非正交多址中继信道复数域网络编码系统性能分析与优化
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摘要
多址中继信道是指两个或两个以上的源节点在一个或多个中继节点的帮助下与目的节点进行通信,是蜂窝通信系统上行链路协作中继传输的一种典型模型。根据源节点的传输方式,可分为正交多址中继信道和非正交多址中继信道。相比正交多址中继信道,非正交多址中继信道有较高的吞吐率。复数域网络编码(CFNC)是指多个用户信息在复数域上进行网络编码,利用“和信号”的星座空间来区分用户,接收端则采用最大似然检测算法识别不同用户信号。采用非正交多址中继信道的CFNC系统可以进一步提高非正交多址中继信道的吞吐率。然而,已有研究很少涉及非正交多址中继信道CFNC系统的CFNC编码系数设计、中继转发策略、功率分配优化和编码增益分析,这些问题就是本论文的主要研究内容。
首先,针对非正交多址接入CFNC系统,通过分析瞬时和统计的误符号概率(SEP)上界,优化设计了源节点和中继节点的CFNC编码系数,这里得到的优化算法适用于任意用户个数的情况。根据提出的中继节点优化CFNC编码系数设计方法,获得了一批优化的CFNC编码系数。研究表明,利用优化后的中继节点CFNC系数,可以避免网络编码后的信号星座的重叠现象,大幅度提高了系统的SEP性能。此外,论文还提出了自适应和非自适应源节点CFNC编码系数优化算法。优化的自适应源节点CFNC系数能提高系统瞬时的SEP性能,进而改善整个系统的平均SEP性能；而优化的非自适应源节点CFNC系数能在多址接入信道相关性较高的情况下,提高系统的SEP性能。
接着,通过分析基于第K个最优中继选择(KBS)的非正交多址接入CFNC系统(N个源节点、M个中继节点和1个目的节点)的SEP上界,得到了KBS-CFNC系统的分集度、编码增益和功率优化算法。理论研究表明：KBS-CFNC系统的分集度为M-K+2,当K=1时达到满分集M+1；在保证分集度前提下,优化功率分配因子能极大地改进KBS-CFNC系统的SEP性能。优化的功率算法表明：当源-中继链路的性能差于中继-目的链路时,源节点应该分配更多的功率资源以便至少满足有一个中继节点被成功选择；随着源-中继链路性能的提高(增大M值或提高源-中继链路信噪比),更多的功率资源应该分配给中继节点以便提高中继-目的链路的性能；中继节点个数M给定时,随着K值的增加,更多的功率资源应该分配给源节点,使得第K个最优中继节点被成功选择的概率增加。
然后,基于自适应译码转发中继,深入地理论分析了三种典型的并行多中继(PR)CFNC系统的SEP性能上界、分集度和编码增益。研究表明：在目的节点没有整个网络的CSI而仅有单跳链路的CSI时,自适应译码转发中继能避免中继节点的错误传播现象；对于Ⅰ型PR-CFNC系统,在2M个时刻内发送NM符号,其吞吐率为1/2sym/S/CU;对Ⅱ型PR-CFNC系统,在2个时刻发送N个符号,吞吐率为1/2sym/S/CU;对Ⅲ型PR-CFNC系统,在M+1个时刻发送了N个符号,吞吐率为1/(M+1) sym/S/CU。此外,Ⅰ型和Ⅲ型PR-CFNC系统能达到满分集度M+1,而Ⅱ型PR-CFNC系统分集度为2；从复杂度比较,Ⅰ型系统复杂度最高,其次是Ⅱ型系统,最低的是Ⅲ型系统；从中高信噪比的误符号性能比较,Ⅲ型系统的误符号性能最优,其次是Ⅰ型系统,最低的是Ⅱ型系统。
通过最小化SEP性能上界,对Ⅲ型PR-CFNC系统的功率分配进行了优化研究。理论和仿真结果表明：在保证分集度的前提下,优化功率分配因子能改进Ⅲ型PR-CFNC系统的SEP性能。优化功率算法表明：随着源-中继链路性能的改善(增大M、提高源-中继链路信噪比、减小源节点的个数或者降低源的调制阶数等),应该减小源节点发射功率,将更多的功率资源分配给中继节点以便提高中继-目的链路的性能,从而提高系统的SEP性能。其次,通过引入信道编码机制,研究了非正交多址接入CFNC系统性能。在源节点和中继节点引入基于软输入软输出译码算法的信道编码,分别给出了中继节点和目的节点的迭代译码结构以及相应的最大后验概率算法(Max-Log-MAP)迭代译码算法。由于在译码结构中采用了多用户的迭代译码算法,本文研究的软输入软输出迭代译码器不是针对单个用户,而是面向整个网络,可以纠正多条链路的信息传输错误,提高系统的可靠性。最后,研究了多址接入中继信道的导频符号设计方案,重点给出了间隔放置导频符号的方法,包括放置的起始位置p和放置的间隔s。通过Cramer-Rao下界分析,得知导频位置p不会影响系统频偏估计性能,而间隔s的增加则能提高系统频偏估计的准确性,由此产生的频偏估计增益称为“放置增益”。接着,论文通过uMMV算法得出了相应的有效信噪比,并揭示了获得“放置增益”的原因是由于间隔放置导频改变了频偏估计值的有效信噪比,有效信噪比越大,则频偏估计的误差越小。理论和仿真分析表明：信道变化越快则系统频偏估计误差越大；系统信噪比越大、导频符号越多则系统频偏估计误差越小,但相比传统的导频符号前置的方法,本文给出的ES放置方法能节省导频符号个数和导频符号发送能量。
The multiple-access relay channel (MARC) represents a typical scenario of cooperative transmissions for uplink cellular networks wherein multiple sources deliver their messages to one common destination with the assistance of one or multiple relays. There are two main MARC schemes based on the source information transmission mode, i.e. orthogonal and non-orthogonal MARC, where the non-orthogonal MARC can attain higher throughput than that of orthogonal one. Complex field network coding (CFNC) uses operations over complex fields and distinguishes the signals by the constellation space of the "summed signal". At the receiver, the received signal is decoded by maximum likelihood detection algorithm. Moreover, the CFNC system with non-orthogonal MARC further improves the throughput. However, existing works have ignored the design of CFNC coding coefficients, relay forwarding strategies, power allocation and coding gain analysis, which are essential to the system design in uplink cellular networks, thus the main focus of this thesis.
Firstly, by analyzing the instantaneous and statistical symbol error probability (SEP) upper bound for the CFNC system with non-orthogonal MARC, the optimal CFNC coding coefficients at the source and relay nodes are presented for arbitrary number of source nodes, together with some specific optimal CFNC coding coefficients. The results unveil that the optimal CFNC coding coefficients at the relay nodes greatly improve the SEP performance by eliminating the superposition of signals. Besides, adaptive and non-adaptive optimization algorithms for CFNC coding coefficients design at the source nodes are proposed. Adaptive optimized CFNC coding coefficients at the source nodes improve the instantaneous SEP performance and hence improve the average SEP performance. Non-adaptive optimized CFNC coding coefficients at the source nodes improve the SEP performance at higher correlated multiple-access channels.
Secondly, for non-orthogonal MARC, the SEP upper bound of the CFNC system with K-th optimal relay selection (KBS-CFNC) is analyzed, which consists of N source nodes, M relay nodes and a destination, then the diversity order, coding gain and optimal power allocation algorithms are obtained. The theoretical results show that the diversity order of KBS-CFNC is M-K+2and full diversity M+1can be achieved when K=1. The optimal power allocation can greatly improve the SEP performance of KBS-CFNC. The optimal power allocation allocates more power to the link with worse quality. When the soruce-relay link is worse than the relay-destination link, more power is allocated to the sources such that at least one of the relays could be successfully chosen. As the quality of relay link is improved (improve M or the source-relay quality), more power should be allocated to the relays such as to improve the relay-destination link. Moreover, more power should be allocated to the source nodes as K increases, such as to improve the success choosing probability of the optimal relay node given the number of relays M.
Thirdly, based on the adaptive decode-and forward (SDF) relay strategy, the SEP upper bound, diversity order and coding gain of three canonical CFNC systems with parallel relay (PR-CFNC) are analyzed. SDF relay strategy can avoid error propagation when the destination owns only single-hop channel side information (CSI). For the type-Ⅰ with PR-CFNC scheme, the throughput is1/2sym/S/CU since NM symbols are transmitted in2M time slots. For the type-Ⅱ with PR-CFNC scheme, the throughput is1/2sym/S/CU since N symbols are transmitted in2time slots. For the type-Ⅲ with PR-CFNC scheme, the throughput is1/(M+1) sym/S/CU since N symbols are transmitted in M+1time slots. Furthermore, type-Ⅰ and type-Ⅲ can achieve full diversity order M+1while type-Ⅱ achieves diversity order2. The implementation complexity of the three PR-CFNC schemes decreases from type-Ⅰ, type-Ⅱ to type-Ⅲ. The SEP performance of type-Ⅲ is the best among the three PR-CFNC schemes, and type-Ⅰ is worse than type-Ⅲ but better than type-Ⅱ.
The optimal power allocation of type-Ⅲ with PR-CFNC scheme is analyzed by minimizing the SEP upper bound. Both the theoretical and simulated results show that the optimal power allocation can improve the SEP performance. In the optimal allocation, in order to improve the SEP performance of type-Ⅲ with PR-CFNC scheme, more power should be allocated to the relays when the quality source-relay channel is improved (M or the source-relay quality is increased, N is decreased, or the modulation level at the source nodes is decreased).
Fourthly, the CFNC scheme with channel coding for the non-orthogonal MARC is studied. Channel coding with soft-in soft-out (SISO) decoding is equipped at the source and relay nodes, the iterative decoding structure and the corresponding Max-Log-MAP iterative decoding algorithm are developed. Note that the SISO iterative decoder is applicable for the whole network and multiple transmission error from different links can be corrected.
Finally, pilot design for multiple-access relay channel is studied and the pilot symbol placement including the start point and the interval is provided. By analyzing the Cramer-Rao lower bound, we show that the selection of start point will not affect the estimation of frequency offset, and increasing the interval will increase the accuracy of frequency offset estimation. The gain over frequency offset estimation by increasing the interval is named as "placement gain". Then the effective SNR is obtained by uMMV algorithm and it is shown that the "placement gain" comes from the increase of the effective SNR, the higher the effective SNR, the smaller the estimation error. Both the theoretical analysis and simulations show that the faster the channel varying, the higher the mean square error (MSE); the higher the SNR and the smaller the number of pilot symbols, then the smaller the MSE. Moreover, the proposed equally space placement method can reduce the number of pilot symbols and hence save the energy for transmitting the pilot symbols.
首先,针对非正交多址接入CFNC系统,通过分析瞬时和统计的误符号概率(SEP)上界,优化设计了源节点和中继节点的CFNC编码系数,这里得到的优化算法适用于任意用户个数的情况。根据提出的中继节点优化CFNC编码系数设计方法,获得了一批优化的CFNC编码系数。研究表明,利用优化后的中继节点CFNC系数,可以避免网络编码后的信号星座的重叠现象,大幅度提高了系统的SEP性能。此外,论文还提出了自适应和非自适应源节点CFNC编码系数优化算法。优化的自适应源节点CFNC系数能提高系统瞬时的SEP性能,进而改善整个系统的平均SEP性能；而优化的非自适应源节点CFNC系数能在多址接入信道相关性较高的情况下,提高系统的SEP性能。
接着,通过分析基于第K个最优中继选择(KBS)的非正交多址接入CFNC系统(N个源节点、M个中继节点和1个目的节点)的SEP上界,得到了KBS-CFNC系统的分集度、编码增益和功率优化算法。理论研究表明：KBS-CFNC系统的分集度为M-K+2,当K=1时达到满分集M+1；在保证分集度前提下,优化功率分配因子能极大地改进KBS-CFNC系统的SEP性能。优化的功率算法表明：当源-中继链路的性能差于中继-目的链路时,源节点应该分配更多的功率资源以便至少满足有一个中继节点被成功选择；随着源-中继链路性能的提高(增大M值或提高源-中继链路信噪比),更多的功率资源应该分配给中继节点以便提高中继-目的链路的性能；中继节点个数M给定时,随着K值的增加,更多的功率资源应该分配给源节点,使得第K个最优中继节点被成功选择的概率增加。
然后,基于自适应译码转发中继,深入地理论分析了三种典型的并行多中继(PR)CFNC系统的SEP性能上界、分集度和编码增益。研究表明：在目的节点没有整个网络的CSI而仅有单跳链路的CSI时,自适应译码转发中继能避免中继节点的错误传播现象；对于Ⅰ型PR-CFNC系统,在2M个时刻内发送NM符号,其吞吐率为1/2sym/S/CU;对Ⅱ型PR-CFNC系统,在2个时刻发送N个符号,吞吐率为1/2sym/S/CU;对Ⅲ型PR-CFNC系统,在M+1个时刻发送了N个符号,吞吐率为1/(M+1) sym/S/CU。此外,Ⅰ型和Ⅲ型PR-CFNC系统能达到满分集度M+1,而Ⅱ型PR-CFNC系统分集度为2；从复杂度比较,Ⅰ型系统复杂度最高,其次是Ⅱ型系统,最低的是Ⅲ型系统；从中高信噪比的误符号性能比较,Ⅲ型系统的误符号性能最优,其次是Ⅰ型系统,最低的是Ⅱ型系统。
通过最小化SEP性能上界,对Ⅲ型PR-CFNC系统的功率分配进行了优化研究。理论和仿真结果表明：在保证分集度的前提下,优化功率分配因子能改进Ⅲ型PR-CFNC系统的SEP性能。优化功率算法表明：随着源-中继链路性能的改善(增大M、提高源-中继链路信噪比、减小源节点的个数或者降低源的调制阶数等),应该减小源节点发射功率,将更多的功率资源分配给中继节点以便提高中继-目的链路的性能,从而提高系统的SEP性能。其次,通过引入信道编码机制,研究了非正交多址接入CFNC系统性能。在源节点和中继节点引入基于软输入软输出译码算法的信道编码,分别给出了中继节点和目的节点的迭代译码结构以及相应的最大后验概率算法(Max-Log-MAP)迭代译码算法。由于在译码结构中采用了多用户的迭代译码算法,本文研究的软输入软输出迭代译码器不是针对单个用户,而是面向整个网络,可以纠正多条链路的信息传输错误,提高系统的可靠性。最后,研究了多址接入中继信道的导频符号设计方案,重点给出了间隔放置导频符号的方法,包括放置的起始位置p和放置的间隔s。通过Cramer-Rao下界分析,得知导频位置p不会影响系统频偏估计性能,而间隔s的增加则能提高系统频偏估计的准确性,由此产生的频偏估计增益称为“放置增益”。接着,论文通过uMMV算法得出了相应的有效信噪比,并揭示了获得“放置增益”的原因是由于间隔放置导频改变了频偏估计值的有效信噪比,有效信噪比越大,则频偏估计的误差越小。理论和仿真分析表明：信道变化越快则系统频偏估计误差越大；系统信噪比越大、导频符号越多则系统频偏估计误差越小,但相比传统的导频符号前置的方法,本文给出的ES放置方法能节省导频符号个数和导频符号发送能量。
The multiple-access relay channel (MARC) represents a typical scenario of cooperative transmissions for uplink cellular networks wherein multiple sources deliver their messages to one common destination with the assistance of one or multiple relays. There are two main MARC schemes based on the source information transmission mode, i.e. orthogonal and non-orthogonal MARC, where the non-orthogonal MARC can attain higher throughput than that of orthogonal one. Complex field network coding (CFNC) uses operations over complex fields and distinguishes the signals by the constellation space of the "summed signal". At the receiver, the received signal is decoded by maximum likelihood detection algorithm. Moreover, the CFNC system with non-orthogonal MARC further improves the throughput. However, existing works have ignored the design of CFNC coding coefficients, relay forwarding strategies, power allocation and coding gain analysis, which are essential to the system design in uplink cellular networks, thus the main focus of this thesis.
Firstly, by analyzing the instantaneous and statistical symbol error probability (SEP) upper bound for the CFNC system with non-orthogonal MARC, the optimal CFNC coding coefficients at the source and relay nodes are presented for arbitrary number of source nodes, together with some specific optimal CFNC coding coefficients. The results unveil that the optimal CFNC coding coefficients at the relay nodes greatly improve the SEP performance by eliminating the superposition of signals. Besides, adaptive and non-adaptive optimization algorithms for CFNC coding coefficients design at the source nodes are proposed. Adaptive optimized CFNC coding coefficients at the source nodes improve the instantaneous SEP performance and hence improve the average SEP performance. Non-adaptive optimized CFNC coding coefficients at the source nodes improve the SEP performance at higher correlated multiple-access channels.
Secondly, for non-orthogonal MARC, the SEP upper bound of the CFNC system with K-th optimal relay selection (KBS-CFNC) is analyzed, which consists of N source nodes, M relay nodes and a destination, then the diversity order, coding gain and optimal power allocation algorithms are obtained. The theoretical results show that the diversity order of KBS-CFNC is M-K+2and full diversity M+1can be achieved when K=1. The optimal power allocation can greatly improve the SEP performance of KBS-CFNC. The optimal power allocation allocates more power to the link with worse quality. When the soruce-relay link is worse than the relay-destination link, more power is allocated to the sources such that at least one of the relays could be successfully chosen. As the quality of relay link is improved (improve M or the source-relay quality), more power should be allocated to the relays such as to improve the relay-destination link. Moreover, more power should be allocated to the source nodes as K increases, such as to improve the success choosing probability of the optimal relay node given the number of relays M.
Thirdly, based on the adaptive decode-and forward (SDF) relay strategy, the SEP upper bound, diversity order and coding gain of three canonical CFNC systems with parallel relay (PR-CFNC) are analyzed. SDF relay strategy can avoid error propagation when the destination owns only single-hop channel side information (CSI). For the type-Ⅰ with PR-CFNC scheme, the throughput is1/2sym/S/CU since NM symbols are transmitted in2M time slots. For the type-Ⅱ with PR-CFNC scheme, the throughput is1/2sym/S/CU since N symbols are transmitted in2time slots. For the type-Ⅲ with PR-CFNC scheme, the throughput is1/(M+1) sym/S/CU since N symbols are transmitted in M+1time slots. Furthermore, type-Ⅰ and type-Ⅲ can achieve full diversity order M+1while type-Ⅱ achieves diversity order2. The implementation complexity of the three PR-CFNC schemes decreases from type-Ⅰ, type-Ⅱ to type-Ⅲ. The SEP performance of type-Ⅲ is the best among the three PR-CFNC schemes, and type-Ⅰ is worse than type-Ⅲ but better than type-Ⅱ.
The optimal power allocation of type-Ⅲ with PR-CFNC scheme is analyzed by minimizing the SEP upper bound. Both the theoretical and simulated results show that the optimal power allocation can improve the SEP performance. In the optimal allocation, in order to improve the SEP performance of type-Ⅲ with PR-CFNC scheme, more power should be allocated to the relays when the quality source-relay channel is improved (M or the source-relay quality is increased, N is decreased, or the modulation level at the source nodes is decreased).
Fourthly, the CFNC scheme with channel coding for the non-orthogonal MARC is studied. Channel coding with soft-in soft-out (SISO) decoding is equipped at the source and relay nodes, the iterative decoding structure and the corresponding Max-Log-MAP iterative decoding algorithm are developed. Note that the SISO iterative decoder is applicable for the whole network and multiple transmission error from different links can be corrected.
Finally, pilot design for multiple-access relay channel is studied and the pilot symbol placement including the start point and the interval is provided. By analyzing the Cramer-Rao lower bound, we show that the selection of start point will not affect the estimation of frequency offset, and increasing the interval will increase the accuracy of frequency offset estimation. The gain over frequency offset estimation by increasing the interval is named as "placement gain". Then the effective SNR is obtained by uMMV algorithm and it is shown that the "placement gain" comes from the increase of the effective SNR, the higher the effective SNR, the smaller the estimation error. Both the theoretical analysis and simulations show that the faster the channel varying, the higher the mean square error (MSE); the higher the SNR and the smaller the number of pilot symbols, then the smaller the MSE. Moreover, the proposed equally space placement method can reduce the number of pilot symbols and hence save the energy for transmitting the pilot symbols.
引文
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