Acknowledgment: This work is supported by the Korea Ministry of Science and Technology through the National Research Laboratory (NRL) and Dual Use Technology Project.
0 IEE 2003 Electronics Letters Online No: 20030519 DOI: IO.I049/el:20030519
Criteria of goodness f o r coded waveform: The two main criteria of goodness of pulse compression sequences or codes are the discrimination and merit factor. Let S= [XO X I x2 x~...xN-I]be a real sequence of length N. Its aperiodic autocorrelation is then defined as
27 February 2003
Du Chang Heo, Jin Dong Song, Won Jun Choi, Jung I1 Lee and I1 Ki Han (Nano Devices Research Center, Korea Institute of Science and Technology, PO. Box 131, Cheongryang, Seoul 130-650, Korea) E-mail:
[email protected] Ji Chai Jung (Department of Radio Engineering, Korea Universiy, Seoul 136-701, Korea)
N-I-*
where k=O, 1, 2, ..., N-1. Ideally, the range-resolution radar signal should have large autocorrelation for zero shift and zero autocorrelation for nonzero shifts. The discrimination is defined as the ratio of main peak in the autocorrelation to the absolute maximum amplitude among the sidelobes [16]:
References ‘Optical coherence tomography (OCT): a review’, IEEE 1 Sel. Top. Quantum Electron., 1999,5, pp. 1205-1215 BURNS, W., CHEN, C.L., and MOELLER, R.: ‘Fiber-optic gyroscopes with broad-band sources’, J: Lightwave TechnoZ., 1983, 1, pp. 98-105 SAMPSON, D.D., and HOLLOWAY, WT.: ‘ 100 mW SpeCtdy-UnifOrm broadband ASE source for spectrum-sliced WDM systems’, Electron. Lett., 1994,30, pp. 1611-1612 LM, C.F., and LEE, 6.L.: ‘Extremely broadband AlGaAs/GaAs superluminescent diodes’, Appl. Phys. Lett., 1997, 71, pp. 1598-1600 YAMATOYA, T., MORI, s., KOYAMA, E, and E A , K.: ‘High power GaInAsP/InP strained quantum well superluminescent diode with tapered active region’, Jpn. 1 Appl. Phys., 1999, 38, pp. 5121-5122 wu, B.R., LIN, C.F., LAIH, L.W., and SHIH, T.T.: ‘Extremely broadband InGaAsP/lnP superluminescent diodes’, Electron. Lett., 2000, 36, pp. 2093-2095 SCHMITT, J.M.:
BIMBERG, D., GRUNDMA”, M., HEINRICHSDOW, E, LEDENTSOY N.N., USTINOY VM,, ZHUKOY A.E., KOVSH, A.R., MAXMOY M.V, SHERNYAKOY YM., VOLOVIK, B,V, TSATSUL”IKO\! A.E, KOP’EY ES., and ALFEROY ZH.1.: ‘QUiXItum
dot lasers: breakthrough in optoelectronics’, Thin Solid Film, 2000, 367, pp. 235-249
Algorithm for design of pulse compression radar codes K. Raja Rajeswari, N. Gangatharan,
G . Ezra Morris Abraham, G.S.V Radha Krishna Rao and D.E. Rani A new algorithm is proposed for the design of radar pulse compression codes from the known Baumert codes using cyclic shifting and
modular permutation techniques. Introduction: An early method for the design of pulse compression codes is skew-symmetry-odd-shift orthonormality, popularly known as Golay codes [l]. Later sieves, e.g. terminal admissibility [2], Barker prefix-variable core-terminal admissibility [3], have been introduced. In this Letter the known Baumert codes [4] have been used for the design of new pulse compression codes by adapting cyclic shifting and modular permutation methods which can be named as sieves. Pulse compression plays an important role in radar applications, where a long modulated pulse is sent. This enables utilisation of the entire energy of the long pulse simultaneously to obtain the resolution of a narrow pulse. Range-resolution is the ability of the radar receiver to discriminate nearby targets. Depending on the application, the codes were developed using different methods to suit requirements. However, the performance of range-resolution radar would be optimal, if the coded waveform has an impulsive autocorrelation [5-71. The binary Barker codes are considered as the optimum sequences [8]. They have the property that the magnitudes of the peak sidelobes of the autocorrelation function are all less than or equal to 1 and the peak mainlobe has a magnitude equal to the length of the sequence N. They are found to exist for lengths 2, 3, 4, 5, 7, 11 and 13, but they are not found to exist over length 13, which has been proved [9]. Longer length binary codes have been obtained [ 10-121 that violate the Barker conditions. Sequences at these lengths were also obtained using polyphase and multilevel codes [13-1.51. In this Letter we present two more sieves, cyclic shifting and modular permutation.
ELECTRONICS LETTERS 29th May 2003
Merit factor F is defined as the ratio of energy in the main peak of the autocorrelation to the total energy in the sidelobes [I]: (3)
The factor 2 appears in the denominator as the autocorrelation is an even function. The factors D and F must be as large as possible for a good sequence or code. Methodology for cyclic shifting: A binary sequence of period N=2”-1 is called balanced if the number of ‘ones’ is one more than the number of ‘zeros’. A complete search on these balanced binary sequences was conducted by Baumert [4] for a period of 127. It is well-known that there are six inequivalent binary sequences of period 127 with ideal autocorrelation property: an m-sequence, a Legender sequence, a Hall’s sequence, and three others. Rao and Reddy [12] obtained larger length binary sequences with minimum sidelobes in their aperiodic autocorrelation pattem by cyclically shifting the Legender sequences. In a similar way, the design procedure proposed in this Letter is based on the cyclic shifting and modular permutation of the difference sets given by Baumert. There are about 85 difference sets and out of that only 49 sequences are considered here for obtaining new sequences. From the aperiodic autocorrelation values of the sequence, first the discrimination and the merit factor of the original sequence are determined. By cyclically shifting the given sequence of length N, one bit at a time, the N-1 new sequences are obtained. Though the periodic autocorrelation remains the same for all cyclic shills, the aperiodic autocorrelation is different for these sequences. For all these sequences the factors such as discrimination and merit factor are determined from their aperiodic autocorrelation values. Among all these sequences obtained, the sequences having the highest discrimination and the sequence having the highest merit factor are searched. If the same sequence has the highest values of D and F, that sequence is retained as a good sequence for comparison with the original sequence and other sequences are not reported. The good sequences thus obtained for different root sequences with different cyclic shifts are reported here. This search has been carried out only up to length 71 along with their cyclic shift position as shown in Table 1. Methodology for modular permutation: Modular permutation is another technique adapted for obtaining good sequences. For a sequence of length N,first all the relative prime factors of N are determined. The relative prime factor is defined as the positive integer which is less than Nand is neither a factor of N nor a multiple of its factors. For all the relative prime factors found, the new sequences can be generated in the following way. For an original sequence xo, xI . . . xN-l, if p is one of the relative prime number of N, then the new sequence can be obtained from the original sequence by applying modular permutation as xo xp, x Z p . . . x i p . . . X(,A.-~)~,where the product ip is to be mod N. For example, if we consider a 15 length sequence, xO 1’
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x2 x3 x4 x5 x6 x7 x8 x9 ’10
xll
x12 ‘13
x14
865
then the relative prime factors are 2, 4, 7 , 8, 11, 13, 14. For the relative prime factor 2, the new sequence obtained using modular permutation can be written as, xo x2 x4 X6 x8 XIO x12XI4 x16 mod 15 X I 8 mod 15 x20 mod 15 x22 mod 15 x24 mod 15 x26 mod 15 x28 mod 15; i.e. XO x2 x4 x6 XE x10 x12 x14 XI xj x5 x7 xg x I 1x I 3 is the new sequence obtained for the permutation performed for a number 2. The same procedure is repeated for other relative prime factors and the discrimination and merit factor are determined from their aperiodic autocorrelation values and they are compared with the original sequence and the good sequences obtained by cyclic shifting method. The sequences that are found better than cyclically shifted sequences are reported.
discrimination obtained is either higher or at least equal to that of the original sequence, but the merit factor is found to be more than that of the original sequence. For example, consider the sequence of length 7 with elements xo x1x2 x3 x4 x5 x6. Then the relative prime numbers are 2, 3,4, 5, 6 and the sequences obtained using the modular permutation method with these numbers are, respectively,
xo x1 x2 xj x4 x5
Position of +ve ones
1, 3, 4, 5 , 9 11.00 12.10
2.75 3.17
1,4,5,6,7,9,11,16,17
(8)
1.40 6.22
m.p. (15)
6.33
6.33
C.S.
m.p. (2) original C.S.
(2)
I I
Original: original Baumert set (sequence); C.S. cyclic shifting method; m.p. modular permutation method
Results: The cyclic shifting algorithm works well compared to the modular permutation method. For almost all sequences taken from Baumerts sets, the cyclic shifting algorithm gives good results for at least one of the shifts without missing for any sequence. For the difference set of length 7 the second cyclic shifted sequence and for length 11 the eighth cyclic shifted sequence have been found on par with Barker sequences; but for length 13, for all cyclic shifted sequences, binary Barker sequence of length 13 was not found. The higher values of D and F have been found to depend on the number of +ve 1’s in the difference set.
I 0 original
El
cyclic R modular
I
xo xj x6 x2 xO
x4
x5
x5 xI x4 and x2 x6 x3
These two sequences have the same periodic autocorrelation function but their aperiodic autocorrelation functions are different. Also it can be observed that the sequence obtained with permutation 4 is same as that of the sequence obtained with permutation 3, if the first bit of the sequence obtained with permutation 4 is shifted to the last bit and the sequence is read backwards. In general the sequence obtained in modular permutation for a relative prime number ‘ 2 ’ can be used to obtain the sequence for relative prime number (N-i) by shifting the first bit to the last bit and reading the sequence backwards. Hence the modular permutation is performed only for relative prime numbers up to N/2, if N is even and up to (N-l)/2, if N is odd. In the modular permutation method, generally higher discrimination has been obtained for relative prime numbers less than 10. Comparing both methods, the cyclic shifting method is not very complex and encouraging results have been obtained. The modular permutation method is a slightly cumbersome procedure and does not have practical importance. In this work, the modular permutation method is considered as the counterpart of the cyclic shifting method. Conclusions: The cyclic shifting method is suitable for online application, is more simple and consumes less time for computing than the modular permutation algorithm. The first technique is more useful for changing the signal without further processing. These concepts will find application mostly in secure communications to change the transmitted signal on hand.
0 IEE 2003 Electronics Letters Online No: 20030281 DOI: I O . 1049/e1:20030281
I I February 2003
K. Raja Rajeswari, N. Gangatharan and G . Ezra Morris Abraham (Faculty of Engineering, Multimedia University, 63100, Cyberjaya, Selangor, Malaysia) G.S.V. Radha Krishna Rao (Faculty of Information Technology, 63100, Cyberjaya, Selangor, Malaysia) D.E. Rani (GITAM College of Engineering, Visakhapatnam, India)
16 I 14
8 12
p 10 E 8 6 6 $
original sequence
The sequences obtained for the relative prime numbers 3 and 4 are,
Table 1: List of some good sequences obtained using original, cyclic shifting, and modular permutation methods
x6
4
2 37
40
43
47
57 length
59
63
67
71
References GOLAY, M.J.E.: ‘Seives
Fig. 1 Comparison of discrimination
1 E3 original
cyclic
modular
I
length Fig. 2 Comparison of merit factor
Figs. 1 and 2 show the comparison plots of maximum discriminations and merit factors, respectively, obtained in these methods at various lengths. The first bar represents the original sequence, the second and third represents the cyclic shifted and modularly permutated sequences, respectively. It can be observed from these plots that sequences with highest discrimination have been obtained for cyclic shift less than 13 up to length 59. In both methods, the
866
for low autocorrelation binary sequences’, IEEE Trans. Int. Theoy, 1977, 23, (l), pp. 43-51 MOHARIR, P.S., RAJA RAJESWARI, K., and VENKATA RAO, K.: ‘Barker progressions’ in ‘Proceedings of Workshop on Signal Processing Communicationsand Networking’ (Tata McGraw Hill, New Delhi, 1990) MOHARIR, P.S., VARMA, S.K., and VENKATA RAO, K.: ‘Ternary puke I Inst. Electron. Telecommun. Eng., 1985, 31, compression sequences’, . pp. 1-8 BAUMERT, L.D.: ‘Cyclic difference sets’ in ‘Lecture notes on mathematics’ (Springer-Verlag. New York, 1971) COOK, C.E., and BERNFELD, M.: ‘Radar signals-an introduction to theory and application’ (Academic Press, New York, 1967) EAVES, J.L., and REEDY, E.K.: ‘Principles of modem radar’ (Nostrand, Reinhold, New York) SKOLNIK, M.1.: ‘Introduction to radar systems’ (McGraw Hill Book Co., New York, 1980, 2nd edn.) BARKER, R.H.: ‘Group synchronization of binary digital systems in communication theory’ in JACKSON, w. (Ed.) (Academic Press, New York, 1953) RAO, B.V, and DESHPANDE, A.A.: ‘Why the Barker sequence bit length does not exceed thirteen’, 1 lETE, 1988,-34, (6), pp. 461462 Trans. Int. 10 BOEHMER, A.M.: ‘Binary pulse compression codes’, Theov, 1967, 13, (2), pp. 156-167
ELECTRONICS LETTERS 29th May 2003
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'Binary sequences upto length 40 with best possible autocorrelation function', Elect". Lett., 1975, 11, (21), pp. 507-508 12 VEERABHADRA RAO, K., and REDDK U,: 'Biphase sequences with low sidelobe autocorrelation fimction', IEEE Trans. Aerosp. Electon. Syst., 1986,22, (2), pp. 128-133 13 ACKROYD, M.H.: 'Amplitude and phase modulated pulse trains for radar', Radio Electron. Eng., 1971, 41, pp. 541-552 14 C m , D.C.: 'Polyphase codes with good periodic autocorrelation properties', IEEE Trans. Int. T h e 0 5 1972, 18, pp. 531-533 15 FRANK, R.L.: 'Comments on polyphase codes with good periodic correlation properties', IEEE Trans. Int. Theov, 1973, 19, p. 244 16 MOHARIR, FS.:'Signal design', 1 IETE, 1976, 41, pp. 381-398 LINDER, J.:
rotation angle. The distance of the phase centre OP from the apex 0 is computed using the equation:
where COis the speed of light. Measurements were made with a 100 MHz frequency step between 1.1 and 2.6 GHz, and with a 200 MHz step up to 5 GHz. The azimuth cp is in a sector of f 3 6 " , by steps of 2". The measured phases are displayed in Fig. 1.
Effect of antenna phase centre displacement on FM-CW measurements: application to radar system C. Barks, C. Brousseau, L. Le Coq and A. Bourdillon In FM-CW measurements,the displacement of the phase centre of the antenna generates a parasitic Doppler effect. Comparisons between measurements and simulations of a LPD antenna are described and validated. The Doppler effect induced by this antenna is then computed for the FM-CW radar application and compared to the classical one due to the aircraft movement.
:,'
4.25
5
._ 4.30 U
-0.35
'
'
1000
1500
2000
2500
3000
3500
4000
4500
5000
frequency, MHz
Introduction: To measure radar cross section (RCS) of aircraft in the HF-VHF frequency band, a FM-CW radar system has been developed at the IETR [l]. This system is able to sweep the 28 to 88 MHz band in a few microseconds. Log-periodic dipole (LPD) antennas are used to transmit this waveform. The main problem with these LPD antennas is the position of the phase centre which is frequency dependent. Thus, when the FM-CW radar sweeps the frequency band, a parasitic Doppler effect is generated by the phase centre displacement. Experimental results: Low frequency band LPD antennas of the radar system are too large to be characterised in an anechoic chamber. Thus we have used a two-step procedure. In the first step, measurements of phase centre positions were performed on a smaller LPD antenna and compared with results of NEC2 simulations for validation purpose. In a second step, the real low frequency antenna was simulated. An EMC03 147 antenna was used for measurements. Its characteristics are summarised in Table 1. As the low cutoff frequency of the anechoic chamber is 1.1 GHz, measurements were made in the 1.1 to 5.0 GHz frequency range. The antenna phase centre moves according to frequency. Its location at each frequency was determined through measurements of the phase $ of the transmission factor between a hom and our LPD antenna. This phase was measured using a network analyser in the E-plane for several azimuths cp by rotating the antenna. To obtain a stable phase centre position [2], measurements were limited to the mainlobe of the antenna and the phase fits the equation:
+= + $0
[U.
Fig. 1 Position of phase centre for EMC03147 against frequency (E-plane, horizontal polarisation. free-space)
Comparisons between simulations and measurements: The EMC03147 antenna was simulated with the NEC2 software. The simulated structure consists of 30 free-space horizontal dipoles connected by a twisted 50 C2 transmission line. The referential centre stands at 69.3 cm from the apex (as for measurements). The far-field pattem is computed for a 0" elevation angle and an azimuth varying between f 3 6 " . The phase of the electrical field is calculated in the E-plane. Distances of the phase centre from the apex are computed as for the measurements. Computed and measured phase centres positions are compared in Fig. 1. A good agreement between measurements and simulations is observed. The discrepancies can be explained by the segmentation of the numerical model. These results prove the capability of the electromagnetic software NEC2, to be used to determine, with a good accuracy, the position of the LPD antenna phase centre. Applications to RACAL 943: The antenna used in the 28 to 88 MHz frequency band is the RACAL 943. Its characteristics are summarised in Table 2. Simulated results for this antenna using NEC2 software are shown in Fig. 2. The position of the phase centre from the apex fits to af-' law. It is located at about 91% of the position of the 1/2 dipole from the apex. Application to Doppler measurements: In the FM-CW radar system, the frequency of the transmitted waveform is a linear function of time t according to the equation:
+
COS(C~b)]
where $0, a and b only depend on the frequency$
f =Af,t++fo Table 1: Characteristics of EMCO 3147 LPD antenna where Afis the frequencyrate. Consequently the antenna phase centre moves with time with a virtual speed V, inducing a Doppler shift& given by:
Number of dipoles Spacing factor
0.066
5 dBi
tvoicallv
As the rotation centre R of the LPD antenna is at 69.3 cm from the antenna apex, the rotation centre is outside the antenna active region [3]. A least mean square method is then applied to the measurements (cp, $) to compute the amplitude a of the phase variation against
ELECTRONICS LETTERS 29th May 2003
with OP variations fitted to - x / j For FM-CW radar application, the frequency rate Af can be very large, around 10 GHz/s. An example of Doppler frequencies computed for this frequency rate Af and for an aircraft speed of 200m/s, is shown in Fig. 3. In this case, the Doppler shift due to the antenna phase centre displacement is larger than the Doppler frequency due to target movement for frequencies below 75MHz.
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