Identify more non-golay complementary sequences for OFDM with low PMEPR using multi-dimensional root pairs

Abstract

Abstract-Recently, sub-root pairs and sequences are introduced to identify Davis-Jedwab (DJ) codes, non-Davis-Jedwab (non-DJ) Golay complementary sequences (GCS) and nonGolay complementary sequences (non-GCS) for OFDM with low PMEPR. In this paper, we extend sub-root pairs to superroot pairs. A discrete version of super-root pairs called multidimensional root pairs are used to build arbitrarily interleaving Boolean functions of long length. The newly identified arbitrarily interleaving Boolean functions can produce more non-DJ GCS and non-GCS with PMEPR at most pre-chosen positive number not always being a power of 2. In this way, we propose an efficient method to identify more codes with low PMEPR for OFDM.Index Term-Golay complementary sequences, OFDM, PMEPR, Root pair.In multicarrier communications, the orthogonal frequency division multiplexing (OFDM) has been made use widely. However, a major drawback of OFDM signals is the high peak to mean envelope power ratio (PMEPR) (1, m).Recently, sub-root pairs which is called seed extension in [15] are introduced to identify Davis-Jedwab (DJ)-codes, non-Davis-Jedwab (non-DJ) Golay complementary sequences (GCS) and non-Golay complementary sequences (non-GCS) for OFDM with low PMEPR [12]. However, the binary variables of the sub-root pairs' Boolean function representations can not employ an arbitrarily interleaving pattern with those of DJ-codes. This is a drawback when come to the non-DJ Galay complementary sequences (GCS) which is discovered recently and explained in [8], [9]. In this paper, we generalize subroot pairs to super-root pairs which can be used to construct longer codes with low PMEPR for OFDM by any arbitrarily interleaving patten with DJ-codes. A discrete version of superroot pairs called multi-dimensional root pairs are used to build arbitrarily interleaving Boolean functions of long length, which can identify more non-DJ GCS and non-GCS with PMEPR at most pre-chosen positive number not always being power of 2. In this way, we propose an efficient method to identify more codes with low PMEPR for OFDM. I. NOTATIONS AND PRELIMINARIESBefore proceeding further, let us introduce the OFDM signals, the PMEPR and the related concepts at first. Throughout this paper ξ = exp (2πj/M ), where M is a positive integer. Let an M -ary phase shift keying (MPSK) constellation be denoted by ξ A. OFDM and Power ControlLet j be the imaginary unit, i.e., j 2 = −1. For an MPSK modulation OFDM, let a codeword c = (c 0 , . . . , c n−1 ) with c ∈ ξ Z M , the frequency separation between any two adjacent subcarriers is ∆f = 1/T . Then the n subcarrier complex baseband OFDM signal can be represented aswhere 0 ≤ t < T . The instantaneous power of the complex envelope s c (t) is defined by P c (t) = |s c (t)| 2 .So the peak-to-mean power ratio (PMEPR) of the codeword c is defined by PMEPR(c) = 1 n sup 0≤t<T |s c (t)| 2 .