Quasi-complementary sequence sets (QCSSs) have attracted sustained research interests for simultaneously supporting more active users in multi-carrier code-division multiple-access (MC-CDMA) systems compared to complete complementary codes (CCCs). In this paper, we investigate a novel class of QCSSs composed of multiple CCCs. We derive a new aperiodic correlation lower bound for this type of QCSSs, which is tighter than the existing bounds for QCSSs. We then present a systematic construction of such QCSSs with a flexible alphabet size and a low maximum correlation magnitude, and also show that the constructed aperiodic QCSSs can meet the newly derived bound asymptotically.

The Z-complementary code set (ZCCS) is well-known for being used in multicarrier code-division multiple access (MC-CDMA) systems to provide interference-free communication in a quasi-synchronous environment. Based on the existing literature, the direct constructions of optimal ZCCSs are limited to their lengths. This letter proposes a direct construction of optimal ZCCSs for all possible even lengths using generalized Boolean functions. The maximum column sequence peak-to-mean envelope power ratio (PMEPR) of the proposed ZCCSs is upper-bounded by two which can benefit in managing PMEPR over a ZCCS-based MC-CDMA system.

This paper aims to construct optimal Z-complementary code set (ZCCS) with non-power-of-two (NPT) lengths to enable interference-free multicarrier code-division multiple access (MC-CDMA) systems. The existing ZCCSs with NPT lengths, which are constructed from generalized Boolean functions (GBFs), are sub-optimal only with respect to the set size upper bound. For the first time in the literature, we advocate the use of pseudo-Boolean functions (PBFs) (each of which transforms a number of binary variables to a real number as a natural generalization of GBF) for direct constructions of optimal ZCCSs with NPT lengths.

The zero correlation zone (ZCZ) ratio, i.e., the ratio of the width of the ZCZ and the length of the sequence plays a major role in reducing interference in an asynchronous environment of communication systems. However, to the best of the authors knowledge, for q = 2, the highest ZCZ ratio for even-length Zcomplementary pairs which are directly constructed using generalized Boolean functions (GBFs), is 2/3. In this letter, we present a direct construction of q-ary even-length Z-complementary pairs through GBFs, which can achieve aZCZ ratio of 3/4.In general, the constructed q-ary even-length Z-complementary pairs are of length 2m-1+ 2 (m ∈ Z+), having a ZCZ width of 2m-2+ 2π(m-3)+ 1 where π is a permutation over m - 2 variables.

A major drawback of orthogonal frequency division multiplexing (OFDM) systems is their high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can be solved by adopting large codebooks consisting of complementary sequences with low PMEPR. In this paper, we present a new construction of polyphase complementary sets (CSs) using generalized Boolean functions (GBFs), which generalizes Schmidt's construction in 2007, Paterson's construction in 2000 and Golay complementary pairs (GCPs) given by Davis and Jedwab in 1999. Compared with Schmidt's approach, our proposed CSs lead to lower PMEPR with higher code-rate for sequences constructed from higher-order (≥ 3) GBFs. We obtain polyphase complementary sequences with maximum PMEPR of 2k+1and 2k+2- 2M where k,M are non-negative integers that can be easily derived from the GBF associated with the CS.

A salient disadvantage of orthogonal frequency division multiplexing (OFDM) systems is the high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can be solved by using complementary sequences with low PMEPR. In this paper, we present a new construction of complementary set (CS) by using generalized Boolean functions (GBFs), which generalizes the constructions given by Davis et al., Paterson and Schmidt. The proposed CS provides lower PMEPR upper bound as compared to Schmidt's method for the sequences corresponding to higher order (≥ 3) GBFs. We obtain complementary sequences with maximum PMEPR of 2k+1and 2k+2- 2M where k, M are non-negative integers that can be easily derived from the GBF associated with the CS.

Z-complementary code set (ZCCS), an extension of perfect CCs, refers to a set of 2-D matrices having zero correlation zone properties. ZCCS can be used in various multi-channel systems to support, for example, quasi-synchronous interference-free multicarrier code-division multiple access communication and optimal channel estimation in multiple-input multiple-output systems. Traditional constructions of ZCCS heavily rely on a series of sequence operations which may not be feasible for rapid hardware generation particularly for long ZCCSs. In this paper, we propose a direct construction of ZCCS using the second-order Reed-Muller codes with efficient graphical representation. Our proposed construction, valid for any number of isolated vertices present in the graph, is capable of generating optimal ZCCS meeting the set size upper bound.