In this paper, we theoretically analyse the influence of intersymbol interference (ISI) and continuous wave interference (CWI) on the bit error rate (BER) performance of the spread spectrum (SS) system using a real-valued Huffman sequence under the additive white Gaussian noise (AWGN) environment. The aperiodic correlation function of the Huffman sequence has zero sidelobes except the shift-end values at the left and right ends of shift. The system can give the unified communication and ranging system because the output of a matched filter (MF) is the ideal impulse by generating transmitted signal of the bit duration T=NTc, N=2n, n=1,2,… from the sequence of length M=2kN+1, k=0,1,…, where Tc is the chip duration and N is the spreading factor. As a result, the BER performance of the system is improved with decrease in the absolute value of the shift-end value, and is not influenced by ISI if the shift-end value is almost zero-value. In addition, the BER performance of the system of the bit duration T=NTc with CWI is improved with increase in the sequence length M=2kN+1, and the system can decrease the influence of CWI.

This paper presents a method of generating sets of orthogonal and zero-correlation zone (ZCZ) periodic real-valued sequences of period 2n, n ≥ 1. The sequences admit a fast correlation algorithm and the sets of sequences achieve the upper bound on family size. A periodic orthogonal sequence has the periodic autocorrelation function with zero sidelobes, and a set with orthogonal sequences whose mutual periodic crosscorrelation function at zero shift is zero. Similarly, a ZCZ set is the set of the sequences with zero-correlation zone. In this paper, we derive the real-valued periodic orthogonal sequences of period 2n from a real-valued Huffman sequence of length 2ν+1, ν being a positive integer and ν ≥ n, whose aperiodic autocorrelation function has zero sidelobes except possibly at the left and right shift-ends. The orthogonal and ZCZ sets of real-valued periodic orthogonal sequences are useful in various systems, such as synchronous code division multiple access (CDMA) systems, quasi-synchronous CDMA systems and digital watermarkings.

The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone for both periodic and aperiodic correlation functions. The proposed sequences can be constructed from a pair of Hadamard matrices of orders n0 and n1. The constructed sequence set consists of n0 n1 ternary sequences, each of length n0(m+2)(n1+Δ), for a non-negative integer m and Δ ≥ 2. The zero-correlation zone of the proposed sequences is |τ| ≤ n0m+1-1, where τ is the phase shift. The proposed sequence set consists of n0 subsets, each with a member size n1. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a zero-correlation zone with a width that is approximately Δ times that of the correlation function of sequences of the same subset (intra-subset correlation function). The inter-subset zero-correlation zone of the proposed sequences is |τ| ≤ Δn0m+1, where τ is the phase shift. The wide inter-subset zero-correlation enables performance improvement during application of the proposed sequence set.

A new class of ternary sequence with a zero-correlation zone is introduced. The proposed sequence sets have a zero-correlation zone for both periodic and aperiodic correlation functions. The proposed sequences can be constructed from a pair of Hadamard matrices of size n0n0 and a Hadamard matrix of size n1n1. The constructed sequence set consists of n0 n1 ternary sequences, and the length of each sequence is (n1+1) for a non-negative integer m. The zero-correlation zone of the proposed sequences is |τ|≤ -1, where τ is the phase shift. The sequence member size of the proposed sequence set is equal to times that of the theoretical upper bound of the member size of a sequence set with a zero-correlation zone.

A new class of ternary sequence having a zero-correlation zone (zcz), based on Hadamard matrices, is presented. The proposed sequence construction can simultaneously generate a finite-length ternary zcz sequence set and a periodic ternary zcz sequence set. The generated finite-length ternary zcz sequence set has a zero-correlation zone for an aperiodic function. The generated periodic ternary zcz sequence set has a zero-correlation zone for even and odd correlation functions.

The present paper introduces a new approach to the construction of a class of ternary sequences having a zero-correlation zone. The cross-correlation function of each pair of the proposed sequences is zero for phase shifts within the zero-correlation zone, and the auto-correlation function of each proposed sequence is zero for phase shifts within the zero-correlation zone, except for zero-shift. The proposed sequence set has a zero-correlation zone for periodic, aperiodic, and odd correlation functions. As such, the proposed sequence can be used as a finite-length sequence with a zero-correlation zone. A set of the proposed sequences can be constructed for any set of Hadamard sequences of length n. The constructed sequence set consists of 2n ternary sequences, and the length of each sequence is (n+1)2m+2 for a non-negative integer m. The periodic correlation function, the aperiodic correlation function, and the odd correlation function of the proposed sequences have a zero-correlation zone from -(2m+1-1) to (2m+1-1). The member size of the proposed sequence set is of the theoretical upper bound of the member size of a sequence having a zero-correlation zone. The ratio of the number of non-zero elements to the the sequence length of the proposed sequence is also .