Optimal design of perfect DFT sequences

In this paper, we propose a novel scheme to construct a large set with N(N+1)N(N+1) perfect sequences of length NN, derived from an Inverse Discrete Fourier Transform (IDFT) of Chu and maximum-length sequences. This optimum set of perfect periodic autocorrelation sequences has a maximum absolute value of periodic cross-correlation strictly lower than NN and close to the well known lower bound SQRT(NN). Moreover, we present a method to transform these perfect sequences into orthogonal sequences. A similar method is also proposed to obtain optimum bipolar codes derived from an alternative set of N2N2 perfect sequences.In the design of perfect sequences, the difficulty is to achieve both low cross-correlation and low peak-to-average power ratio (PAPR). Many of the proposed perfect DFT sequences should have low PAPR and thus can be applied in an OFDM–CDMA (Orthogonal Frequency-Division Multiplexing–Code Division Multiple Access) communication system or in a simple CDMA communication system. Alternatively, the proposed perfect DFT sequences may be useful for pre-coded mapping in OFDM communication systems or for the design of radar waveform diversity sets.