A Direct Construction of Intergroup Complementary Code Set for CDMA

A collection of mutually orthogonal complementary codes (CCs) is said to be complete complementary codes (CCCs) where the number of CCs are equal to the number of constituent sequences in each CC. Intergroup complementary (IGC) code set is a collection of multiple disjoint code groups with the following correlation properties: (1) inside the zero-correlation zone (ZCZ), the aperiodic autocorrelation function (AACF) of any IGC code is zero for all nonzero time shifts; (2) the aperiodic cross-correlation function (ACCF), of two distinct IGC codes, is zero for all time shifts inside the ZCZ when they are taken from the same code groups; and (3) the ACCF, for two IGC codes from two different code groups, is zero everywhere. IGC code set has a larger set size than CCC, and both can be applicable in multicarrier code-division multiple access (CDMA). In this chapter, we present a direct construction of IGC code set by using second-order generalized Boolean functions (GBFs), and our IGC code set can support interference-free code-division multiplexing. We also relate our construction with a graph where the ZCZ width depends on the number of isolated vertices present in a graph after the deletion of some vertices. Here, the construction that we propose can generate IGC code set with more flexible parameters

A Direct Construction of 2D-CCC with Arbitrary Array Size and Flexible Set Size Using Multivariable Function

Recently, two-dimensional (2D) array codes have been found to have applications in wireless communication.In this paper, we propose direct construction of 2D complete complementary codes (2D-CCCs) with arbitrary array size and flexible set size using multivariable functions (MVF). The Peak-to-mean envelope power ratio (PMEPR) properties of row and column sequences of the constructed 2D-CCC arrays are investigated. The proposed construction generalizes many of the existing state-of-the-art such as Golay complementary pair (GCP), one-dimensional (1D)-CCC, 2D Golay complementary array set (2D-GCAS), and 2D-CCC with better parameters compared to the existing work

A Direct and Generalized Construction of Polyphase Complementary Set with Low PMEPR and High Code-Rate for OFDM System

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 ($\geq 3$) GBFs. We obtain polyphase complementary sequences with maximum PMEPR of $2^{k+1}$ and $2^{k+2}-2M$ where $k,M$ are non-negative integers that can be easily derived from the GBF associated with the CS

A Direct Construction of Optimal Symmetrical Z-Complementary Code Sets of Prime Power Lengths

This paper presents a direct construction of an optimal symmetrical Z-complementary code set (SZCCS) of prime power lengths using a multi-variable function (MVF). SZCCS is a natural extension of the Z-complementary code set (ZCCS), which has only front-end zero correlation zone (ZCZ) width. SZCCS has both front-end and tail-end ZCZ width. SZCCSs are used in developing optimal training sequences for broadband generalized spatial modulation systems over frequency-selective channels because they have ZCZ width on both the front and tail ends. The construction of optimal SZCCS with large set sizes and prime power lengths is presented for the first time in this paper. Furthermore, it is worth noting that several existing works on ZCCS and SZCCS can be viewed as special cases of the proposed construction

A direct construction of even length ZCPs with large ZCZ ratio

This paper presents a direct construction of aperiodic q-ary (q is a positive even integer) even length Z-complementary pairs (ZCPs) with large zero-correlation zone (ZCZ) width using generalised Boolean functions (GBFs). The applicability of ZCPs increases with the increasing value of ZCZ width, which plays a significant role in reducing interference in a communication system with asynchronous surroundings. For q = 2, the proposed ZCPs reduce to even length binary ZCPs (EB-ZCPs). However, to the best of the authors’ knowledge, the highest ZCZ ratio for even length ZCPs which are directly constructed to date using GBFs is 3/4. In the proposed construction, we provide even length ZCPs with ZCZ ratios 5/6 and 6/7, which are the largest ZCZ ratios achieved to date through direct construction.acceptedVersio