Zi Long Liu

New Constructions of General QAM Golay Complementary Sequences

There have been five constructions (Cases I to V) of 64-QAM Golay complementary sequences (GCSs), of which the Cases IV and V constructions were identified by Chang in 2010. The Generalized Cases I-III constructions for 4q-QAM (q ≥ 1) GCSs were additionally proposed by Li. In this paper, the Generalized Case IV and Generalized Case V constructions for 4q-QAM (q > =3) GCSs are proposed using selected Gaussian integer pairs, each of which contains two distinct Gaussian integers with identical magnitude and which are not conjugate with each other.

Correlation and Set Size Bounds of Complementary Sequences with Low Correlation Zone

The correlation lower bounds, as well as the set size upper bounds, of low-correlation-zone complementary sequences are presented in this paper. They can be treated as an extension of Tang-Fan-Matsufuji bounds in and , which considered only the conventional (non-complementary) low-correlation-zone sequence sets.

New Complete Complementary Codes for Peak-to-Mean Power Control in Multi-Carrier CDMA

Owing to the zero non-trivial aperiodic correlation sum properties, complete complementary codes (CCC) have been applied to asynchronous multi-carrier code-division multiple-access (MC-CDMA) communications in order to provide zero interference performance. When each complementary code is arranged to be a matrix, the peak-to-mean envelope power ratio (PMEPR) of the CCC-MC-CDMA system is determined by the column sequences of the complementary matrices. The existing CCC have the column sequence PMEPR of M, where M denotes the number of subcarriers in a CCC-MC-CDMA system. In practice, M is generally large and a PMEPR approaching this value is unacceptable. To solve this problem, a new class of CCC using generalized Boolean functions and with a column sequence PMEPR of at most 2 is proposed in this paper.

A Tighter Correlation Lower Bound for Quasi-Complementary Sequence Sets

Levenshtein improved the famous Welch bound on aperiodic correlation for binary sequences by utilizing some properties of the weighted mean square aperiodic correlation. Following Levenshteins idea, a new correlation lower bound for quasi-complementary sequence sets (QCSSs) over the complex roots of unity is proposed in this paper. The derived lower bound is shown to be tighter than the Welch bound for QCSSs when the set size is greater than some value. The conditions for meeting the new bound with equality are also investigated.

Fractional-Delay-Resilient Receiver Design for Interference-Free MC-CDMA Communications Based on Complete Complementary Codes

Complete complementary codes (CCC) refer to a set of two-dimensional matrices, which have zero non-trivial aperiodic auto- and cross- correlation sums. A modern application of CCC is in interference-free multicarrier code-division multiple-access (MC-CDMA) communications. In this paper, we first show that in asynchronous “fractional-delay” uplink channels, CCC-MC-CDMA systems suffer from orthogonality loss, which may lead to huge interference increase when a conventional correlator based receiver is deployed. Then, by exploiting the correlation properties of CCC, we present a fractional-delay-resilient receiver which is comprised of a chip-spaced correlating array. Analysis and simulations validate the interference-free achievability of the proposed CSCA receiver in strong interference scenarios.

Optimal odd-length binary Z-complementary pairs

A pair of sequences is called a Golay complementary pair (GCP) if their aperiodic autocorrelation sums are zero for all out-of-phase time shifts. Existing known binary GCPs only have even-lengths in the form of 2α 10β 26γ (where \(α, β, γ) are nonnegative integers). To fill the gap left by the odd-lengths, we investigate the optimal odd-length binary (OB) pairs, which display the closest correlation property to that of GCPs. Our criteria of closeness is that each pair has the maximum possible zero-correlation zone (ZCZ) width and minimum possible out-of-zone aperiodic autocorrelation sums. Such optimal pairs are called optimal OB Z-complementary pairs (OB-ZCP) in this paper. We show that each optimal OB-ZCP has maximum ZCZ width of (N+1)/2, and minimum out-of-zone aperiodic sum magnitude of 2, where N denotes the sequence length (odd). Systematic constructions of such optimal OP-ZCPs are proposed by insertion and deletion of certain binary GCPs, which settle the 2011 Li-Fan-Tang-Tu open problem positively. The proposed optimal OB-ZCPs may serve as a replacement for GCPs in many engineering applications, where odd sequence lengths are preferred. In addition, they give rise to a new family of base-two almost difference families, which are useful in studying partially balanced incomplete block design.

Improved lower bound for quasi-complementary sequence set

The Welch bound for aperiodic correlation for binary sequence set was improved by Levenshtein by weighting the cyclic shifts of the sequence vectors. Taking Levenshteins idea, a new lower bound for quasi-complementary sequence set (QCSS) over the complex roots-of-unity is derived in this paper. It is shown to be tighter than the Welch bound for QCSS in one of the following cases: 1) K = 4M − 1, M ≥ 2 and equation; 2) K ≥ 4M, M ≥ 2 and N ≥ 2. where K,M,N respectively denotes the set size, number of channels, elementary sequence length of QCSS.

On Even-Period Binary Z-Complementary Pairs with Large ZCZs

For an even-period binary Z-complementary pair (EB-ZCP), if it is not a Golay complementary pair (GCP), we show that Z ≤ N-2, where N and Z denote the sequence length and the zero correlation zone (ZCZ) width, respectively. This result partially answers the Fan-Yuan-Tu conjecture in 2007. In addition, we present a construction of EB-ZCPs with large ZCZ widths, where N=2m+1+2m and Z=2m+1. Interestingly, each of the proposed EB-ZCPs features zero out-of-phase aperiodic auto-correlation sums except for the time-shift of ±2m+1, thus displaying a very close correlation property to that of GCPs.

Training Sequence Design for Efficient Channel Estimation in MIMO-FBMC Systems

This paper is focused on training sequence design for efficient channel estimation in multiple-input multiple-output filterbank multicarrier (MIMO-FBMC) communications using offset quadrature amplitude modulation (OQAM). MIMO-FBMC is a promising technique to achieve high spectrum efficiency as well as strong robustness against dispersive channels due to its feature of time-frequency localization. A salient drawback of FBMC/OQAM signals is that only real-field orthogonality can be kept, leading to the intrinsic imaginary interference being a barrier for high-performance channel estimations. Also, conventional channel estimations in the MIMO-FBMC systems mostly suffer from high training overhead especially for large number of transmit antennas. Motivated by these problems, in this paper, we propose a new class of training sequences, which are formed by concatenation of two identical zero-correlation zone sequences whose auto-correlation and cross correlation are zero within a time-shift window around the in-phase position. Since only real-valued symbols can be transmitted in MIMO-FBMC systems, we propose “complex training sequence decomposition (CTSD)” to facilitate the reconstruction of the complex-field orthogonality of MIMO-FBMC signals. Our simulations validate that the proposed CTSD is an efficient channel estimation approach for practical preamble-based MIMO-FBMC systems.

A New Weight Vector for a Tighter Levenshtein Bound on Aperiodic Correlation

The Levenshtein bound on aperiodic correlation, which is a function of the weight vector, is tighter than the Welch bound for sequence sets over the complex roots of unity when M ≥ 4 and n ≥ 2, where M denotes the set size and n the sequence length. Although it is known that the tightest Levenshtein bound is equal to the Welch bound for M ∈ {1,2}, it is unknown whether the Levenshtein bound can be tightened for M=3, and Levenshtein, in his paper published in 1999, postulated that the answer may be negative. A new weight vector is proposed in this paper, which leads to a tighter Levenshtein bound for M=3, n ≥ 3 and M ≥ 4, n ≥ 2. In addition, the explicit form of the weight vector (which is derived by relating the quadratic minimization to the Chebyshev polynomials of the second kind) in Levenshteins paper is given. Interestingly, this weight vector also yields a tighter Levenshtein bound for M=3, n ≥ 3 and M ≥ 4, n ≥ √M, a fact not noticed by Levenshtein.