4 research outputs found
Modifications on Character Sequences and Construction of Large Even Length Binary Sequences
It has been noticed that all the known binary sequences having the asymptotic
merit factor are the modifications to the real primitive characters. In
this paper, we give a new modification of the character sequences at length
, where 's are distinct odd primes and is finite.
Based on these new modifications, for with 's distinct
odd primes, we can construct a binary sequence of length with asymptotic
merit factor $6.0
Sequences with Low Correlation
Pseudorandom sequences are used extensively in communications and remote
sensing. Correlation provides one measure of pseudorandomness, and low
correlation is an important factor determining the performance of digital
sequences in applications. We consider the problem of constructing pairs
of sequences such that both and have low mean square
autocorrelation and and have low mean square mutual crosscorrelation.
We focus on aperiodic correlation of binary sequences, and review recent
contributions along with some historical context.Comment: 24 page
Advances in the merit factor problem for binary sequences
The identification of binary sequences with large merit factor (small
mean-squared aperiodic autocorrelation) is an old problem of complex analysis
and combinatorial optimization, with practical importance in digital
communications engineering and condensed matter physics. We establish the
asymptotic merit factor of several families of binary sequences and thereby
prove various conjectures, explain numerical evidence presented by other
authors, and bring together within a single framework results previously
appearing in scattered form. We exhibit, for the first time, families of
skew-symmetric sequences whose asymptotic merit factor is as large as the best
known value (an algebraic number greater than 6.34) for all binary sequences;
this is interesting in light of Golay's conjecture that the subclass of
skew-symmetric sequences has asymptotically optimal merit factor. Our methods
combine Fourier analysis, estimation of character sums, and estimation of the
number of lattice points in polyhedra.Comment: 31 pages, minor revision
Designing Sequence with Minimum PSL Using Chebyshev Distance and its Application for Chaotic MIMO Radar Waveform Design
Controlling peak side-lobe level (PSL) is of great importance in
high-resolution applications of multiple-input multiple-output (MIMO) radars.
In this paper, designing sequences with good autocorrelation properties are
studied. The PSL of the autocorrelation is regarded as the main merit and is
optimized through newly introduced cyclic algorithms, namely; PSL Minimization
Quadratic Approach (PMQA), PSL Minimization Algorithm, the smallest Rectangular
(PMAR), and PSL Optimization Cyclic Algorithm (POCA). It is revealed that
minimizing PSL results in better sequences in terms of autocorrelation
side-lobes when compared with traditional integrated side-lobe level (ISL)
minimization. In order to improve the performance of these algorithms,
fast-randomized Singular Value Decomposition (SVD) is utilized. To achieve
waveform design for MIMO radars, this algorithm is applied to the waveform
generated from a modified Bernoulli chaotic system. The numerical experiments
confirm the superiority of the newly developed algorithms compared to
high-performance algorithms in mono-static and MIMO radars.Comment: 14 page