In this research paper, we present a novel method for obtaining the patterns of inputs that generate low-weight codewords in Recursive Systematic Convolutional (RSC) codes, hereafter referred to as low-weight inputs. RSC codes are commonly used as component codes for various concatenated schemes, including the popular Turbo codes. Efficient interleaver design is crucial in improving the error-correcting performance of Turbo codes; therefore, understanding the low-weight input patterns specific to the selected RSC code is essential. Existing graph-based search algorithms face increasing complexity as the constraint length of the RSC code increases. To address this issue, we introduce a method that directly derives the critical low-weight input patterns (up to Hamming weight 4) from the generator function of the RSC code. The proposed method addresses the complexity issue and can be extended to non-recursive systematic convolutional (NRSC) codes by modifying the generator function. To validate our novel method, we compare the union bound obtained using our approach to that obtained via the transfer function method and the simulation results for selected RSC codes. This comparison demonstrates the effectiveness of our method, which shows no significant counting losses.

In this paper, we present a novel design framework for Turbo codes (TCs). Referring to the generator functions of the employed recursive systematic convolutional (RSC) codes, we develop a method to determine not only the multiplicity, but also detailed patterns of low-weight (LW) input and LW parity-check (LWPC) sequences for the component codes. Next, we select the component RSC code based on the knowledge obtained by the proposed method and derive expressions necessary to evaluate the free distance dfof the resultant TC. Finally, we propose a novel interleaver class, named Coset interleaver, with its parameter selection criteria to enlarge df. Based on the proposed design framework, we succeed in designing a rate 1=3 TC with df= 42 for frame size N = 1024. At an Eb=N0of 2dB, our proposed design demonstrates a bit-error rate (BER) of 1:232 × 1010, which represents a significant improvement of 6:18 × 108and 2:207 108when compared to the BERs exhibited by the Quadratic Permutation Polynomial (QPP, df= 30) and S-random (df= 21) interleavers, respectively.

Over multipath channels, complete complementary code division multiple access and convolutional spreading code division multiple access provide inter-channel interference free transmission with an enhanced spectral efficiency. However, the convolutional spreading (CS) operation of the systems is computationally complex and involves a high peak-to-average power ratio. To address such issues, we propose the concatenative complete complementary code (CCCC) division multiple access, named (CCC-CDMA). Since the CCCCs can be generated from the rows of the Walsh-Hadamard or discrete Fourier transform matrices, the CS operation can be implemented using corresponding fast transforms to reduce computational complexity. Simulation results show that the enlargement of the spreading factor strengthens the robustness against clipping noise. The binary CCCC generated by Walsh-Hadamard matrix exhibited excellent robustness against Doppler frequency shifts.

Convolutional spreading code division multiple access (CS-CDMA) system provides an inter-channel interference-free transmission. However, the CS operation of CS-CDMA involves high computational complexity and high peak-to-average power ratio. Addresing such drawbacks, we propose the use of binary Z-connectable complete complementary codes (BZ-CCC) to implement CS operation based on fast Walsh Hadamard transform. With the proposed implementation structure, the CS-CDMA based on BZ-CCC dramatically reduces the computational complexity of CS operation. Simulation results demonstrate that with inherited performance of the traditional CS-CDMA over Rayleigh fading channel, the proposed system has acceptable robustness against clipping noise and excellent robustness against Doppler frequency shifts.

The behavior of single-carrier frequency-division multiaccess with localized subcarrier assignment (localized SC-FDMA) over doubly selective, that is, frequency and time selective, fading channels has not yet been studied well. In this paper, we study a behavior of the localized SC-FDMA channel called the user channel instability, where the standard linear minimum mean-squared error (MMSE) equalizer fails to work properly due to a few excessively small eigenvalues of the user channel matrix, and show that, although it has a crucial effect on the performance of linear minimum mean-square error (MMSE) equalization, its effect can be alleviated with the use of advanced techniques, such as stepwise decision detection and diversity reception with multiple receive antennas.

In this paper, we propose the use of coded constellation rotated vector OFDM (CRV-OFDM) to alleviate the necessity for a convolutional code with a large free distance dfin coded OFDM. Theoretical analysis indicates that CCRV-OFDM of vector length-M attains diversity order min{P, Mdf} over a length-P Rayleigh fading channel with an appropriately designed interleaver. We employ Almost linear interleaver (ALI) to CCRV-OFDM and introduce a union bit error rate (BER) bound which is used for the purpose of the parameter selection of ALI. The effectiveness of our design and the superiority of CCRV-OFDM on BER over coded OFDM are demonstrated through simulations.

In this paper, we study pairwise error probability (PEP) of a system employing constellation-rotated vector orthogonal frequency-division multiplexing (CRV-OFDM), which is an enhancement of vector OFDM (V-OFDM) with enhanced diversity, over a frequency-selective channel with both carrier frequency offset (CFO) and Doppler frequency spread. First, we extend the work of Rugini and Banelli, which is known to give a good bit-error rate (BER) approximation for the standard OFDM system only with CFO, to PEP evaluation for CRV-OFDM and discuss its limitations. Then, we discuss the conditionally Gaussian characteristi2cs of the Doppler-induced interference and propose a conditionally Gaussian PEP approximation. Confirming a good match of the conditionally Gaussian PEP approximation and with simulation results, we propose a new semianalytical PEP lower bound. The new lower bound is computationally feasible and is shown by simulation to be tight for small to moderate CFO. Finally, a computationally more feasible approximation of the lower bound is also proposed. Our discussion reveals, as a by-product, why the Gaussian assumption for the Doppler-induced interference works for standard OFDM systems although the assumption is actually incorrect.

This paper proposes a novel deterministic inter-leaver, called almost linear interleaver (ALI) as the generalization of block and linear interleavers, and discusses its parameter/depth selection for coded orthogonal frequency division multiplexing (COFDM) system over Rayleigh fading channel. The concept of diversity guard is introduced to guarantee the achievable maximum diversity order with a reasonable complexity. Simulation results shown that the proposed design always outperforms random interleaver (RI) and the block interleaver (BI) adopted by the IEEE 802.11a standard.

In this paper, we propose the use of constellation rotated vector OFDM (CRV-OFDM) to combat a fast fading channel, which accompanies with carrier frequency offset (CFO) and Doppler frequency spread (DFS). Employing Gaussian approximation of interference, we give pair-wise error probability bounds of CRV-OFDM in terms of the CFO and DFS. The theoretical analysis indicates that robustness of CRV-OFDM against fast fading increases with M, the length of vectorized symbols, and such argument is confirmed by running computer simulations.

In this paper, convolutional spreading CDMA with cyclic prefix (CS-CDMA/CP) employing the zero-correlation-zone (ZCZ) code generated from the Chu sequence is proposed as a novel multi-access scheme for fast fading multipath channels. Analysis results demonstrate that the system remains approximately multiuser interference (MUI)-free even when the system is heavily loaded and subject to severe Doppler spreads. An effective channel estimation method based on B-spline approximation is also proposed. Simulation results show, in combination with the Probabilistic Data Association (PDA) equalization, the system significantly outperforms the DS-CDMA system employing Linear Minimum Mean Squared Error (LMMSE) chip-wise equalization and polynomial interpolation-based channel estimation from medium to high user population.

The complete complementary code (CCC) that was proposed by Suehiro and Hatori is a sequence family, that is a set of sequence sets, with ideal correlation sums. Numerous studies in the literature show its applications to direct-spread code-division multiple access (DS-CDMA) systems for interchannel interference (ICI)-free communication with improved spectral efficiency. In this paper, we propose a systematic framework for the construction of CCCs based onN-shift cross-orthogonal sequence families (N-CO-SFs) . We show theoretical bounds on the size ofN-CO-SFs and CCCs and give a set of four algorithms for their generation and extension. The algorithms are optimal in the sense that the size of the resultant sequence families achieves theoretical bounds and, with the algorithms, we can construct an optimal CCC consisting of sequences whose lengths are not only almost arbitrary but even variable between sequence sets. We also discuss the family size, alphabet size, and length of constructible CCCs based on the proposed algorithms.

Although the single antenna vector OFDM (VOFDM) proposed by Xia shows performance robust to channel spectral nulls, it does not necessarily attain full diversity for multi-path fading channels. It is known that the degradation in diversity order is sometimes rescued by the rotation of constellation. A simple application of constellation rotation to the V-OFDM system does not, however, improve its performance. In this paper, we discuss the sub-channel spectral structure of the V-OFDM signal and give upper bounds on its pair-wise error probability over multi-path Rayleigh fading channels and propose a novel constellation-rotated V-OFDM (CRV-OFDM) with improved diversity. To this end, we design rotation angles for sub-channel symbols to minimize upper bounds on BER. Simulation results show that the proposed CRV-OFDM attains diversity order min{M,P} for the vector length M and the number of paths P. As the results, for BER 10¿4, CRV-OFDM improves the performance of V-OFDM by 2 dB for both BPSK and QPSK modulation when M is 2, and, for M = 4, the improvement factor is about 1.3 dB. We also discuss the effects of M on the transmitter and receiver complexities and on the peak-to-averate power ratio. Finally, we compare several methods for rotational angle determination.

Convolutional spreading CDMA with cyclic prefix (CS-CDMA/CP) enables multiuser interference-free (MUI-free) transmission over multipath downlink channels with the use of zero correlation zone (ZCZ) codes. However, MUI-free transmission is guaranteed only when the data length D, channel delay L, and ZCZ length Z satisfy Z+1 ≥ D + L. In this paper, we consider the situation that MUI-free transmission is not realized inevitably because of excessive multipath delays or deliberately because of the necessity to get a higher bandwidth efficiency, clarify the structure of MUI in the CS-CDMA/CP system employing M-ZCZ codes, and propose iterative partial multiuser detection (IPMUD). The detection is implemented at symbol-level (after despreading) and the number of users jointly considered can be adjusted flexibly to offer a tradeoff between system performance and receiver complexity. The performance of the proposed scheme is verified numerically by density evolution approach and BER simulations. The CS-CDMA/CP system with IPMUD is shown to be much less complex than the DS-CDMA system with Wang and Poor's turbo MUD receiver and to be less complex and better, in terms of bit error rate (BER) performance, than the DS-CDMA system with iterative chip-wise equalization receivers.

Although the single antenna vector OFDM (V-OFDM) proposed by Xia is robust to channel spectral nulls, it does not necessarily attain full diversity for multi-path fading channels. In this paper, we propose a novel constellation-rotated V-OFDM (CRV-OFDM) system based on modified V-OFDM, and analyze its performance over Rayleigh fading channels. In CRV-OFDM, we design rotation angles for each symbol to minimize upper bounds on bit error rate (BER) with full diversity order. Our simulation results show that, compared with V-OFDM, proposed CRV-OFDM always attains the maximum diversity order determined by the vector length M. As a result, for BER 10-4, CRV-OFDM improves the performance of V-OFDM by 2 dB for both BPSK and QPSK modulation for M = 2, and, for M = 4, the improvement is about 1.3 dB. To verify optimality of the derived angles, we also test, in therms of BER, some other angles including the angles derived from minimum product distance (MPD) criterion and compare with the theoretical union bounds and show that the BERs take the smallest values at our derived optimal angles.

Convolutional spreading CDMA with cyclic prefix (CS-CDMA/CP) enables multiuser interference-free (MUI-free) transmission over multipath downlink channels with the use of zero correlation zone (ZCZ) codes. However, MUI-free transmission is guaranteed only when the data length D, channel delay L, and ZCZ length Z satisfy Z + 1 ges D + L, and the user population is constraint to be K les [N/(Z+1)], where N is the code length. In this paper, for the purpose of allowing higher bandwidth efficiency for more active users, we propose an iterative partial multiuser detector for CS-CDMA/CP with M-ZCZ code to allow Z + 1 < D + L. Because the detector is implemented in the symbol-level (after despreading) and only a partion of users are jointly considered, its receiver complexity is expected to be acceptable for a mobile terminal. Comparison with the DS-CDMA system employing chip-equalization receiver shows that the CS-CDMA/CP system employing the proposed receiver offers a better tradeoff between the performance and receiver complexity, which indicates its potential application in future wireless communications.

A code-division multiple access (CDMA) communication system achieves the maximum spectral efficiency over multipath fading channels if employed spreading sequences have ideal correlations, i.e., the ideal auto-correlation that are zero except for zero shift and the ideal cross-correlations that are zero for all shifts. Unfortunately, such sequences are known non-existent and, Suehiro and Hatori proposed a sequence family with ideal correlation sum called the complete complementary code (CCC). For (quasi-) synchronous CDMA systems, the ideal correlation sum of CCC provides an inter-channel interference (ICI)-free communication and CCC based CDMA (CCC-CDMA) improves spectral efficiency significantly. In previous work, we have proposed a general and systematic construction of the optimal CCC. However, in special cases, the proposed construction results in CCCs with extra interesting properties. In this paper, we propose a new type of CCC called the Z-connectable CCC (Z-CCC), which gives a sequence set with zero correlation zone (ZCZ) by connecting codes in its complementary codes. We also present two Z-CCCs which consist of rows of the discrete Fourier transform (DFT) and Hadamard matrices. Due to Z-CCC provides the guard-part reduced sub-packet structure, Z-CCC based CDMA (Z-CCC-CDMA) realizes higher spectral efficiency than the traditional CCC-CDMA and, intimate relationships of the present Z-CCCs and the DFT matrix or Hadamard matrix allows low implementation complexity.

This paper studies the impact of fast fading on the performance of coded convolutional spreading CDMA with cyclic prefix (CS-CDMA/CP) combined with iterative detection, which was originally proposed for multiuser interference-free (MUI-free) downlink transmission over a quasi-static multipath fading channel. We show that the CS-CDMA/CP system in conjunction with a single pilot, with zero-correlation-zone code from an M-sequence (M-ZCZ), and with iterative detection works also well for fast fading, and the impacts of Doppler spreads can be made negligible without bandwidth efficiency loss by the employment of excess channel spread configuration and iterative partial multiuser detection. We compare the proposed system and the standard W-CDMA system for downlink transmission by simulation and show that both systems enjoy time-diversity effects of fast fading and that, although the W-CDMA system performs better for a small number of users, the CS-CDMA/CP system performs much better for the number of users from moderate to as large as processing gain.

In an approximately synchronous CDMA (ASCDMA) system, zero correlation zone (ZCZ) sequences are known as the sequences to eliminate co-channel and multi-path interferences. Therefore, numerous constructions of zero correlation zone (ZCZ) sequences have been introduced e.g. based on perfect sequences, m-sequences and complete complementary codes etc.. However, the previous construction method which based on complete complementary code is lacking for merit figure. In this paper, a new construction method of ZCZ sequences based on complete complementary codes is proposed. By proposed method, the ZCZ sequences with greater than 1/2 merit figure are constructable.

N-shift cross-orthogonal sequences are powerful materials for constructing complete complementary codes. In this paper, we present six theorems concerning general construction and expansion methods with the least upper bounds for N-shift cross-orthogonal sequences and complete complementary codes. Applying the theorems that about construction and expansion method of N-shift cross-orthogonal sequences, many types of N-shift cross orthogonal sequences are constructed systematically. Those include the sequence sets consisting of different lengths and include previous classes as special cases. Based on the generated N-shift cross orthogonal sequences, a complete complementary code are constructed by the theorem of construction method of complete complementary code. The last theorem which is about expansion method of complete complementary code are given for increase the number of sequence sets.