Design, analysis, and performance evaluation for BICM-ID withsquare QAM constellations in Rayleigh fading channels

We consider bit-interleaved coded modulation with iterative decoding (BICM-ID) for bandwidth-efficient transmission over Rayleigh fading channels. We propose the design criteria that utilize a large Hamming distance inherited in a low-rate code and a new labeling technique designed specifically for fading channels. This results in a large coding gain over noniterative coded modulation and performance close to that of “turbo” coded modulation with less complexity. We also show that BICM-ID designed for fading channels usually has a very good performance over the additive white Gaussian noise (AWGN) channel while the converse is difficult to achieve. When combined with signal space diversity, diversity order can be improved to twice the diversity order of conventional BICM-ID; therefore, the code complexity can further be reduced while maintaining the same level of performance. Specifically, with the bandwidth efficiency of 2 bits/s/Hz over Rayleigh fading channels, a bit error rate (BER) of 10^-6 can be achieved with 16-QAM, a four-state rate 1/2 code at E_b/N₀ of about seven dB. We also derive performance bounds for BICM-ID with and without signal space diversity over Rayleigh fading channels, which can be easily extended for other types of fading channels     

基于软判决的BICM-ID在Rayleigh信道下的性能研究

从理论上对不同映射方式下的BICM-ID系统在Rayleigh衰落信道中的性能做了分析和估计,通过3种映射方式(SP,SSP,Gray)下BICM-ID系统的性能仿真,对理论分析进行了验证。仿真结果和理论分析吻合,在Rayleigh衰落信道下,SSP映射性能最佳。与其他编码调制方式(TTCM,BICM)的性能相比,在Rayleigh衰落信道下,随着信噪比的增加,BICM-ID性能要优于其他编码调制方式。     

一种高效的联合编码调制分集——迭代接收方案

本文研究了加入迭代解调译码的比特交织编码调制方案,并通过联合编码调制分集扩展此方案。BICM-ID通过信号空间分集增加分集数,并选择最优旋转角度使性能上进一步取得了明显增益。     

Bit-interleaved coded modulation with iterative decoding and 8 PSK signaling

We have suggested bit-interleaved coded modulation with soft decision iterative decoding (BICM-ID) for bandwidth-efficient transmission over Gaussian and fading channels. Unlike trellis coded modulation, BICM-ID has a small free Euclidean distance but large diversity order due to bit interleaving. With iterative decoding, soft bit decisions can be employed to significantly improve the conditional intersignal Euclidean distance. This leads to a large coding gain, comparable to that of turbo TCM, over both Gaussian and Rayleigh fading channels with much less system complexity. We address critical design issues to enhance the decoding performance and provide the analytical bounds on the performance with an ideal feedback assumption. We investigate the performance characteristics of BICM-ID through extensive simulations and show that at high signal to noise ratios, the performance of BICM-ID converges to the performance assuming error-free feedback.     

一种稀疏码本多址接入码本优化设计方法

稀疏码多址接入(SCMA)作为一种具有竞争力的非正交多址接入(NOMA)技术,该技术通过高维调制与稀疏扩频的结合,有效地提升了系统的频谱效率。该文针对现有SCMA码本设计中存在的问题,提出一种同时适用于高斯信道和瑞利衰落信道的SCMA码本优化设计方法。在该方法中,首先通过旋转基准星座和母星座,实现母星座在各个维度上投影点间的最小欧氏距离以及叠加在单个资源块上的总星座中与各用户对应的星座图上星座点间的最小欧氏距离的最大化,以提升SCMA码本在高斯信道下的性能;进而在保持总星座上星座点间最小欧氏距离不变的条件下,通过旋转叠加在单个资源块上多个用户的星座,优化叠加在单个资源块上的与各用户对应的星座图中星座点间最小乘积距离和信号空间分集(SSD)阶数,最后结合Q路坐标交织技术获得额外的分集增益,以提升系统抗信道衰落的能力。仿真结果显示:在高斯信道和瑞利衰落信道下,该文设计的SCMA码本的性能均明显优于华为公司提出的SCMA码本和低密度扩频多址接入(LDS-MA)技术。     

Bit-interleaved coded modulation with iterative decoding using constellation shaping over Rayleigh fading channels

We propose to investigate the performance of bit-interleaved coded modulation with iterative decoding (BICM-ID) over Rayleigh fading channel by using constellation shaping (CS). The (CS) is implemented by inserting shaping block codes between mapping and channel coding functions, in order to generate non-equiprobable distribution of a 16-ary QAM signal constellation. Simulation results carried out on 2-bit/s/Hz 16-QAM BICM-ID indicate that is possible to obtain a gain of 1.2 dB at a BER of 10^-3 compared to the equiprobable 16-QAM BICM-ID schemes. It is also shown that, the error floor level can reduced by applying the signal space diversity technique.     

Maximum achievable diversity order for cascaded Rayleigh fading channels

In this Letter, we investigate the error rate performance of coherent M-ary phase shift keying (M-PSK) modulation over cascaded Rayleigh fading with receive antenna diversity. Through the derived symbol error rate (SER) expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degradation in comparison to conventional Rayleigh channels.     

Performance analysis of coded modulation with generalized selection combining in Rayleigh fading

We consider coded modulation with generalized selection combining (GSC) for bandwidth-efficient-coded modulation over Rayleigh fading channels. Our results show that reception diversity with generalized selection combining can conveniently trade off system complexity versus performance. We provide a number of new results by calculating the cutoff rate, and by deriving analytical upper bounds on symbol-interleaved trellis-coded modulation (TCM) and bit-interleaved-coded modulation (BICM) with GSC. All are verified by simulation. We show that our new bounds on TCM with GSC, which includes maximum ratio combining and selection combining as special cases, are tighter than the previously derived bounds. A new asymptotic analysis on the pairwise error probability, which can be used as a guideline for designing coded modulation over GSC channels, is also given. Finally, we show that BICM with iterative decoding (BICM-ID) can achieve significant coding gain over conventional coded modulation in a multiple-receiving-antenna channel.     

A Communication System Based on Walsh–Hadamard Codes and Constellations for Fading Environments

In this paper, we investigate a new digital communication system based on Walsh-Hadamard codes. The modulator maps a uniformly distributed binary source to a set of symbols with a Gaussian-like distribution. These symbols are then mapped to a 2-D constellation in such a way that performance is improved when transmission occurs over Rayleigh fading channels. We assess the performance of these modulation schemes when the channel is of the nonfrequency-selective Rayleigh fading plus white Gaussian noise type and compare the results to conventional quadrature-amplitude modulation (QAM) schemes with comparable spectral efficiencies. The proposed system provides excellent robustness to fading without the use of common diversity schemes employed in M-ary signaling systems to improve bit-error-rate (BER) performance in such environments.     

Multidimensional Subcarrier Mapping for Bit-Interleaved Coded OFDM With Iterative Decoding

A power and bandwidth-efficient bit-interleaved coded modulation (BICM) with orthogonal frequency-division multiplexing (OFDM) and iterative decoding (BI-COFDM-ID) using combined multidimensional mapping and subcarrier grouping is proposed for broadband transmission in a frequency-selective fading environment. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence, they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multidimensional mapping for bit-interleaved coded modulation with iterative decoding (BICM-ID) in frequency-flat Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with linear constellation preceding (LCP). Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using LCP and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth, and receiver complexity.     

A Novel and Efficient Mapping of 32-QAM Constellation for BICM-ID Systems

Bit-interleaved coded modulation with iterative decoding (BICM-ID) is a bandwidth-efficient technique for both additive white Gaussian noise and fading channels. The asymptotic performance of BICM-ID is strongly determined by how the coded bits are mapped to the symbols of the signal constellation. In this paper an explicit mapping method is presented for 32-QAM using two criteria: (i) maximization of the minimum Euclidean distance between the symbols with Hamming distance one, and (ii) minimizing the number of symbols which have jointly the minimum Hamming distance and the minimum Euclidean distance from each other. Our method is much simpler than the previously-known methods. Compared to previously-known best mapping, the mapping obtained by our method performs significantly better in a BICM-ID system implemented with hard-decision feedback, while its asymptotic performance is almost the same in a BICM-ID system using soft-decision feedback.     

Optimum Pilot Symbol Assisted Modulation

Optimum detectors for pilot symbol assisted modulation (PSAM) signals in Rayleigh and Rician fading channels are derived. Conventional PSAM as used on Rayleigh fading channels is also employed on Rician fading channels. It is shown that the conventional PSAM receiver is optimal for binary phase shift keying in Rayleigh fading but suboptimal for Rician fading and suboptimal for 16-ary quadrature amplitude modulation in Rayleigh fading. The optimum PSAM signal detector uses knowledge of the specular component and also jointly processes the pilot symbols and the data symbol. The performance of the optimum detector is analyzed and compared with that of the conventional detector. It is concluded that substantial gains can be achieved by exploiting knowledge of the specular component while joint processing of the data symbol with the pilot symbols may offer small benefits.     

Performance Analysis and Design Criteria of BICM-ID With Signal Space Diversity for Keyhole Nakagami-$m$ Fading Channels

This paper generalizes the application bit-interleaved coded modulation with iterative decoding (BICM-ID) using signal space diversity (SSD) over keyhole Nakagami-$m$ fading channels. The tight union bound on the asymptotic error performance is first analytically derived. The near-optimal rotation matrix with respect to both the asymptotic performance and the convergence behavior is then determined. In particular, it is demonstrated that the suitable rotation matrix is the one that has 1) all entries equal in magnitude, 2) a high diversity order, and 3) a large minimum product of the ratios between squared distances to the power $m$ and log-squared distances to the power $m$ of the rotated constellation scaled by factors of signal-to-noise ratio (SNR) and the parameter $m$ . Various analytical and simulation results show that by employing SSD with a sufficiently large dimension, the error performance can closely approach that over an additive white Gaussian noise (AWGN) channel, even in the worst case of keyhole fading.      

Error Performance of Rotated Phase Shift Keying Modulation over Fading Channels

In this paper, the modulation diversity is used to improve the performance of M-PSK modulation over fading channels. Modulation diversity can be achieved by rotating the signal constellation and using component interleaving. We derive symbol error probability expressions for rotated uncoded M-PSK over Ricean fading channels and obtain optimal rotation angles for M-PSK (M = 2, 4, 8). We show that rotated signal constellations with component interleaving improve the performance of M-PSK significantly as compared to the unrotated one over Rayleigh and Ricean fading channels. For example, when the ratio of the direct path power to the multipath signal power, K is 0 and 10, 8 and 1.5 dB gains are obtained, respectively, at a symbol error probability of 10⁻³ for 8PSK modulation. We also show that as K gets larger, the gain obtained by the rotation rapidly decreases. We develop a new asymmetric 8PSK signal constellation obtained from two QPSK signal constellations that are optimally rotated by different angles. This asymmetric 8PSK and also the rotated 8PSK signal constellation together with component interleaving are applied to four-state trellis-coded schemes. Simulation results show that these new schemes provide good performance improvements over the original TCM schemes and previous relevant works over Rayleigh and Ricean fading channels.     

A Tight BER Upper Bound for Bit-Interleaved Coded Modulation with Square QAM and Gray Labeling

Bit-interleaved coded modulation (BICM) is a bandwidth-efficient coded system with diversity order higher than that of Ungerboeck's trellis-coded modulation on fading channels. In this paper, we investigate the BER (bit error rate) performance of BICM in the additive white Gaussian and Rayleigh fading channels. A new upper bound is given for the square QAM constellation with gray labeling, which constitutes a large portion of practical applications of BICM systems. The new upper bound is tighter than the well-known BICM union bound proposed in G. Caire et al. (1998)     

Diversity analysis of space-time coding in cascaded Rayleigh fading channels

Cascaded Rayleigh distribution is used to model multipath fading in mobile-to-mobile communication scenarios and provides a better fit to experimental data in such scenarios compared to the conventional Rayleigh channel model. In this letter, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the cascaded Rayleigh fading channel, which is in the form of a simple single finite-range integral. Through the derived PEP expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degradation in comparison to conventional Rayleigh channels. Monte-Carlo simulations are further demonstrated to confirm the analytical results.     

Trellis-coded modulation with bit interleaving and iterativedecoding

This paper considers bit-interleaved coded modulation (BICM) for bandwidth-efficient transmission using software radios. A simple iterative decoding (ID) method with hard-decision feedback is suggested to achieve better performance. The paper shows that convolutional codes with good Hamming-distance property can provide both high diversity order and large free Euclidean distance for BICM-ID. The method offers a common framework for coded modulation over channels with a variety of fading statistics. In addition, BICM-ID allows an efficient combination of punctured convolutional codes and multiphase/level modulation, and therefore provides a simple mechanism for variable-rate transmission     

A sensitivity matched multicarrier modulation

We develop a multicarrier modulation scheme for transmission of compressed data. The energy allocation among subcarriers is optimized by minimizing a modified symbol error function in either AWGN or Rayleigh fading channels. It is observed that our sensitivity matched multicarrier modulation significantly outperforms the conventional multi carrier modulation. The performance gain in Rayleigh fading channels varies from 0.58 to 3.26 dB depending upon the relative sensitivity of bit groups associated with subchannels     

Rayleigh衰落信道中多级编码调制的不等错误保护

本文研究了Rayleigh衰落信道中以信道容量规则为设计准则的多级编码调制系统的不等错误保护性能的实现及其改进.在详细分析了多级编码调制的不等错误保护原理的基础上,设计了一种针对8ASK调制的非均匀信号星座.理论分析与计算机仿真均表明,非均匀信号星座的设计能够增强多级编码调制系统的不等错误保护能力,在不展宽频带的前提下有效地提高Rayleigh衰落环境下数字通信系统的传输质量.     

On the symbol error rates for signal space diversity schemes over a rician fading channel

A signal space diversity (SSD) scheme is one of techniques to achieve diversity gain in fading channels. This method consists of two key operations: constellation rotation and component-wise interleaving. Because of these operations, the decision boundaries for the SSD are no longer perpendicular, and thus, different coordination approaches are required for the analysis of error rates compared to conventional rectangular coordinates. In this letter, we derive an exact expression of the symbol error rate for the SSD scheme in Rician fading channels with M-QAM and M-PSK. By defining the ratio of the standard deviation of the inphase and quadrature components, we introduce a new signal model for the SSD. Based on this signal model, we can compute the exact symbol error rate using polar coordinates. The computer simulation results confirm the accuracy of our analysis for fading channels.