Complementary Code Pairs Research Articles

Good code sets from complementary pairs via symmetrical/antisymmetrical chips

Golay complementary code pairs have the advantage of being biphase codes, available at a variety of lengths, with exact sidelobe cancellation. However, they require transmission at two frequencies or channels. At the receiver, the two codes require reception in their own matched filters. The two matched filter outputs are then added, resulting in complete sidelobe cancellation. However, frequency- or channel-selective fading could result in inexact sidelobe cancellation. This paper introduces a new code constructed from the complementary code pair (A, B) by concatenating them with a gap in between, using one frequency band or one channel. The autocorrelation of this code contains a zero-sidelobe region on either side of the mainlobe and an adjacent region of small cross-correlation sidelobes. This is achieved by having the chips used for A and B satisfy the following two conditions: The two chips are symmetrical/antisymmetrical mirror images of each other and the cross-correlation between them is small-i.e., they are quasiorthogonal in the convolution sense. The symmetry/antisymmetry property results in the zero-sidelobe region, while the quasiorthogonality makes the adjacent region of cross-correlation sidelobes small. Linear frequency-modulated (LFM) and piecewise LFM chips satisfy both the symmetry/ antisymmetry and quasiorthogonality conditions. The symmetry/antisymmetry property is shown to be invariant under frequency-selective fading; therefore, sidelobe cancellation is also fading invariant. Any good code set that satisfies the symmetry/antisymmetry condition could be used as chips with the same Golay complementary code pair to generate a good code set with a zero-sidelobe region and an adjacent region of small cross-correlation sidelobes. Such sets are generated by varying the slope of the LFM and piecewise LFM chips.

Complementary Binary Code Design based on Mismatched Filter

Complementary code (CC) pairs have the interesting characteristic that the superposition of the two related autocorrelation functions (ACFs) has zero sidelobes in range direction. This is an important property for radar applications to avoid range sidelobes. However, CC pairs exist only for limited codeword lengths. Therefore, the general idea of CC design is extended here by applying a mismatched filter (MMF) procedure to the binary phase codeword pairs. There are two objectives considered. The first objective is to design MMF impulse responses to fulfill the zero sidelobe property. The second objective is to find binary phase codeword pairs in cooperation with the MMFs which have a high gain in signal-to-noise ratio (SNR). It is shown that for all codeword lengths (even where the classic CC pair does not exist) there exist binary phase codeword pairs and the related MMF impulse response coefficients which also have the zero sidelobe property. Furthermore, these codeword pairs have high gains in SNR which are nearly the same as for the classic matched filter technique.

Subcomplementary code pairs: new codes for ST/MST radar observations

A new type of codes, named subcomplementary codes, are introduced. These codes are close to, but not strictly, complementary. Each of the two sequences of the pair has an equal number of opposite elements, which enables the codes to have very high interference-suppression-factor (ISF) performances in and around the radar center frequency. The disadvantage of these codes is the presence of sidelobes of amplitude of -N in their autocorrelation functions for lag 1 (N being the code length). Some properties of these codes are presented along with a technique for generating the code pairs. Subcomplementary code pairs have been found for values of N equal to 4, 8, 16, 20, and 32. A simulation study confirms a major improvement in ISF over complementary code pairs around the zero Doppler frequency. Experimental observations were performed with the middle and upper atmosphere radar in Japan using complementary and subcomplementary code pairs of length 16 and an uncoded pulse for range resolution performance comparisons. The results obtained so far indicate that the effects of the sidelobes in the subcomplementary code pair are minimal for wind observations, although significant for shear velocity observations. The degradation in performance in signal-to-noise ratio observations is found to be noticeable but not severe. The subcomplementary code pairs may, therefore, be used in situations where their advantages for interference suppression are exploited and where the effects of their weaknesses are not so important as in the case of observations for applications in meteorology.

Complementary sequences with high sidelobe suppression factors for ST/MST radar applications

Under ideal conditions, complementary code pairs produce no sidelobes. In practice, sidelobes are produced, among other things, when the period of the Doppler frequency shift as well as the time of coherence of clear air turbulence are comparable (or smaller) than the interpulse period. The intensity of sidelobes increases with the radar operating frequency and becomes a real problem in the upper VHF and UHF bands. In this paper, a new technique for reducing sidelobes originating from atmospheric characteristics for clear air radar systems using pulse coding is presented. For this, a generalized analytic expression for a sidelobe suppression factor applicable to any number of binary code sequences is first derived. This is then used to develop the technique, which in the case of complementary codes consists of manipulating the order of transmission of the code sequences. For such codes, improvements in sidelobe suppression of the order of 80 dB on the VHF frequency band are obtained. The modifications required to implement the technique into existing systems are very few and simple.

Sequences of complementary codes for the optimum decoding of truncated ranges and high sidelobe suppression factors for ST/MST radar systems

A new technique of full decoding of truncated ranges applicable to complementary codes is presented. For code length of N, the technique uses a set of N/2 complementary code pairs to obtain a diagonal decoding matrix M that enables the full decoding of truncated ranges without the need of matrix inversion, and resulting in optimum performance with regards to the signal-to-noise ratio degradation (SNRD) in the truncated ranges. Techniques of constructing the required code sequences for code length of 4, 8, 16, 32, etc., are given. By arranging the order of transmission of the code sequences systematically to increase the suppression of sidelobes resulting from atmospheric characteristics, and by performing appropriate steps to reduce the effects of interferences, it is shown that a coding system that simultaneously optimizes the performances with regards to SNRD, sidelobe suppression, and interference rejection can be obtained. Examples are given to illustrate this.

On full decoding of truncated ranges for ST/MST radar applications

In a coding system that uses a complementary code pair of length N, the first N-1 sampled ranges are not normally fully decoded due to truncation. However, these ranges can be fully decoded by performing two processing stages. In the first stage, the truncated ranges are partially decoded and during the second stage, the vector of the fully decoded values is obtained as a product of the vector of the partially decoded values and a decoding matrix. Three performance parameters appropriate to the full decoding of truncated ranges are considered. These are the signal-to-noise power ratio degradation of the truncated ranges, the interference suppression performance of the codes, and a parameter related to the magnitudes of the elements of the decoding matrix which may influence the complexity of implementation. It is shown that by choosing suitable code pairs significant performance improvements can be obtained. >

New quasi‐complementary code sets for atmospheric radar applications

The basics of using low‐autocorrelation binary sequences in high‐resolution atmospheric radar experiments are briefly reviewed. An exact cancellation of correlation side lobes with repeated complementary code pairs is often not attained due to transmitter nonlinearities and due to poor coherence of atmospheric targets. Sulzer and Woodman (1984) have recently introduced quasi‐complementary code sets (QCCS) of low‐autocorrelation binary sequences, obtained by an extensive computer search, for which the side lobes nearly cancel on accumulation over the set. Improved performance of QCCS over complementary pairs has been confirmed in experiments with the Arecibo UHF radar. We report here an exhaustive computer search for a base set of 32‐bit binary sequences with correlation side lobes at level 3. These codes are then combined in optimal QCCS of several even set sizes with a residual correlation side lobe level of 2, or 6 dB better than for a sample QCCS of 48 codes given by Sulzer and Woodman. A similar search for 64‐bit codes, using a partial base set of ∼4000 codes with correlation side lobes at level 5 and 6, gives QCCS with a residual correlation side lobe level of 6.

Principles of high-resolution radar based on nonsinusoidal waves. III. Radar-target reflectivity model

For pt.II see ibid., vol.31, no.4, p.369-75 (1989). A target-reflectivity model is developed for carrier-free nonsinusoidal waves with the time variation of a Gaussian pulse or a sequence of positive and negative Gaussian pulses representing a binary code, as was introduced in pt.I (see ibid., vol.31, no.4, p.359-68 (1989)). It is shown that the impulse response of a complex target that is composed of a finite number of scattering centers can be expressed as a sequence of Gaussian pulses. The characteristics of the Gaussian pulses, e.g. peak amplitude and nominal duration, are functions of the physical properties of the scattering centers, which are unique for each target. Hence, the impulse response waveform of a target can be regarded as a one-dimensional image in time (or range), which is valuable information for target classification and recognition. A signal processing technique is developed for obtaining an approximation of a target impulse response waveform from the backscattered and received signals. The signal processor is specifically developed for radar signals with the structure of complementary code pairs whose autocorrelation function is a single narrow pulse with no time sidelobes. >