MIMO系统中低复杂度空时编码技术研究
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摘要
空时编码(Space-Time Coding)技术能够充分利用MIMO信道中多个独立的传输通路获得空间分集增益,从而大幅提高无线系统抗衰落的能力。本文围绕低复杂度利于实现的空时编码技术开展研究,利用多维代数网格信号设计思想,提出了四种新的编码设计方案。
满足广义正交约束(GOC)条件的空时码能把MIMO信道等效成若干个并行的虚拟SISO信道,消除信号间的耦合。目前以提高可靠性为目的设计的空时码中,满足GOC条件的已有正交空时码(Orthogonal Space-Time Block Code,OSTBC)和约束满秩单符号可译设计(Restricted Full-rank Single-symbol Decodable Design,RFSDD),但前者码速率很低,后者虽然码速率有所提高,但具有功率分布不平衡的缺点,而且码速率仍然有限。本文构造了一种新的满足GOC条件的全分集空时码——GOC-STBC,它在OSTBC的基础上通过放松对权矩阵满秩的要求从而获得码速率的提升,利用多维实网格星座来获得全分集,并系统地分析了该码的编码增益、码速率、译码复杂度等问题。GOC-STBC不但比OSTBC大幅提高了码速率,还解决了RFSDD功率分布不平衡的缺陷。与另一类典型的低译码复杂度的准正交空时码(Quasi-Orthogonal STBC,QSTBC)相比,GOC-STBC利用现有的代数网格理论来设计全分集和最大化编码增益,因而节省了设计开销,而且在相同译码复杂度的情况下比QSTBC具有相等或者更优的性能。
基于GOC-STBC构造,研究了有限比特反馈的闭环系统中GOC-STBC的全分集方案,提出了一种自适应的GOC-STBC设计。该设计只需2~4比特反馈信息来指导发送端自适应地选择预编码码本,通过改善码的等效虚拟信道特性,使得自适应GOC-STBC用简单的迫零(ZF)译码就能获得全分集,而且性能与最大似然(ML)译码完全等价。即使用ML译码也具备最低的译码复杂度——单符号可译。自适应GOC-STBC在两种译码下都是星座自由的,对于任意发送天线数目时都能达到码速率1。与另一种码速率为1且用ZF译码也具有全分集的自适应QSTBC(Adaptive-QSTBC,A-QSTBC)比较,本文提出的码采用2比特反馈时就已经与使用完全反馈(无限比特)的A-QSTBC性能相当,采用大于2比特反馈时的性能统统优于完全反馈的A-QSTBC。
码速率1的QSTBC编码增益的上界由星座的最小欧氏距离决定。在不增加星座能量的前提下,当前复数星座(如4QAM、16QAM)的最小欧氏距离很难进一步提高。为了改善QSTBC的编码增益,本文将码速率为1的4×4和8×8-QSTBC通过一定的结构变形,使其适合采用多维复网格星座这种信号设计形式,提出了一种基于多维复分圆网格的QSTBC(CL-QSTBC),并证明了CL-QSTBC编码增益的上界由网格间的最小欧氏距离决定,且该上界是可达到的,从而让CL-QSTBC的编码增益直接取决于多维网格星座的最小欧氏距离。最后,利用网格球形封装原理最大化该最小欧氏距离,从而达到最大化编码增益的目的。这样,CL-QSTBC的编码增益不再受传统复数星座的限制。经比较,CL-QSTBC的编码增益高于传统QSTBC编码增益的上界,获得了更好的性能,而且保持同样的译码复杂度。
空时编码一个重要的设计思路是开发空间分集,在获得全部空间分集之后,再通过提高编码增益来一步步改善性能。然而,编码增益的对性能的影响总是有限的,对空时编码性能起主导作用的仍然是分集增益。空时编码系统假设信道是“块状衰落”的,即在一个码字时间内保持不变,在不同码字之间可独立地变化。考虑到时域上的独立衰落具有提供时间分集的潜力,论文提出了一种基于多维网格的联合正交空时编码方案(Joint-OSTBC)。该方案充分利用了OSTBC等效信道模型并结合多维代数网格抗衰落的特性,采用时域上多个码字联合编码,在确保全部空间分集的前提下能获得额外的时间分集。然后推导了Joint-OSTBC的符号成对错误概率的Chernoff界,证明了在块状独立衰落信道中Joint-OSTBC获得的分集增益等于发送天线数、接收天线数和联合码字的个数三者的乘积。换而言之,M个码字联合编码可使原来OSTBC的分集增益放大M倍。仿真表明成对码字联合的Joint-OSTBC,其性能已显著优于QSTBC甚至目前性能最好的Golden码,而且译码复杂度低很多。
Space-time coding techniques can exploit the space diversity gains by utilizing the multi mutual independent transmission paths of MIMO systems to greatly increase the ability against channel fadings. In this thesis, we study the space-time coding techniques with low complexity, which is easy to implement, and propose four new coding design schemes based on multi-dimensional algebraic lattices.
The MIMO channel can be equivalent to multi parallel virtual SISO channels if space-time codes satisfy so-called generalized orthogonal constraint (GOC) conditions, so that the transmitted signals can be decoupled. In the current space-time codes designed for improving reliability, Orthogonal Space-Time Block Codes (OSTBC) and Restricted Full-rank Single-symbol Decodable Designs (RFSDD) have already satisfied the GOC condition. However, the OSTBC has just very low code rate and the RFSDD has the defect of unbalanced power distribution though its code rate is a little higher than the OSTBC. In this thesis, we propose a new space-time block code with generalized orthogonal constraint (named as GOC-STBC) to achieve full diversity, where the code rate is enhanced much compared with the OSTBC by relaxing the full-rank condition of weight matrices; the full diversity is obtained by using multi-dimensional real lattice constellations; in addition, we systematically analyze the coding gain, code rate and decoding complexity issues of the proposed GOC-STBC. In the meanwhile, the GOC-STBC resolves the unbalanced power distribution problem of the RFSDD. As the coding gain is maximized by using the ready-made algebraic lattice theory, the GOC-STBC has smaller design expense than another typical STBC with lower decoding complexity- Quasi-Orthogonal STBC (QSTBC). Moreover, the performance of GOC-STBC is the same or even better than the QSTBC when the decoding complexity is comparable.
Based on the structured GOC-STBC, we investigate its full diversity strategy in closed-loop systems with limited feedback bits and propose an adaptive GOC-STBC design. Because the property of equivalent virtual channel matrices of the proposed code is improved by the precoding codebooks, which are adaptively choosen by 2~4 bits feedback information at the transmitter, the proposed code can obtain full diversity under the simple zero-forcing (ZF) decoding. Furthermore, the performance of ZF decoding is equivalent to that of maximum likelihood (ML) decoding, which is single-symbol decodable (SSD). In addition, the proposed adaptive GOC-STBC is constellation free for both of the aforementioned decoding methods and at the same time the code rate achieve one for any number of transmit antennas. In contrast to the adaptive-QSTBC (A-QSTBC), which is a typical code with rate one and also has full diversity under ZF decoding, the proposed code with just 2 feedback bits has the same performance as the A-QSTBC with perfect feedback; when the proposed code uses more that 2 feedback bits, its performance is better than that of the A-QSTBC with perfect feedback.
The coding gain of rate-one QSTBCs is upper-bounded by the minimum Euclidean distance of signal constellations. When the constellation energy is fixed, it is very difficult to increase the minimum Euclidean distance of the current complex constellations (such as 4QAM and 16QAM). To further improve the coding gain of QSTBCs, in this thesis we propose a Cyclotomic Lattice-based QSTBC (CL-QSTBC) where the previous rate one 4×4- and 8×8- QSTBCs are transformed so that they are suitable to use multi-dimensional complex lattice constellations. Then, we prove that the coding gain of the CL-QSTBC is upper-bounded by the minimum Euclidean distance of lattice points and then the upper-bound is reachable. Thus, the coding gain is completely determined by the the minimum Euclidean distance of multi-dimensional lattice constellations. So, we maximize the above minimum Euclidean distance by lattice packing theory, which is equivalent to maximize the coding gain. As a result, the coding gain of the proposed CL-QSTBC will not be constrained by the common complex constellations. According to the comparison of simulations, the CL-QSTBC has higher coding gain than the upper-bound of previous QSTBCs and obtains better performance than the current best QSTBCs but with comparable decoding complexity.
The mainest factor which dominates the performance of space-time codes is the diversity gain instead of coding gain. In this thesis, we propose a Joint Orthogonal Space-Time Code (Joint-OSTBC) scheme, where the anti-fading property of multi-dimensional algebraic lattices is combined with the equivalent channel model of OSTBCs, so that the extra time diversity can be obtained by jointly coding multi OSTBC codewords along time domain. In the meanwhile, the full space diversity can be still kept in the above coding scheme. In addition, we derive the Chernoff bound of symbol pairwise error probability and prove that the total diversity gain of the proposed Joint-OSTBC is equal to the product of the number of transmit antennas, receive antennas and jointed codewords. In other words, the Joint-OSTBC with M codewords jointed has the M times diversity gains than the previous OSTBCs. From simulations, we find that the Joint-OSTBC with just double codewords jointed has already significant performance gain over both the QSTBC and even the Golden code, which is the best known code currently, but the decoding complexity is lower much.
满足广义正交约束(GOC)条件的空时码能把MIMO信道等效成若干个并行的虚拟SISO信道,消除信号间的耦合。目前以提高可靠性为目的设计的空时码中,满足GOC条件的已有正交空时码(Orthogonal Space-Time Block Code,OSTBC)和约束满秩单符号可译设计(Restricted Full-rank Single-symbol Decodable Design,RFSDD),但前者码速率很低,后者虽然码速率有所提高,但具有功率分布不平衡的缺点,而且码速率仍然有限。本文构造了一种新的满足GOC条件的全分集空时码——GOC-STBC,它在OSTBC的基础上通过放松对权矩阵满秩的要求从而获得码速率的提升,利用多维实网格星座来获得全分集,并系统地分析了该码的编码增益、码速率、译码复杂度等问题。GOC-STBC不但比OSTBC大幅提高了码速率,还解决了RFSDD功率分布不平衡的缺陷。与另一类典型的低译码复杂度的准正交空时码(Quasi-Orthogonal STBC,QSTBC)相比,GOC-STBC利用现有的代数网格理论来设计全分集和最大化编码增益,因而节省了设计开销,而且在相同译码复杂度的情况下比QSTBC具有相等或者更优的性能。
基于GOC-STBC构造,研究了有限比特反馈的闭环系统中GOC-STBC的全分集方案,提出了一种自适应的GOC-STBC设计。该设计只需2~4比特反馈信息来指导发送端自适应地选择预编码码本,通过改善码的等效虚拟信道特性,使得自适应GOC-STBC用简单的迫零(ZF)译码就能获得全分集,而且性能与最大似然(ML)译码完全等价。即使用ML译码也具备最低的译码复杂度——单符号可译。自适应GOC-STBC在两种译码下都是星座自由的,对于任意发送天线数目时都能达到码速率1。与另一种码速率为1且用ZF译码也具有全分集的自适应QSTBC(Adaptive-QSTBC,A-QSTBC)比较,本文提出的码采用2比特反馈时就已经与使用完全反馈(无限比特)的A-QSTBC性能相当,采用大于2比特反馈时的性能统统优于完全反馈的A-QSTBC。
码速率1的QSTBC编码增益的上界由星座的最小欧氏距离决定。在不增加星座能量的前提下,当前复数星座(如4QAM、16QAM)的最小欧氏距离很难进一步提高。为了改善QSTBC的编码增益,本文将码速率为1的4×4和8×8-QSTBC通过一定的结构变形,使其适合采用多维复网格星座这种信号设计形式,提出了一种基于多维复分圆网格的QSTBC(CL-QSTBC),并证明了CL-QSTBC编码增益的上界由网格间的最小欧氏距离决定,且该上界是可达到的,从而让CL-QSTBC的编码增益直接取决于多维网格星座的最小欧氏距离。最后,利用网格球形封装原理最大化该最小欧氏距离,从而达到最大化编码增益的目的。这样,CL-QSTBC的编码增益不再受传统复数星座的限制。经比较,CL-QSTBC的编码增益高于传统QSTBC编码增益的上界,获得了更好的性能,而且保持同样的译码复杂度。
空时编码一个重要的设计思路是开发空间分集,在获得全部空间分集之后,再通过提高编码增益来一步步改善性能。然而,编码增益的对性能的影响总是有限的,对空时编码性能起主导作用的仍然是分集增益。空时编码系统假设信道是“块状衰落”的,即在一个码字时间内保持不变,在不同码字之间可独立地变化。考虑到时域上的独立衰落具有提供时间分集的潜力,论文提出了一种基于多维网格的联合正交空时编码方案(Joint-OSTBC)。该方案充分利用了OSTBC等效信道模型并结合多维代数网格抗衰落的特性,采用时域上多个码字联合编码,在确保全部空间分集的前提下能获得额外的时间分集。然后推导了Joint-OSTBC的符号成对错误概率的Chernoff界,证明了在块状独立衰落信道中Joint-OSTBC获得的分集增益等于发送天线数、接收天线数和联合码字的个数三者的乘积。换而言之,M个码字联合编码可使原来OSTBC的分集增益放大M倍。仿真表明成对码字联合的Joint-OSTBC,其性能已显著优于QSTBC甚至目前性能最好的Golden码,而且译码复杂度低很多。
Space-time coding techniques can exploit the space diversity gains by utilizing the multi mutual independent transmission paths of MIMO systems to greatly increase the ability against channel fadings. In this thesis, we study the space-time coding techniques with low complexity, which is easy to implement, and propose four new coding design schemes based on multi-dimensional algebraic lattices.
The MIMO channel can be equivalent to multi parallel virtual SISO channels if space-time codes satisfy so-called generalized orthogonal constraint (GOC) conditions, so that the transmitted signals can be decoupled. In the current space-time codes designed for improving reliability, Orthogonal Space-Time Block Codes (OSTBC) and Restricted Full-rank Single-symbol Decodable Designs (RFSDD) have already satisfied the GOC condition. However, the OSTBC has just very low code rate and the RFSDD has the defect of unbalanced power distribution though its code rate is a little higher than the OSTBC. In this thesis, we propose a new space-time block code with generalized orthogonal constraint (named as GOC-STBC) to achieve full diversity, where the code rate is enhanced much compared with the OSTBC by relaxing the full-rank condition of weight matrices; the full diversity is obtained by using multi-dimensional real lattice constellations; in addition, we systematically analyze the coding gain, code rate and decoding complexity issues of the proposed GOC-STBC. In the meanwhile, the GOC-STBC resolves the unbalanced power distribution problem of the RFSDD. As the coding gain is maximized by using the ready-made algebraic lattice theory, the GOC-STBC has smaller design expense than another typical STBC with lower decoding complexity- Quasi-Orthogonal STBC (QSTBC). Moreover, the performance of GOC-STBC is the same or even better than the QSTBC when the decoding complexity is comparable.
Based on the structured GOC-STBC, we investigate its full diversity strategy in closed-loop systems with limited feedback bits and propose an adaptive GOC-STBC design. Because the property of equivalent virtual channel matrices of the proposed code is improved by the precoding codebooks, which are adaptively choosen by 2~4 bits feedback information at the transmitter, the proposed code can obtain full diversity under the simple zero-forcing (ZF) decoding. Furthermore, the performance of ZF decoding is equivalent to that of maximum likelihood (ML) decoding, which is single-symbol decodable (SSD). In addition, the proposed adaptive GOC-STBC is constellation free for both of the aforementioned decoding methods and at the same time the code rate achieve one for any number of transmit antennas. In contrast to the adaptive-QSTBC (A-QSTBC), which is a typical code with rate one and also has full diversity under ZF decoding, the proposed code with just 2 feedback bits has the same performance as the A-QSTBC with perfect feedback; when the proposed code uses more that 2 feedback bits, its performance is better than that of the A-QSTBC with perfect feedback.
The coding gain of rate-one QSTBCs is upper-bounded by the minimum Euclidean distance of signal constellations. When the constellation energy is fixed, it is very difficult to increase the minimum Euclidean distance of the current complex constellations (such as 4QAM and 16QAM). To further improve the coding gain of QSTBCs, in this thesis we propose a Cyclotomic Lattice-based QSTBC (CL-QSTBC) where the previous rate one 4×4- and 8×8- QSTBCs are transformed so that they are suitable to use multi-dimensional complex lattice constellations. Then, we prove that the coding gain of the CL-QSTBC is upper-bounded by the minimum Euclidean distance of lattice points and then the upper-bound is reachable. Thus, the coding gain is completely determined by the the minimum Euclidean distance of multi-dimensional lattice constellations. So, we maximize the above minimum Euclidean distance by lattice packing theory, which is equivalent to maximize the coding gain. As a result, the coding gain of the proposed CL-QSTBC will not be constrained by the common complex constellations. According to the comparison of simulations, the CL-QSTBC has higher coding gain than the upper-bound of previous QSTBCs and obtains better performance than the current best QSTBCs but with comparable decoding complexity.
The mainest factor which dominates the performance of space-time codes is the diversity gain instead of coding gain. In this thesis, we propose a Joint Orthogonal Space-Time Code (Joint-OSTBC) scheme, where the anti-fading property of multi-dimensional algebraic lattices is combined with the equivalent channel model of OSTBCs, so that the extra time diversity can be obtained by jointly coding multi OSTBC codewords along time domain. In the meanwhile, the full space diversity can be still kept in the above coding scheme. In addition, we derive the Chernoff bound of symbol pairwise error probability and prove that the total diversity gain of the proposed Joint-OSTBC is equal to the product of the number of transmit antennas, receive antennas and jointed codewords. In other words, the Joint-OSTBC with M codewords jointed has the M times diversity gains than the previous OSTBCs. From simulations, we find that the Joint-OSTBC with just double codewords jointed has already significant performance gain over both the QSTBC and even the Golden code, which is the best known code currently, but the decoding complexity is lower much.
引文
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