MIMO干扰对齐预编码与信道反馈研究
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摘要
干扰对齐（Interference alignment, IA）是一种有效的干扰控制机制，能够通过发送端预编码使多个发送用户的干扰在接收端重叠在一起，可以实现干扰系统最大自由度（Degree of Freedom, DoF）并显著提高系统容量，近年来受到学术界的广泛关注。多输入多输出(MIMO)技术是提高频谱效率的关键技术，MIMO技术能够提供大量的空间自由度，适合于应用到干扰对齐系统之中。将MIMO技术与干扰对齐相结合能够大幅度提高多用户干扰系统的通信速率，是当前无线通信领域的一个重要研究方向。
干扰对齐技术的研究还处于起步阶段，还有许多的问题没有解决。例如，干扰对齐的预编码在大多数情况下难以获得显式解，只能获得数值解，并且只能得到次优解。干扰对齐需要发送端具有全局信道状态信息（CSI）。一方面获取发送端全局信道状态信息会带来大量的开销，另一方面信道状态信息误差导致预编码产生误差，使系统性能下降。此外，干扰对齐最初是在对称干扰网络的背景下被提出的，将干扰对齐应用到现有网络，例如蜂窝网中，需要根据现有系统的特点对传统干扰对齐算法进行改进。
本文针对MIMO干扰对齐系统中的预编码算法、信道状态信息反馈以及蜂窝网中的预编码算法进行如下的研究工作：
首先，本文对干扰对齐的自由度和预编码算法进行了分析和研究。在进行MIMO干扰对齐预编码设计之前需要确定预编码的自由度，并且这一自由度不能大于系统能够实现的最大自由度。本文对几种主要MIMO干扰信道下的自由度进行了分析，研究了自由度的实现方法，并对干扰对齐预编码的解析算法和数值算法进行了分析。在此基础上，本文提出了一种基于二次规划的干扰对齐预编码算法，该算法以系统容量为优化目标，联合设计预编码矩阵和接收解码矩阵，在每次迭代中都同时更新预编码矩阵和接收解码矩阵。仿真表明该算法能够实现较高的系统速率。这些分析和研究为本文后续研究工作的展开进行了铺垫。
其次，研究了非理想信道状态信息下基于最小均方误差（MMSE）的干扰对齐预编码算法。干扰对齐需要发送端具有全局信道状态信息，由于实际系统中能够获得的信道状态信息与真实信道状态信息会存在一定的误差，本文对高斯信道误差模型和范数有界信道误差模型进行了分析，然后在高斯信道误差模型下，提出一种每用户功率受限的MMSE干扰对齐算法。仿真表明该算法与传统MMSE算法相比，在信道状态信息存在高斯误差时能够获得更好的性能。在范数有界信道误差模型下提出了用户功率受限时的极小极大总MSE和极小极大用户MSE两种干扰对齐算法。两种算法都是以信道误差范数有界时，最差信道下的性能为优化目标，是鲁棒的预编码算法。极小极大总MSE算法从系统总体性能考虑，能够实现更好的总体MSE性能，而极小极大用户MSE算法能够实现更好的用户MSE性能，是一种实现用户间公平的预编码算法。
再次，研究了干扰对齐信道状态信息反馈过程中的比特分配算法。由于干扰信道各链路增益不同，在各链路之间平均分配反馈比特数是一种次优算法。针对这一问题，本文分析了随机向量量化下的量化失真与量化比特数的关系，给出了有限反馈下干扰对齐的平均速率下限。根据平均速率下限与量化比特数和信道增益的关系，提出了干扰对齐系统中的分布式反馈比特分配算法和集中式反馈比特分配算法。分布式反馈比特分配算法以最大化每个用户的平均速率下限为目标，以每个用户的反馈比特数为约束，集中式反馈比特分配算法以最大化总平均速率下限为优化目标，总反馈比特数为约束。仿真表明，提出的两种反馈比特分配算法与等比特分配算法相比能够在相同的总反馈比特数下实现更高的总速率。集中式算法比分布式算法性能稍好，但是需要在中心处理单元进行，需要占用更多的控制链路资源，并且算法复杂度也高于分布式算法。
最后，研究了蜂窝网中基于级联预编码的干扰对齐算法。针对传统级联预编码算法在多小区边缘速率下降的问题，提出了基于干扰空间扩展的级联预编码算法和基于干扰最小化的级联预编码算法。改进算法能够在多小区边缘实现更好的性能。针对干扰对齐不能对期望信号的功率进行控制，有可能导致期望信号功率损失较大，进而造成速率下降的问题，结合级联预编码算法的特点，提出了基于等效信道矩阵范数的多用户选择算法，从而利用多用户增益来提高系统性能。仿真表明提出的多用户选择算法能够实现系统性能的大幅度提升。
Interference alignment is an effective interference management strategy. With properly designed transmit precoder such that multiple interference from different transmitters overlapped at each receiver. Interference alignment can realizes the maximum degree of freedom (DoF) in interference system and significantly improve system capacity. Multiple input multiple output (MIMO) technology is the key technology to improve the spectrum efficiency. MIMO system can provide a large number of spatial degrees of freedom, which is very suitable for the implementation of interference alignment. Combining MIMO technology and the interference alignment will greatly improve the interference network capacity, therefore becomes an important research area in today’s wireless communication field.
Research on interference alignment is still in its infancy and there are many problems unsolved. For example, explicit precoder of interference alignment is difficult to obtain in most cases, and only suboptimal numerical solution can be achieved by numerical methods. Interference alignment requires global channel state information at transmitter. On the one hand, acquisition of the global channel state information will bring a lot of overhead. On the other hand, imperfect channel state information bring about precoding error and lead to performance degradation. Further, the origin interference alignment algorithms are proposed based on symatric interference channel, and modifications are needed before the implementation of interference alignment in to the current networks such as cellular network.
Focus on MIMO interference alignment, the research works in this thesis include precoder design, channel state information feedback and transceiver design for cellular networks, which are detailed as follows:
Firstly, degree of freedom and precoding algorithms for interference alignment are analyzed. Since degrees of freedom should be known before designing the precoder in MIMO interference alignment, degree of freedom for several MIMO interference networks are analyzed and the methods of realize degree of freedom are evaluated. After that, precoder design algorithms are analyzed, which include closed form algorithms and numerical algorithms. This thesis gives an interference alignment algorithm based on quadratic programming which jointly design the transmit precoder and receive decoder to optimize the system capacity. In each iteration, precoders and decoders are updated simultaneously. Simulation results show that the proposed algorithm outperforms traditional interference alignment algorithm in the expanse of higher complexity. However, this algorithm can be used to evaluate the performance of interference alignment.
Secondly, MMSE interference alignment strategy under imperfect channel state information is studied. Interference aligned requires global channel state information at transmitters (CSIT). Channel state information obtained at transmitter usually have some errors. Gaussian statistic channel error model and norm bounded channel model are analyzed. Based on the Gaussian statistic channel error model, this thesis gives interference alignment strategy which minimize the mean square error with per transmitter power constraint. Simulation results show that compared with traditional MMSE algorithm，the proposed algorithm achieves better performance. Based on norm bounded channel model, two interference alignment algorithms which minimize the worst case sum MSE and minimize worst case user MSE are proposed. These two algorithms are robust transceiver algorithms mini-max total MSE algorithm can achieve better total MSE performance, from the viewpoint of system and the mini-max users MSE algorithm can achieve better user MSE performance, which is a fair precoding algorithm.
Thirdly, bit allocation algorithm in the process of channel state information feedback for MIMO interference alignment is studied. Since channel gains of interference channels are differenc, allocation feedback bits equally on different channels is sub-optimal. In order to solve this problem, relationship between quantization distortion and quantization bits is studied, and lower bound of average rate for interference alignment with limited feedback is derived. Based on the relationship between lower bound of average rate and the quantization bits and channel gains, distributed and centralized feedback bit allocation algorithms are proposed. Distributed feedback bit allocation algorithm maximize the lower bound of the average rate of each user with per user feedback bits constraint, while centralized feedback bit allocation algorithm maximize the average sum rate lower bound with the total number of feedback bits constraint. Simulation results show that the proposed two feedback bit allocation algorithms achieve higher sum rate compared with the equal bit allocation algorithm. Performance of centralized feedback bit allocation algorithm is slightly better than distributed algorithm, but centralized feedback bit allocation should be processed at central processing unit, so more control and feedback resources are needed. Also, the centralized feedback bit allocation algorithm is more computational complex than distributed algorithm.
Lastly, interference alignment based on cascade precoding for cellular networks is studied. In order to solve the rate degradation for cell edge user due to inter cell interference, two modified interference alignment precoding algorithms are proposed. Cascade precoding algorithm based on interference space expansion and interference minimization are proposed. Proposed algorithms can achieve better performance when there are multiple interference base stations. Since desired signal power cannot be controlled in interference alignment, which could lead to signal power degradation and therefore the degradation of throughput. Considering the characteristics of the cascade precoding algorithm, multi-user selection algorithm based on the Frobenius norm of equivalent channel matrices are proposed. Simulation results show that the proposed multi-user selection algorithm can greatly improve system performance.
干扰对齐技术的研究还处于起步阶段，还有许多的问题没有解决。例如，干扰对齐的预编码在大多数情况下难以获得显式解，只能获得数值解，并且只能得到次优解。干扰对齐需要发送端具有全局信道状态信息（CSI）。一方面获取发送端全局信道状态信息会带来大量的开销，另一方面信道状态信息误差导致预编码产生误差，使系统性能下降。此外，干扰对齐最初是在对称干扰网络的背景下被提出的，将干扰对齐应用到现有网络，例如蜂窝网中，需要根据现有系统的特点对传统干扰对齐算法进行改进。
本文针对MIMO干扰对齐系统中的预编码算法、信道状态信息反馈以及蜂窝网中的预编码算法进行如下的研究工作：
首先，本文对干扰对齐的自由度和预编码算法进行了分析和研究。在进行MIMO干扰对齐预编码设计之前需要确定预编码的自由度，并且这一自由度不能大于系统能够实现的最大自由度。本文对几种主要MIMO干扰信道下的自由度进行了分析，研究了自由度的实现方法，并对干扰对齐预编码的解析算法和数值算法进行了分析。在此基础上，本文提出了一种基于二次规划的干扰对齐预编码算法，该算法以系统容量为优化目标，联合设计预编码矩阵和接收解码矩阵，在每次迭代中都同时更新预编码矩阵和接收解码矩阵。仿真表明该算法能够实现较高的系统速率。这些分析和研究为本文后续研究工作的展开进行了铺垫。
其次，研究了非理想信道状态信息下基于最小均方误差（MMSE）的干扰对齐预编码算法。干扰对齐需要发送端具有全局信道状态信息，由于实际系统中能够获得的信道状态信息与真实信道状态信息会存在一定的误差，本文对高斯信道误差模型和范数有界信道误差模型进行了分析，然后在高斯信道误差模型下，提出一种每用户功率受限的MMSE干扰对齐算法。仿真表明该算法与传统MMSE算法相比，在信道状态信息存在高斯误差时能够获得更好的性能。在范数有界信道误差模型下提出了用户功率受限时的极小极大总MSE和极小极大用户MSE两种干扰对齐算法。两种算法都是以信道误差范数有界时，最差信道下的性能为优化目标，是鲁棒的预编码算法。极小极大总MSE算法从系统总体性能考虑，能够实现更好的总体MSE性能，而极小极大用户MSE算法能够实现更好的用户MSE性能，是一种实现用户间公平的预编码算法。
再次，研究了干扰对齐信道状态信息反馈过程中的比特分配算法。由于干扰信道各链路增益不同，在各链路之间平均分配反馈比特数是一种次优算法。针对这一问题，本文分析了随机向量量化下的量化失真与量化比特数的关系，给出了有限反馈下干扰对齐的平均速率下限。根据平均速率下限与量化比特数和信道增益的关系，提出了干扰对齐系统中的分布式反馈比特分配算法和集中式反馈比特分配算法。分布式反馈比特分配算法以最大化每个用户的平均速率下限为目标，以每个用户的反馈比特数为约束，集中式反馈比特分配算法以最大化总平均速率下限为优化目标，总反馈比特数为约束。仿真表明，提出的两种反馈比特分配算法与等比特分配算法相比能够在相同的总反馈比特数下实现更高的总速率。集中式算法比分布式算法性能稍好，但是需要在中心处理单元进行，需要占用更多的控制链路资源，并且算法复杂度也高于分布式算法。
最后，研究了蜂窝网中基于级联预编码的干扰对齐算法。针对传统级联预编码算法在多小区边缘速率下降的问题，提出了基于干扰空间扩展的级联预编码算法和基于干扰最小化的级联预编码算法。改进算法能够在多小区边缘实现更好的性能。针对干扰对齐不能对期望信号的功率进行控制，有可能导致期望信号功率损失较大，进而造成速率下降的问题，结合级联预编码算法的特点，提出了基于等效信道矩阵范数的多用户选择算法，从而利用多用户增益来提高系统性能。仿真表明提出的多用户选择算法能够实现系统性能的大幅度提升。
Interference alignment is an effective interference management strategy. With properly designed transmit precoder such that multiple interference from different transmitters overlapped at each receiver. Interference alignment can realizes the maximum degree of freedom (DoF) in interference system and significantly improve system capacity. Multiple input multiple output (MIMO) technology is the key technology to improve the spectrum efficiency. MIMO system can provide a large number of spatial degrees of freedom, which is very suitable for the implementation of interference alignment. Combining MIMO technology and the interference alignment will greatly improve the interference network capacity, therefore becomes an important research area in today’s wireless communication field.
Research on interference alignment is still in its infancy and there are many problems unsolved. For example, explicit precoder of interference alignment is difficult to obtain in most cases, and only suboptimal numerical solution can be achieved by numerical methods. Interference alignment requires global channel state information at transmitter. On the one hand, acquisition of the global channel state information will bring a lot of overhead. On the other hand, imperfect channel state information bring about precoding error and lead to performance degradation. Further, the origin interference alignment algorithms are proposed based on symatric interference channel, and modifications are needed before the implementation of interference alignment in to the current networks such as cellular network.
Focus on MIMO interference alignment, the research works in this thesis include precoder design, channel state information feedback and transceiver design for cellular networks, which are detailed as follows:
Firstly, degree of freedom and precoding algorithms for interference alignment are analyzed. Since degrees of freedom should be known before designing the precoder in MIMO interference alignment, degree of freedom for several MIMO interference networks are analyzed and the methods of realize degree of freedom are evaluated. After that, precoder design algorithms are analyzed, which include closed form algorithms and numerical algorithms. This thesis gives an interference alignment algorithm based on quadratic programming which jointly design the transmit precoder and receive decoder to optimize the system capacity. In each iteration, precoders and decoders are updated simultaneously. Simulation results show that the proposed algorithm outperforms traditional interference alignment algorithm in the expanse of higher complexity. However, this algorithm can be used to evaluate the performance of interference alignment.
Secondly, MMSE interference alignment strategy under imperfect channel state information is studied. Interference aligned requires global channel state information at transmitters (CSIT). Channel state information obtained at transmitter usually have some errors. Gaussian statistic channel error model and norm bounded channel model are analyzed. Based on the Gaussian statistic channel error model, this thesis gives interference alignment strategy which minimize the mean square error with per transmitter power constraint. Simulation results show that compared with traditional MMSE algorithm，the proposed algorithm achieves better performance. Based on norm bounded channel model, two interference alignment algorithms which minimize the worst case sum MSE and minimize worst case user MSE are proposed. These two algorithms are robust transceiver algorithms mini-max total MSE algorithm can achieve better total MSE performance, from the viewpoint of system and the mini-max users MSE algorithm can achieve better user MSE performance, which is a fair precoding algorithm.
Thirdly, bit allocation algorithm in the process of channel state information feedback for MIMO interference alignment is studied. Since channel gains of interference channels are differenc, allocation feedback bits equally on different channels is sub-optimal. In order to solve this problem, relationship between quantization distortion and quantization bits is studied, and lower bound of average rate for interference alignment with limited feedback is derived. Based on the relationship between lower bound of average rate and the quantization bits and channel gains, distributed and centralized feedback bit allocation algorithms are proposed. Distributed feedback bit allocation algorithm maximize the lower bound of the average rate of each user with per user feedback bits constraint, while centralized feedback bit allocation algorithm maximize the average sum rate lower bound with the total number of feedback bits constraint. Simulation results show that the proposed two feedback bit allocation algorithms achieve higher sum rate compared with the equal bit allocation algorithm. Performance of centralized feedback bit allocation algorithm is slightly better than distributed algorithm, but centralized feedback bit allocation should be processed at central processing unit, so more control and feedback resources are needed. Also, the centralized feedback bit allocation algorithm is more computational complex than distributed algorithm.
Lastly, interference alignment based on cascade precoding for cellular networks is studied. In order to solve the rate degradation for cell edge user due to inter cell interference, two modified interference alignment precoding algorithms are proposed. Cascade precoding algorithm based on interference space expansion and interference minimization are proposed. Proposed algorithms can achieve better performance when there are multiple interference base stations. Since desired signal power cannot be controlled in interference alignment, which could lead to signal power degradation and therefore the degradation of throughput. Considering the characteristics of the cascade precoding algorithm, multi-user selection algorithm based on the Frobenius norm of equivalent channel matrices are proposed. Simulation results show that the proposed multi-user selection algorithm can greatly improve system performance.
引文
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