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.

A set consisting of K subsets of Msequences of length L is called a complementary sequence set expressed by A(L, K, M), if the sum of the out-of-phase aperiodic autocorrelation functions of the sequences within a subset and the sum of the cross-correlation functions between the corresponding sequences in any two subsets are zero at any phase shift. Suehiro et al. first proposed complementary set A(Nn, N, N) where N and n are positive integers greater than or equal to 2. Recently, several complementary sets related to Suehiro's construction, such as N being a power of a prime number, have been proposed. However, there is no discussion about their inclusion relation and properties of sequences. This paper rigorously formulates and investigates the (generalized) logic functions of the complementary sets by Suehiro et al. in order to understand its construction method and the properties of sequences. As a result, it is shown that there exists a case where the logic function is bent when n is even. This means that each series can be guaranteed to have pseudo-random properties to some extent. In other words, it means that the complementary set can be successfully applied to communication on fluctuating channels. The logic functions also allow simplification of sequence generators and their matched filters.

This paper proposes an accurate and efficient method to calculate probability distributions of pulse-shaped complex signals. We show that the distribution over the in-phase and quadrature-phase (I/Q) complex plane is obtained by a recursive probability mass function of the accumulator for a pulse-shaping filter. In contrast to existing analytical methods, the proposed method provides complex-plane distributions in addition to instantaneous power distributions. Since digital signal processing generally deals with complex amplitude rather than power, the complex-plane distributions are more useful when considering digital signal processing. In addition, our approach is free from the derivation of signal-dependent functions. This fact results in its easy application to arbitrary constellations and pulse-shaping filters like Monte Carlo simulations. Since the proposed method works without numerical integrals and calculations of transcendental functions, the accuracy degradation caused by floating-point arithmetic is inherently reduced. Even though our method is faster than Monte Carlo simulations, the obtained distributions are more accurate. These features of the proposed method realize a novel framework for evaluating the characteristics of pulse-shaped signals, leading to new modulation, predistortion and peak-to-average power ratio (PAPR) reduction schemes.

In this paper, we propose a hybrid crystal oscillator which achieves both quick startup and low steady-state power consumption. At startup, a large negative resistance is realized by configuring a Pierce oscillating circuit with a multi-stage inverter amplifier, resulting in high-speed startup. During steady-state oscillation, the oscillator is reconfigured as a class-C complementary Colpitts circuit for low power consumption and low phase noise. Prototype chips were fabricated in 65nm CMOS process technology. With Pierce-type configuration, the measured startup time and startup energy of the oscillator are reduced to 1/11 and 1/5, respectively, compared with the one without Pierce-type configuration. The power consumption during steady oscillation is 30 µW.

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.

We developed a self-controllable voltage level (SVL) circuit and applied this circuit to a single-power-supply, six-transistor complementary metal-oxide-semiconductor static random-access memory (SRAM) to not only improve both write and read performances but also to achieve low standby power and data retention (holding) capability. The SVL circuit comprises only three MOSFETs (i.e., pull-up, pull-down and bypass MOSFETs). The SVL circuit is able to adaptively generate both optimal memory cell voltages and word line voltages depending on which mode of operation (i.e., write, read or hold operation) was used. The write margin (VWM) and read margin (VRM) of the developed (dvlp) SRAM at a supply voltage (VDD) of 1V were 0.470 and 0.1923V, respectively. These values were 1.309 and 2.093 times VWM and VRM of the conventional (conv) SRAM, respectively. At a large threshold voltage (Vt) variability (=+6σ), the minimum power supply voltage (VMin) for the write operation of the conv SRAM was 0.37V, whereas it decreased to 0.22V for the dvlp SRAM. VMin for the read operation of the conv SRAM was 1.05V when the Vt variability (=-6σ) was large, but the dvlp SRAM lowered it to 0.41V. These results show that the SVL circuit expands the operating voltage range for both write and read operations to lower voltages. The dvlp SRAM reduces the standby power consumption (PST) while retaining data. The measured PST of the 2k-bit, 90-nm dvlp SRAM was only 0.957µW at VDD=1.0V, which was 9.46% of PST of the conv SRAM (10.12µW). The Si area overhead of the SVL circuits was only 1.383% of the dvlp SRAM.

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.

To mitigate the interference caused by range sidelobes in multiple-input multiple-output (MIMO) radar, we propose a new method to construct Doppler resilient complementary waveforms from complete complementary code (CCC). By jointly designing the transmit pulse train and the receive pulse weights, the range sidelobes can vanish within a specified Doppler interval. In addition, the output signal-to-noise ratio (SNR) is maximized subject to the Doppler resilience constraint. Numerical results show that the designed waveforms have better Doppler resilience than the previous works.

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.

It has been demonstrated that large-scale labeled datasets facilitate the success of machine learning. However, collecting labeled data is often very costly and error-prone in practice. To cope with this problem, previous studies have considered the use of a complementary label, which specifies a class that an instance does not belong to and can be collected more easily than ordinary labels. However, complementary labels could also be error-prone and thus mitigating the influence of label noise is an important challenge to make complementary-label learning more useful in practice. In this paper, we derive conditions for the loss function such that the learning algorithm is not affected by noise in complementary labels. Experiments on benchmark datasets with noisy complementary labels demonstrate that the loss functions that satisfy our conditions significantly improve the classification performance.

A new construction of shift sequences is proposed under the condition of P|L, and then the inter-group complementary (IGC) sequence sets are constructed based on the shift sequence. By adjusting the parameter q, two or three IGC sequence sets can be obtained. Compared with previous methods, the proposed construction can provide more sequence sets for both synchronous and asynchronous code-division multiple access communication systems.

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.

Inspired by an idea due to Levenshtein, we apply the low correlation zone constraint in the analysis of the weighted mean square aperiodic correlation. Then we derive a lower bound on the measure for quasi-complementary sequence sets with low correlation zone (LCZ-QCSS). We discuss the conditions of tightness for the proposed bound. It turns out that the proposed bound is tighter than Liu-Guan-Ng-Chen bound for LCZ-QCSS. We also derive a lower bound for QCSS, which improves the Liu-Guan-Mow bound in general.

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.

In an OFDM communication system using quadrature amplitude modulation (QAM) signals, peak envelope powers (PEPs) of the transmitted signals can be well controlled by using QAM Golay complementary sequence pairs (CSPs). In this letter, by making use of a new construction, a family of new 16-QAM Golay CSPs of length N=2m (integer m≥2) with binary inputs is presented, and all the resultant pairs have the PEP upper bound 2N. However, in the existing such pairs from other references their PEP upper bounds can arrive at 3.6N when the worst case happens. In this sense, novel pairs are good candidates for OFDM applications.

Hadamard matrix is defined as a square matrix where any components are -1 or +1, and where any pairs of rows are mutually orthogonal. In this work, we consider the similar matrix on finite field GF(p) where p is an odd prime. In such a matrix, every component is one of the integers on GF(p){0}, that is, {1,2,...,p-1}. Any additions and multiplications should be executed under modulo p. In this paper, a method to generate such matrices is proposed. In addition, the paper includes the applications to generate n-shift orthogonal sequences and complete complementary codes. The generated complete complementary code is a family of multi-valued sequences on GF(p){0}, where the number of sequence sets, the number of sequences in each sequence set and the sequence length depend on the various divisors of p-1. Such complete complementary codes with various parameters have not been proposed in previous studies.

This paper improves the family size of quadrature amplitude modulation (QAM) complementary sequences with binary inputs. By employing new mathematical description: B-type-2 of 4q-QAM constellation (integer q ≥ 2), a new construction yielding 4q-QAM complementary sequences (CSs) with length 2m (integer m ≥ 2) is developed. The resultant sequences include the known QAM CSs with binary inputs as special cases, and the family sizes of new sequences are approximately 22·2q-4q-1(22·2q-3-1) times as many as the known. Also, both new sequences and the known have the same the peak envelope power (PEP) upper bounds, when they are used in an orthogonal frequency-division multiplexing communication system.