CN102017553B - 用于多信道宽带通信系统中的基带预失真线性化的方法和系统 - Google Patents

用于多信道宽带通信系统中的基带预失真线性化的方法和系统 Download PDF

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CN102017553B
CN102017553B CN200780051434.2A CN200780051434A CN102017553B CN 102017553 B CN102017553 B CN 102017553B CN 200780051434 A CN200780051434 A CN 200780051434A CN 102017553 B CN102017553 B CN 102017553B
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金钟宪
赵庚浚
金完锺
S·P·斯特普尔顿
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    • H03F1/32—Modifications of amplifiers to reduce non-linear distortion
    • H03F1/3241—Modifications of amplifiers to reduce non-linear distortion using predistortion circuits
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    • H04L25/49—Transmitting circuits; Receiving circuits using code conversion at the transmitter; using predistortion; using insertion of idle bits for obtaining a desired frequency spectrum; using three or more amplitude levels ; Baseband coding techniques specific to data transmission systems
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    • H—ELECTRICITY
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    • H03F2201/00—Indexing scheme relating to details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements covered by H03F1/00
    • H03F2201/32—Indexing scheme relating to modifications of amplifiers to reduce non-linear distortion
    • H03F2201/3233—Adaptive predistortion using lookup table, e.g. memory, RAM, ROM, LUT, to generate the predistortion
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    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
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    • H04L2025/0335—Arrangements for removing intersymbol interference characterised by the type of transmission
    • H04L2025/03375—Passband transmission
    • H04L2025/03414—Multicarrier

Abstract

公开了一种有效的基带预失真线性化方法，该方法用于在使用有效的多路复用调制技术的宽度通信系统中减少频谱再生并且补偿记忆效应，其中有效的复用调制技术诸如宽度码分多址以及正交频分复用。本发明基于使用分段预均衡的查找表的预失真方法，以利用针对宽度发射器系统的记忆效应补偿来针对所需线性性能降低计算复杂度和数值不稳定性，其中分段预均衡的查找表的预失真是查找表预失真和分段预均衡器的级联。因此，本发明可以在相邻信道功率比方面降低计算负载，这节省了实现中的硬件资源并且改进了性能。

Description

用于多信道宽带通信系统中的基带预失真线性化的方法和系统
相关申请
本申请要求与本申请具有相同发明人的、于2006年12月26日提交的美国临时专利申请S.N.60/877,035的优先权，并且还要求于2007年12月7日提交的美国临时专利申请S.N.61/012416的优先权，通过引用将以上二者合并于此。将美国临时专利申请S.N.61/012,416作为附录1包括进来。
技术领域
本发明一般地涉及使用多路复用调制技术的宽带通信系统。更具体地，本发明涉及用于基带预失真线性化以补偿多信道宽带无线发射器的非线性和记忆效应的方法和系统。
背景技术
由于无线通信系统中频谱效率的重要性增加，射频(RF)功率放大器(PA)的线性和效率对于非恒定包络数字调制方案而言已经成为关键的设计问题，其中非恒定包络数字调制方案具有高的峰值平均功率比(PAR)。RF PA具有非线性，该非线性在PA的输出处产生幅度调制-幅度调制(AM-AM)以及幅度调制-相位调制(AM-PM)失真。这些效应产生了使误差向量幅度(EVM)恶化的相邻信道中的频谱再生和带内失真。
线性和效率之间的关系是一种权衡，因为当放大器在其线性区域中操作时，功率效率非常低，而当驱使放大器进入其压缩区域时，功率效率增大。为了同时增强线性和效率，通常对RF PA应用线性化技术。已经提出了各种线性化技术，诸如反馈、前馈和预失真。
一个技术是基带数字预失真(PD)，其通常使用数字信号处理器。与广泛使用的传统的前馈线性化技术相比，数字预失真可以实现改进的线性和改进的功率效率，同时降低了系统复杂度。软件实现为数字预失真器提供了适于多标准环境的重配置性。此外，使用效率增强技术的PA，例如Doherty功率放大器(DPA)，能够以线性为代价实现比传统PA设计更高的效率。因此，将数字预失真与使用效率增强技术的PA组合具有改进系统线性和总效率的潜力。
然而，大部分数字PD预设PA没有记忆或具有弱记忆。这在记忆效应使得输出信号是当前以及过去的输入信号的函数的宽带应用中是不切实际的。PA中的记忆效应源包括有源设备的自加热(也称为长时恒定或热记忆效应)以及有源设备的频率依赖性(也称为短时恒定或电子记忆效应)，这涉及匹配网络或偏置电路。随着信号带宽增大，PA的记忆效应也变得显著并且限制了无记忆数字PD的性能。
为了克服数字PD中的记忆效应，已经提出了各种方法。对于短期记忆效应，应用Volterra滤波器结构以使用间接学习算法补偿记忆效应，但是优化系数的数量随着阶的增大而非常大。该复杂度使得基于Volterra滤波器的PD在实际的硬件中极难实现。为了减少系数的数量，已经提出了作为Volterra滤波器简化版本的记忆多项式结构，但是就算是该简化版本也仍旧需要大的计算负载。此外，基于记忆多项式的PD在包括高阶多项式项时遭受了数值不稳定性，因为为了估计多项式系数而需要对矩阵取逆。已经利用同样基于正交多项式的复杂结构的备选方案来减轻与传统多项式相关联的数值不稳定性。为了以性能为代价进一步降低复杂度，已经提出了Hammerstein预失真器，其是有限冲激响应(FIR)滤波器或线性时变(LTI)系统，其后跟随有无记忆多项式PD。Hammerstein预失真器假设使用的PA模型遵守是无记忆非线性的Wiener模型结构，其后跟随有有限冲激响应(FIR)滤波器或线性时变(LTI)系统。
该实现意味着Hammerstein结构仅可以补偿来自于RF频率响应的记忆效应。因此，如果RF频率响应非常平坦，则Hammerstein PD不能修正任何其他类型的记忆效应，诸如偏置感应(bias-induced)以及热记忆效应。
最近，使用了与子带滤波块级联的静态查找表(LUT)数字基带PD，这不是为补偿电子记忆效应，而是为了解决由于在针对固定LUTPD进行了初始设置之后，PA的温度改变而引起的增益和相位变化。
因此，在多信道宽带无线发射器中，存在对不仅能够补偿RF频率响应记忆效应而且能够补偿偏置感应或热记忆效应的基带预失真方法的长期需要。
发明内容
因而，本发明基本上克服了现有技术的很多前述限制，并且提供了基带预失真线性化的系统和方法，其补偿了在多信道宽带无线发射器中发现的非线性以及记忆效应。通过使用利用查找表的分段(piecewise)预均衡PD实现了该结果。利用该方法，本发明能够补偿电子以及热记忆效应，而同时与使用记忆多项式PD算法的现有技术系统相比，降低了系统的计算复杂度以及数值不稳定性，同时本发明在得到的多带PA性能中的线性方面可与记忆多项式PD相媲美。
可以从结合附图的以下详细描述中更全面地理解本发明的其他目的和优势，在附图中：
附图说明
图1是示出了根据本发明的分段预均衡LUT预失真系统的示意图。
图2是示出了图1均衡器107的基于多项式的实施方式的示意图。
图3A是示出了复数增益调节器响应的图示。
图3B是示出了根据本发明的分段均衡器响应的图示。
图3C是示出了根据本发明的复数增益调节器和分段均衡器级联的响应的图示。
图3D是示出了功率放大器响应的图示。
图3E是示出了来自于复数增益调节器和分段均衡器级联的响应和复数增益调节器响应的详细响应的图示。
图4A是示出了表示利用使用具有500kHz间隔的八音测试信号的无记忆LUT PD的实施方式进行线性化之前以及之后的线性化结果的图示。
图4B是示出了表示利用使用具有500kHz间隔的八音测试信号的LUT Hammerstein PD进行线性化之前以及之后的线性化结果的图示。
图4C是示出了表示利用使用具有500kHz间隔的八音测试信号的本发明的分段预均衡PD进行线性化之前以及之后的线性化结果的图示。
图4D是示出了表示利用使用具有500kHz间隔的八音测试信号的记忆多项式PD进行线性化之前以及之后的线性化结果的图示。
图5是示出了表示四个类型PD分别使用单个W-CDMA载波的线性化结果的图示，这四种类型的PD包括无记忆LUT PD、LUTHammerstein PD、本发明的分段预均衡PD和记忆多项式PD。
图6是示出了四个类型PD分别使用单个W-CDMA载波的ACPR仿真结果分别性能比较的图示，这四种类型的PD包括无记忆LUTPD、LUT Hammerstein PD、本发明的分段预均衡PD和记忆多项式PD。
图7是示出了四个类型PD分别使用单个W-CDMA载波的测量的线性化结果的图示，这四种类型的PD包括无记忆LUT PD、LUTHammerstein PD、本发明的分段预均衡PD和记忆多项式PD。
图8是示出了四个类型PD分别使用单个W-CDMA载波的ACPR的测量结果的性能比较的图示，这四种类型的PD包括无记忆LUTPD、LUT Hammerstein PD、本发明的分段预均衡PD和记忆多项式PD。
图9是示出了本发明的分段预均衡的PD的复杂度估计的图示。
图10是示出了记忆多项式PD的复杂度估计的图示。
具体实施方式
为了克服在现有技术中发现的记忆多项式PD的计算复杂度和数值不稳定性，因此，本发明利用具有已经被预均衡来补偿记忆效应的LUT的基于LUT的自适应数字预失真系统，从而实现比现有技术更小的计算负载，而同时还将相邻信道功率比(ACPR)降低到基本上与记忆多项式PD已经实现的相同的程度。因此，本发明提供的系统在下文称为分段预均衡的、基于查找表的预失真(PELPD)系统。
现在，将参考附图详细描述根据本发明的PELPD系统的优选和备选实施方式。
图1是示出了根据本发明的PELPD系统的实施方式的示意图。如图所示，用于索引LUT 106的线性幅度寻址(addressing)方法使用如下：
m＝round(|u(n)|·N)
其中，u(n)是输入信号101并且所述round函数返回作为索引(m)的最接近整数并且N是LUT 106的大小。
在进行预均衡107之前，将数字复数基带输入信号采样101与从LUT条目中抽取的复数系数102相乘，如下
x(n)＝u(n)·Fm(|u(n)|)
其中Fm(|u(n)|)是对应于输入信号101幅度的复数系数102，用于补偿PA 110的AM到AM以及AM到PM失真。
分段预均衡器107的LUT中的N乘K-1个滤波器系数用于补偿记忆效应，其中N是LUT的深度并且FIR滤波器具有K个抽头。在某些实施方式中，由于稳定性问题，分段预均衡器107使用FIR滤波器而不是无限冲激响应(IIR)滤波器，尽管不是所有实施方式都需要FIR滤波器。预均衡器的输出104可以由以下方程描述
z ( n ) = Σ k = 0 K - 1 W k m ( | u ( n ) | ) · x ( n - k )
= Σ k = 0 K - 1 W k m ( | u ( n ) | ) · u ( n - k ) · F m ( | u ( n - k ) | )
其中Wk m(|u(n)|)是对应于所述输入信号u(n)101幅度的第k个抽头的第m个索引的系数。而且，Wk m(|u(n)|)是|u(n)|的函数并且Fm102是|u(n-k)|的函数。出于分析目的，可以由如下多项式模型替代无记忆LUT 106(Fm)结构：
F m ( | u ( n - k ) | ) = Σ p = 1 P b 2 p - 1 · | u ( n - k ) | 2 ( p - 1 )
其中2p-1是多项式阶并且b是对应于该多项式阶的复数系数。此外，注意，抽头系数和无记忆LUT系数(Fm)102分别取决于u(n)和u(n-k)。
因此，可以使用以下多项式方程表示每段均衡器：
z ( n ) = Σ k = 0 K - 1 W k m ( | u ( n ) | ) · Σ p = 1 P b 2 p - 1 · u ( n - k ) · | u ( n - k ) | 2 ( p - 1 )
其中Wk m(|u(n)|)是具有作为|u(n)|函数的第m个索引的第k个抽头系数。不失一般性地，分段预均衡器107可以使用一个I阶多项式进行类似地定义，
z ( n ) = Σ k = 0 K - 1 Σ l = 1 L w k , 2 l - 1 · | u ( n ) | 2 ( l - 1 )
× Σ p = 1 P b 2 p - 1 · u ( n - k ) · | u ( n - k ) | 2 ( p - 1 )
其中Wk，I是第k个抽头的第I阶系数。
在z(n)104的数模转换108之后，该信号上变频109至RF，由生成失真的PA 110放大、衰减113、下变频114至基带并且继而最终进行模数转换115并且应用于延迟116估计算法117。可以由以下方程描述反馈信号y(n-Δ)105，该反馈信号是具有延迟的、PA 110的输出，
y(n-Δ)＝G(|z(n-Δ)|)·ej·Φ(|z(n-Δ)|)
其中G(·)和Φ(·)分别是PA 110的AM/AM和AM/PM失真，并且Δ是反馈环路延迟。为了估计Δ，相关技术应用如下：
R ( d ) = 1 N Σ n = 0 N - 1 z ( n ) · y * ( n + d )
其中d是延迟变量并且N是用于进行相关的块大小。
在延迟116估计之后，可以通过以下方程估计无记忆LUT 106系数，该方程是具有间接学习的最小均方(LMS)算法。
Fm(|u(n+1)|)＝Fm(|u(n)|)+μ·u(n)·e(n)
其中n是迭代数量，μ是稳定性因子并且e(n)是x(n)-y(n)·Fm(|x(n)|)。
应该指出，已经生成的寻址可以重新用于对y(n)105进行索引，该y(n)105是失真信号，其能够因为不正确的索引而引起另一误差。在该过程期间，将通过分段预均衡器107旁路采样x(n)103。在该间接学习LMS算法收敛之后，激活均衡器107。已经将利用LMS算法的间接学习方法用于对分段滤波器系数进行自适应调整。以向量格式将反馈路径中的多个均衡器107的输入写为
yFI(n)＝[yF(n)yF(n-1)…yF(n-K+1)]
其中yF(n)是过去的LUT输出，即，y(n)·Fm(|y(n)|)。
因此，多个FIR滤波器输出yFO(n)可以使用以下方程以向量的格式导出
yFO(n)＝Wm·yFI(n)T
W n = W 0 m W 1 m . . . W K - 1 m
其中T是转置算子。
可以如下获得预均衡器107的抽头系数的自适应：
Wm(|u(n+1)|)＝Wm(|u(n)|)+μ·(yFI(n)T)*·E(n)
其中E(n)是z(n)和yFO(n)之间的误差信号，并且μ是步长(*表示复数共轭)。自适应算法通过比较反馈信号和输入信号的延迟版本来确定系数值。
参考开始于输出111的反馈路径，应该理解，存在多个备选方案来使用此类反馈以更新LUT值或多项式系数。在某些实施方式中，将PA的输出转换到基带，并且将得到的基带信号与输入信号进行比较。将产生的误差用于修正LUT值和系数。在其他实施方式中，从频谱方面监视来自于PA的输出，并且使用下变频器、带通滤波器和功率检测器监视带外(out of band)失真。然后，将功率检测器值用于调整LUT值或多项式系数。
图2示出了使用多项式方程时分段预均衡器107PD的相应框图。多项式表示需要类似于Volterra系列的太多的复数乘法。如图1所示，当利用基于PELPD的方法时，降低了复杂度，因为所需的计算较少，尽管可能需要更多的存储器。从本文中应该理解，预均衡部分是自适应的并且设计用于修正记忆效应，同时lut主要用于进行预失真以修正在商业PA中发现的其他非线性。
图3A-3D是本发明的PELPD的图示。在图3A中示出了典型的无记忆预失真器响应。图3B示出了划分为N段的分段预失真器产生的滞后。由于功率放大器的滞后不一定均匀分布在整个输入幅度范围上，所以应用分段预均衡器以在整个输入范围获得均匀的补偿。在图3C中示出了本发明的PELPD的输出，其可以被认为源自图3A和图3B的级联。图3D示出了典型的功率放大器响应的响应，并且图3B导致了如图3C所示的本发明的PELPD。图3D示出了具有记忆的典型功率放大器响应的响应。在级联了图3C和图3D之后获得了图3E中希望的线性响应。
为了检验本发明的PELPD的性能，首先执行基于时域测量采样的PA行为建模。该行为模型基于截断的Volterra模型。设计了在最终极处使用两个170W推挽式横向扩散金属氧化物半导体(LDMOS)的300W峰值包络功率(PEP)Doherty PA。该DohertyPA工作于2140MHz频带并且具有61dB的增益，和平均30W输出功率处的28％的功率附加效率(PAE)。为了基于实际PA的测量来构建PA模型，使用测试工作台(test bench)[K.Mekechuk，W.Kim，S.Staleton和J.Kim，“Linearinzing Power Amplifiers Using DigitalPredistortion，EDA Tools and Test hardware”High FrequencyElectronics，pp.18-27，2004年4月]。基于该行为模型，已经仿真了包括无记忆LUT PD、Hammerstein PD、本发明的PELPD和记忆多项式PD的各类PD，并且比较了相邻信道功率比(ACPR)性能。在所有仿真中，将LUT的大小固定为128个条目，这是在考虑量化效应以及存储器大小的情况下的折衷大小。本领域的技术人员应该认识到，针对非线性的补偿量涉及LUT 106的大小。增加LUT大小，虽然产生了更准确的非线性表示，但是在自适应方面付出了更多的代价。因此，LUT大小的选择是准确度和复杂度之间的权衡。
作为测试信号的是单个下行链路W-CDMA载波，其基于第三代合作伙伴计划(3GPP)标准规范的测试模式，具有64个专用物理信道(DPCH)，该载波具有3.84Mchips/s和9.8db的波峰因子。首先，将具有9.03db的PAR和4MHz带宽的、具有500kHz间隔的八音信号用于验证所提出的方法，其中该八音信号可与W-CDMA信号相媲美。
图4A-4D是示出了四种类型的PD的线性化之前以及之后的代表性线性化结果的图示。如图4A所示，传统无记忆LUT PD能够改进线性并且还补偿记忆效应。图4B示出了传统的Hammerstein PD，其在10MHz以上使性能恶化，而在10MHz带宽内使其发生改进。如果主信号路径中的RF频率响应非常平坦，则Hammerstein PD不能修正除了频率响应记忆效应之外的任何其他记忆效应。也不存在使用传统Hammerstein PD，对于减小频谱再生而言，也没有显而易见的改进。非常清楚的是：Hammerstein PD对来自于记忆效应的失真进行抑制的能力非常有限。图4C示出了本发明的PELPD(具有2个抽头)的性能。图4D示出了传统记忆多项式PD(具有第5阶和两个记忆项)的性能。通过比较图4A-4D，可以看到，本发明的PELPD在ACPR性能方面可以与记忆多项式PD相媲美。
图5是示出了针对上述四个类型的PD的线性化结果的图示。将单个W-CDMA载波应用于LUT PD、LUT Hammerstein PD、本发明的PELPD以及记忆多项式PD。
图6是示出了分别针对4个类型的ACPR仿真结果的性能比较的图示。与无记忆PD相比，传统Hammerstein PD不能改进来自记忆效应的失真。本发明的PELPD可以抑制归因于非线性和PA记忆效应的失真。
在基于行为PA模型验证了仿真中本发明的PELPD的ACPR性能之后，使用测试工作台中的实际Doherty PA执行实验。发射器原型包括具有两个数模转换器(DAC)和RF上变频器的ESG以及PA。接收器包括RF下变频器、高速模数转换器以及数字下变频器。该接收器原型可以通过VSA构造。对于主DSP，PC用于延迟补偿和预失真算法。作为测试信号，为了验证不同PD的补偿性能，在测量中，将具有3.84Mchips/s和9.8db波峰因子的测试模型1的、具有64DPCH的两个下行链路W-CDMA载波用作输入信号。PD的所有系数通过间接学习算法来标识，该间接学习算法被认为是PA的逆建模。在验证过程期间，使用了256条目LUT、5抽头FIR滤波器的Hammerstein PD、本发明的PELPD(具有2抽头)以及第5阶-2延迟记忆多项式。根据多个测量优化抽头数量的选择。
图7是示出了分别使用单个W-CDMA载波的4类PD在线性化之前和之后的测量的线性化结果的图示。从距中心频率的频率偏移量(5MHz和-5MHz)处执行原型发射器输出处的ACPR计算。
图8是示出了分别使用单个W-CDMA载波的4类PD的ACPR测量结果的性能比较的图示。对于具有带有5抽头滤波器的Hammerstein PD的发射器，ACPR值在上ACPR(5MHz偏移)处比LUT PD大约好1dB，而在下ACPR(-5MHz偏移)处与之相同。本发明的PELPD和第5阶-2记忆多项式PD在ACPR方面显示处接近的补偿性能。对于下ACPR和上ACPR而言，这二者对ACPR的改进比Hammerstein PD和无记忆LUT PD分别好出大约4dB和6dB。
还评估了本发明的PELPD和记忆多项式方法的复杂度(忽略LUT读、写、编索引以及信号幅度的平方根(SQRT)的计算，因为LUT索引不仅取决于方法，还取决于变量，例如幅度、对数、幂等，并且SQRT运算可以以不同的方式实现)。因此，仅通过对每个输入采样的加法(减法)和乘法数量进行计数来评估复杂度。为了考虑实数硬件实现，将复数运算转换为实数运算并且考虑存储器大小。例如，一次复数乘法需要两次实数加法和四次实数乘法。如果N是LUT条目的数量，则所需的存储器大小是2N(I和Q LUT)。
图9是示出了本发明的PELPD的复杂度仿真的图示。如果LUT具有256个条目并且滤波器具有2个抽头，则PD每个采样需要进行40次实数加法(减法)、54次实数乘法以及1542的存储器大小。本发明的PELPD需要与传统Hammerstein PD相同的加法和乘法数量，但是需要更多的存储器。
图10是示出了使用RLS间接学习算法的记忆多项式PD的复杂度估计的图示。在图11中给出了算术运算的数量，其中O等于P(k+1)。例如，P＝5并且K＝1每个采样需要进行1342次实数加法(减法)，1644次实数乘法，以及24的存储器大小。在将乘法数量与本发明的PELPD进行比较时，记忆多项式PD每个采样需要进行多于300次实数乘法。因此，PELPD方法显著降低了复杂度。此外，记忆多项式方法的实数乘法的数量随着多项式阶数和记忆长度的平方指数(square power)增长。
总之，与传统Hammerstein方法比较，本发明的PELPD可以更有效地减小频谱再生并且与记忆多项式PD获得相似的修正能力，但是仅需要更小的复杂度。
尽管已经参考优选和备选实施方式描述了本发明，但是应该理解，本发明不限于所描述的细节。在前面的描述中已经提出了各种变形和修改，并且本领域的技术人员将进行其他变形和修改。因此，旨在将所有此类变形和修改包括在如所附权利要求书所定义的发明范围内。

Claims (10)

1.一种方法，用于减小使用多路复用调制技术的多信道宽带通信系统的相邻信道功率比并且补偿所述多信道宽带通信系统的记忆效应，所述方法包括以下步骤：
根据通信系统的基带输入信号的采样生成地址；
根据所述地址从无记忆查找表中获取条目；以及
将所述基带输入信号和所述查找表条目相乘；以及
对所述相乘步骤进行预均衡，
所述预均衡步骤由以下方程执行：
z ( n ) = Σ k = 0 K - 1 W k m ( | u ( n ) | ) · x ( n - k ) = = Σ k = 0 K - 1 W k m ( | u ( n ) | ) · u ( n - k ) · F m ( | u ( n - k ) | ) ,
其中，是对应于所述输入信号u(n)的幅度的第k个抽头的第m个索引的系数，并且
x(n)＝u(n)·Fm(|u(n)|)，Fm(|u(n)|)是所述无记忆查找表的复数系数。
2.根据权利要求1所述的方法，其中所述查找表中的所述条目是复数系数。
3.根据权利要求1所述的方法，其中所述预均衡步骤包括分段均衡。
4.根据权利要求1所述的方法，其中所述预均衡步骤使用有限冲激响应滤波。
5.根据权利要求3所述的方法，其中所述分段均衡使用有限冲激响应滤波器，而不是使用无限冲激响应滤波器。
6.根据权利要求1所述的方法，进一步包括使用间接学习方法来更新所述条目。
7.根据权利要求6所述的方法，其中所述间接学习方法使用最小均方算法。
8.根据权利要求1所述的方法，其中通过确定以下方程执行所述获取步骤：
m＝round(|u(n)|·N)，
其中，u(n)是输入信号，并且所述round函数返回作为索引(m)的最接近整数，并且N是所述查找表的大小。
9.根据权利要求1所述的方法，进一步包括由以下方程获得所述索引的系数的自适应：
wm(|u(n+1)|)＝wm(|u(n)|)+μ·(yFI(n)T)*·E(n)，
其中yFI(n)是反馈路径中多个均衡器的输入，E(n)是误差信号，μ是步长并且*是复数共轭，并且
10.一种系统，用于减小使用多路复用调制技术的多信道宽带通信系统的相邻信道功率比并且补偿所述多信道宽带通信系统的记忆效应，所述系统包括：
地址生成器，用于根据通信系统的基带输入信号的采样生成地址；
无记忆查找表，其中具有根据所述地址而可寻址的系数；
乘法器，用于组合所述基带输入信号和所述系数即查找表条目；以及
均衡器，用于对乘法器进行预均衡，以补偿所述通信系统的功率放大器中的记忆效应，
所述均衡器通过以下方程执行预均衡：
z ( n ) = Σ k = 0 K - 1 W k m ( | u ( n ) | ) · x ( n - k ) = = Σ k = 0 K - 1 W k m ( | u ( n ) | ) · u ( n - k ) · F m ( | u ( n - k ) | ) ,
其中，是对应于所述输入信号u(n)的幅度的第k个抽头的第m个索引的系数，并且
x(n)＝u(n)·Fm(|u(n)|)，Fm(|u(n)|)是所述无记忆查找表的复数系数。
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