Peak-to-mean Envelope Power Ratio Research Articles

Construction of type-II ZCCS for the MC-CDMA system with low PMEPR

This paper introduces a novel construction method for Type-II Z complementary code set (ZCCS) based on the Kronecker product between complete complementary code and mutually orthogonal sequences. Type-II ZCCS offer significant advantages over their Type-I counterparts, boasting larger zero correlation zone (ZCZ) width and a larger number of codes with identical constituent sequences and lengths. Moreover, we propose a strategy to reduce column peak-to-mean envelope power ratio (PMEPR) to a low values upto smaller than 2. This construction framework also facilitates the creation of Z complementary pairs (ZCPs) with flexible parameters. Furthermore, we present a Type-II ZCCS based multi-carrier code division multiple access (MC-CDMA) system and conduct performance comparisons against existing Type-I ZCCS based counterparts. Simulation results demonstrate the superiority of the proposed system, showcasing improved reliability and efficiency. Additionally, we establish a novel relationship among set size, code size, sequence length, and ZCZ width for Type-II ZCCS.

A Direct Construction of Golay Complementary Pairs and Binary Complete Complementary Codes of Length Non-Power of Two

Golay complementary pairs (GCPs) and complete complementary codes (CCCs) have found a wide range of practical applications in coding, signal processing and wireless communication due to their ideal correlation properties. The binary CCCs have special advantages in spread spectrum communication for their simple modulo-2 arithmetic operation, modulation, and correlation simplicity; however, they are limited in length. In this paper, we present a direct construction of GCPs, mutually orthogonal Golay complementary sets (MOGCSs) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -ary, including binary CCCs of non-power of two lengths to widen their application in the recent communication field. First, a generalised Boolean function (GBF) based truncation technique is used to construct GCPs of non-power of two lengths which has never been reported before. Then Golay complementary sets (GCSs) and MOGCSs of lengths of the form <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{m-1}+2^{m-3}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m \geq 5$ </tex-math></inline-formula> ) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{m-1}+2^{m-2}+2^{m-4}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m \geq 6$ </tex-math></inline-formula> ) are generated by higher order GBFs. The later length of MOGCSs with direct construction is not available in the literature. Finally, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -ary sequences including binary CCCs with non-power of two lengths are constructed using the union of MOGCSs. There is no such direct construction of binary CCC of non-power of two lengths available in the literature. The column sequence peak to mean envelope power ratio (PMEPR) have been investigated for GCSs and CCCs respectively, and compared with existing works. The column sequence PMEPR of resultant CCCs is effectively upper bounded by 2, which is much lower than that of paraunitary based CCC construction. The proposed construction is also compared with existing works.

Integrated Radar and Communications Waveform Design Based on Multi-Symbol OFDM

Integrated radar and communications (IRC) technology has become very important for civil and military applications in recent years, and IRC waveform design is a major challenge for IRC development. In this paper, we focus on the IRC waveform design based on the multi-symbol orthogonal frequency division multiplexing (OFDM) technique. In view of the defects resulting from high peak-to-mean envelope power ratios (PMEPRs) and high range sidelobes in IRC systems, an intelligent and effective IRC waveform design method jointly optimized with the PMEPR and peak-to-sidelobe ratio (PSLR) is proposed. Firstly, a flexible tone reservation (TR)-based IRC waveform structure is applied in both temporal and frequency domains, i.e., multi-symbol OFDM waveform. Secondly, the optimization problem considering PMEPR and PSLR and extending them to the Lp-norm form is reformulated. Then, the conjugate gradient of the objective function is analytically derived and the conjugate gradient algorithm (CGA) is presented to simultaneously improve the PMEPR and PSLR. Finally, the simulation results show that the proposed algorithm can efficiently generate IRC waveforms with an excellent PMEPR, PSLR, radar signal-to-noise ratio (SNR), and bit error rate (BER) performance.

A New Construction of 4q-QAM Golay Complementary Sequences.

Quadrature amplitude modulation (QAM) constellation and Golay complementary sequences (GCSs) are usually applied in orthogonal frequency division multiplexing (OFDM) systems to obtain a higher data rate and a lower peak-to-mean envelope power ratio (PMEPR). In this paper, after a sufficient search of the literature, it was found that increasing the family size is an effective way to improve the data rate, and the family size is mainly determined by the number of offsets in the general structure of QAM GCSs. Under the guidance of this idea, we propose a new construction for -QAM GCSs through generalized Boolean functions (GBFs) based on a new description of a -QAM constellation, which aims to enlarge the family size of GCSs and obtain a low PMEPR. Furthermore, a previous construction of -QAM GCSs presented by Li has been proved to be a special case of the new one, and the family size of new sequences is much larger than those previously mentioned, which means that there was a great improvement in the data rate. On the other hand, a previous construction of 16-QAM GCSs presented by Zeng is also a special case of the new one in this paper, when . In the meantime, the proposed sequences have the same PMEPR upper bound as the previously mentioned sequences presented by Li when applied in OFDM systems, which increase the data rate without degrading the PMEPR performance. The theoretical analysis and simulation results show that the proposed new sequences can achieve a higher data rate and a low PMEPR.

Index Modulation With Circularly-Shifted Chirps for Dual-Function Radar and Communications

In this study, we propose index modulation (IM) with circularly-shifted chirps (CSCs) (CSC-IM) for dual-function radar and communication (DFRC) systems. The proposed scheme encodes the information bits with the CSC indices and the phase-shift keying (PSK) symbols. It allows the receiver to exploit the frequency selectivity naturally in fading channels by combining IM and wideband CSCs. It also leverages the fact that a CSC is a constant-envelope signal to achieve a controllable peak-to-mean envelope power ratio (PMEPR). For radar functionality, CSC-IM maintains the good autocorrelation (AC) properties of a chirp by ensuring that the transmitted CSCs are separated apart sufficiently in the time domain through index separation (IS). We investigate the impact of IS on spectral efficiency (SE) and obtain the corresponding mapping functions. For theoretical results, we derive the union bound (UB) of the block error rate (BLER) for arbitrary chirps and the Cramer-Rao lower bounds (CRLBs) for the range and reflection coefficients for the matched filter (MF)- based estimation. We also prove that complementary sequences (CSs) can be constructed through CSCs by linearly combining the Fourier series of CSCs. Finally, through comprehensive comparisons, we demonstrate the efficacy of the proposed scheme for DFRC scenarios.

High-Efficiency Optimization Algorithm of PMEPR for OFDM Integrated Radar and Communication Waveform Based on Conjugate Gradient

The tone reservation (TR) approach is mainly adopted to reduce the peak-to-mean envelope power ratio (PMEPR) of orthogonal frequency division multiplexing (OFDM) waveform with low TR ratio (TRR) in classic 4G communication systems. However, for the OFDM integrated radar and communication waveform, high TRR is necessary to simultaneously maintain the radar detection performance as well as communication performance. For cases with high TRR, the traditional waveform optimization algorithms have low execution efficiency and a poor PMEPR convergence level, and thus a new algorithm is needed. This paper proposes a new PMEPR optimization algorithm based on conjugate gradient. Firstly, by introducing the concept of Lp-norm, the PMEPR of the OFDM waveform is accurately remodeled as the objective function of the waveform optimization problem. Secondly, the conjugate gradient of the objective function is analytically derived to form the basis of the efficient PMEPR optimization. Finally, a PMEPR optimization algorithm based on the Polak–Ribière–Polyak (PRP) conjugate gradient is proposed. The simulation results verified the proposed algorithm in terms of optimization efficiency, as well as convergence level, and the initial experimental results suggested the practicality of the proposed algorithm.

New Construction of Multiple Complete Complementary Codes With Inter-Set Zero Cross-Correlation Zone

Controlling the peak-to-mean envelope power ratio (PMEPR) of multi-carrier code division multiple access (MC-CDMA) transmissions is a notoriously important problem. In this letter, a direct construction of multiple complete complementary codes (CCCs) with inter-set zero cross-correlation zone (ZCCZ) is proposed based on multivariable functions. The presented construction has an advantage over the previous works with regard to the new flexible parameters and low column sequence PMEPR, which may give an extra benefit in fulfilling different requirements and managing PMEPR in MC-CDMA systems with multiple cells. In addition, it turns out that the combination of the constructed CCCs results in a new optimal Z-complementary code set (ZCCS).

A Generic Complementary Sequence Construction and Associated Encoder/Decoder Design

In this study, we propose a flexible construction of complementary sequences (CSs) that can contain zero-valued elements. To derive the construction, we use Boolean functions to represent a polynomial generated with a recursion. By applying this representation to recursive CS constructions, we show the impact of construction parameters such as sign, amplitude, phase rotation used in the recursion on the elements of the synthesized CS. As a result, we extend Davis and Jedwab’s CS construction by obtaining independent functions for the amplitude and phase of each element of the CS, and the seed sequence positions in the CS. The proposed construction shows that a set of distinct CSs compatible with non-contiguous resource allocations for orthogonal frequency-division multiplexing (OFDM) and various constellations can be synthesized systematically. It also leads to a low peak-to-mean-envelope-power ratio (PMEPR) multiple accessing scheme in the uplink and a low-complexity recursive decoder. We demonstrate the performance of the proposed encoder and decoder through comprehensive simulations.

Constructions of Z-optimal Type-II quadriphase Z-complementary pairs

Investigating (periodic) and design sequences with good correlation properties have numerous applications in communications. Research on designing sequence pairs with good correlation properties started in the early 1950's thanks to M.J. Golay. Ideally, one of our ultimate aims in this context is to design a set of sequences whose out-of-phase auto-correlation magnitudes and cross-correlation magnitudes are very small, preferably zero. The so-called Z-complementary pair (ZCP) is one of the suitable candidates. 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). ZCPs have been widely used in different communication systems and are closely related with almost difference families, which are useful in studying partially balanced incomplete block design. Despite remarkable progress in designing ZCPs, only a few constructions of quadriphase ZCPs (QZCPs) have been reported in the literature up to now. Aiming to reducing this gap, we explore in this article several methods to design such sequences. More specifically, we propose a recursive construction based on the concatenation of sequences aimed to design Type-II QZCPs. Also, based on Turyn's construction method, we present another new Type-II QZCPs. The proposed constructions lead to Z-optimal Type-II even-length QZCPs (E-QZCPs) and Type-II odd-length QZCPs (O-QZCPs) with large ZCZ widths. Finally, we derive upper bounds for the peak-to-mean envelope-power ratio (PMEPR) of the proposed ZCPs. It turns out that our constructions lead to ZCPs with low PMEPR. These characteristics allow our QZCPs to be seen as promising for practical uses in some modern communication systems.

Reduction of sidelobe levels in multicarrier radar signals via the fusion of hill patterns and geometric progression

Multi-carrier waveforms have several advantages over single-carrier waveforms for radar communication. Employing multi-carrier complementary phase-coded (MCPC) waveforms in radar applications has recently attracted significant attention. MCPC radar signals take advantage of orthogonal frequency division multiplexing properties, and several authors have explored the use of MCPC signals and the difficulties associated with their implementation. The sidelobe level and peak-to-mean-envelope-power ratio (PMEPR) are the key issues that must be addressed to improve the performance of radar signals. We propose a scheme that applies pattern-based scaling and geometric progression methods to enhance sidelobe and PMEPR levels in MCPC radar signals. Numerical results demonstrate the improvement of sidelobe and PMEPR levels in the proposed scheme. Additionally, autocorrelations are obtained and analyzed by applying the proposed scheme in extensive simulation experiments.

New Mutually Orthogonal Complementary Sets With Non-Power-of-Two Lengths

Mutually orthogonal complementary sets (MOCSs) have found a number of practical applications in wireless communications and radar owing to their perfect aperiodic auto-correlation and cross-correlation properties. Recently, toward the challenge of designing MOCSs with non-power-of-two lengths, direct constructions were presented by Wu et al. using generalized Boolean functions (GBFs). In this letter, a new construction of MOCSs is proposed based on GBFs, which leads to MOCSs with flock size 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sup> and length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> + 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> , whose set size is 1/2 of the flock size, where integers 0 ≤ t <; k ≤ m. In addition, the constructed MOCSs can yield column sequence peak-to-mean envelope power ratio (PMEPR) of at most 2.

A Direct Construction of Optimal ZCCS With Maximum Column Sequence PMEPR Two for MC-CDMA System

The high peak-to-mean envelope power ratio (PMEPR) is a major problem in multicarrier code-division multiple-access (MC-CDMA) system. In this letter, we have proposed a new optimal Z-complementary code set (ZCCS) using higher-order (≥ 2) generalized Boolean functions (GBFs). The proposed ZCCS has maximum column sequence PMEPR of 2 and it achieves the theoretical upper bound of optimality.

A Direct and Generalized Construction of Polyphase Complementary Sets 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 (≥ 3) GBFs. We obtain polyphase complementary sequences with maximum PMEPR of 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sup> and 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+2</sup> - 2M where k,M are non-negative integers that can be easily derived from the GBF associated with the CS.

Joint Reduction of PMEPR and Sidelobe in Multicarrier Radar Signals using ZC and SC Method

Employing the multitone waveforms for radar applications has attracted many authors in recent days. Several researchers have investigated the use of multitone waveform and challenges associated while implementation. The serious drawback of using multicarrier waveforms is the high Peak to Mean Envelope Power Ratio (PMEPR) values recorded and large sidelobes. To overcome PMEPR and sidelobe drawbacks a novel method is suggested for reducing sidelobe levels. The projected method applies zad-off chu phase sequence for multicarrier complementary phase coded (MCPC) signals. The comparison of integrated sidelobe ratio and peak sidelobe is obtained. Autocorrelations and complex envelope of the MCPC signal is obtained from the above methods are analyzed with extensive simulations. It is also possible to reduce the PMEPR and sidelobe simultaneously by using secondary user method. The suggested technique results with reduction in sidelobe and PMEPR levels.

Low-PMEPR Preamble Sequence Design for Dynamic Spectrum Allocation in OFDMA Systems

Orthogonal Frequency Division Multiple Access (OFDMA) with Dynamic spectrum allocation (DSA) is able to provide a wide range of data rate requirements. This paper is focused on the design of preamble sequences in OFDMA systems with low peak-to-mean envelope power ratio (PMEPR) property in the context of DSA. We propose a systematic preamble sequence design which gives rise to low PMEPR for possibly non-contiguous spectrum allocations. With the aid of Golay-Davis-Jedwab (GDJ) sequences, two classes of preamble sequences are presented. We prove that their PMEPRs are upper bounded by 4 for any DSA over a chunk of four contiguous resource blocks.

Multiple Complete Complementary Codes With Inter-Set Zero Cross-Correlation Zone

Complete complementary codes (CCCs) have found a number of practical applications in wireless communications owing to their perfect aperiodic auto-correlation and cross-correlation properties. In particular, an important application of CCCs is in interference-free multi-carrier code-division multiple-access (MC-CDMA) systems. The available number of complementary codes determines the system capacity. To enlarge the system capacity, this paper focuses on constructing multiple CCCs with inter-set zero cross-correlation zone (ZCCZ) property based on generalized Boolean functions (GBFs). To the best of our knowledge, such multiple CCCs have not been reported in the literature. The obtained multiple CCCs can provide advantages in applications to MC-CDMA systems with multiple cells. As a byproduct, optimal aperiodic Z-complementary code sets (ZCCSs) with low peak-to-mean envelope power ratio (PMEPR) can be derived by combining these CCCs.

Golay complementary sets with large zero odd-periodic correlation zones

<p style='text-indent:20px;'>Golay complementary sets (GCSs) are widely used in different communication systems, i.e., GCSs could be used in OFDM systems to control peak-to-mean envelope power ratio (PMEPR). In this paper, inspired by the work on GCSs with large zero correlation zone given by Chen et al in 2018, we investigate the relationship between GCSs and zero odd-periodic correlation zone (ZOCZ) sequence sets, and present GCSs with flexible sequence set sizes, sequence lengths, large ZOCZ and low PMEPR. Those proposed sequences could be applied in OFDM system for synchronization.

Two constructions for 16-QAM complementary sequence sets with non-power-of-two length

Complementary sequences with quadrature amplitude modulation (QAM) symbols have important applications in OFDM communication systems. The objective of this paper is to present two constructions of 16-QAM complementary sequence sets of size 4. The first construction generates four complementary sequences of length L = 2m− 1 + 2v, where m and v are two positive integers with 1 ≤ v ≤ m − 1. The second one leads to four complementary sequences of length L = 2m− 1 + 1. It turns out that the peak-to-mean envelope power ratios (PMEPRs) of constructed complementary sequence sets are upper bounded by 4.

Binary Z-Complementary Pairs With Bounded Peak-to-Mean Envelope Power Ratios

Three constructions of Z-complementary pairs (ZCPs) were proposed with upper bounds on their peak-to-mean envelope power ratios (PMEPRs) by Xie and Sun. However, there were no derivations of the PMEPR bounds given by Xie and Sun and, actually, one of those is incorrect. In this letter, a corresponding correct PMEPR bound is provided with the proof. In addition, the PMEPR property of binary ZCPs is studied in this letter. Based on specific autocorrelation properties of some existing ZCPs, the upper bound on PMEPR can be obtained. Therefore, ZCPs with bonus PMEPR properties can be regarded as potential alternatives of Golay complementary pairs (GCPs) in practical applications since they can exist for more lengths.

Complementary M ‐ary orthogonal spreading OFDM architecture for HF communication link

A complementary M-ary orthogonal spreading (CMOS) architecture with orthogonal frequency division multiplexing (OFDM) is proposed to improve performance of bit-error rate (BER) and spectrum efficiency for high frequency (HF) communications. The CMOS-OFDM architecture is based on orthogonal complementary pairs with their central elements being zero. It is well known that complementary pairs theoretically reduce peak-to-mean envelope power ratio (PMEPR) of OFDM due to their ideal aperiodic auto-correlation properties. However, many practical OFDM applications, such as HF OFDM and IEEE 802.11, require that no data should be modulated to direct current (DC) subcarrier, which will destroy ideal properties of traditional complementary pairs and hence increase their PMEPRs. Compared with traditional complementary pairs, the proposed zero-centre complementary pairs (ZCCPs) in CMOS-OFDM architecture may maintain ideal properties and hence be more suitable for OFDM systems as long as zero element in the centre is modulated to DC subcarrier. The corresponding simulation results and numerical analyses over the HF fading channel modelled by ITU-R F.1487 are provided. Different from the previous researches on HF OFDM systems, the proposed HF CMOS-OFDM architecture using the constructed ZCCPs not only possesses excellent BER performance, but also may firmly resist PMEPR to 3 dB or near to 3 dB.