A single-symbol-decodable space-time block code with full rate and low peak-to-average power ratio

Three desirable properties of a four-antenna spacetime block code are full rate, full diversity, and single-symbol decodability. Previously reported space-time codes that achieve all three properties do so at the expense of the peak-to-average power ratio (PAPR). A fourth desirable property of a space-time block code is that its PAPR be the same as that of the underlying quadrature-amplitude modulation alphabet. In this letter we introduce space-time codes for three and four transmit antennas that achieve all four properties; these codes use a diversity technique based on constellation stretching. Numerical results for quasistatic Rayleigh-fading channels show that, despite their low PAPR, the proposed codes are comparable in SNR performance to the best-performing single-symbol decodable space-time codes for three and four transmit antennas.     

No-Zero-Entry Space-Time Block Codes Over Time-Selective Fading Channels for MIMO Systems

In MIMO systems, space-time block code (STBC) is good solution for improving system performance. Among the STBCs, coordinate interleaved orthogonal designs (CIODs) combined with QR-decomposition-based decision-feedback decoding (QR-DDF) allow achieving good performance for time-selective fading channels. However, half of entries in codeword matrix of CIODs are zeros. These zero entries result in high peak-to-average power ratio (PAPR) and also impose a severe constraint on hardware implementation of the code when turning off some of the transmitting antennas whenever a zero is transmitted. In this paper, we propose a new design of space-time block codes without zero entry in codeword matrix (NZE-STBCs) for time-selective fading channels. The main advantage of the proposed NZE-STBCs is that its peak-to-average ratio (PAPR) is 3 dB lower than that of CIODs, and its hardware implementation is also easier due to eliminating on-off switchers without sacrificing performance. Moreover, similar as CIODs, the proposed NZE-STBCs can use low complexity QR-DDF decoder over time-selective fading channels to enhance performance and reduce decoding complexity. Simulation results show that the proposed NZE-STBCs outperform CIODs for three transmit antennas while performing the same for two and four transmit antennas.     

Reduction of PAPR in coded OFDM using fast Reed-Solomon codes over prime Galois fields

In this work, two new techniques using Reed–Solomon (RS) codes over GF(257) and GF(65,537) are proposed for peak-to-average power ratio (PAPR) reduction in coded orthogonal frequency division multiplexing (OFDM) systems. The lengths of these codes are well-matched to the length of OFDM frames. Over these fields, the block lengths of codes are powers of two and we fully exploit the radix-2 fast Fourier transform algorithms. Multiplications and additions are simple modulus operations. These codes provide desirable randomness with a small perturbation in information symbols that is essential for generation of different statistically independent candidates. Our simulations show that the PAPR reduction ability of RS codes is the same as that of conventional selected mapping (SLM), but contrary to SLM, we can get error correction capability. Also for the second proposed technique, the transmission of side information is not needed. To the best of our knowledge, this is the first work using RS codes for PAPR reduction in single-input single-output systems.     

Concatenated space-time block coding with trellis coded modulation in fading channels

Trellis coded modulation (TCM) is a bandwidth efficient transmission scheme that can achieve high coding gain by integrating coding and modulation. This paper presents an analytical expression for the error event probability of concatenated space-time block coding with TCM which reveals some dominant factors affecting the system performance over slow fading channels when perfect interleavers are used. This leads to establishing the design criteria for constructing the optimal trellis codes of such a concatenated system over slow flat fading channels. Through simulation, significant performance improvement is shown to be obtained by concatenating the interleaved streams of these codes with space-time block codes over fading channels. Simulation results also demonstrate that these trellis codes have better error performance than traditional codes designed for single-antenna Gaussian or fading channels. Performance results over quasi-static fading channels without interleaving are also compared in this paper. Furthermore, it is shown that concatenated space-time block coding with TCM (with/without interleaving) outperforms space-time trellis codes under the same spectral efficiency, trellis complexity, and signal constellation.     

Multilevel block codes for Rayleigh-fading channels

New multilevel block codes for Rayleigh-fading channels are presented. At high signal-to-noise ratios (SNRs), the proposed block codes can achieve better bit error performance over TCM codes, optimum for fading channels, with comparable decoder complexity and bandwidth efficiency. The code construction is based on variant length binary component block codes. As component codes for the 8-PSK multilevel block construction, the authors propose two modified forms of Reed-Muller codes giving a good trade-off between the decoder complexity and the effective code rates. Code design criteria are derived from the error performance analysis. Multistage decoding shows very slight degradation of bit error performance relative to the maximum likelihood algorithm     

A Low-BER Clipping Scheme for PAPR Reduction in STBC MIMO-OFDM Systems

Clipping is a simple scheme to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. Further, it can be extended to space-time block coding (STBC) multiple-input multiple-output (MIMO) OFDM systems for the PAPR reduction. In the conventional clipping schemes for STBC MIMO-OFDM systems, the input symbols are first encoded and then clipped. In this paper, a new scheme is proposed, where the clipping operation is performed before space-time block coding. We theoretically prove that the proposed scheme has better bit-error rate (BER) performance while maintaining the same PAPR reduction as the conventional schemes. Additionally, we derive the symbol-error rate (SER) and BER expressions for the new scheme over multipath fading channels. The simulation results show a good match with our analysis.     

Constructing LDPC codes by error minimization progressive edge growth

A novel approach to constructing Tanner graphs using progressive edge growth (PEG) is introduced. It yields LDPC codes providing minimized block error probability in Binary Erasure Channels (BEC). The constructed codes exhibit superior performance over codes generated by previously known algorithms, both for BEC and AWGN channels. Furthermore, an upper bound on the expected block error probability in the error floor region of the generated codes is derived. This allows analytical prediction of the codes' error floor performance. Finally, the method is generalized for generating simple in implementation LDPC codes based on lifted graphs.     

Performance of the deliberate clipping with adaptive symbolselection for strictly band-limited OFDM systems

The performance of the strictly band-limited OFDM systems with deliberate clipping is examined in terms of the peak-to-average power ratio (PAPR) and the resultant bit error performance. The clipping is performed on the OFDM signals sampled at the Nyquist rate, followed by the ideal low-pass filter, Since the low-pass filter considerably enlarges the PAPR, there is a severe limitation in PAPR reduction capability. Thus, in order to achieve further reduction of the PAPR, the application of the adaptive symbol selection scheme is also considered. It is shown that the significant PAPR reduction with moderate complexity can be achieved by the combination of the clipping and the adaptive symbol selection. The price to be paid for PAPR reduction by this scheme is its performance degradation. The paper theoretically analyzes the bit error rate performance of the OFDM system with the Nyquist-rate clipping combined with the adaptive symbol selection, and considers the use of the forward error correction for compensation of the degradation. It is shown that even though the clipping scheme causes severe loss in required signal-to-noise ratio, the use of a powerful channel coding scheme such as turbo codes significantly alleviates the bit error rate performance degradation     

An erasure-based scheme for reduction of PAPR in spatial multiplexing MIMO-OFDM using Reed-Solomon codes over GF(216 + 1)

In this paper, a novel erasure-based scheme which uses long Reed-Solomon (RS) codes over GF(65537) is proposed for the reduction of the peak-to-average power ratio (PAPR) in coded orthogonal frequency division multiplexing (OFDM). The motivation for using the field GF(65537) is to generate long code words (up to 65536 symbols in just one code word). Using long codes results in greater flexibility to search for low PAPR OFDM frames within the subsets of symbols of a code word because RS codes are maximum distance separable and any subset of a high enough number of symbols is sufficient for the recovery of data. Over this field, the lengths of code words are exponents of 2. Hence, low-complexity radix-2 fast Fourier transform can be exploited. RS codes are deployed for both PAPR reduction and error correction. Simulation results show that in similar PAPR reduction performances, the proposed scheme outperforms the previously reported work with RS codes in both error correction and computation complexity. The proposed scheme can be applied to both single-input single-output and multi-input multi-output systems.     

Comparison of decoding algorithms of binary linear block codes inRayleigh fading channels with diversity reception

The word error probability of binary linear block codes is evaluated in Rayleigh fading channels with diversity reception for three decoding algorithms: error correction (EC), error/erasure correction (EEC), and maximum likelihood (ML) soft decoding algorithms. The performance advantage of EEC over EC in the required average SNR decreases as the number of diversity channels increases. The performance advantage of EEC over EC does not depend on the specific value of word error probability although the advantage of ML soft decoding over EC increases for lower word error probability     

Peak‐to‐average power ratio reduction of orthogonal frequency division multiplexing systems using modified tone reservation techniques

This paper proposed a modified tone reservation (TR) technique that can reduce the peak‐to‐average power ratio (PAPR) of the orthogonal frequency division multiplexing (OFDM) system and is able to correct errors to avoid channel interference. The TR technique is a widely used PAPR reduction technique, which divides subcarriers of the OFDM system into two sets to generate peak‐canceling signals and transmit modulated data. The subcarriers used to reduce the PAPR are called the peak reduction tone sets. The mechanism of peak‐canceling signal generation is a primary factor in determining the quality of the PAPR reduction performance of the TR technique. Currently, two signal generation mechanisms exist: TR‐gradient‐based and TR‐clipping‐based techniques. Although TR techniques can effectively reduce the high PAPR in the OFDM system, TR techniques lack the ability to correct errors. Therefore, this paper combined block coded modulation codes and TR techniques to provide the modified TR techniques with error correction abilities. From the simulation results, the modified TR techniques had a superior effect on PAPR reduction performance compared with the conventional TR technique. The modified TR technique also possessed the ability to correct errors during signal transmission. Copyright © 2015 John Wiley & Sons, Ltd.     

Universally optimum block codes and convolutional codes with maximum likelihood decoding

A new proof is presented for the existence of block codes whose error probability under maximum likelihood decoding is bounded asymptotically by the random coding bound universally over all discrete memoryless channels. On the basis of this result, the existence of convolutional codes with universally optimum performance is shown. Furthermore the existence of block codes which attain the expurgated bound universally over all discrete memoryless channels is proved under the use of maximum likelihood decoding.     

Peak-to-average power ratio of selective mapping technology involving a phase generation mechanism based on polar codes for orthogonal frequency division multiplexing with index modulation systems

In this paper, a novel selective mapping (SLM) method is proposed for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing with index modulation (OFDM-IM) systems. In the proposed method, polar codes are used to construct the SLM phase generation mechanism. This systematic structural design is superior to conventional methods in which phases are randomly generated. Moreover, polar codes and Reed–Muller codes are selected to protect the input data of the OFDM-IM system. The weight distribution of the Reed–Muller codes is then used to determine the location data of the active subcarriers in the OFDM-IM system, and these data are used to determine the error correction capacity. Simulation results indicated that the PAPR improvement achieved using the proposed method is similar to that achieved with conventional SLM methods. Moreover, linear block codes are used to construct the active subcarrier selection and SLM phase generation mechanisms to ensure that both mechanisms have systematic structural designs.     

一种利用标准阵列降低PAPR的新方法

针对正交频分复用系统中峰均功率比较大的问题,从分析选择映射法的基本原理和实现框图入手,详细描述了利用线性分组码标准阵列降低OFDM系统PAPR的算法,其核心思想是通过选择陪集中PAPR较小的向量代替选择映射法中的加权向量。最后进行了蒙特卡罗仿真,仿真结果表明,该方法能够明显改善PAPR特性。     

Utilizing a novel root companding transform technique to reduce PAPR in OFDM systems

One major defect in orthogonal frequency division multiplexing systems is the high peak‐to‐average power ratio (PAPR) at the transmitter. The linear nonsymmetrical transform (LNST) technique, one of the companding transform (CT) techniques for PAPR reduction, offers excellent performance, but requires additional side information. In this paper, a new ‘root CT’ technique without additional side information is proposed, and it can reach a good trade‐off between the PAPR reduction and the bit error rate (BER). The theoretical analysis of the proposed root technique is also derived. The simulation results show that the proposed root CT technique can achieve more efficient PAPR reduction and better power spectrum density than those of the LNST technique. The BER of the proposed CT technique without additional side information is close to that of the LNST technique with additional side information when the AWGN or multipath fading channels are considered. Furthermore, the simulation results also demonstrate that the proposed technique offers better performance than that of the µ‐law technique over the AWGN and multipath fading channels. Copyright © 2010 John Wiley & Sons, Ltd.     

Convolutional Spreading CDMA and Comparison With the DS-CDMA With RAKE Receiver

For synchronous downlink direct-sequence code-division multiple access (DS-CDMA), we introduce a cyclic-prefix (CP)-based convolutional spreading CDMA (CS-CDMA/CP) scheme employing zero correlation zone (ZCZ) codes, which gives a class of multiuser interference (MUI)-free CDMA schemes, including Suehiro's CDMA and block spreading (BS) CDMA as special cases. We show that CS-CDMA/CP employing appropriately selected binary and ternary ZCZ codes have good user capacity, peak-to-average power ratio (PAPR), and transmission power loss, compared with previously proposed BS-CDMA schemes. By simulation, we show the effect of PAPR to its bit-error rate (BER) performance when nonlinear amplifiers are used, and also compare its BER performance with the conventional DS-CDMA scheme employing a RAKE receiver     

Analysis of Single-Symbol Detectable Space-Time Block Codes With COD and GCIOD

In this paper, we present a simplified maximum likelihood detection metric for the newly emerging space-time block codes (STBCs) with generalized coordinate interleaved orthogonal design (GCIOD). We also derive the symbol pairwise error probability (PEP) and the union bound on symbol error rate (SER) for a space-time block coded (STBCed) system with single-symbol detection and rotated QAM scheme over flat Rayleigh fading channels. In particular, linear STBCs with complex orthogonal design (COD) and GCIOD are considered. Based on the theoretical analysis, the symbol PEP of the GCIOD codes is related to the transmit power, signal-to-noise ratio, and the rotated angle of the rotated QAM scheme. However, the symbol PEP of the COD code is irrelevant to the rotated angle. It is shown that simulation results match well with our analysis. Thus, the union bounds on SER can be applied to predict the performance of a STBCed system with adaptive code selection between the full-rate COD and GCIOD codes.     

Peak-to-average power control in OFDM using standard arrays of linear block codes

We propose an efficient scheme to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems by using the standard arrays of linear block codes. Our scheme may be regarded as a modified version of the selective mapping (SLM), which is a probabilistic method to reduce the PAPR by selecting a signal with minimum PAPR from several candidates as the transmit signal. Because the coset leaders of a linear code are used for scrambling in our scheme, no side information is required to be transmitted and the received signal can be easily decoded by syndrome decoding. Simulation results show that our scheme has good performance in PAPR reduction.     

一种非线性信道MIMO-OFDM系统性能改进算法

多输入多输出正交频分复用(MIMO-OFDM)可以提高系统在频率选择性衰落信道的传输性能.与OFDM系统一样,MIMO-OFDM系统也存在高峰值平均功率比(PAPR)的问题.为此,提出了一种降低空时分组编码MIMO-OFDM系统PAPR的正交部分传输序列算法,运用这种算法,利用傅里叶变换的性质,通过调整空时编码与基带正交调制的顺序,对两天线发射端,可以降低算法近一半的复杂度,且可以减少一半的边信息.利用高功率放大器的非线性模型,得到了瑞利衰落信道下PAPR降低后系统的误码率性能.仿真结果证明了该方法的有效性.     

Effect of joint spatial correlation on the diversity performance of space?time block codes

We characterize the effect of joint spatial correlation on the diversity performance of multiple-input multiple-output (MIMO) systems. The joint spatial correlation is structured by the coupling matrix whose elements determine the average power coupling between the transmit and receive eigenmodes. We first derive the closed-form expression for the exact symbol error probability (SEP) of orthogonal space?time block codes over jointly correlated MIMO Rayleigh-fading channels. We then show that the achievable diversity order is equal to the number of nonzero elements of the power coupling matrix and establish the Schur monotonicity theorems on the SEP and the effective fading figure as a functional of elements of the power coupling matrix. Diversity, orthogonal space?time block code (OSTBC), Schur monotonicity, spatial correlation, symbol error probability (SEP).