3-D Array Processing Of Ternary Pulse Compression

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Prmeedings of 1CSP 96

3-0ARRAY PROCESSING OF TERNARY PULSE COMPRESSION SEQUENCES K.Raja Rajeswari, K.Venkata Rao and D.Elizabath Rani Department of ECE, A.U. College of Engineering, Visakhapatnam - 530 003, INDIA.

If N is the length of the sequence such that

N = rst, all factors (r,s,t) being relatively prime, without repetition, then the array can be formed with dimension of r layers, s rows, and t columns. Here an arbitrary temary sequence of length 60 (1 0 -1 0 1 -1 1 1 1 -1 0 -1 -1 0 1 1 1

Pulse compression is playing an important role in radar applications in the sense of sending a long modulated pulse of utilizing its entire energy and simultaneously obtaining resolution of a narrow pulse. Range resolution is the ability of the receiver to separately detecting targets that are close together. In this paper the emphasis is on the formation of these sequences in three dimensional array and to see how its autocorrelation pattem can be recognized easily. This makes observation of the sequence as well as its autocorrelation pattern easier.

-1 -1 0 - 1 1 1 -1 1 1 -1 0 0 0 1 1 1 1 0 0 - 1 -1 -1 0 0 1 - 1 -1 1 1 1 1 -1 -1 0 0 0 1 - 1 -1 -1 1 - 1 1 ) is taken for illustration. The array is formed in (3 x 4 x 5) that is with 3 planes, in each plane with 4 rows and 5 columns. Starting from the left top most corner of the first plane the elements are filled along the diagonal of the three dimensional volume. When the face is reached, the next element is filled on the opposite face of the next row or column of the next plane. This procedure is repeated till the bottom right-most corner of the last layer is reached. The index location for filling the elements of 60 length sequence is shown in fig.1. Then the elements of the sequence are filled in the 3-D array as per the index location shown in fig.1. Fig.2 is the 3-D array which is formed with 3 tiers, 4 rows and 5 columns for the above 60 length sequence. The keys shown in fig.1 for determining the progressions on the rows, columns and tiers are seen to be 36, 45 and 40. The element R produces rows on 4 x 5 plane, C generates the columns on the 4 x 5 plane and T generates the tiers (vertical columns).

TRODUCTION: Two-dimensional and three-dimensional array processing of maximal length sequences and its effect on autocorrelation is reported in the earlier literature [1,2,3]. Here the same principle is adopted for temary (with 0, k 1 as alphabet) pulse compression sequences. For maximal length PN Sequences, the autocorrelation pattem is simple because it has two-level autocorrelation valued. i.e., R(0) = N and R(i) =-I. But for temary pulse compression i#O

sequences this property cannot be matched as it has uneven distribution. Two-dimensional array formation of ternary pulse compression sequences was reported [4]. Now it is extended to threedimensional array which improves storage capacity but logic becomes difficult.

3. COMPARISON OF AUTOCORRELATI PATTERN WITH lNDEX LOCATIONS: The autocorrelation for a 3-D array is formed by the 3-D array multiplication. r s t [Al. PI/ R(i,j,k) =

ETHODOLOGY FOR FORMATION OF

3-0ARRAY:

i = lj = 1 k = l

The following procedure is used for folding the given sequence in a 3-D array form.

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where A is the original 3-D array and B is the 3D array of A which is shifted cyclically by i-I layers, j-1 rows and k-I columns. By using the above formula the autocorrelation of 3-0 array is formed. An interesting and useful property was found that, the periodic autocorrelation structure of the 3-D array maintains the same structure as that of the original sequence even for any cyclic shift of the array in terms of its dimensions. The autocorrelation of the array is shown in Fig.3. This autocorrelation pattern is compared with the periodic autocorrelation of the sequence which is obtained as;

i=l

'

45 6 -5-5-13 -13 8 7 2 0 -7 -2 -8 -1 5 5 5 5 -2 -20 -5 3 1 - 3 5 - 2 -6 1 5 - 4 5 1 - 6 -2 5 -3 1 3 -5 0 -2-2 5 5 5 5 -1 -8 -2 -7 0 2 7 8 -13 -13 -5 -5 6. i=l

1 46

37 22

13 58

49 34

Fig. 2

25 10

i=2

5

5 6

-7

5

-13

5

0

2 1 3 7

1 -1 -5 5

-13 -2 -2 -2

i=3

Fig. 1

6

Fig. 3

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Making use of this sort of techniques the entire sequence need not be read bit wise. At a glance the sequence as well its autocorrelation pattem can be viewed. Compared with 2-D arrays, in 3-D arrays the storage capacity can be tremendously improved but logic and hardware implementation become difficult task. The 3-D array processing is more suitable for larger lengths data rather than smaller lengths. But some restrictions are imposed on selection of sequence as explained in section 2. Hence this technique can be adopted only for selected lengths. Compared with 2-D arrays, this can be preferred for larger lengths only. This technique leads to hybrid packages also.

5. REFERENCES: Green.D.H. and 'Families of sequen good periodic correl Proc. E, Vol. 138, July 1991, PP 260-268. Macwil1iams.F.J. and Sloane N.J.A., 'Pseudorandom Sequence and arrays', Proc. IEEE 1976,64 (12),PP 1715-1729. Green D.H., 'Structural properties of Pseudorandom arrays and volumes and their related sequences', IEE Proc. E, 1985, 132 (3),PP 133-145. Elizabath Rani.D, Raja f3ajeswari.K and Venkata Rao.K., 'Array formation of temary pulse compression sequences'. Proc. of National Symposium on Modem Trends in Electronics and Communication Systems (NASMOTECS), Visakhap~tnam, Feb. 23-25, 1995.

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