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Register a new userSequences with Low Correlation
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Added by
Daniel Katz
Publication date
2018
fields
Informatics Engineering
and research's language is
English
Authors
Daniel J. Katz
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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 $(f,g)$ of sequences such that both $f$ and $g$ have low mean square autocorrelation and $f$ and $g$ have low mean square mutual crosscorrelation. We focus on aperiodic correlation of binary sequences, and review recent contributions along with some historical context.
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In this study, we propose partitioned complementary sequences (CSs) where the gaps between the clusters encode information bits to achieve low peak-to-average-power ratio (PAPR) orthogonal frequency division multiplexing (OFDM) symbols. We show that the partitioning rule without losing the feature of being a CS coincides with the non-squashing partitions of a positive integer and leads to a symmetric separation of clusters. We analytically derive the number of partitioned CSs for given bandwidth and a minimum distance constraint and obtain the corresponding recursive methods for enumerating the values of separations. We show that partitioning can increase the spectral efficiency (SE) without changing the alphabet of the nonzero elements of the CS, i.e., standard CSs relying on Reed-Muller (RM) code. We also develop an encoder for partitioned CSs and a maximum-likelihood-based recursive decoder for additive white Gaussian noise (AWGN) and fading channels. Our results indicate that the partitioned CSs under a minimum distance constraint can perform similar to the standard CSs in terms of average block error rate (BLER) and provide a higher SE at the expense of a limited signal-to-noise ratio (SNR) loss.
Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared to random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation values (for each sequence in the pair) and significantly lower mean square crosscorrelation values. If we define crosscorrelation merit factor analogously to the usual merit factor for autocorrelation, and if we define demerit factor as the reciprocal of merit factor, then randomly selected binary sequence pairs are known to have an average crosscorrelation demerit factor of $1$. Our constructions provide sequence pairs with crosscorrelation demerit factor significantly less than $1$, and at the same time, the autocorrelation demerit factors of the individual sequences can also be made significantly less than $1$ (which also indicates better than average performance). The sequence pairs studied here provide combinations of autocorrelation and crosscorrelation performance that are not achievable using sequences formed from single characters, such as maximal linear recursive sequences (m-sequences) and Legendre sequences. In this study, exact asymptotic formulae are proved for the autocorrelation and crosscorrelation merit factors of sequence pairs formed using linear combinations of multiplicative characters. Data is presented that shows that the asymptotic behavior is closely approximated by sequences of modest length.
In this study, we propose two schemes for uplink control channels based on non-contiguous complementary sequences (CSs) where the peak-to-average-power ratio (PAPR) of the resulting orthogonal frequency division multiplexing (OFDM) signal is always less than or equal to 3 dB. To obtain the proposed schemes, we extend Golays concatenation and interleaving methods by considering extra upsampling and shifting parameters. The proposed schemes enable a flexible non-contiguous resource allocation in frequency, e.g., an arbitrary number of null symbols between the occupied resource blocks (RBs). The first scheme separates the PAPR minimization and the inter-cell interference minimization problems. While the former is solved by spreading the sequences in a Golay complementary pair (GCP) with the sequences in another GCP, the latter is managed by designing a set of GCPs with low cross-correlation. The second scheme generates reference symbols (RSs) and data symbols on each RB as parts of an encoded CS. Therefore, it enables coherent detection at the receiver side. The numerical results show that the proposed schemes offer significantly improved PAPR and cubic metric (CM) results in case of non-contiguous resource allocation as compared to the sequences defined in 3GPP New Radio (NR) and Zadoff-Chu (ZC) sequences.
A class of binary sequences with period $2p$ is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over ${mathbb{F}_{{q}}}$ as well as 2-adic complexity are determined using Gauss period and group ring theory. The results show that the linear complexity of these sequences attains the maximum when $pequiv pm 1(bmod~8)$ and is equal to {$p$+1} when $pequiv pm 3(bmod~8)$ over extension field. Moreover, the 2-adic complexity of these sequences is maximum. According to Berlekamp-Massey(B-M) algorithm and the rational approximation algorithm(RAA), these sequences have quite good cryptographyic properties in the aspect of linear complexity and 2-adic complexity.
In this paper, we determine the 4-adic complexity of the balanced quaternary sequences of period $2p$ and $2(2^n-1)$ with ideal autocorrelation defined by Kim et al. (ISIT, pp. 282-285, 2009) and Jang et al. (ISIT, pp. 278-281, 2009), respectively. Our results show that the 4-adic complexity of the quaternary sequences defined in these two papers is large enough to resist the attack of the rational approximation algorithm.
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