Page 99 - Radar Technology Encyclopedia

CODE, CODING code, Gray 89

The basic code that is used in coding information for data forms of binary phase codes are binary phase code represen-
transmission is the Gray code. Some other codes for specific tations in any one of four forms, all of which have the same
tasks can be formed from the Gray codes (e.g., Gillham code correlation characteristics. These forms are the code itself, the
for transmitting information about the height of aircraft). SAL inverted code (i.e., written in reverse order), the comple-
Ref.: IEEE (1993), p. 202; Cook (1967), Ch. 8. mented code (1s changed to 0s and vice versa), and the
inverted complemented code. SAL
The Barker code is a binary (phase) code with the property
that the peak of the autocorrelation function is equal to N, Ref.: Hovanessian (1984), p. 241; Skolnik (1990), p. 10.17.
where N is the code length, and all the time sidelobes have The combined [compound] Barker code is a code using
unit amplitude. The time duration of a Barker code is equal to known Barker codes to generate codes longer than 13 bits.
Nd, where d is the chip width. The peak-to-sidelobe ratio is For example, either a 5-´-4 or a 4-´-5 combined Barker code
equal to 20logN. The only Barker codes possible are listed in can be used to devise a system with 20:1 pulse-compression
Table C6, and the longest of these has length N = 13. ratio. SAL
The Barker codes have a sidelobe structure containing Ref.: Morris (1988), pp. 135–138; Skolnik (1980), p. 432.
the minimum energy theoretically possible, uniformly distrib-
Complementary codes are the codes in which a pair of
uted among the sidelobes (Fig. C32). That is why Barker
equal-length codes have the property that the time sidelobes
codes are sometimes called perfect codes. They can serve as
of one code are the negative of the other, so the autocorrela-
building blocks for much longer codes (see combined
tion function of a complementary pair is equal to zero except
Barker codes). SAL
for the central peak. Complementary codes are used to form
Ref.: Barton (1988), p. 221; Barton (1991), p. 7.30; Skolnik (1990), p. 10.17;
complementary-code phase-coded waveforms with no resi-
Morris (1988), p. 134.
dues due to sidelobe cancellation. (See Golay code, Welti
Voltage code.) SAL
13 Ref.: Skolnik (1980), p. 432; Nathanson (1990), p. 491.
The Frank code is a polyphase code composed of N sets of
phase sequences that can be described as an N ´ N matrix in
which the phase in the ith row and jth column is given by
f = (2p/N) (i - 1) (j - 1).
ij
SAL
1 Time
Ref.: Barton (1991), p. 7.17; Skolnik (1990), p. 10.25.
26 d
frequency coding (see MODULATION, frequency)
Figure C32 Matched-filter output of Barker code of length
The Gillham code is a special digital code based on the Gray
13.
code and used in the air traffic control systems with second-
Table C6
ary surveillance radars. It is approved by the International
The Barker Codes
Civil Aviation Organization for transmission of data on the
height of aircraft. SAL
Sidelobe level (dB)
Code Code Ref.: Pereverzentsev (1981), p. 71; Stevens (1988), p. 113.
length elements
Peak Integrated The Golay code is a binary phase code using a pair of com-
plementary codes transmitted and received over two chan-
1 + 0.0 – nels. The Golay code pair of length 8, their autocorrelation
functions, and the zero sidelobe sum of their autocorrelations
2 + - , or - - 6.0 - 3.0
-
are shown in Fig. C33. The two channels must preserve phase
-
3 + + , or + - + - 9.5 - 6.5 and amplitude matching so that the sidelobes are canceled.
For radar, this implies transmission on alternating pulse repe-
-
4 + + +, or + + + - - 12.0 - 6.0
tition intervals (PRIs), with a delay of one PRI introduced in
5 + + + - + - 14.0 - 8.0 one of the channels before the final summing, and with target
scatterers preserving the same phase over that interval t . The
r
7 + + + - - + - - - 9.1
16.9
resulting doppler sensitivity corresponds to f << 1/t = f , a
d
r
r
difficult requirement that explains the lack of practical appli-
+
11 + + + - - -- - + - - 20.8 - 11.5
cation of complementary codes. SAL
13 + + + + + - - + + - + - + - 22.3 - 11.5 Ref.: Morris (1988), p. 142; Barton (1991), p. 7.31.
The Gray code is a cyclical binary code used as the basis for
A binary (phase) [biphase] code is the sequence of symbols, systems of data transmission. The cyclical codes have an
each plus or minus, used to form binary-coded waveforms advantage over conventional binary codes when transmitted
(sometimes called binary code or biphase code). Allomorphic information continuously varies in time, since cyclical codes