Efficient Optimization of the Merit Factor of Long Binary Sequences

Baden, J. M.

doi:10.1109/tit.2011.2164778

Cited by 34 publications

(19 citation statements)

References 8 publications

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“…The state-of-the-art WeCAN algorithm proposed in [17] is considered for comparison. The metrics Peak Side-lobe Level (PSL), Integrated Side-lobe Level (ISL) and the Isolation (I) are used to evaluate the performance of the sequences which are defined as follows [4] PSL = 20log 10 max r pp,l (k)…”

Section: Numerical Resultsmentioning

confidence: 99%

Designing Constant Modulus Sequences with Good Correlation and Doppler Properties for Simultaneous Polarimetric Radar

Wang

Pang

et al. 2018

Electronics

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Abstract:Simultaneous polarimetric radar transmits a pair of orthogonal waveforms both of which must have good auto-and cross-correlation properties. Besides, high Doppler tolerance is also required in measuring the highly maneuvering targets. A new method for the design of sequences with good correlation and Doppler properties is proposed. We formulate a fourth-order polynomial, but unconstrained, minimization problem. An iterative algorithm based on the gradient method on the phases is applied to solve it. Numerical results demonstrate the superiority of the proposed algorithm compared to the previous state-of-the-art method.

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Section: Numerical Resultsmentioning

confidence: 99%

Designing Constant Modulus Sequences with Good Correlation and Doppler Properties for Simultaneous Polarimetric Radar

Wang

Pang

et al. 2018

Electronics

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“…Using the sequence appending operation, the modified Legendre sequence with a length m can be generated from any rotated Legendre sequence with a prime length n for m 2 ≤ n ≤ m. Flipping. In a recent work [3], Baden presented an efficient optimization method of the merit factor of binary sequences by deriving a formulation for measuring the change in the merit factor by a change of value in an element (flipping) in the sequence. The formulation is given by…”

Section: Modified Legendre Sequence For Coded Exposurementioning

confidence: 99%

“…6). To determine the elements to flip among the candidates, we apply a variant of the steep decent algorithm in [3], which is described in Algorithm 1. Since the number of candidates in Δ is usually small, the computational load for Algorithm 1 is small.…”

Section: Modified Legendre Sequence For Coded Exposurementioning

confidence: 99%

Fluttering Pattern Generation Using Modified Legendre Sequence for Coded Exposure Imaging

Jeon

Lee

Han

et al. 2013

2013 IEEE International Conference on Computer Vision

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Finding a good binary sequence is critical in determining the performance of the coded exposure imaging, but previous methods mostly rely on a random search for finding the binary codes, which could easily fail to find good long sequences due to the exponentially growing search space. In this paper, we present a new computationally efficient algorithm for generating the binary sequence, which is especially well suited for longer sequences. We show that the concept of the low autocorrelation binary sequence that has been well exploited in the information theory community can be applied for generating the fluttering patterns of the shutter, propose a new measure of a good binary sequence, and present a new algorithm by modifying the Legendre sequence for the coded exposure imaging. Experiments using both synthetic and real data show that our new algorithm consistently generates better binary sequences for the coded exposure problem, yielding better deblurring and resolution enhancement results compared to the previous methods for generating the binary codes.

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“…However this too may be improved upon. A recent paper [1] showed that the gradient of the sidelobe energy of binary sequences could be recast as a correlation, or more precisely as the sum of terms from several correlations. The correlations may be computed using a Fast Fourier Transform (FFT), yielding a total computational cost of O(N log N ).…”

Section: Introductionmentioning

confidence: 99%

Efficient energy gradient calculations for binary and polyphase sequences

Baden

Davis

Schmieder

2015

2015 IEEE Radar Conference (RadarCon)

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Methods for optimization of phase coded waveforms often entail a nearest-neighbor search used in reducing autocorrelation or crosscorrelation sidelobes. Computing the energy gradient -the change in sidelobe energy that results from single -element modifications to the sequence -is a computationally expensive component of the nearest-neighbor search. A recent paper showed that the autocorrelation sidelobe energy gradient for binary sequences could be computed with O(N log N ) operations in initialization and O(N ) operations in iteration, substantially faster than previous methods which required O(N 2 ) operations both initially and in iteration. In this paper the same approach is extended to additional sequence optimizations -polyphase sequences, biphase cross-correlations, and biphase sequence filtering. It is shown that similarly efficient equations are available for those gradient calculations.

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Efficient Optimization of the Merit Factor of Long Binary Sequences

Cited by 34 publications

References 8 publications

Designing Constant Modulus Sequences with Good Correlation and Doppler Properties for Simultaneous Polarimetric Radar

Designing Constant Modulus Sequences with Good Correlation and Doppler Properties for Simultaneous Polarimetric Radar

Fluttering Pattern Generation Using Modified Legendre Sequence for Coded Exposure Imaging

Efficient energy gradient calculations for binary and polyphase sequences

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