CN101630965B - Multi-antennae multiplexing receiving device based on GMC - Google Patents
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Abstract
本发明提供一种基于GMC系统多天线复用接收装置,包括射频接收模块,同步与信道估计模块,去除循环前缀模块,串并转换模块,以及,还包括:频域均衡模块,其与串并转换模块、同步与信道估计模块的输出端相连接;第一并串转换模块,其与频域均衡模的输出端相连接;匹配滤波器组,其与第一并串转换模块的输出端相连接;线性逆变换模块,其与匹配滤波器组模块的输出端相连接,用于将各子带传输的信号恢复到时域去;第二并串转换模块,其与线性逆变换模块的输出端相连接,用于将输入的并行数据序列变换成串行的输出数据序列,用于恢复在原始星座点上的串行符号。该接收装置大大降低了系统的开销。
The present invention provides a multi-antenna multiplexing receiving device based on the GMC system, including a radio frequency receiving module, a synchronization and channel estimation module, a cyclic prefix removal module, a serial-to-parallel conversion module, and also includes: a frequency domain equalization module, which is combined with a serial-to-parallel The conversion module is connected with the output terminal of the channel estimation module synchronously; the first parallel-serial conversion module is connected with the output terminal of the frequency domain equalization module; the matched filter bank is connected with the output terminal of the first parallel-serial conversion module connection; a linear inverse transform module, which is connected to the output of the matched filter bank module, and is used to restore the signals transmitted by each sub-band to the time domain; a second parallel-serial conversion module, which is connected to the output of the linear inverse transform module The terminals are connected to convert the input parallel data sequence into a serial output data sequence, which is used to restore the serial symbols on the original constellation points. The receiving device greatly reduces the overhead of the system.
Description
本申请是申请号为200510111450.9、申请日为2005年12月13日、发明名称为基于GMC的多天线复用发送、接收装置及频域均衡方法的发明专利的分案申请。This application is a divisional application for an invention patent with the application number 200510111450.9, the application date is December 13, 2005, and the invention name is GMC-based multi-antenna multiplexing transmission and reception device and frequency domain equalization method.
技术领域 technical field
本发明涉及一种基于GMC的多天线复用接收装置,特别是在接收端做均衡处理时,得不到调制映射后星座图上符号的无线通信系统,在衰落信道情况下多天线复用接收装置。The invention relates to a multi-antenna multiplexing receiving device based on GMC, especially in a wireless communication system where symbols on the constellation diagram after modulation and mapping cannot be obtained when the receiving end performs equalization processing, and multi-antenna multiplexing receiving under the condition of a fading channel device.
背景技术 Background technique
多输入多输出MIMO(Multiple Input Multiple Output)的多天线技术是未来移动通信系统实现高数据速率,提高传输质量的重要途径,是现代通信技术中的重大突破之一,提供了解决未来Internet无线网络中的业务容量需求瓶颈问题。多天线技术已经出现在宽带无线接入系统、无线局域网WLAN和3G及后3G等商用无线通信产品和网络中。多天线通信系统定义为:在发射端和接收端分别采用多个天线,也就是信号通过发射端和接收端的多个天线传送和接收,从而改善每个用户得到的服务质量(误比特率或数据速率)。利用多天线技术可以提高网络服务性能并给网络运营商带来巨大收益。Multiple Input Multiple Output MIMO (Multiple Input Multiple Output) multi-antenna technology is an important way for future mobile communication systems to achieve high data rates and improve transmission quality. It is one of the major breakthroughs in modern communication technology and provides solutions for future Internet wireless networks. The bottleneck problem of business capacity demand in . Multi-antenna technology has appeared in commercial wireless communication products and networks such as broadband wireless access system, wireless local area network WLAN and 3G and post-3G. A multi-antenna communication system is defined as: multiple antennas are used at the transmitter and receiver respectively, that is, signals are transmitted and received through multiple antennas at the transmitter and receiver, thereby improving the quality of service (bit error rate or data rate) obtained by each user. rate). Using multi-antenna technology can improve network service performance and bring huge benefits to network operators.
多天线复用信号处理技术是一种采用多天线实现并行传输数据的结构。该信号处理技术能够使无线链接的容量提高20到30倍。即每个发送信号采用不同的发送天线,在接收端也利用多个天线以及独特的信号处理技术把互相干扰的信号分离出来,从而可在给定的信道频段上,容量随天线的数量成比例增加。Multi-antenna multiplexing signal processing technology is a structure that uses multiple antennas to transmit data in parallel. The signal processing technology can increase the capacity of wireless links by 20 to 30 times. That is, each transmitted signal uses a different transmitting antenna, and multiple antennas and unique signal processing technology are used at the receiving end to separate the mutually interfering signals, so that the capacity can be proportional to the number of antennas in a given channel frequency band Increase.
现有的频域均衡器利用MMSE原理进行工作时,假设使用n根发送天线和n根接收天线,发送的数据块记为x,有:When the existing frequency domain equalizer uses the MMSE principle to work, it is assumed that n transmitting antennas and n receiving antennas are used, and the transmitted data block is denoted as x, which is:
x=[x1;x2;...xn] (1)x=[x 1 ; x 2 ; . . . x n ] (1)
其中,xi为第i根天线上发送的长度为N的数据块序列,为列向量。Wherein, x i is a sequence of data blocks with a length of N sent on the i-th antenna, which is a column vector.
接收到的块记为y,则有:The received block is recorded as y, then:
其中:in:
为从发送天线q到接收天线p的信道矩阵,为循环矩阵,且有: is the channel matrix from the transmitting antenna q to the receiving antenna p, which is a circulant matrix, and has:
Hi,j=FHΛi,jF (4)H i, j = F H Λ i, j F (4)
其中,H表示共轭转置,
分别对yi作FFT,可得:Perform FFT on y i respectively, we can get:
其中:in:
以(5)式为目标,在频域对Y乘以一个矩阵W进行均衡,再变回时域,则有:Taking Equation (5) as the goal, multiply Y by a matrix W to equalize in the frequency domain, and then change back to the time domain, then:
使用MMSE方法,即有:Using the MMSE method, there are:
即:Right now:
在(9)式两边对WH取偏导,则有:Take the partial derivative of W H on both sides of equation (9), then:
即:Right now:
WMMSE=σs 2ΛH[σs 2ΛΛH+σn 2I]-1 (11)W MMSE =σ s 2 Λ H [σ s 2 ΛΛ H +σ n 2 I] -1 (11)
其中,WMMSE为MMSE方法乘性矩阵,σs为信号能量,Λ包含M×M个N×N对角矩阵,其中M为发射天线数目,N为FFT长度,σn为噪声能量,在步骤3.3之均衡器中设计中,必须对一MN×MN的矩阵求逆,WMMSE的计算复杂度主要由[σs 2ΛΛH+σn 2I]-1决定,若直接计算[σs 2ΛΛH+σn 2I]-1,其算法复杂度为O((MN)3),在多天线GMC系统中,M=2,3,4 N=512,1024,此时,该矩阵求逆过程给接收机带来巨大的计算开销,浪费着系统的大量资源。Among them, W MMSE is the multiplicative matrix of MMSE method, σ s is the signal energy, Λ contains M×M N×N diagonal matrices, where M is the number of transmitting antennas, N is the length of FFT, σ n is the noise energy, in step In the design of the equalizer in 3.3, an MN×MN matrix must be inverted. The computational complexity of W MMSE is mainly determined by [σ s 2 ΛΛ H +σ n 2 I] -1 . If [σ s 2 ΛΛ H +σ n 2 I] -1 , its algorithm complexity is O((MN) 3 ), in the multi-antenna GMC system, M=2, 3, 4 N=512, 1024, at this time, the matrix The inverse process brings huge calculation overhead to the receiver and wastes a lot of resources of the system.
使用一般的方法,该步骤算法复杂度为O((MN)3),在GMC系统中,块长一般为:N=512或者N=1024,而发送天线数目一般选择为:M=2,3,4。于是,从而浪费大量的资源。Using a general method, the algorithm complexity of this step is O((MN) 3 ), in the GMC system, the block length is generally: N=512 or N=1024, and the number of transmitting antennas is generally selected as: M=2,3 , 4. Thus, a lot of resources are wasted.
发明内容 Contents of the invention
本发明所要解决的技术问题是提供一种基于GMC的多天线复用发送、接收装置及频域均衡方法,该发射装置发明装置要利用多天线系统发送复用和接收分集的优势,从而实现在发送端不同天线发送不同信号;相应的在接收端大大降低了系统的开销。The technical problem to be solved by the present invention is to provide a GMC-based multi-antenna multiplexing transmission and reception device and frequency domain equalization method. Different antennas at the sending end send different signals; correspondingly, the overhead of the system is greatly reduced at the receiving end.
为了解决上述技术问题,本发明所采用的技术方案是:In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:
提供一种基于GMC系统多天线复用传输发送装置,包括依次连接的串并转换模块,线性变换模块,成形滤波器组,加循环前缀模块和射频发送模块,以及,还包括:A GMC system-based multi-antenna multiplexing transmission transmission device is provided, including serial-to-parallel conversion modules, linear conversion modules, shaping filter banks, cyclic prefix adding modules and radio frequency transmission modules connected in sequence, and also includes:
多天线复用发射模块,其连接成形滤波器组的输出端及加循环前缀模块的输入端,用于将成形滤波后的信号交替分块到多路上,作为相应多个天线发射的信道组;A multi-antenna multiplexing transmission module, which is connected to the output end of the shaping filter bank and the input end of the cyclic prefix adding module, is used to alternately divide the signal after shaping filtering into multiple channels, as a channel group for corresponding multiple antennas to transmit;
相应地,本发明还提供一种基于GMC系统多天线复用传输接收装置,包括射频接收模块,同步与信道估计模块,去除循环前缀模块,串并转换模块,以及,还包括:Correspondingly, the present invention also provides a multi-antenna multiplexing transmission receiving device based on the GMC system, including a radio frequency receiving module, a synchronization and channel estimation module, a cyclic prefix removal module, a serial-to-parallel conversion module, and also includes:
频域均衡模块,其与串并转换模块、同步与信道估计模块的输出端相连接,其利用估计的信道衰落系数对采样信号进行频域均衡;A frequency domain equalization module, which is connected to the output of the serial-to-parallel conversion module and the synchronization and channel estimation module, uses the estimated channel fading coefficient to perform frequency domain equalization on the sampled signal;
第一并串转换模块,其与频域均衡模的输出端相连接,用于将输入的并行数据序列变换成串行的输出数据序列;The first parallel-to-serial conversion module, which is connected to the output end of the frequency domain equalization module, is used to convert the input parallel data sequence into a serial output data sequence;
匹配滤波器组,其与第一并串转换模块的输出端相连接,用于将串行输入符号序列进行与发射机子带成行滤波组相对应的子带匹配滤波处理,以生成多个子带并行输出的符号数据序列;A matched filter bank, which is connected to the output terminal of the first parallel-to-serial conversion module, is used to perform subband matched filter processing on the serial input symbol sequence corresponding to the transmitter subband row filter group, so as to generate multiple subband parallel output symbolic data sequence;
线性逆变换模块,其与匹配滤波器组模块的输出端相连接,用于将各子带传输的信号恢复到时域去;A linear inverse transform module, which is connected to the output end of the matched filter bank module, is used to restore the signals transmitted by each sub-band to the time domain;
第二并串转换模块,其与线性逆变换模块的输出端相连接,用于将输入的并行数据序列变换成串行的输出数据序列,用于恢复在原始星座点上的串行符号。The second parallel-to-serial conversion module is connected to the output terminal of the linear inverse conversion module, and is used to convert the input parallel data sequence into a serial output data sequence, and is used to restore the serial symbols on the original constellation points.
同时,本发明还提供一种基于本发明的多天线复用传输发送装置的简化频域均衡方法,包括计算WMMSE=σs 2ΛH[σs 2ΛΛH+σn 2I]-1,其包括如下步骤:At the same time, the present invention also provides a simplified frequency domain equalization method based on the multi-antenna multiplexing transmission sending device of the present invention, including calculating W MMSE =σ s 2 Λ H [σ s 2 ΛΛ H +σ n 2 I] -1 , which includes the following steps:
步骤1、首先记[σs 2ΛΛH+σn 2I]-1为Λ’,设∧’包括M×M个小矩阵,且每个小矩阵均为对角矩阵;Step 1. First record [σ s 2 ΛΛ H +σ n 2 I] -1 as Λ', let ∧' include M×M small matrices, and each small matrix is a diagonal matrix;
步骤2、将∧’分解为沿主对角线准对角矩阵和沿反对角线准对角矩阵的和;Step 2, decompose ∧' into the sum of the quasi-diagonal matrix along the main diagonal and the quasi-diagonal matrix along the anti-diagonal;
步骤3、将∧’的逆过程转化为对角矩阵或块对角矩阵的求逆从而计算WMMSE;Step 3, converting the inverse process of ∧' into the inversion of a diagonal matrix or a block diagonal matrix to calculate W MMSE ;
其中,WMMSE为MMSE方法乘性矩阵,σs为信号能量,Λ包含M×M个N×N对角矩阵,其中M为发射天线数目,N为FFT长度,σn为噪声能量,∧’为过程参数。Among them, W MMSE is the multiplicative matrix of MMSE method, σ s is the signal energy, Λ contains M×M N×N diagonal matrices, where M is the number of transmitting antennas, N is the length of FFT, σ n is the noise energy, ∧' is a process parameter.
采用本发明的多天线复用发射装置,显著的提高了频谱效率,相应的本发明简化了传统均衡方法的大矩阵求逆过程,在不影响系统性能的前提下,充分利用频域信道矩阵的特殊结构,设计出简化的均衡器,使得MMSE均衡中矩阵求逆的算法复杂度从O((MN)3)下降到O(M3N),在GMC系统中,块长一般为:N=512或者N=1024,而发送天线数目一般选择为:M=2,3,4。简化的均衡器大大地减少了系统的开销。The multi-antenna multiplexing transmitting device of the present invention significantly improves the spectrum efficiency, and the corresponding present invention simplifies the large matrix inversion process of the traditional equalization method, and makes full use of the channel matrix in the frequency domain without affecting the system performance. Special structure, designed a simplified equalizer, so that the algorithm complexity of matrix inversion in MMSE equalization is reduced from O((MN) 3 ) to O(M 3 N), in the GMC system, the block length is generally: N= 512 or N=1024, and the number of transmitting antennas is generally selected as: M=2, 3, 4. Simplified equalizers greatly reduce system overhead.
附图说明 Description of drawings
图1是本发明的发射装置的结构示意图。Fig. 1 is a structural schematic diagram of the transmitting device of the present invention.
图2是本发明的接收装置的结构示意图。Fig. 2 is a schematic structural diagram of the receiving device of the present invention.
具体实施方式 Detailed ways
如图1,本发明中发送装置由串并转换模块,线性变换模块,成形滤波器组,多天线复用发射模块,加循环前缀模块和射频发送模块依次连接而成。As shown in Fig. 1, the transmitting device in the present invention is composed of a serial-to-parallel conversion module, a linear conversion module, a shaping filter bank, a multi-antenna multiplexing transmission module, a cyclic prefix adding module and a radio frequency transmission module connected in sequence.
串并转换模块1,其输出端与线性变换模块2相连,用于将已调制的串行符号数据序列变成并行符号数据序列。The serial-to-parallel conversion module 1, whose output terminal is connected to the linear conversion module 2, is used to convert the modulated serial symbol data sequence into a parallel symbol data sequence.
线性变换模块2,与串并转换模块1的输出端相连,用于将输入的数据符号进行FFT变换后,映射到多个子带上传输,一方面可以获得频率复用增益,另一方面可以降低发射信号的峰均比。The linear transformation module 2 is connected to the output terminal of the serial-to-parallel conversion module 1, and is used to map the input data symbols to multiple subbands for transmission after FFT transformation. On the one hand, frequency multiplexing gain can be obtained, and on the other hand, it can reduce The peak-to-average ratio of the transmitted signal.
成形滤波器组3,与线性变换模块的输出端相连,用于将整个信道带宽分割成若干个相互正交(拟正交)的子信道(或子带),成形滤波器组中每个子滤波器对应一个子信道。这样,经过线性变换所得的并行符号数据块的列向量中的每个元素符号被分别映射到相应的子信道上。Shaping filter bank 3 is connected to the output terminal of the linear transformation module, and is used to divide the entire channel bandwidth into several mutually orthogonal (quasi-orthogonal) sub-channels (or sub-bands), and each sub-filter in the shaping filter bank device corresponds to a sub-channel. In this way, each element symbol in the column vector of the parallel symbol data block obtained through the linear transformation is mapped to the corresponding sub-channel respectively.
多天线复用发射模块4,与成形滤波器组3的输出端相连,将成形滤波后的信号交替分块到多路上,作为相应多路发射的信道组,本具体实施例中信道可以是2路、3路、4路。Multi-antenna multiplexing transmission module 4 is connected to the output end of shaping filter group 3, and the signal after shaping filtering is alternately divided into multiple paths, as a channel group for corresponding multi-path transmission. In this specific embodiment, the channel can be 2 Road, Road 3, Road 4.
加循环前缀模块5,与多天线复用发射模块4的输出端相连,在信号块之前加上循环前缀,用于消除块间干扰,隔离信道时延扩展的影响,以利于接收机的频域均衡。The cyclic prefix adding module 5 is connected to the output of the multi-antenna multiplexing transmission module 4, and a cyclic prefix is added before the signal block to eliminate inter-block interference and isolate the influence of channel delay expansion, so as to benefit the frequency domain of the receiver balanced.
射频发送模块6,和加循环前缀模块5的输出端相连,并与发送天线连接,用于将基带信号上变频到射频。经过和射频发送模块和发送天线,发射机输出射频信号。The radio frequency sending module 6 is connected to the output end of the cyclic prefix adding module 5 and connected to the sending antenna, and is used for up-converting the baseband signal to a radio frequency. The transmitter outputs a radio frequency signal through the radio frequency sending module and the sending antenna.
如图2,本发明的对应的接收装置包括:射频接收模块,同步与信道估计模块,去除循环前缀模块,串并转换模块,频域均衡模块,第一并串转换模块,匹配滤波器组模块,线性逆变换模块和第二并串转换模块。其中所述的频域均衡模块均包括依次连接的:FFT变换模块、线性组合器模块,子信道均衡模块、IFFT变换模块。As shown in Figure 2, the corresponding receiving device of the present invention includes: a radio frequency receiving module, a synchronization and channel estimation module, a cyclic prefix removal module, a serial-to-parallel conversion module, a frequency domain equalization module, a first parallel-to-serial conversion module, and a matched filter bank module , a linear inverse transform module and a second parallel-to-serial transform module. The frequency domain equalization modules mentioned therein all include sequentially connected: FFT transformation module, linear combiner module, sub-channel equalization module, and IFFT transformation module.
射频接收模块11,其与接收天线相连接,用于将无线信道中的信号接收下来,变频到基带进行处理。经过接收天线和射频处理模块,接收机输出基带信号。The radio frequency receiving module 11 is connected with the receiving antenna, and is used to receive the signal in the wireless channel, convert the frequency to the baseband for processing. After the receiving antenna and the radio frequency processing module, the receiver outputs the baseband signal.
同步与信道估计模块12,其与射频接收模块11的输出端相连接,用于完成接收信号的时频同步和信道衰落系数估计。Synchronization and channel estimation module 12, which is connected to the output terminal of radio frequency receiving module 11, is used to complete the time-frequency synchronization and channel fading coefficient estimation of the received signal.
去除循环前缀模块13,其与射频接收模块11的输出端相连接,用于删除受到符号间干扰的信号循环前缀,消除块间干扰,隔离信道时延扩展的影响,以利于接收机的频域均衡。Remove the cyclic prefix module 13, which is connected to the output of the radio frequency receiving module 11, and is used to delete the signal cyclic prefix subject to intersymbol interference, eliminate interblock interference, and isolate the influence of channel delay expansion, so as to benefit the frequency domain of the receiver balanced.
串并转换模块14,其与去除循环前缀模块13的输出端相连接,用于将输入的串行数据序列变换成并行的输出数据序列。A serial-to-
频域均衡模块,其与串并转换模块14、同步与信道估计模块12的输出端相连接,其利用估计的信道衰落系数对采样信号进行频域均衡。The frequency domain equalization module is connected with the serial-to-
第一并串转换模块19,其与频域均衡模的输出端相连接,用于将输入的并行数据序列变换成串行的输出数据序列。The first parallel-to-serial conversion module 19 is connected to the output terminal of the frequency domain equalization module, and is used to convert the input parallel data sequence into a serial output data sequence.
匹配滤波器组110,其与第一并串转换模块19的输出端相连接,用于将串行输入符号序列进行与发射机子带成行滤波组相对应的子带匹配滤波处理,以生成多个子带并行输出的符号数据序列。Matched
线性逆变换模块111,其与匹配滤波器组模块110的输出端相连接,用于将各子带传输的信号恢复到时域去。The inverse
第二并串转换模112,其与线性逆变换模块111的输出端相连接,用于将输入的并行数据序列变换成串行的输出数据序列。这样就恢复出了在原始星座点上的串行符号。The second parallel-to-
所述的频域均衡模块包括依次连接的:The frequency domain equalization module includes sequentially connected:
FFT变换模块15,其与串/并转换模块14的输出端相连接,用于将一定长度的接收信号数据块变换到频域,以便于频域均衡消除信道对该数据块的影响;FFT transformation module 15, it is connected with the output end of serial/
线性组合器16,用于将多个时间块内接收到的符号进行线性变换,重新组合,利于均衡模块进行简单的线性均衡;The
均衡模块17,其与线性组合器模块16的输出端和相连接,用于在频域对信道损伤进行相位和幅度的补偿;Equalization module 17, it is connected with the output end of
IFFT变换模块18,其与均衡模块17的输出端相连接,用于将已经经过频域均衡的频域子带信号恢复到时域去,以便于进一步处理。The IFFT transformation module 18 is connected to the output terminal of the equalization module 17, and is used to restore the frequency domain sub-band signal that has undergone frequency domain equalization to the time domain for further processing.
基于上述发射及接收装置,由于数据符号串要经过线性变换和成形滤波器,经过空时处理模块的复信号不再是星座图上的符号,使得在接收端要使用星座点信息的进行检测和均衡方法不可行,即:最大似然(ML)、干扰抵消(SIC)、QR分解等译码方法不可行。而最小均方误差频域均衡(MMSE-FDE)不需要原始星座点的信息,从而成为一种可行的均衡方法,但该均衡方法复杂度高。所以,对应地,本发明还需提供一种简化的频域均衡方法,具体说明如下:Based on the above-mentioned transmitting and receiving device, since the data symbol string needs to undergo a linear transformation and a shaping filter, the complex signal passing through the space-time processing module is no longer a symbol on the constellation diagram, so that the constellation point information must be used for detection and processing at the receiving end. Equalization methods are not feasible, that is, decoding methods such as maximum likelihood (ML), interference cancellation (SIC), and QR decomposition are not feasible. The Minimum Mean Square Error Frequency Domain Equalization (MMSE-FDE) does not require the information of the original constellation points, so it becomes a feasible equalization method, but the equalization method has high complexity. Therefore, correspondingly, the present invention also needs to provide a simplified frequency domain equalization method, which is specifically described as follows:
记[σs 2ΛΛH+σn 2I]-1为Λ’,设Record [σ s 2 ΛΛ H +σ n 2 I] -1 as Λ', set
∧’为过程参数,当M=2时,∧' is the process parameter, when M=2,
令make
则but
Λ’2=A2+B2.Λ' 2 =A 2 +B 2 .
于是then
注意到(I2-(A2 -1B2)2)是一对角矩阵,从而求(I2-(A2 -1B2)2)-1的复杂度为2N。故总的求Λ2’-1的过程共执行20N次乘法,4N次加法。Note that (I 2 -(A 2 -1 B 2 ) 2 ) is a diagonal matrix, so the complexity of calculating (I 2 -(A 2 -1 B 2 ) 2 ) -1 is 2N. Therefore, a total of 20N times of multiplication and 4N times of addition are performed in the process of calculating Λ 2 ' -1 .
当M=3时,When M=3,
令make
则but
Λ3=A3+B3 Λ 3 =A 3 +B 3
注意到(I3-(A3 -1B3)2)是一块对角矩阵,从而可用一个Λ2的求逆以及一个对角矩阵的求逆完成(I3-(A3 -1B3)2)-1。总的求Λ3 -1的过程共执行64N次乘法,17N次加法。Note that (I 3 -(A 3 -1 B 3 ) 2 ) is a diagonal matrix, so it can be done with one Λ 2 inversion and one diagonal matrix inversion (I 3 -(A 3 -1 B 3 ) 2 ) -1 . In total, 64N times of multiplication and 17N times of addition are performed in the process of finding Λ 3 -1 .
当M=4时,When M=4,
令make
则but
Λ4=A4+B4 Λ 4 =A 4 +B 4
注意到(I4-(A4 -1B4)2)是一块对角矩阵,从而可用两个Λ’2的求逆完成(I4-(A4 -1B4)2)-1。总的求Λ4’-1的过程共执行152N次乘法,56N次加法。Note that (I 4 -(A 4 -1 B 4 ) 2 ) is a diagonal matrix, so (I 4 -(A 4 -1 B 4 ) 2 ) -1 can be done with two inversions of Λ' 2 . In total, 152N times of multiplication and 56N times of addition are performed in the process of finding Λ 4 ' -1 .
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CN1697360A (en) * | 2005-06-29 | 2005-11-16 | 北京邮电大学 | A detection method for multiple-input multiple-output (MIMO) antenna array system |
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