Serious multiple access interference (MAI) exists in uplink transmission of a multi-carrier code division multiple access (MC-CDMA) system in frequency-selective fading channels because orthogonality among codes cannot be restored. A novel MC-CDMA system is proposed in this paper to avoid MAI by employing Fourier duals of sparse perfect Gaussian integer sequences (SPGISs) as frequency-domain spreading codes. The SPGISs are obtained by linearly combining four base sequences or their cyclic-shift equivalents using nonzero Gaussian integer coefficients of equal magnitudes. The number of nonzero elements of SPGISs is 16 at most. The Fourier dual is the fast Fourier transform (FFT) of a SPGIS. Thus, when the Fourier duals of SPGISs are employed as frequency-domain spreading codes, the corresponding time-domain spreading codes are SPGISs. Furthermore, the modulated symbols of users should be properly allocated and the receiver architecture should be redesigned to avoid MAI. The computational complexity of the proposed MC-CDMA system is much lower than that of the traditional MC-CDMA system at the transmitter. Simulation results demonstrate both the bit error rate and peak-to-average power ratio performance of the proposed MC-CDMA system outperform those of the orthogonal frequency division multiple access, single-carrier frequency division multiple access, and the traditional MC-CDMA systems.

A complex number whose real and imaginary parts are both integers is called a Gaussian integer . A Gaussian integer sequence is said to be perfect if it has an ideal periodic autocorrelation function (PACF) where all out‐of‐phase values are zero. Further, the degree of a Gaussian integer sequence is defined as the number of distinct non‐zero Gaussian integers within one period of the sequence. Recently, the perfect Gaussian integer sequences have been found important practical applications as signal processing tools for orthogonal frequency‐division multiplexing systems. The present article generalises the authors’ earlier paper by Lee et al. (2015) related to the Gaussian integer sequences with ideal PACFs. By the applications of two‐tuple‐balanced binary sequences and cyclic difference sets, a number of new degree‐2 perfect Gaussian integer sequences with different periods are obtained.

A Gaussian integer is a complex number whose real and imaginary parts are both integers. Meanwhile, a sequence is defined as perfect if and only if it has an ideal periodic autocorrelation function. This paper proposes a method for constructing sparse perfect Gaussian integer sequences (SPGISs) in which most of the sequence elements are zero. The proposed SPGISs are obtained by linearly combining four base sequences or their cyclic-shift equivalents using nonzero Gaussian integer coefficients of equal magnitudes. Each base sequence contains four nonzero elements belonging to the set {±1, ±j}. The number of nonzero elements of the constructed SPGISs depends on the choice of complex coefficients and cyclic shifts. However, each SPGIS has at most 16 nonzero elements, irrespective of the sequence length. A systematic investigation is performed into the properties of the SPGISs and their Fourier dual equivalents. Finally, a general expression is derived for a perfect Gaussian integer sequence (PGIS) of length 4n, where n is any positive integer and most of the sequence elements are nonzero.

Multi-carrier code division multiple access (MC- CDMA) systems experience serious multiple access interference in uplink transmission since the orthogonality among codes is destroyed by the frequency-selective fading channels. The comb- spectrum (CS) CDMA system was proposed to overcome this drawback by orthogonally assigning subcarriers to various users. However, the CS-CDMA system has three main drawbacks: 1) the numbers of nonzero elements of various frequency-domain CS codes are different, 2) the nonzero elements of the frequency-domain CS codes have unequal magnitude, and 3) the computational complexity of the transmitter and receiver is extremely high. This study proposes a novel CS-CDMA system, wherein the perfect Gaussian integer sequences are adopted as the frequency-domain CS codes. The proposed CS-CDMA system inherits all the advantages of the traditional CS-CDMA system, and all three drawbacks are overcome. Simulation experiments demonstrate that the improvements of the proposed scheme for quadrature phase-shift keying and 16-quadrature amplitude modulation are approximately 7.5 dB and 4.5 dB, respectively.

A composite number can be factored into either N=mp or N=2n, where p is an odd prime and m, n ≥ 2 are integers. This paper proposes a method for constructing degree-3 and degree-4 perfect Gaussian integer sequences (PGISs) of an arbitrary composite length utilizing an upsampling technique and the base sequence concept proposed by Hu, Wang, and Li. In constructing the PGISs, the degree of the sequence is defined as the number of distinct nonzero elements within one period of the sequence. This paper commences by constructing degree-3 PGISs of odd prime length, followed by degree-2 PGISs of odd prime length. The proposed method is then extended to the construction of degree-3 and degree-4 PGISs of composite length N=mp. Finally, degree-3 and degree-4 PGISs of length N=4 are built to facilitate the construction of degree-3 and degree-4 PGISs of length N=2n, where n ≥ 3.

The symbol interleaving scheme is one of the peak-to-average power ratio (PAPR) reduction schemes for the orthogonal frequency division multiplexing (OFDM) system. Compared with the selected mapping (SLM) and the partial transmit sequence (PTS) schemes, it does not require any extra complex multiplications to generate candidate signals aside from the complex multiplications of inverse fast Fourier transform (IFFT) operations. However, the interleaving scheme still has high computational complexity since it also requires a bank of IFFT operations. In this paper, two time-domain properties of IFFT operations are used to construct the proposed low-complexity PAPR reduction scheme. Simulation results show that the complementary cumulative distribution function (CCDF) of the proposed scheme is close to that of the traditional interleaving scheme when the given threshold γ <; 7.2 dB and N = 256 subcarriers. The CCDF of the proposed scheme is lower than that of the traditional interleaving scheme when γ ≥ 7.2 dB and N = 256 subcarriers.

Multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with space-frequency block coding (SFBC) have a high computational complexity since the number of inverse fast Fourier transforms (IFFTs) required scales in direct proportion to the number of antennas at the transmitter. This paper proposes to generate the SFBC encoded signals of the various antennas in time domain by exploiting the time-domain signal properties and signal correlations among the various transmitter antennas, achieving a significant reduction in computational complexity. In particular, it is demonstrated that the time domain SFBC encoded signals of the various antennas can be obtained from the time domain signal of the first antenna. Therefore, the proposed scheme requires only one IFFT irrespective of the number of transmission antennas. In addition, a low-complexity peak-to-average power ratio (PAPR) reduction scheme is presented based on the proposed transmitter architectures.

A Gaussian integer is a complex number whose real and imaginary parts are both integers. In addition, a sequence is defined to be perfect if and only if the out-of-phase value of the periodic autocorrelation function (PACF) equals zero. This paper commences by presenting a novel class of perfect sequences. The investigated perfect sequences are generated by two groups of base sequences with four base sequences in each group. The nonzero elements of these base sequences belong to the set {±1,±j}. A perfect sequence can be obtained by linearly combining these base sequences or their cyclic shift equivalents with arbitrary nonzero complex coefficients of equal magnitude. In particular, if the complex coefficients are Gaussian integers, the resulting perfect sequences are Gaussian integer sequences and are termed as the Gaussian integer perfect sequences (GIPSs).

Selected mapping (SLM) schemes are commonly employed to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. To decrease the number of inverse fast Fourier transform (IFFT) operations in traditional SLM schemes, the candidate signals can be generated in the time domain by linearly combining the original time-domain transmitted signal with multiple cyclic shift equivalents. However, the weighting coefficients and the number of cyclic shifts should be properly chosen to ensure that the elements of the corresponding frequency domain phase rotation vectors have an equal magnitude. This study presents a number of expressions for meeting this equal-gain-magnitude constraint in orthogonal frequency division multiple access (OFDMA) uplink systems. Of these various solutions, a low-complexity expression is selected to construct the proposed low-complexity scheme that requires only one IFFT. The proposed architecture is proven to be applicable to OFDMA uplink systems using either an interleaved or a sub-band sub-carrier assignment strategy.

Recently, multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with space-frequency block coding (SFBC) has attracted substantial attention because of its robustness toward time selective fading channel. However, SFBC MIMO-OFDM system needs the same number of inverse fast Fourier transforms (IFFTs) as the number of antennas at the transmitter and the computational complexity is extremely high. In addition, it also inherits the disadvantage of a high peak-to-average power ratio (PAPR) from OFDM technique. In this paper, a low-complexity transmitter architecture is proposed for SFBC MIMO-OFDM systems with a general encoding matrix and an arbitrary number of transmitter antennas. The proposed scheme fully exploits the time-domain signal properties and requires only one IFFT. Then, a PRPR reduction scheme is presented by using the proposed transmitter architecture. The PAPR reduction performance of the proposed scheme is slightly worse than that of the traditional selected mapping (SLM) scheme. However, the proposed scheme achieves a substantially lower computational complexity.

The cell search procedure of the third generation partnership project long term evolution (3GPP LTE) includes the time synchronization, the frequency synchronization of frames, and the acquisition of cell identity (Cell ID). The traditional cell search scheme detects the Cell ID by computing the correlation between the received signal and all transmitted sequences. However, it causes high computational complexity and considerable processing time which effect the delay time of services power on, the standby time, the energy consumption, and the cost of manufacture. This paper firstly proposes a perfect sequence with special structure as preamble, and the sequence is linear combination of two base sequences. In addition, a low complexity cell search scheme, which utilizes the proposed perfect sequence, is then proposed in this paper.

High peak-to-average power ratio (PAPR) of the transmitted signals is a major drawback of orthogonal frequency division multiple access (OFDMA) systems. The selected mapping (SLM) method is one of the major schemes employed for PAPR reduction. Unfortunately, the computational complexity of traditional SLM scheme is relatively high since a number of inverse fast Fourier transforms (IFFTs) are required. A low-complexity SLM PAPR reduction scheme is proposed in this paper for interleaved OFMDA uplink, where only one IFFT is needed. The proposed scheme exploits the interleaved mechanism and the time-domain signal property to construct a low-complexity architecture. The candidate signals are generated in time-domain by combining the original time-domain transmitted signal with its cyclic shift equivalents. The PAPR reduction performance of the proposed scheme is marginally poorer than that of the traditional SLM scheme. However, the proposed scheme achieves a substantially lower computational complexity.

The multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with space-frequency block coding (SFBC) is an attractive technique due to its robustness for time selective fading channels. However, the SFBC MIMO-OFDM system also inherits from OFDM systems the drawback of high peak-to-average power ratio (PAPR) of the transmitted signal. The selected mapping (SLM) method is a major scheme for PAPR reduction. Unfortunately, computational complexity of the traditional SLM scheme is relatively high since it requires a number of inverse fast Fourier transforms (IFFTs). In this letter, a low-complexity PAPR reduction scheme is proposed for SFBC MIMO-OFDM systems, needing only one IFFT. The proposed scheme exploits the time-domain signal properties of SFBC MIMO-OFDM systems to achieve a low-complexity architecture for candidate signal generation.

The selected mapping (SLM) is a major scheme for peak-to-average power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) systems. It has been shown that the complexity of the traditional SLM scheme can be substantially reduced by adopting the conversion vectors to replace the inverse fast Fourier transform (IFFT) operations. Each conversion vector is obtained by taking the IFFT of the phase rotation vector. Unfortunately, the corresponding phase rotation vectors of the conversion vectors in do not have equal magnitude, leading to significant degradation in bit error rate (BER) performance. This drawback can be remedied by adopting the perfect sequences as the conversion vectors. This paper presents two novel classes of perfect sequences, which are shown to be compositions of certain base vectors and their cyclic-shift versions. Then, two novel low-complexity SLM schemes are proposed by utilizing the special structures of the perfect sequences. The BER performances of both the proposed schemes are exactly the same as the traditional SLM scheme.