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...nces [6] as codewords in OFDM, since their PMEPR is at most 2 in q-ary phase-shift keying (PSK) modulation [27]. Major progress has been made by Davis and Jedwab [4]; slightly generalized by Paterson =-=[23]-=-, it was proved that a large family of polyphase Golay sequences of length 2 m organizes in m!/2 cosets of a ∗ This work was supported in part by the German Science Foundation (DFG) under Grant FI 470...

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...hogonal frequency-division multiplexing (OFDM), due to their small peak-to-mean envelope power ratio (PMEPR). However, the major advances in this context are due to Davis and Jedwab [24] and Paterson =-=[25]-=-, who derived tight bounds for the PMEPR of Golay complementary sequences 0018-9448/$25.00 © 2008 IEEEPEZESHKI et al.: DOPPLER RESILIENT GOLAY COMPLEMENTARY WAVEFORMS 4255 and related codes from cose...

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...mmunications Standards Institute (ETSI) Broadband Radio Access Networks (BRAN) committee. These classes of sequences enjoy PMEPR as low as and are very attractive for this reason [5], [6], [10], [9], =-=[12]-=-. In [6], Davis and Jedwab developed a powerful theory which yields -PSK Golay sequences as unions of cosets of the classical Reed–Muller codes and new generalizations of them. Special realization of ...

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...ngth N = 2 m Complementary Sequences (CS) are (Almost) Orthogonal to F1m [4,3]. Length 2 m CS over Z 2 h, as formed using the Davis-Jedwab construction, DJm, are also Roughly Orthogonal to each other =-=[3,8]-=-. This paper shows that DJm is (Almost) Orthogonal to Lm, and therefore each member of DJm has a Peak-to-Average Power Ratio (PAPR) ≤ 2.0 under all Linear Unimodular Unitary Transforms (LUUTs) of leng...

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...al form of the Golay sequence pair (a[x]) and (b[x]) of Theorem 9 is immediate, as stated in Corollary 10; the case H = 2h of this corollary was given by Davis and Jedwab [4, Theorem 3], and Paterson =-=[17]-=- showed that the case H ̸= 2h holds without modification to the construction in [4]: Corollary 10. Let m ≥ 1 be integer and let e ′ 0 , e0, e1, . . . , em ∈ ZH. For any permutation π of {1, . . . , m}...

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... 1.97. It is evident from the figure that their power sum is 2.00 everywhere. Length 2 m CS over Z 2 h, as formed using the Davis-Jedwab construction, DJm,h, are also Roughly Orthogonal to each other =-=[16, 9, 26, 33, 21]-=-, i.e. they form a codeset with reasonable Euclidean distance. For example, here are the 48 codewords in DJ3,1, having a minimum Hamming Weight of 2 m−2 = 2 between codewords, and where each codeword ...

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...der to increase the code rate at the cost of a slightly larger PMEPR. While in [4] such cosets have been identified with an exhaustive search, a more sophisticated theory was developed by Paterson in =-=[12]-=-; it was shown that each coset of RM2h(1, m) inside RM2h(2, m) can be partitioned into complementary sets of size 2k+1 , where k is a nonnegative integer that can be easily determined from a represent...