Aperiodic quadriphase Z-complementary sequences, which include the conventional complementary sequences as special cases, are introduced. It is shown that, the aperiodic quadriphase Z-complementary pairs are normally better than binary ones of the same length, in terms of the number of Z-complementary pairs, and the maximum zero correlation zone. New notions of elementary transformations on quadriphase sequences and elementary operations on sets of quadriphase Z-complementary sequences are presented. In particular, new methods for analyzing the relations among the formulas relative to sets of quadriphase Z-complementary sequences and for describing the sets are proposed. The existence problem of Z-complementary pairs of quadriphase sequences with zero correlation zone equal to 2, 3, and 4 is investigated. Constructions of sets of quadriphase Z-complementary sequences and their mates are given.

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The logistic map is a chaotic mapping. Although several studies have examined logistic maps over real domains with infinite/finite precisions, there has been little analysis of the logistic map over integers. Focusing on differences between the logistic map over the real domain with infinite precision and the logistic map over integers with finite precision, we herein show the characteristic properties of the logistic map over integers and discuss the sequences generated by the map.

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We investigate binary sequence pairs with two-level correlation in terms of their corresponding cyclic difference pairs (CDPs). We define multipliers of a cyclic difference pair and present an existence theorem for multipliers, which could be applied to check the existence/nonexistence of certain hypothetical cyclic difference pairs. Then, we focus on the ideal case where all the out-of-phase correlation coefficients are zero. It is known that such an ideal binary sequence pair exists for length v= 4u for every u ≥ 1. Using the techniques developed here on the theory of multipliers of a CDP and some exhaustive search, we are able to determine that, for lengths v ≤ 30, (1) there does not exist “any other” ideal binary sequence pair and (2) every example in this range is equivalent to the one of length v = 4u above. We conjecture that if there is a binary sequence pair with an ideal two-level correlation then its in-phase correlation must be 4. This implies so called the circulant Hadamard matrix conjecture.

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Let n, k, e, m be positive integers such that n ≥ 3, 1 ≤ k ≤ n - 1, gcd(n, k) = e, and $m={n\\over e}$ is odd. In this paper, for an odd prime p, we derive a lower bound for the minimal distance of a large class of p-ary cyclic codes C_l with nonzeros α^-1, α^-(pk+1), α^-(p3k+1), …, α^{-(p(2l-1)k+1)}, where $1\\leq l\\leq {m-1\\over 2}$ and α is a primitive element of the finite field F_pⁿ. Employing these codes, p-ary sequence families with a flexible tradeoff between low correlation and large size are constructed.

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Binary sequence pairs as a class of mismatched filtering of binary sequences can be applied in radar, sonar, and spread spectrum communication system. Binary sequence pairs with two-level periodic autocorrelation function (BSPT) are considered as the extension of usual binary sequences with two-level periodic autocorrelation function. Each of BSPT consists of two binary sequences of which all out-phase periodic crosscorrelation functions, also called periodic autocorrelation functions of sequence pairs, are the same constant. BSPT have an equivalent relationship with difference set pairs (DSP), a new concept of combinatorial mathematics, which means that difference set pairs can be used to research BSPT as a kind of important tool. Based on the equivalent relationship between BSPT and DSP, several families of BSPT including perfect binary sequence pairs are constructed by recursively constructing DSP on the integer ring. The discrete Fourier transform spectrum property of BSPT reveals a necessary condition of BSPT. By interleaving perfect binary sequence pairs and Hadamard matrix, a new family of binary sequence pairs with zero correlation zone used in quasi-synchronous code multiple division address is constructed, which is close to the upper theoretical bound with sequence length increasing.

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This paper presents a ZCZ code which are combinedly used for spreading sequences and a synchronization symbol in quasi-synchronous CDMA systems using PSK, ASK or BFSK. Furthermore a simple matched filter is presented, which simultaneously calculates correlations with any sequences in the ZCZ code.

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In this paper, the optimum combination of optical pseudo-noise (PN) code and modulation scheme to achieve high total data transmission rate is presented. Moreover, the bit error rate (BER) performance of a wireless OCDMA system using chip-level detection is evaluated through theoretical analysis in the multi-user case. It is shown that, in a wireless OCDMA system with chip-level detection, the total data transmission rate of a multi-pulse pulse position modulation (MPPM) systems with optical pseudo-noise code generated by an M-sequence is better than that of an MPPM system with optical orthogonal code and that of an MPPM system with an extended prime code sequence. Moreover, the total data transmission rate of an MPPM/SIK system using modified pseudo orthogonal M-sequence sets can achieve more than 1.0[bit/chip].

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In this paper, newly-found properties of the pseudo-ternary maximum-length shift register sequences (pseudo-ternary M-sequences) are described. In particular, the balance properties, the run-length distribution, the cross-correlation properties, and the decimation relationships are shown. The pseudo-ternary M-sequence is obtained by subtracting the one-chip shifted version from the {+1, -1}-valued M-sequence. Moreover, in this paper, performances of the direct sequence spread spectrum (DS/SS) system using the pseudo-ternary M-sequence are analyzed. In the performance evaluation, tracking error performance (jitter) and bit error rate (BER) performance that takes the jitter into account in DS/SS system with a pseudo-ternary M-sequence non-coherent DLL are evaluated. Using the pseudo-ternary M-sequence instead of the conventional M-sequences can improve the tracking error performance about 2.8[dB]. Moreover, BER of the DS/SS system using the pseudo-ternary M-sequence is superior about 0.8[dB]to that using the {+1, -1}-valued M-sequence.

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Spreading sequences with appropriate negative auto-correlation can reduce average multiple access interference (MAI) in asynchronous DS/CDMA systems compared with the conventional Gold Sequences generated by linear feedback shift registers (LFSRs). We design spreading sequences with negative auto-correlation based on Gold sequences and the chaos theory for the Bernoulli map. By computer simulations, we evaluate BER performances of asynchronous DS/CDMA systems using the proposed sequences.

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Continuously increasing the bandwidth to enhance the capacity is impractical because of the scarcity of spectrum availability. Fortunately, on the basis of the characteristics of the multihop cellular networks (MCNs), a new compact frequency reuse scheme has been proposed to provide higher spectrum utilization efficiency and larger capacity without increasing the cost on network. Base stations (BSs) and relay stations (RSs) could transmit simultaneously on the same frequency according to the compact frequency reuse scheme. In this situation, however, mobile stations (MSs) near the coverage boundary will suffer serious interference and their traffic quality can hardly be guaranteed. In order to mitigate the interference while maintaining high spectrum utilization efficiency, this paper introduces a fractional frequency reuse (FFR) scheme into multihop cellular networks, in which the principle of FFR scheme and characteristics of frequency resources configurations are described, then the transmission (Tx) power consumption of BS and RSs is analyzed. The proposed scheme can both meet the requirement of high traffic load in future cellular system and maximize the benefit by reducing the Tx power consumption. Numerical results demonstrate that the proposed FFR in compact frequency reuse achieves higher cell coverage probability and larger capacity with respect to the conventional schemes.

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Being a new feature of next generation of wireless networks, Mobile Multi-hop Relay (MMR) is proposed for the purpose of coverage extension and throughput enhancement in LTE-Advanced, IEEE 802.16j/m. Besides, with the help of relay, the system energy consumption could be well saved. In this paper, an energy saving scheduling scheme is proposed for OFDMA based two-hop relay systems. The novel scheme adjusts the modulation and coding (MC) mode and allocates the transmit power dynamically according to the resource intensity. It can also guarantee the Quality of Service (QoS) of different services by setting the scheduling priority. The simulation results show that the novel scheduling scheme can reduce energy consumption up to 76.27% compared to the conventional scheduling scheme, and achieve higher throughput while guaranteeing QoS.

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In this paper, we proposed the compact construction of a matched filter for integrand code, which do not require the high-rate clock pulse in two-valued PWM (pulse width modulation) code, using a real-valued shift-orthogonal finite-length sequence, which has a sharp aperiodic autocorrelation function with zero sidelobes except at left and right shift-ends. This matched filters are implemented on a field programmable gate array (FPGA) corresponding to 400, 000 logic gates. A proposed matched filter for the sequence of length 129 can be constructed by the circuit scale of about 47% compared with conventional filter.

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In frequency-hopping (FH) multiple access systems, frequency-hopping sequences (FHSs) with optimal Hamming correlation properties are needed. Based on the d-form functions with ideal autocorrelation properties, a new set of FHSs is constructed. The new FHS set is optimal with respect to the Peng-Fan bounds and each FHS in the set is optimal with respect to the Lempel-Greenberger bound.

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The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone (ZCZ). This sequence set is referred to as a ZCZ sequence set. The proposed sequence construction generates a ZCZ sequence set from a perfect sequence pair or a single perfect sequence. The proposed method can generate an optimal ZCZ sequence set, the member size of which reaches the theoretical bound.

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In this paper, we calculate autocorrelation of new generalized cyclotomic sequences of period pⁿ for any n > 0, where p is an odd prime number.

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