No abstract

Spatial modulation (SM) is a new paradigm of multiple-input multiple-output (MIMO) systems, in which only one antenna at the transmitter is activated during each symbol period. Recently, it is observed that SM training sequences derived from corss Z-complementary pairs (CZCPs) lead to optimal channel estimation performance over frequency-selective channels. CZCPs are special form of sequence pairs which have zero aperiodic autocorrelation zones and cross-correlation zone at certain time-shifts. Recent paper by Liu et al. discussed only perfect CZCPs. In this paper, we focus on non-perfect CZCPs. We introduce the term cross Z-complementary ratio and re-categorise the CZCPs, both perfect and non-perfect, based on that. We propose a systematic construction of CZCPs based on generalised Boolean functions (GBFs). We further extend the lengths of the CZCPs by using the insertion method. The proposed CZCPs are all of new lengths of the form 2 α 10 β 26 γ + 2 (α ≥ 1), 10 β + 2, 26 γ + 2 and 10 β 26 γ + 2. Finally we propose a construction of optimal binary CZCPs having parameters (12, 5) and (24, 11) from binary Barker sequences. These CZCPs are also extended to (12N, 5N )-CZCPs and (24N, 11N )-CZCPs, where N is the length of a binary Golay complementary pair (GCP). During the proof, we also found a new structural property of binary CZCPs and concluded all binary GCPs are CZCPs too. Finally, we give some numerical simulations to confirm that depending on the number of multipaths, the proposed CZCPs can be used to design SM training matrix which attains the minimum mean square error.

In this Letter, a new construction of aperiodic Z-complementary sequence sets (ZCSSs) is proposed. The constituent sequences of ZCSSs have odd-length of the form 2 a 10 b 26 g + 1 (where a, b and g are non-negative integers). The resultant ZCSSs are optimal with respect to the Welch bound.

A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs) display closest correlation properties to Golay complementary pairs (GCPs) in that each OB-ZCP achieves maximum ZCZ of width (N + 1)/2 (where N is the sequence length) and every outof-zone AACSs reaches the minimum magnitude value, i.e. 2. Till date, systematic constructions of optimal OB-ZCPs exist only for lengths 2 α ± 1, where α is a positive integer. In this paper, we construct optimal OB-ZCPs of generic lengths 2 α 10 β 26 γ + 1 (where α, β, γ are non-negative integers and α ≥ 1) from inserted versions of binary GCPs. The key leading to the proposed constructions is several newly identified structure properties of binary GCPs obtained from Turyn's method. This key also allows us to construct OB-ZCPs with possible ZCZ widths of 4×10 β−1 +1, 12×26 γ−1 +1 and 12×10 β 26 γ−1 +1 through proper insertions of GCPs of lengths 10 β , 26 γ , and 10 β 26 γ , respectively. Our proposed OB-ZCPs have applications in communications and radar (as an alternative to GCPs).

In recent years, complementary sequence sets have found many important applications in multi-carrier code-division multiple-access (MC-CDMA) systems for their good correlation properties. In this paper, we propose a construction, which can generate multiple sets of complete complementary codes (CCCs) over ZN , where N (N ≥ 3) is a positive integer of the form N = p e 0 0 p e 1 1 . . . p e n−1 n−1 , p0 < p1 < · · · < pn−1 are prime factors of N and e0, e1, · · · , en−1 are non-negative integers. Interestingly, the maximum inter-set aperiodic cross-correlation magnitude of the proposed CCCs is upper bounded by N . When N is odd, the combination of the proposed CCCs results to a new set of sequences to obtain asymptotically optimal and near-optimal aperiodic quasi-complementary sequence sets (QCSSs) with more flexible parameters.Index Terms-Complete complementary codes (CCCs), asymptotically optimal quasi-complementary sequence set (QCSSs), maximum aperiodic cross-correlation magnitude, multi-carrier code-division multiple-access (MC-CDMA).