 100)
0
-10
-20
-30
-40
-50
-60
0 10 20
40 50 60
30
time in s
Amplitude in dB
Fig 1. Auto-correlation function of Frank code
Autocorrelation function of P1 code (PCR = 100)
0
-10
-20
-30
-40
-50
-60
0
10
20
30
time in s
50
60
40
Amplitude in dB
Fig 2. Auto-correlation function of P1 code
Autocorrelation function of P2 code (PCR = 100)
0
-10
-20
-30
-40
-50
-60
0
10
20
30
time in s
50
60
Fig 3. Autocorrelation function of P2 code
40
Fig 3. Autocorrelation function of P2 code
40 50 60
Amplitude in dB
Fig 4. Auto-correlation function of P3 code
Autocorrelation function of P4 code (PCR = 100)
0
-10
-20
-30
-40
-50
-60
0 10 20
40 50 60
30
time in s
Fig 5. Auto-correlation function of P4 code
Peak Side Lobe Ratio (PSLR) for a PCR = 100
Frank
P1
P2
P3
P4
-30 dB
-30 dB
-30 dB
-26.3 dB
-26.3 dB
Table 1. PSLR of Polyphase codes
It is evident from the simulation that, the Peak Side Lobe Ratio (PSLR) of P3 and P4 codes are higher than that of Frank, P1 and P2 codes by 3.7 dB at a PCR = 100.
-
DOPPLER TOLERANCE OF POLYPHASE CODES Any pulse compression code will exhibit some sensitivity
to Doppler and to the number of bits used to represent elements of the sequence. In pulse Doppler Radars matched iltering is performed in receiver which involves the computation of cross-correlation of the received waveform and reference signal for signal detection. Because of the Doppler shift introduced by the moving targets matched filter performance will decrease. Doppler tolerance describes the maximum obtainable Doppler shift for a known waveform such that still a correlation peak bigger than threshold is achieved.
Autocorrelation function of Frank code (PCR = 100) with Doppler 0
-10
-20
-30
-40
-50
Autocorrelation function of P4 code (PCR = 100) with Doppler
40 50 60
30
time in s
-60
0 10 20
40 50 60
30
time in s
0
-10
-20
-30
-40
-50
-60
0 10 20
Amplitude in dB
Amplitude in dB
Amplitude in dB
Fig 6.Doppler tolerance of Frank code
Autocorrelation function of P1 code (PCR = 100) with Doppler
0
-10
-20
-30
-40
-50
-60
0 10 20
40 50 60
30
time in s
Amplitude in dB
Fig 7. Doppler tolerance of P1 code
Autocorrelation function of P2 code (PCR = 100) with Doppler
0
-10
-20
-30
-40
-50
-60
0 10 20
40 50 60
30
time in s
Amplitude in dB
Fig 8. Doppler tolerance of P2 code
Autocorrelation function of P3 code (PCR = 100) with Doppler
0
-10
-20
-30
-40
-50
-60
0
10 20
40 50 60
30
time in s
Fig 9. Doppler tolerance of P3 code
Fig 10. Doppler tolerance of P4 code
Figures [6-10] shows the matched filter response by auto- correlation of Polyphase codes in the presence of Doppler frequency shift of 30 KHz.
PSLR with Doppler for a PCR = 100
Frank
P1
P2
P3
P4
-16.9 dB
-13.9 dB
-13.6 dB
-19.3 dB
-19.3 dB
Table 2. PSLR of Polyphase codes with Doppler
It is evident from the above Table 1 and 2 that P3 and P4 codes have better Doppler tolerance compared to Frank, P1 and P2 codes.
-
PRE-COMPRESSION BAND-LIMITING EFFECTS ON POLYPHASE CODES
Amplitude in dB
Before the application of pulse compression algorithm, the base band signal will be undergoing band-limiting to minimize the effect to out-of-band noise. If a receiver designed so that it has an approximate rectangular bandwidth with respect to 3-dB bandwidth of the received waveform, the received waveform contains errors and mismatch occur later in the pulse compression stage. This band-limiting would normally occur before sampling process in order to prevent noise and aliasing effects. The result of any band-limiting is to smooth the vectors constituting the coded waveform. This weighing causes an unwanted mismatch with the pulse compressor which results in a degradation of the sidelobe level.
Autocorrelation function of Frank code (PCR = 100) with Bandlimiting
0
-50
-150
0
10 20
40 50 60
30
time in s
-100
Fig 11. Bandlimiting effects on Frank code
Autocorrelation function of P1 code (PCR = 100) with Bandlimiting
0
-50
-150
0
10 20
40 50 60
30
time in s
-100
Amplitude in dB
Amplitude in dB
Fig 12. Bandlimiting effects on P1 code
Autocorrelation function of P2 code (PCR = 100) with Bandlimiting
0
-50
-150
0
10 20
40 50 60
30
time in s
-100
Fig 13. Band-limiting effects on P2 code
Fig 14. Bandlimiting effects on P3 code
/
Amplitude in dB
Fig 14. Band-limiting effects on P3 code
Autocorrelation function of P4 code (PCR = 100) with bandlimiting 0
-50
-100
-150
-200
-250
-300
0
10
20
30
time in s
50
60
40
Fig 15. Band-limiting effects on P4 code
Figures [11-15] shows the matched filter response of Polyphase codes in the presence of pre-compression bandlimiting. Sampling rate chosen was 4 times the bandwidth to improve the time resolution.
Bandlimiting effects for a PCR = 100
Frank
P1
P2
P3
P4
PSLR (dB)
-13.4
-13.5
-13.5
-13.8
-13.8
Range Resolution (m)
125
125
125
125
125
Table 3.Band-limiting effects on Polyphase codes
The band-limiting filter carries out a smoothing process that combines the slower varying phase terms resulting in the increased side lobes close to the end of the code. Band- limiting also widens the main lobe, which reduces the range resolution. Polyphase codes given in the Table 3 are designed for a range resolution of 50 m, but due to bandlimiting process the actual range resolution resulted is 125 m.
-
SUMMARY
Pulse compression permits us to trade-off between the average transmitted power of a reasonably long pulse and the range resolution corresponding to a short pulse. Polyphase codes for pulse compression applications are investigated and a comparison between different Polyphase codes (Frank, P1, P2, P3 and P4) is analyzed with respect to main lobe width, side lobe reduction Doppler tolerance and pre-compression band-limiting effects are analyzed by means of simulation.
It is clear that Peak Side Lobe Ratio (PSLR) of P3 and P4 codes are higher than that of Frank, P1 and P2 codes by 3.7 dB at a PCR = 100, range resolution of 50m.
It is evident from the Table 1 and 2 that P3 and P4 codes have better Doppler tolerance compared to Frank, P1 and P2 codes. The better Doppler tolerance of P3 and P4 codes allows large time-bandwidths to be effective even in the presence of high Doppler shifts on received signal.
Pre-compression band-limiting widens the main lobe, which reduces the range resolution. Pre-compression band- limiting results in the increased side lobes close to the end of the code.
ACKNOWLEDGEMENTS
The authors would like to thank. Sri N.Suresh, General Manager, NS2, BEL, for giving us theopportunity to work on this project. He provided the motivation through his vast knowledgeand experience in BEL Radars.
It is our duty to thank Sri. Narasimhaprasad, Sr.DGM, NS2, BEL, Ms. Dharani, Sr.DGM, NS2, BEL, Ms.KN Vani,
DGM, NS2, BEL, Sri.Vidyanand, DGM, NS2, BEL, for their valuable suggestions and support during the course of the project. It was a good learning experience for us to work with their vast experience in Radar Signal Processing areas.
REFERENCES
-
Bassem R. Mahafza, Radar system analysis and design using Matlab, CRC Press LLC, 2000.
-
F.F. Kretschmer JR. and B.L. Lewis, Polyphase Pulse Compression Waveforms, Naval Research Laboratory, Washington DC, January 5, 1982.
-
B.L. Lewis and F.F. Kretschmer, Linear Frequency Modulation Derived Polyphase Pulse Compression Codes, IEEE Transactions on Aerospace and Electronic Systems, September 1982.
-
Carroll J. Nunn, Gregory E. Coxson Polyphase Pulse Compression Codes with Optimal Peak and Integrated Sidelobes Technology Service Corporation Suite 800, 962 Wayne Avenue, Silver Spring, Maryland 20910
ABOUT AUTHORS
Shri. N.Muralidhara is currently working in Bharat Electronics Limited, Bangalore as Manager. He obtained his
-
E in Electronics in the year 1993 SJCE, Mysore University and M.Tech degree in Digital Electronics and Advanced Communications from NIT Surathkal, Karnataka in 1997. His area of interests is 3D Radar signal processing, recent trends in SAR and ISAR.
Shri. Vinod V is currently working in Bharat Electronics Limited, Bangalore as Dy.Manager. He obtained his B.Tech in Electronics in the year 2000 from NSSCE, Calicut University and M.Tech degree in Digital Systems and Communications Engineering from NIT Calicut, Kerala in 2004. His areas of interest are Digital Signal Processing and Radar signal processing.
Shri. Santhoshkumar D is currently working in Bharat Electronics Limited, Bangalore as Sr.Deputy General Manager. He obtained his B.E in Electronics in the year 1984 SJCE, Mysore University and has vast experience in testing of Radar modules of various types of BEL Radars. His area of interest are Radar signal processing and Digital Beam forming.
Shri. Kiran V is currently working in Bharat Electronics Limited, Bangalore as Additional General Manager. He obtained his B.E in Electronics in the year 1982 UVCE, Bangalore and has extensive experience in design and development of Magnetron, Klystron and TWTs. His area of interest is Phased Array Radar.