线性MIMO系统预编码技术的研究
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摘要
无线通信正经历着它自诞生以来发展最快的时期,它的迅速发展归功于先进通信技术的研究与应用。随着无线通信系统实际应用的迅猛普及,无线通信用户数和用户服务需求成指数性增长,但可用于无线通信服务的无线电频谱资源极其有限,使得不断增长的无线服务需求与有限的无线电频谱资源之间的矛盾日益突出。MIMO多天线技术正是在这一背景下发展起来的一种新型无线通信技术,它能够极大地提高通信系统的频谱利用率、满足用户的高速率通信需求,因此得到了国内外广泛的关注和研究,它已经成为下一代移动通信系统中极具发展前景的技术之一。
本论文侧重于线性MIMO系统预编码技术的研究,方向导数理论和盖理论是本论文研究得以进行的数学理论基础。本论文主要研究内容包括：基于方向导数理论的最优线性MIMO预编码设计的研究、基于盖理论的最优能量分配策略的研究、多用户MIMO系统中用户选择与QOS控制策略的研究。本论文的主要贡献和创新之处列举如下：
·基于最小化均方误差准则,提出了一种适用于多种能量约束(lp范数能量约束)的最优线性MIMO系统预编码设计框架,并且从方向导数理论的角度证明了最大化信道容量准则和最小化MSE矩阵行列式准则的等价性。
·在联合总能量约束和峰值能量约束下,提出了一个适用于多种设计准则的最优线性MIMO系统预编码设计框架。与近似的lp范数约束问题相比,该设计框架能取得最优的系统性能。此外,在理论上证明了联合能量约束下的能量分配具有分段线性性,从而推导出了一种极其快速的能量分配策略。
·基于最大化信道容量准则,提出了一种QoS约束下最大化上行链路信道容量的最优能量分配策略,从盖理论的角度给出了能量分配的最优结构。与现有算法相比,采用搜索变量代换的改进最优能量分配算法的计算复杂度大幅度降低,即使在最坏情况下也仅需原有一半的计算复杂度。
·最大化信道容量准则可获得高的传输速率,但有失用户间的公平性原则。基于最大化最小速率准则,提出了一种QoS约束下具有公平性原则的最优能量分配策略,并利用盖理论,证明了能量分配的最优结构,且导出了-个接近具有闭式解的最优能量分配方案。
·贪婪用户选择方案的瓶颈在于随着用户数的增加,用户选择算法的计算复杂度急剧增加。基于Householder变换,提出了一种适用于迫零编码和脏纸编码下的快速贪婪用户选择算法。在与现有算法获得相同性能的前提下,该算法只需微乎其微的计算复杂度,从本质上解决了贪婪用户选择算法的瓶颈。
·基于Perron-Frobenius定理,在发射能量加权和受限且系统资源已过载情况下,提出了一种适用于接纳更多用户数的最优QOS等比例控制算法,并推导出了具有闭式解的能量分配方案。由于无需迭代过程,所提算法具有合理的计算复杂度和稳定性。
It is all about spectrum. Wireless industry is experiencing its fastest growing since Marconi pioneered the wireless technology one hundred years ago, which is due to the research and application of advanced communications technology. The gradual evolution of mobile communication system follows the quest for high data rates, and the demands on bandwidth and spectral availability seem to be endless. So, wireless designers have to face an uphill task of limited availability of radio frequency spectrum problem in the wireless channel. Multiple-input multiple-output (MIMO) technology has attracted a large amount of attention in wireless communications, because it offers a promising solution to support greater data rate and higher reliability over wireless links without additional bandwidth or transmit power. As a result, MIMO systems have been a current theme of international wireless research.
To achieve better performance, precoding and decoding design becomes an im-portant challenge in the future wireless MIMO communication systems. The main objective of this thesis is to provide a series of optimal designs for MIMO transceivers including:optimal design for linear MIMO transceivers by using directional derivative, optimal power allocation via Majorization theory with quality of service (QoS) con-straints, and optimal user selection and QoS control for multi-users MIMO systems. Directional derivative and Majorization theory are the underlying mathematical theo-ries on which our methods hinge. The concrete contributions and innovations of the thesis are listed as follows:
Optimal design for minimizing the combination of symbol estimation errors sub-ject to lp-norm constraint is investigated. Instead of considering each constraint in a separate way, we develop a unifying framework to obtain the optimal solution by employing a directional derivative method. Moreover, based on directional derivative, we show that the minimization of the determinant of mean-square er-ror matrix and the maximization of mutual information are equivalent criteria.
A unified framework is developed to obtain the optimal precoder designs for several different criteria with the realistic power constraints jointly imposed on both the sum power and the peak power. It is shown that power allocation is piecewise linear in the sum power, and thus finding the entire path of solution for every value of the sum power just requires checking a finite number of points. Our method is computationally efficient and outperforms existing methods in the literature which can only give approximate solutions.
Optimal power allocation for maximizing the sum capacity of the reverse link of multi-rate CDMA systems with QoS constraints is investigated. It is shown that the structure of the optimal solution can be easily obtained via Majorization theory. Furthermore, based on our new approach, an efficient searching method for power allocation is developed. Our new method requires only approximately a half of the computational cost of existing methods in the worst case and is even much faster in general.
Max-min fair power allocation brings higher average throughput and better uti-lization of the resources than a work-conserving equal sharing policy. Instead of achieving a common maximum sum-rate objective, an optimal power allo-cation design for maximizing the minimum rate of the reverse-link of CDMA systems with QoS constraints is investigated. We first try to derive the structure of the optimal solution via Majorization theory. Then, we propose a very effi-cient search method to find the max-min fair solution. Compared with existing methods, much lighter computational complexity is required by our method.
An efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel ma-trix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.
In an attempt to admit new users into CDMA communication systems in the case of overload, an optimal proportional QoS reduction method subject to a weighted sum power constraint is investigated. Based on the Perron-Frobenius Theorem, we successfully derive an optimal closed-form solution. Compared to existing methods, our method greatly reduces the computational complexity, as well as maintains high reliability.
本论文侧重于线性MIMO系统预编码技术的研究,方向导数理论和盖理论是本论文研究得以进行的数学理论基础。本论文主要研究内容包括：基于方向导数理论的最优线性MIMO预编码设计的研究、基于盖理论的最优能量分配策略的研究、多用户MIMO系统中用户选择与QOS控制策略的研究。本论文的主要贡献和创新之处列举如下：
·基于最小化均方误差准则,提出了一种适用于多种能量约束(lp范数能量约束)的最优线性MIMO系统预编码设计框架,并且从方向导数理论的角度证明了最大化信道容量准则和最小化MSE矩阵行列式准则的等价性。
·在联合总能量约束和峰值能量约束下,提出了一个适用于多种设计准则的最优线性MIMO系统预编码设计框架。与近似的lp范数约束问题相比,该设计框架能取得最优的系统性能。此外,在理论上证明了联合能量约束下的能量分配具有分段线性性,从而推导出了一种极其快速的能量分配策略。
·基于最大化信道容量准则,提出了一种QoS约束下最大化上行链路信道容量的最优能量分配策略,从盖理论的角度给出了能量分配的最优结构。与现有算法相比,采用搜索变量代换的改进最优能量分配算法的计算复杂度大幅度降低,即使在最坏情况下也仅需原有一半的计算复杂度。
·最大化信道容量准则可获得高的传输速率,但有失用户间的公平性原则。基于最大化最小速率准则,提出了一种QoS约束下具有公平性原则的最优能量分配策略,并利用盖理论,证明了能量分配的最优结构,且导出了-个接近具有闭式解的最优能量分配方案。
·贪婪用户选择方案的瓶颈在于随着用户数的增加,用户选择算法的计算复杂度急剧增加。基于Householder变换,提出了一种适用于迫零编码和脏纸编码下的快速贪婪用户选择算法。在与现有算法获得相同性能的前提下,该算法只需微乎其微的计算复杂度,从本质上解决了贪婪用户选择算法的瓶颈。
·基于Perron-Frobenius定理,在发射能量加权和受限且系统资源已过载情况下,提出了一种适用于接纳更多用户数的最优QOS等比例控制算法,并推导出了具有闭式解的能量分配方案。由于无需迭代过程,所提算法具有合理的计算复杂度和稳定性。
It is all about spectrum. Wireless industry is experiencing its fastest growing since Marconi pioneered the wireless technology one hundred years ago, which is due to the research and application of advanced communications technology. The gradual evolution of mobile communication system follows the quest for high data rates, and the demands on bandwidth and spectral availability seem to be endless. So, wireless designers have to face an uphill task of limited availability of radio frequency spectrum problem in the wireless channel. Multiple-input multiple-output (MIMO) technology has attracted a large amount of attention in wireless communications, because it offers a promising solution to support greater data rate and higher reliability over wireless links without additional bandwidth or transmit power. As a result, MIMO systems have been a current theme of international wireless research.
To achieve better performance, precoding and decoding design becomes an im-portant challenge in the future wireless MIMO communication systems. The main objective of this thesis is to provide a series of optimal designs for MIMO transceivers including:optimal design for linear MIMO transceivers by using directional derivative, optimal power allocation via Majorization theory with quality of service (QoS) con-straints, and optimal user selection and QoS control for multi-users MIMO systems. Directional derivative and Majorization theory are the underlying mathematical theo-ries on which our methods hinge. The concrete contributions and innovations of the thesis are listed as follows:
Optimal design for minimizing the combination of symbol estimation errors sub-ject to lp-norm constraint is investigated. Instead of considering each constraint in a separate way, we develop a unifying framework to obtain the optimal solution by employing a directional derivative method. Moreover, based on directional derivative, we show that the minimization of the determinant of mean-square er-ror matrix and the maximization of mutual information are equivalent criteria.
A unified framework is developed to obtain the optimal precoder designs for several different criteria with the realistic power constraints jointly imposed on both the sum power and the peak power. It is shown that power allocation is piecewise linear in the sum power, and thus finding the entire path of solution for every value of the sum power just requires checking a finite number of points. Our method is computationally efficient and outperforms existing methods in the literature which can only give approximate solutions.
Optimal power allocation for maximizing the sum capacity of the reverse link of multi-rate CDMA systems with QoS constraints is investigated. It is shown that the structure of the optimal solution can be easily obtained via Majorization theory. Furthermore, based on our new approach, an efficient searching method for power allocation is developed. Our new method requires only approximately a half of the computational cost of existing methods in the worst case and is even much faster in general.
Max-min fair power allocation brings higher average throughput and better uti-lization of the resources than a work-conserving equal sharing policy. Instead of achieving a common maximum sum-rate objective, an optimal power allo-cation design for maximizing the minimum rate of the reverse-link of CDMA systems with QoS constraints is investigated. We first try to derive the structure of the optimal solution via Majorization theory. Then, we propose a very effi-cient search method to find the max-min fair solution. Compared with existing methods, much lighter computational complexity is required by our method.
An efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel ma-trix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.
In an attempt to admit new users into CDMA communication systems in the case of overload, an optimal proportional QoS reduction method subject to a weighted sum power constraint is investigated. Based on the Perron-Frobenius Theorem, we successfully derive an optimal closed-form solution. Compared to existing methods, our method greatly reduces the computational complexity, as well as maintains high reliability.
引文
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