This letter presented several new constructions of complementary sets (CSs) with flexible sequence lengths using matrix transformations. The constructed CSs of size 4 have different lengths, namely N + L and 2N + L, where N and L are the lengths for which complementary pairs exist. Also, presented CSs of size 8 have lengths N + P, P + Q and 2P + Q, where N is length of complementary pairs, P and Q are lengths of CSs of size 4 exist. The achieved designs can be easily extended to a set size of 2n+2 by recursive method. The proposed constructions generalize some previously reported constructions along with generating CSs under fewer constraints.

Spatial modulation (SM) is a type of multiple-input multiple-output (MIMO) technology that provides several benefits over traditional MIMO systems. SM-MIMO is characterized by its unique transmission principle, which results in lower costs, enhanced spectrum utilization, and reduced inter-channel interference. To optimize channel estimation performance over frequency-selective channels in the spatial modulation system, cross Z-complementary pairs (CZCPs) have been proposed as training sequences. The zero correlation zone (ZCZ) properties of CZCPs for auto-correlation sums and cross-correlation sums enable them to achieve optimal channel estimation performance. In this paper, we systematically construct CZCPs based on binary Golay complementary pairs and binary Golay complementary pairs via Turyn’s method. We employ a special matrix operation and concatenation method to obtain CZCPs with new lengths 2M + N and 2(M + L), where M and L are the lengths of binary GCP, and N is the length of binary GCP via Turyn’s method. Further, we obtain the perfect CZCP with new length 4N and extend the lengths of CZCPs.

This letter is devoted to constructing new Type-II Z-complementary pairs (ZCPs). A ZCP of length N with ZCZ width Z is referred to in short by the designation (N, Z)-ZCP. Inspired by existing works of ZCPs, systematic constructions of (2N+3, N+2)-ZCPs and (4N+4, 7/2N+4)-ZCPs are proposed by appropriately inserting elements into concatenated GCPs. The odd-length binary Z-complementary pairs (OB-ZCPs) are Z-optimal. Furthermore, the proposed construction can generate even-length binary Z-complementary pairs (EB-ZCPs) with ZCZ ratio (i.e. ZCZ width over the sequence length) of 7/8. It turns out that the PMEPR of resultant EB-ZCPs are upper bounded by 4.

Type-II Z-complementary pairs (ZCPs) play an important role in suppressing asynchronous interference in a wideband wireless communication system where the minimum interfering-signal delay is large. Based on binary Golay complementary pairs (BGCPs) and interleaving technique, new construction for producing Z-optimal Type-II even-length quadriphase ZCPs (EL-QZCPs) is presented, and the resultant pairs have new lengths in the form of 2 × 2α10β26γ (α, β, γ non-negative integers), which are not included in existing known Type-II EL-QZCPs.

This letter provides a direct construction of binary even-length Z-complementary pairs. To date, the maximum zero correlation zone ratio of Type-I Z-complementary pairs has reached 6/7, but no direct construction of Z-complementary pairs can achieve the zero correlation zone ratio of 6/7. In this letter, based on Boolean function, we give a direct construction of binary even-length Z-complementary pairs with zero correlation zone ratio 6/7. The length of constructed Z-complementary pairs is 2m+3 + 2m + 2+2m+1 and the width of zero correlation zone is 2m+3 + 2m+2.

Almost-complementary pairs (ACPs) are sequence pairs whose autocorrelations sum up to zero at all but one non-zero time-shifts. Periodic ACPs (P-ACPs) display almost similar correlation properties to that of the periodic complementary pairs (PCPs). In this letter, we propose systematic constructions of quadriphase P-ACPs (QP-ACPs) from aperiodic (periodic) complementary pairs and almost perfect binary (quadriphase) sequences. The proposed construction gives QP-ACPs of new lengths which are not covered in the literature.

In this letter, we give a recursive construction of q-ary almost periodic complementary pairs (APCPs) based on an interleaving technique of sequences and Kronercker product. Based on this construction, we obtain new quaternary APCPs with new lengths.

Z-complementary pairs (ZCPs) were proposed by Fan et al. to make up for the scarcity of Golay complementary pairs. A ZCP of odd length N is called Z-optimal if its zero correlation zone width can achieve the maximum value (N + 1)/2. In this letter, inserting three elements to a GCP of length L, or deleting a point of a GCP of length L, we propose two constructions of Z-optimal ZCPs with length L + 3 and L - 1, where L=2α 10β 26γ, α ≥ 1, β ≥ 0, γ ≥ 0 are integers. The proposed constructions generate ZCPs with new lengths which cannot be produced by earlier ones.

This paper is focused on constructing even-length binary Z-complementary pairs (EB-ZCPs) with new length. Inspired by a recent work of Adhikary et al., we give a construction of EB-ZCPs with length 8N+4 (where N=2α 10β 26γ and α, β, γ are nonnegative integers) and zero correlation zone (ZCZ) width 5N+2. The maximum aperiodic autocorrelation sums (AACS) magnitude of the proposed sequences outside the ZCZ region is 8. It turns out that the generated sequences have low PAPR.

We present a low-complexity complementary pair affine projection (CP-AP) adaptive filter which employs the intermittent update of the filter coefficients. To achieve both a fast convergence rate and a small residual error, we use a scheme combining fast and slow AP filters, while significantly reducing the computational complexity. By employing an evolutionary method which automatically determines the update intervals, the update frequencies of the two constituent filters are significantly decreased. Experimental results show that the proposed CP-AP adaptive filter has an advantage over conventional adaptive filters with a parallel structure in that it has a similar convergence performance with a substantial reduction in the total number of updates.

In this paper, a novel pseudo-random noise complementary pair (PNCP) is proposed and adopted as the guard intervals in the time-domain synchronous OFDM (TDS-OFDM) system. The proposed PNCP has nearly ideal aperiodic auto-correlation property and inherits the differential property of the PN sequence. Simulations demonstrate the proposed TDS-OFDM system padded with PNCP could achieve better performance in both synchronization and channel estimation than the conventional TDS-OFDM system.