MIMO系统中球形译码算法的研究

针对多输入多输出（MIMO）通信系统中球形译码检测算法在较低信噪比和较高的调制阶数时复杂度仍然很高的问题,提出一种不影响检测性能同时又能大大降低其复杂度的方案。首先,对传统的球形译码算法进行研究;其次,介绍改进的球形译码算法;最后,通过仿真结果对其进行验证。     

降低高条件数信道下的球形译码算法复杂度的方法

MIMO系统中,球形译码可以在保证接近ML检测性能的前提下大大降低检测复杂度。但当信道矩阵条件数很高时,球形译码的复杂度仍然会很高。在分析了这一现象的原因后,本文提出了在高层对权值进行合并的一种球形译码算法,因为其减小了译码搜索过程中对树的高层节点的访问的概率,由此降低了搜索复杂度。仿真结果表明,这种算法在低信噪比、高条件数时可以节约20％的浮点运算操作次数。     

PSK调制下空频块码的低复杂度复数球形译码

对于PSK调制下的空频块码,复数球形译码相对实数球形译码有较低的复杂度.当复数球形译码的初始半径趋向无穷大时,排序的复杂度高.本文针对PSK符号提出每层符号以排序中心点为中心,在极坐标角度维按照之字(Zigzag)排序的方法.通过查表可以快速获得排序后的符号序列,查表排序球形译码算法相对于通用复数球形译码算法在16-PSK调制14dB平均比特信噪比下节省约61%的复杂度.     

MIMO-OFDM中基于KSDA和SQRD的联合检测算法

球形译码算法的检测性能最接近最大似然检测算法,但其计算复杂度仍然较高。为了在计算复杂度和系统性能之间取得良好折中,在研究标准球形译码的基础上,提出一种新的球形译码改进算法。新算法由快速球形译码与基于MMSE准则的SQRD算法构成。该算法在高信噪比时采用SQRD算法,低信噪比时采用KSDA算法。仿真结果表明,该算法在降低球形译码算法复杂度的同时获得了较好的系统性能。     

New SNR Adaptive Sphere Decoding Algorithm

针对多输入多输出(MIMO)无线通信系统中基于球形译码算法(Sphere Decoding Algorithm,SDA)在低信噪比区域较高的复杂度,提出一种半定松弛算法和有限星座SDA相结合的信噪比自适应的SDA.通过仿真得知,所提出的算法与已有的SDA相比,在低信噪比区域有较低的算法复杂度,并且误比特性能逼近于最优的SDA.     

多天线系统中逼近最大似然的快速检测算法

该文针对无编码的多输入多输出无线通信系统中的最大似然检测接收机在发端天线数较多、调制阶数较高时计算复杂度过高的问题,提出了一种低复杂度的球形译码算法。该算法首先利用信道信息对待检测的发送信号矢量进行分组,然后对各组内的信号矢量采用球形译码进行最大似然检测,并在组间做干扰消除。理论分析和仿真表明,该算法不仅复杂度低,而且能够逼近最大似然检测的性能。     

标准球形译码算法在发射相关MIMO信道下的平均复杂度分析

球形译码算法作为实现MIMO系统最大似然检测的一种有效方法,受到广泛重视.目前,几乎所有对球形译码算法的研究,均是基于假设信道衰落系数完全统计独立并且同分布,而在实际环境下,天线之间通常存在相关性,这样会使球形译码算法的复杂度发生变化.本文针对标准的球形译码算法,对其在发射相关MIMO信道下的复杂度进行了数学分析,推导了平均复杂度的数学表达式,并利用计算机仿真,比较了在不同的信噪比和不同的发射天线数下,发射相关性强弱对算法复杂度的影响.     

编码MIMO系统中一种低复杂度次优软检测算法

提出了一种低复杂度次优编码MIMO系统软检测算法.在编码MIMO系统的迭代译码中,信道译码需要MIMO检测输出每一比特的软信息,而软信息的计算需要巨大的计算量.本文在不同的迭代次数中分别利用球形译码的硬判决信息和编码比特先验信息得到发射向量的估计值.在这个估计值的基础上计算MIMO检测中每一比特的软信息,从而避免了常规的穷尽搜索检测算法,减少了复杂度.通过分析和仿真,本算法在有限性能损失的前提下使复杂度得到了极大减少.在相同没置下,本算法的一帧数据仿真时间不到原算法的1/20,并且对于不同的调制方式复杂度基本不变,达到了性能和复杂度的较好折中.     

一种新的信噪比自适应的球形译码算法

针对多输入多输出(MIMO)无线通信系统中基于球形译码算法(Sphere Decoding Algorithm,SDA)在低信噪比区域较高的复杂度,提出一种半定松弛算法和有限星座SDA相结合的信噪比自适应的SDA。通过仿真得知,所提出的算法与已有的SDA相比,在低信噪比区域有较低的算法复杂度,并且误比特性能逼近于最优的SDA。     

一种用于高频谱利用率非确定性MIMO系统的高效球形译码算法

球形译码是多输入多输出(MIMO)系统中一种高效的检测算法。但对于非确定性MIMO系统,已有球形译码算法不能同时获得最优解和最低搜索树。针对该问题,提出了一种高效球形译码检测算法,通过增加常量对最大似然代价函数进行等价转化,使得球形译码算法获得最优解的同时具有最低搜索树,大大降低了球形译码算法中的搜索复杂度。仿真结果表明,对于高阶正交幅度调制(M-QAM,M>4)方式,本文算法优于修正的CT(Modified Cui and Tellambura,MCT)算法,大大提高了球形译码中的搜索效率。此外,仿真结果给出了最小复杂度下的最优参数值。     

基于分段循环冗余校验的极化码自适应连续取消列表译码算法

针对极化码连续取消列表(SCL)译码算法为获取较好性能而采用较多的保留路径数,导致译码复杂度较高的缺点,自适应SCL译码算法虽然在高信噪比下降低了一定的计算量,却带来了较高的译码延时。根据极化码的顺序译码结构,该文提出了一种分段循环冗余校验(CRC)与自适应选择保留路径数量相结合的SCL译码算法。仿真结果表明,与传统CRC辅助SCL译码算法、自适应SCL译码算法相比,该算法在码率R=0.5时,低信噪比下(–1 dB)复杂度降低了约21.6%,在高信噪比下(3 dB)复杂度降低了约64%,同时获得较好的译码性能。     

基于动态分组的球形译码算法

在MIMO信号检测中,采用最大似然算法可以使系统的误码率最低,但最大似然算法要搜索整个信号空间,计算速度相当慢。球形译码算法性能最接近最大似然算法,它通过减少需要比较的信号点可大大降低计算量。提出了动态分组的球形译码算法,对传统球形译码算法进行了改进。仿真结果表明,所提算法可以根据M IMO系统的需要进行动态调整,可在小信噪比时降低误码率,大信噪比时提高译码速率。     

Speeding up the Sphere Decoder With H∞ and SDP Inspired Lower Bounds

It is well known that maximum-likelihood (ML) decoding in many digital communication schemes reduces to solving an integer least-squares problem, which is NP hard in the worst-case. On the other hand, it has recently been shown that, over a wide range of dimensions N and signal-to-noise ratios (SNRs), the sphere decoding algorithm can be used to find the exact ML solution with an expected complexity that is often less than N³. However, the computational complexity of sphere decoding becomes prohibitive if the SNR is too low and/or if the dimension of the problem is too large. In this paper, we target these two regimes and attempt to find faster algorithms by pruning the search tree beyond what is done in the standard sphere decoding algorithm. The search tree is pruned by computing lower bounds on the optimal value of the objective function as the algorithm proceeds to descend down the search tree. We observe a tradeoff between the computational complexity required to compute a lower bound and the size of the pruned tree: the more effort we spend in computing a tight lower bound, the more branches that can be eliminated in the tree. Using ideas from semidefinite program (SDP)-duality theory and H^infin estimation theory, we propose general frameworks for computing lower bounds on integer least-squares problems. We propose two families of algorithms, one that is appropriate for large problem dimensions and binary modulation, and the other that is appropriate for moderate-size dimensions yet high-order constellations. We then show how in each case these bounds can be efficiently incorporated in the sphere decoding algorithm, often resulting in significant improvement of the expected complexity of solving the ML decoding problem, while maintaining the exact ML-performance.     

Combined simplified maximum likelihood and sphere decoding algorithm for MIMO system

In this article, a new system model for sphere decoding （SD） algorithm is introduced. For the 2 × 2 multipleinput multiple-out （MIMO） system, a simplified maximum likelihood （SML） decoding algorithm is proposed based on the new model. The SML algorithm achieves optimal maximum likelihood （ML） performance, and drastically reduces the complexity as compared to the conventional SD algorithm. The improved algorithm is presented by combining the sphere decoding algorithm based on Schnorr-Euchner strategy （SE-SD） with the SML algorithm when the number of transmit antennas exceeds 2. Compared to conventional SD, the proposed algorithm has low complexity especially at low signal to noise ratio （SNR）. It is shown by simulation that the proposed algorithm has performance very close to conventional SD.     

一种低复杂度的差分酉空时调制多符号球形译码算法

该文提出了一种瑞利衰落信道下差分酉空时调制系统中多符号差分球形译码的改进算法。该算法在执行球形译码的最大似然度量搜索时,仅对具有较小最大似然度量的部分测试符号进行搜索,从而大大减少了搜索的次数,同时提出了一种逐项进行的最大似然度量计算方法,可以尽早发现超过搜索范围的测试符号并终止计算,在避免无谓的运算负担的同时得到所需的具有较小最大似然度量的部分测试符号。仿真表明,在适中的信噪比范围内,该算法在牺牲少量系统性能的基础上降低了超过50%的运算量。     

Decoding the Golden Code: A VLSI Design

The recently proposed Golden code is an optimal space-time block code for 2$,times,$ 2 multiple-input–multiple-output (MIMO) systems. The aim of this work is the design of a VLSI decoder for a MIMO system coded with the Golden code. The architecture is based on a rearrangement of the sphere decoding algorithm that achieves maximum-likelihood (ML) decoding performance. Compared to other approaches, the proposed solution exhibits an inherent flexibility in terms of QAM modulation size and this makes our architecture particularly suitable for adaptive modulation schemes. Relying on the flexibility of this approach two different architectures are proposed: a parametric one able to achieve high decoding throughputs ($>$ 165 Mb/s) while keeping low overall decoder complexity (45 KGates), a flexible implementation able to dynamically adapt to the modulation scheme (4-,16-,64-QAM) retaining the low complexity and high throughput features.      

低密度奇偶校验码在EBPSK系统中的应用

扩展的二元相移键控(EBPSK)是一种高效调制,为了降低其在低信噪比下的误码率,引入了低密度奇偶校验码(LDPC)。用BP算法对LDPC码进行译码时,需要计算译码初始信息。根据所用EBPSK解调器的特点,本文定义了解调输出的近似似然比,不仅可以降低系统的复杂性,同时通过仿真发现,利用其作为译码初始消息可以得到较高的信噪比增益。因此,在EBPSK系统中应用LDPC码以抵抗噪声、降低误码率是一种较有效的方式。     

On the complexity of sphere decoding in digital communications

Sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications. In some cases, the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure. Another claim is that although worst-case complexity is exponential, the expected complexity of the algorithm is polynomial. Herein, we study the expected complexity where the problem size is defined to be the number of symbols jointly detected, and our main result is that the expected complexity is exponential for fixed signal-to-noise ratio (SNR), contrary to previous claims. The sphere radius, which is a parameter of the algorithm, must be chosen to ensure a nonvanishing probability of solving the detection problem. This causes the exponential complexity since the squared radius must grow linearly with problem size. The rate of linear increase is, however, dependent on the noise variance, and thus, the rate of the exponential function is strongly dependent on the SNR. Therefore sphere decoding can be efficient for some SNR and problems of moderate size, even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size.