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73
OFDM or SingleCarrier Block Transmissions?
, 2004
"... We compare two block transmission systems over frequencyselective fading channels: orthogonal frequencydivision multiplexing (OFDM) versus singlecarrier modulated blocks with zero padding (ZP). We first compare their peaktoaverage power ratio (PAR) and the corresponding power amplifier backoff ..."
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Cited by 39 (0 self)
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We compare two block transmission systems over frequencyselective fading channels: orthogonal frequencydivision multiplexing (OFDM) versus singlecarrier modulated blocks with zero padding (ZP). We first compare their peaktoaverage power ratio (PAR) and the corresponding power amplifier backoff for phaseshift keying or quadrature amplitude modulation. Then, we study the effects of carrier frequency offset on their performance and throughput. We further compare the performance and complexity of uncoded and coded transmissions over random dispersive channels, including Rayleigh fading channels, as well as practical HIPERLAN/2 indoor and outdoor channels. We establish that unlike OFDM, uncoded block transmissions with ZP enjoy maximum diversity and coding gains within the class of linearly precoded block transmissions. Analysis and computer simulations confirm the considerable edge of ZPonly in terms of PAR, robustness to carrier frequency offset, and uncoded performance, at the price of slightly increased complexity. In the coded case, ZP is preferable when the code rate is high (e.g., 3 4), while coded OFDM is to be preferred in terms of both performance and complexity when the code rate is low (e.g., 1 2) and the errorcorrecting capability is enhanced. As ZP block transmissions can approximate serial singlecarrier systems as well, the scope of the present comparison is broader.
On Cosets of the Generalized FirstOrder Reed–Muller Code with Low PMEPR
, 2006
"... Golay sequences are well suited for use as codewords in orthogonal frequencydivision multiplexing (OFDM) since their peaktomean envelope power ratio (PMEPR) in qary phaseshift keying (PSK) modulation is at most 2. It is known that a family of polyphase Golay sequences of length 2m organizes in ..."
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Cited by 23 (3 self)
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Golay sequences are well suited for use as codewords in orthogonal frequencydivision multiplexing (OFDM) since their peaktomean envelope power ratio (PMEPR) in qary phaseshift keying (PSK) modulation is at most 2. It is known that a family of polyphase Golay sequences of length 2m organizes in m!/2 cosets of a qary generalization of the firstorder Reed–Muller code, RMq(1, m). In this paper a more general construction technique for cosets of RMq(1, m) with low PMEPR is established. These cosets contain socalled nearcomplementary sequences. The application of this theory is then illustrated by providing some construction examples. First, it is shown that the m!/2 cosets of RMq(1, m) comprised of Golay sequences just arise as a special case. Second, further families of cosets of RMq(1, m) with maximum PMEPR between 2 and 4 are presented, showing that some previously unexplained phenomena can now be understood within a unified framework. A lower bound on the PMEPR of cosets of RMq(1, m) is proved as well, and it is demonstrated that the upper bound on the PMEPR is tight in many cases. Finally it is shown that all upper bounds on the PMEPR of cosets of RMq(1, m) also hold for the peaktoaverage power ratio (PAPR) under the Walsh–Hadamard transform.
Doppler resilient Golay complementary pairs for radar,” presented at the
 IEEE Statist. Signal Process. Workshop (SSP
, 2007
"... We present a systematic way of constructing a Doppler resilient sequence of Golay complementary waveforms for radar, for which the composite ambiguity function maintains ideal shape at small Doppler shifts. The idea is to determine a sequence of Golay pairs that annihilates the loworder terms of th ..."
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Cited by 17 (1 self)
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We present a systematic way of constructing a Doppler resilient sequence of Golay complementary waveforms for radar, for which the composite ambiguity function maintains ideal shape at small Doppler shifts. The idea is to determine a sequence of Golay pairs that annihilates the loworder terms of the Taylor expansion of the composite ambiguity function. The ProuhetThueMorse sequence plays a key role in the construction of Doppler resilient sequences of Golay pairs. We extend this construction to multiple dimensions. In particular, we consider radar polarimetry, where the dimensions are realized by two orthogonal polarizations. We determine a sequence of twobytwo Alamouti matrices, where the entries involve Golay pairs and for which the matrixvalued composite ambiguity function vanishes at small Doppler shifts. 1.
Two Constructions of 16QAM Golay Complementary Sequences
 IEEE Trans. Inform. Theory
"... We present twocL8Lx4kx[8[g of 16QAM Golayc omplementary sequenc4k The size of the set ofc onstrucxI sequenc is (14+ 12m)(m!/2)4 m+1 . Of these, when employed in an OFDM system, (m!/2)4 m+1sequenc4 have PMEPR (peak to mean envelope power ratio) bounded above by 3.6, three subsets of size (4+4m)( ..."
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Cited by 16 (0 self)
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We present twocL8Lx4kx[8[g of 16QAM Golayc omplementary sequenc4k The size of the set ofc onstrucxI sequenc is (14+ 12m)(m!/2)4 m+1 . Of these, when employed in an OFDM system, (m!/2)4 m+1sequenc4 have PMEPR (peak to mean envelope power ratio) bounded above by 3.6, three subsets of size (4+4m)(m!/2)4 m+1 c4 tainsequencfi having PMEPRs less than of 2.8, 2.0, and 1.2 respec40 ely, and a subset of size (m!/2)4 m+1 c4 tains sequenc4 that have PMEPR upperbounded by 0.4. 1 Introducti6 In an excIx4k paper [2], Golayc0xfi04k0L thec40NNIg4k0L ofc4Ifi]]x4 tary binary Golay sequencxg Thesesequenc[ have found numerousapplicg8fi]4 in various fields ofscx[x] and engineering. An important applic4k00 of Golay c0[8]I4k tary sequenc4 is to orthogonalfrequenc division multiplexing (OFDM). This is ac0I unic0L4k tec hnique with a long historywhic h is rapidly emerging as atec hnology ofc hoic in wireless applic4k8L[fi International standards suc h as IEEE 802.11 are employing OFDM for wireless LANapplic4k8][x For wireless applic4k8][x an OFDMbased systemc an be ofpartic4k8 interest becLgI it provides a greater immunity to impulse noise and fast fades and eliminates the need for equalizers, while e#ce4 t hardware implementationsci be realized using FFTtec hniques. One of the major issues in deploying OFDM is the high peak to mean enevelope power ratio (PMEPR) ofunc ded OFDM signals. To prevent spec080 growth of the OFDM signal in the form of intermodulation amongst subc arriers and outofband radiation, the transmit amplifier must be operated in its linear region. Amplifiers with large linear range are expensive and thisc anincNNgI the ce4 of the implementation of OFDM. Moreover, If the peak transmit power is limited, either 1 by regulatory or applic4k]I c onstraints, then a h...
Generalised RudinShapiro Constructions
 WCC2001, WORKSHOP ON CODING AND CRYPTOGRAPHY, PARIS(FRANCE
, 2001
"... A Golay Complementary Sequence (CS) has PeaktoAveragePowerRatio (PAPR) ≤ 2.0 for its onedimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2 m CS, (GDJ CS), originate from certain quadratic cosets of ReedMuller (1, m). These can be g ..."
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Cited by 15 (8 self)
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A Golay Complementary Sequence (CS) has PeaktoAveragePowerRatio (PAPR) ≤ 2.0 for its onedimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2 m CS, (GDJ CS), originate from certain quadratic cosets of ReedMuller (1, m). These can be generated using the RudinShapiro construction. This paper shows that GDJ CS have PAPR ≤ 2.0 under all unitary transforms whose rows are unimodular linear (Linear Unimodular Unitary Transforms (LUUTs)), including one and multidimensional generalised DFTs. We also propose tensor cosets of GDJ sequences arising from RudinShapiro extensions of nearcomplementary pairs, thereby generating many infinite sequence families with tight low PAPR bounds under LUUTs.
A Construction for Binary Sequence Sets with Low PeaktoAverage Power Ratio
"... A recursive construction is provided for sequence sets which possess good Hamming Distance and low PeaktoAverage Power Ratio (PAR) under any Local Unitary Unimodular Transform (including all one and multidimensional Discrete Fourier Transforms). An important instance of the construction identifie ..."
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Cited by 14 (9 self)
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A recursive construction is provided for sequence sets which possess good Hamming Distance and low PeaktoAverage Power Ratio (PAR) under any Local Unitary Unimodular Transform (including all one and multidimensional Discrete Fourier Transforms). An important instance of the construction identifies an iteration and specialisation of the MaioranaMcFarland (MM) construction. I.
A multidimensional approach to the construction and enumeration of Golay complementary sequences
 J. Combin. Theory (A
, 2006
"... We argue that a Golay complementary sequence is naturally viewed as a projection of a multidimensional Golay array. We present a threestage process for constructing and enumerating Golay array and sequence pairs: 1. construct suitable Golay array pairs from lowerdimensional Golay array pairs; 2. a ..."
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Cited by 14 (8 self)
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We argue that a Golay complementary sequence is naturally viewed as a projection of a multidimensional Golay array. We present a threestage process for constructing and enumerating Golay array and sequence pairs: 1. construct suitable Golay array pairs from lowerdimensional Golay array pairs; 2. apply transformations to these Golay array pairs to generate a larger set of Golay array pairs; and 3. take projections of the resulting Golay array pairs to lower dimensions. This process greatly simplifies previous approaches, by separating the construction of Golay arrays from the enumeration of all possible projections of these arrays to lower dimensions. We use this process to construct and enumerate all 2 hphase Golay sequences of length 2 m obtainable under any known method, including all 4phase Golay sequences obtainable from the length 16 examples given in 2005 by Li and Chu [12]. 1
GolayDavisJedwab Complementary Sequences and RudinShapiro Constructions
 IEEE TRANS. INFORM. THEORY
, 2001
"... A Golay Complementary Sequence (CS) has a PeaktoAveragePowerRatio (PAPR) ≤ 2.0 for its onedimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2 m CS, (GDJ CS), originate from certain quadratic cosets of ReedMuller (1, m). These can b ..."
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Cited by 12 (4 self)
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A Golay Complementary Sequence (CS) has a PeaktoAveragePowerRatio (PAPR) ≤ 2.0 for its onedimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2 m CS, (GDJ CS), originate from certain quadratic cosets of ReedMuller (1, m). These can be generated using the RudinShapiro construction. This paper shows that GDJ CS have a PAPR ≤ 2.0 under all 2 m ×2 m unitary transforms whose rows are unimodular linear (Linear Unimodular Unitary Transforms (LUUTs)), including one and multidimensional generalised DFTs. In this context we define Constahadamard Transforms (CHTs) and show how all LUUTs can be formed from tensor combinations of CHTs. We also propose tensor cosets of GDJ sequences arising from RudinShapiro extensions of nearcomplementary pairs, thereby generating many more infinite sequence families with tight low PAPR bounds under LUUTs. We m m−⌊ then show that GDJ CS have a PAPR ≤ 2 2 ⌋ under all 2m × 2m unitary transforms whose rows are linear (Linear Unitary Transforms (LUTs)). Finally we present a radix2 tensor decomposition of any 2 m × 2 m LUT.
Complementary Sets, Generalized ReedMuller Codes, and Power Control for OFDM
 IEEE Trans. Inform. Theory
, 2007
"... The use of errorcorrecting codes for tight control of the peaktomean envelope power ratio (PMEPR) in orthogonal frequencydivision multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each qphase (q is even) sequence of len ..."
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Cited by 10 (1 self)
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The use of errorcorrecting codes for tight control of the peaktomean envelope power ratio (PMEPR) in orthogonal frequencydivision multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each qphase (q is even) sequence of length 2 m lies in a complementary set of size 2 k+1, where k is a nonnegative integer that can be easily determined from the generalized Boolean function associated with the sequence. For small k this result provides a reasonably tight bound for the PMEPR of qphase sequences of length 2m. A new 2hary generalization of the classical Reed–Muller code is then used together with the result on complementary sets to derive flexible OFDM coding schemes with low PMEPR. These codes include the codes developed by Davis and Jedwab as a special case. In certain situations the codes in the present correspondence are similar to Paterson’s code constructions and often outperform them.