Pilot sequence design over doubly selective channels (DSC) is challenging due to the variations in both the time- and frequency-domains. Against this background, the contribution of this paper is twofold: Firstly, we investigate the optimal sequence design criteria for efficient channel estimation in orthogonal frequency division multiplexing systems under DSC. Secondly, to design pilot sequences that can satisfy the derived criteria, we propose a new metric called oversampled ambiguity function (O-AF), which considers both fractional and integer Doppler frequency shifts. Optimizing the sidelobes of O-AF through a modified iterative twisted approximation (ITROX) algorithm, we develop a new class of pilot sequences called “oversampled low ambiguity zone (O-LAZ) sequences”. Through numerical experiments, we evaluate the efficiency of the proposed O-LAZ sequences over the traditional low ambiguity zone (LAZ) sequences, Zadoff-Chu (ZC) sequences and m-sequences, by comparing their channel estimation performances over DSC.

In this paper, a general class of polyphase sequences called Generalized Zadoff-Chu (GZC) sequences is presented, which is based on a quadratic function with real-valued coefficients. The conventional ZC sequences, P3, and P4 codes are included as special cases of GZC sequences. It is shown that, with the help of grid search algorithm, the optimized GZC sequences have significantly lower PMEPR than the well-known sequences such as Golay sequences, m-sequences, P3 and P4 codes, and ZC sequences. Numerical simulations suggest that the minimum PMEPR tends to a small constant of less than 1.43 dB as the sequence length approaches infinity.

With the explosive growth of spectrum demand for various wireless devices and applications, it is more and more difficult to allocate contiguous spectral bands for radar and communication nowadays. In this paper, the problem of dual-functional radar-communication (DFRC) multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) waveform design under non-contiguous spectrum bands is studied. We consider a flexible spectrum structure where a large number of non-contiguous bands are used for communication and some idle bands which are complementary to the communication bands are exploited for radar detection. The symbols transmitted on the communication bands are first designed by minimizing the multi-user interference (MUI) to enhance the performance of communication. Meanwhile, the radar performance is improved by designing the waveform of idle bands. We formulate the radar beampattern design as a rank-1 approximation problem, which can be solved with a closed-form solution. Numerical results show that we can achieve omnidirectional strict beampattern design and data transmission with zero MUI.

Iterative Twisted Approximation (ITROX), proposed in 2012 by Soltanalian et al., is an interesting algorithm for designing sequences with desired correlation properties. However, when aperiodic correlation of unimodular complementary and Zcomplementary sets (ZCSs) are considered, the correlation magnitudes of the resultant sequence sets of the ITROX algorithm, are not as good as desired. In this work, we have proposed a new modified ITROX algorithm, which can design unimodular ZCSs. Also the correlation levels of the resultant unimodular complementary sequence sets are better as compared to the previous ITROX.

Sequences with low correlation sidelobes have found a wide range of applications in communication systems and RADAR. In this work, we have proposed a computational framework of aperiodic mismatched filtering sequence pairs using iterative twisted approximation (ITROX). A mismatched-filter is a filter where the transmitting sequence and receiving sequence are different (not matched). We have used singular value decomposition (SVD) instead of eigenvalue decomposition (EVD), which is more general, to obtain the resultant sequences. Numerical simulation shows that the resultant aperiodic mismatched filtering sequences have lower sidelobes without reducing too much loss-in-processing gain.

Since its inception in 2013, Golay complementary sequences with periodic zero autocorrelation zones (ZACZs) and cross-correlation zones (ZCCZs), or Golay-ZCZ (zero correlation zone) sequences have special importance in modern communication systems. Till date, all the proposed complementary sequences with periodic ZACZs and ZCCZs have lengths in the form$2^{m}$, where$m$is a natural number. In this paper, we extend such complementary sequences with large periodic ZACZs and ZCCZs to more flexible lengths in the form of non-power-of-two.

A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums at each of the non-zero time-shifts within a certain region, called the zero correlation zone (ZCZ). ZCPs are categorised into two types: Type-I ZCPs and Type-II ZCPs. Type-I ZCPs have the ZCZ around the in-phase position and Type-II ZCPs have the ZCZ around the end-shift position. Till now only a few constructions of Type-II ZCPs are reported in the literature, and all have lengths of the form 2m±1 or N+1 where N=2a10b26cand a, b, c are non-negative integers. In this paper, we propose a recursive construction of ZCPs based on concatenation of sequences. Inspired by Turyn's construction of Golay complementary pairs, we also propose a construction of Type-II ZCPs from known ones. The proposed constructions can generate optimal Type-II ZCPs with new flexible parameters and Z-optimal Type-II ZCPs with any odd length. In addition, we give upper bounds for the PMEPR of the proposed ZCPs. It turns out that our constructions lead to ZCPs with low PMEPR.