WO2022037021A1 - 基于混合软信息的块迭代均衡器及双向块迭代均衡器 - Google Patents
基于混合软信息的块迭代均衡器及双向块迭代均衡器 Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03178—Arrangements involving sequence estimation techniques
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L2025/03433—Arrangements for removing intersymbol interference characterised by equaliser structure
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- the invention belongs to the technical field of communication, and particularly relates to a hybrid soft information-aided block linear equalizer (HBLE) and a bidirectional block iterative equalizer.
- HBLE hybrid soft information-aided block linear equalizer
- the block transmission system is suitable for time-varying and frequency-selective fading channels, and the channel fading characteristics will seriously affect the quality of the communication system.
- the channel equalizer in the receiver can reduce the effect of intersymbol interference caused by channel time-frequency dispersion.
- Iterative equalization is a technique in which a channel equalizer and a channel decoder jointly process the received signal. Since the equalizer and the decoder constantly exchange soft information, the iterative equalizer can greatly improve the performance of the communication system.
- the original iterative equalizer, channel equalization and decoding all use the maximum posteriori probability (MAP) algorithm.
- MAP-based equalizer algorithm complexity grows exponentially with the modulation constellation size and channel length. Therefore, iterative equalization techniques based on transversal filters have attracted great interest.
- a linear equalizer using prior information is proposed.
- An exact solution to LE requires recomputing the inverse for each symbol.
- a low-complexity scheme using time-invariant filtering vectors is proposed, but the performance is slightly worse than that of time-varying filters.
- the filter coefficients are obtained using a diagonal approximation.
- a decision feedback equalizer (DFE) based on the MMSE criterion has been proposed in the literature. The DFE assumes that the hard decisions of the estimated symbols are correct and is used to eliminate causal symbol interference. However, error propagation can affect the performance of the DFE equalizer.
- a soft-decision feedback-assisted time-domain iterative equalizer is proposed to mitigate the effects of error propagation in DFE equalizers.
- a time-domain iterative equalizer uses a posteriori soft-decision symbols that are more precise than a priori soft-decision to cancel causal ISI, and assumes that the decision and transmitted symbols have the same statistical properties.
- the above iterative equalizers all detect each symbol through a sliding window, and usually only use a few adjacent symbols to reduce the influence of ISI.
- Another type of iterative equalizer exists that utilizes entire block symbols to eliminate ISI.
- a block iterative equalizer based on constrained minimum variance filter design is also proposed in some literatures.
- a block iterative equalizer using prior information is proposed for single-carrier high-frequency communication systems. Compared with Exact-MMSE-LE, BLE has a faster convergence rate, but the latter has higher computational complexity.
- BLE only uses the a priori information provided by the decoder to eliminate ISI.
- the performance of the iterative equalizer can be greatly improved by utilizing the a posteriori information at the output of the equalizer.
- Some literatures use a more accurate a posteriori decision for channel estimation and equalization, which greatly improves the performance of the communication system.
- For the underwater acoustic communication system some literatures have also studied the adaptive iterative equalizer using a posteriori soft decision, which can improve the convergence speed. It is worth noting that BLE equalizers using both prior and posterior information have not been studied.
- the present invention proposes a block iterative equalizer based on mixed soft information, the equalizer utilizes the prior information corresponding to the unestimated symbols and the a posteriori information corresponding to the estimated symbols in the symbol sequence Compute the filter vector to obtain the final estimated symbol sequence.
- h n is the nth column vector of the channel matrix.
- ⁇ n-1 is the channel covariance matrix at time n-1; is the posterior variance at time n-1, v n-1 is the prior variance of the symbol x n-1 ; h n-1 is the n-1th column vector of the channel matrix, is the inverse matrix of the channel covariance matrix at time n-1, is the filter coefficient at time n-1; in particular, time n in the present invention refers to the time when symbol x n is processed, and time n-1 refers to the time when symbol x n-1 is processed.
- the mean value of the preprocessing vector is calculated, and the mean value of the preprocessing vector is expressed as:
- a fixed covariance matrix is used when calculating each unknown symbol.
- the present invention also proposes another bidirectional block iterative equalizer based on mixed soft information, including any of the aforementioned equalizers, wherein one equalizer is a forward equalizer, and is used to sequentially calculate the extrinsic information of the symbol sequence; One is an inverse equalizer, which is used to calculate the extrinsic information of the symbol sequence in reverse.
- the extrinsic information is obtained by combining the two equalizers with the set weights, and the final result is obtained.
- the process of obtaining the optimal weight combination includes: if the weight of the forward equalizer is ⁇ j and the weight of the reverse equalizer is (1- ⁇ j ), the weight ⁇ j of the forward equalizer is expressed as:
- ⁇ j arg min(E ⁇
- ⁇ j arg min(E ⁇
- L e (cn ,j ) is the extrinsic information obtained by the forward equalizer
- L c (c n,j ) is the extrinsic information obtained by the reverse equalizer
- E ⁇ * ⁇ represents the expectation.
- the present invention proposes an HBLE equalizer that uses both a priori and a posteriori information, and provides two fast recursion methods to reduce the computational complexity of the HBLE equalizer; in order to further reduce the computational complexity
- an LC-HBLE equalizer using a fixed covariance matrix is proposed; in addition, on the basis of the existing equalizer, an inverse equalizer is added to obtain diversity gain and further improve the system Performance; EXIT diagram and simulation results show that the performance of the various equalizers proposed in this paper is better than that of traditional BLE equalizers, but their complexity is the same as that of BLE, and when the unknown symbols are large, LC-HBLE and BLE can be used.
- Bi-LC-HBLE equalizer to avoid large computational complexity; when unknown symbols are small, using Bi-HBLE and HBLE equalizers can achieve better performance.
- 1 is a schematic diagram of an existing transmitter and an ISI channel structure
- FIG. 2 is a schematic structural diagram of an existing block transmission system
- FIG. 3 is a schematic structural diagram of the HBLE equalizer proposed by the present invention.
- FIG. 5 is a schematic diagram of the Bi-HBLE/Bi-LC-HBLE equalizer symbol detection sequence of the present invention
- FIG. 6 is a schematic diagram of BPSK bit error rate curves of various equalizers and traditional BLE equalizers in the present invention
- FIG. 7 is an EXIT diagram of various equalizers in the present invention and a conventional BLE equalizer under BPSK modulation.
- the present invention provides a block iterative equalizer based on mixed soft information in a fast time-varying channel, which utilizes the prior decision corresponding to the unestimated symbol and the a posteriori decision of the estimated symbol to obtain the estimated symbol.
- the detection block consists of three sub-blocks.
- One block is composed of N training data adjacent to the previous detection block
- the second block is composed of M unknown symbols
- the third block is also composed of N training symbols.
- the ISI channel impulse response with L taps can be expressed as:
- h k is the k-th tap coefficient
- ⁇ [nk] is the value of the impulse function at time nk
- the independent and identically distributed noise sampling is expressed as w n
- the variance of the real part and the imaginary part is the noise power. Therefore, the received symbol is written as:
- H is represented as is the value range of the matrix
- K represents the column of the channel matrix, and its value is M+L-1
- h L-1 is the Lth channel of the channel -1 tap coefficient
- H 1 is represented as H2 is represented as ⁇ indicates that all elements at these positions are 0
- t 1 and t 2 indicate the training symbols close to the unknown symbol x
- w is the noise vector.
- d [d 1 , d 2 , . . . , d M ] T represent the filter matrix and the error vector, respectively.
- the prior mean and variance of the symbol x n can be expressed as:
- the estimated transmit symbols can be Expressed as:
- ⁇ is represented as ⁇ is expressed as I K is a K ⁇ K identity matrix.
- the estimated transmitted symbol nth estimated symbol in can be expressed as:
- f' n is further transformed into:
- the estimated symbol Obedience is the additive Gaussian channel output, and the channel input is the transmitted symbol x n , then the estimated symbol is expressed as:
- ⁇ n represents additive white Gaussian noise with zero mean and variance
- ⁇ n,i is the ratio of estimated noise power to real noise power, expressed as
- This embodiment provides, on the basis of Embodiment 1, a hybrid soft information aided block linear equalizer (hybrid soft information aided block linear equalizer) based on minimum mean square error (MMSE) criterion applied to a block transmission system equalizer, HBLE), the HBLE equalizer calculates filter coefficients and eliminates inter-symbol interference (ISI) simultaneously using the a posteriori information of the estimated symbols and the prior information of the unestimated symbols.
- MMSE minimum mean square error
- the structure of the equalizer in this embodiment is shown in FIG. 3 .
- the equalizer includes a filter unit, a soft information calculation unit, and a statistical information calculation unit.
- the preprocessing symbol z is input to the filter unit, and the filter unit performs filtering to obtain an estimated value.
- the soft information calculation unit based on the estimated value Calculate the extrinsic information Le (c n,j ) of the transmitted symbol x n in the current iteration and the posterior information L p (c n ,j ) of the transmitted symbol x n in the current iteration, and calculate the transmitted symbol x in the current iteration.
- the posterior information L p (c n ,j ) of n is fed back to the statistical information calculation unit, and the statistical information calculation unit is based on the posterior information L p (c n,j ) of the transmitted symbol x n in the current iteration Obtained prior information L(c n-1,j ) obtains the estimated symbol and the variance matrix ⁇ n at time n , as the relevant parameters of the filtering unit at time n+1.
- L(c n-1,j ) obtains the estimated symbol and the variance matrix ⁇ n at time n , as the relevant parameters of the filtering unit at time n+1.
- L e (c n-1,j ) represents the extrinsic information of the transmitted symbol x n-1 in the current iteration
- L(c n-1,j ) represents the prior information obtained from the previous iteration
- the posterior mean and variance of x n-1 can be expressed as:
- the estimated symbol can be expressed as:
- ⁇ n is the variance matrix at time n, expressed as is the posterior variance at time n-1, and v n is the prior variance at time n; is the filter coefficient at time n, expressed as ⁇ n is the channel covariance matrix at time n; is the filter scalar at time n, expressed as
- the extrinsic information corresponding to the transmitted symbol x n is obtained from the extrinsic information expression in Example 1, the only difference is that k n and f n are replaced by and
- L e (cn ,j ) is the extrinsic information corresponding to the bits cn ,j
- Lp (cn ,j ) is the information corresponding to the bits cn ,j Posterior information.
- Embodiment 2 since the HBLE equalizer needs to recalculate the inverse matrix for each unknown symbol, its computational complexity is much higher than that of the traditional BLE equalizer. Therefore, in order to avoid a large number of direct matrix inversion operations, this embodiment uses the matrix
- the inverse criterion proposes a fast recursive method to obtain the filter vector.
- ⁇ n is the channel covariance matrix at time n
- the matrices ⁇ n and ⁇ n-1 can be expressed as:
- the inverse matrix can be expressed as:
- Example 2 the preprocessing vector mean needs to be recalculated for each unknown symbol The computational complexity is much higher than that of traditional BLE equalizers. Therefore, another fast recursion algorithm is proposed to further reduce the computational complexity of the HBLE equalizer.
- the covariance matrix ⁇ n of the HBLE equalizer will change continuously with time n, so that the inverse matrix needs to be recalculated for each unknown symbol. Therefore, the computational complexity of the HBLE equalizer is much higher than that of the traditional BLE equalizer.
- the estimated symbols can be expressed as:
- ⁇ n can be approximated by ⁇ , so ⁇ n,i can be simplified to:
- this embodiment proposes a bidirectional-HBLE (Bi-HBLE) equalizer based on mixed soft information, which can
- the HBLE equalizer is replaced by the LC-HBLE equalizer, that is, the bi-directional block iterative equalizer based on mixed soft information includes the Bi-HBLE/Bi-LC-HBLE equalizer, thereby further improving the equalizer performance.
- the structure of the equalizer in this embodiment is shown in FIG.
- the equalizer includes forward HBLE/LC-HBLE, reverse HBLE/LC-HBLE, and a soft information combiner, and the preprocessing symbols z are respectively input to the forward HBLE/LC-HBLE HBLE, reverse HBLE/LC-HBLE, forward HBLE/LC-HBLE get the extrinsic information output by the forward equalizer Inverse HBLE/LC-HBLE to get extrinsic information of the output of the inverse equalizer
- the soft information combiner is Allocate the weights to obtain the extrinsic information Le (c n ,j ) output by the final bidirectional structural equalizer.
- Bi-HBLE/Bi-LC-HBLE consists of a forward HBLE/LC-HBLE equalizer and a reverse HBLE/LC-HBLE equalizer.
- the forward equalizer processes the symbol x 1 all the way to x M
- the processing order of the inverse equalizer is just the opposite, that is, the inverse equalizer processes the symbol x M until it reaches x 1 .
- the dotted line represents the detection order of the equalizer.
- the forward equalizer can effectively eliminate causal interference.
- the inverse equalizer is able to cancel the acausal interference with a posteriori soft decision of the acausal symbols. Therefore, the Bi-HBLE/Bi-LC-HBLE equalizer is able to cancel both causal and acausal interferences.
- ⁇ j represents the weighting coefficient. Based on the MMSE criterion, ⁇ j can be expressed as:
- ⁇ j arg min(E ⁇
- the weighting factor can be expressed as:
- the merging method is mean merging.
- the extrinsic information output by the forward and reverse equalizers is the same, therefore, the BLE-based bidirectional equalizer will fail and the diversity gain cannot be obtained.
- This embodiment compares the complexity of the proposed various equalizers and the traditional BLE equalizer in terms of complex multiplication (CM).
- the main sources of computational complexity include computing filter coefficients, posterior moments, and symbol estimates, and the results are shown in Table 1.
- Figure 6 shows the BER curves of various equalizers under BPSK modulation, where the abscissa is the signal-to-noise ratio Eb/No, the ordinate is the bit error rate (BER), and the number of iterations is 4.
- the performance of the HBLE that is, any of the equalizers proposed in Embodiments 1 to 4
- the LC-HBLE that is, the equalizer proposed in Embodiment 5
- Bi-HBLE and Bi-LC-HBLE ie the equalizer proposed in Example 6) can achieve the best performance.
- Bi-HBLE and Bi-LC-HBLE use an additional inverse equalizer, so time diversity gain can be obtained.
- Figure 7 shows the convergence performance of the equalizer. in, and respectively represent the input and output mutual information (MI) of the equalizer; and represent the input and output mutual information of the decoder, respectively.
- MI input and output mutual information
- Bi-HBLE produces the largest output MI, followed by HBLE or Bi-LC-HBLE, LC-HBLE and BLE. Therefore, Bi-HBLE has the fastest convergence rate and the best performance.
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Abstract
本发明属于通信技术领域，特别涉及一种基于混合软信息的块迭代均衡器及双向块迭代均衡器，块迭代均衡器包括利用未估计符号对应的先验判决和已估计符号的后验判决来获取估计符号，每次利用未估计符号对应的先验判决和已估计符号的后验判决来获取估计符号时，计算预处理向量均值以及每个未知符号时使用固定的协方差矩阵；本发明当未知符号数量较大时，可以使用LC-HBLE和Bi-LC-HBLE均衡器，避免较大的计算复杂度；当未知符号数量较小时，使用Bi-HBLE和HBLE均衡器能够获得更好的性能。
Description
本申请要求于2020年08月20日提交中国专利局、申请号为202010841978.6、发明名称为“基于混合软信息的块迭代均衡器双向块迭代均衡器”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
本发明属于通信技术领域，特别涉及一种基于混合软信息的块迭代均衡器(hybrid soft information aided block linear equalizer，HBLE)及双向块迭代均衡器。
块传输系统适用于时变和频率选择性衰落信道，信道衰落特性会严重影响通信系统质量。接收机中的信道均衡器可以减弱由信道时频色散造成的码间干扰的影响。迭代均衡是一种信道均衡器和信道译码器联合处理接收信号的技术。由于均衡器和译码器不断交换软信息，迭代均衡器可以极大改善通信系统性能。原始的迭代均衡器，信道均衡和译码都使用最大后验概率(maximum posteriori probability，MAP)算法。但是，基于MAP的均衡器算法复杂度随调制星座大小和信道长度呈指数增长。因此，基于横向滤波器的迭代均衡技术引起了极大兴趣。
基于MMSE准则，提出了一种利用先验信息的线性均衡器(linear equalizer，LE)。对于每个符号，LE的准确解决方案(Exact-MMSE-LE)都需要重新计算逆矩阵。为了降低计算复杂度，提出了一种利用时不变滤波向量的低复杂度方案，但是性能比时变滤波器稍差。为了进一步降低计算复杂度，利用对角近似来求滤波器系数。有文献提出了一种基于MMSE准则的判决反馈均衡器(decision feedback equalizer，DFE)，DFE假设已估计符号的硬判决是正确的，并且用来消除因果符号干扰。然而，误差传播会影响DFE均衡器的性能。提出了一种软判决反馈辅助的时域迭代均衡器，用来减轻DFE均衡器中的误差传播的影响。时域迭代均衡器利用比先验软判决更精确的后验软判决符号来消除因果ISI，并且假设判决符号和发射符号具有相同的统计特性。上述迭代均衡器都是通过滑动窗口方式来检测每个符号，通常只用了相邻的几个符号来减弱ISI的影响。还存在另外一种迭代均衡器，利用整个块符号来消除ISI。针对正交频分复用系统中的未知信道，也有文献提出一种基于约束最小方差滤波器设计的块迭代均衡器。针对单载波高频通信系统提出一种使用先验信息的块迭代均衡器，和Exact-MMSE-LE相比，BLE具有更快收敛速率，但是后者的计算复杂度更高。
然而，BLE仅仅利用了译码器提供的先验信息来消除ISI，在实际应用上，通过利用均衡器输出端的后验信息可以大大改善迭代均衡器的性能。有文献使用更加准确的后验判决来进行信道估计和均衡，极大提高了通信系统性能。针对水声通信系统，也有文献研究了利用后验软判决的自适应迭代均衡器，可以提高收敛速度。值得注意的是，同时使用先验信息和后验信息的BLE均衡器还没有得到研究。
发明内容
为了改进了块迭代均衡器的性能，本发明提出一种基于混合软信息的块迭代均衡器，所述均衡器利用符号序列中未估计符号对应的先验信息和已估计符号对应的后验信息计算滤波器向量，获取最终估计的符号序列。
进一步的，估计符号表示为：
其中，
为滤波器标量；
为均衡器的滤波器的滤波系数；z为预处理序列；H为信道相关矩阵；
为均值向量，表示为
为符号x
n-1的后验均值，
为符号x
n的先验均值；h
n为信道矩阵的第n列向量。
进一步的，均衡器的滤波器向量
表示为：
其中，
为信道协方差矩阵的逆矩阵。
进一步的，信道协方差矩阵的逆矩阵
表示为：
其中，Σ
n-1为n-1时刻的信道协方差矩阵；
为n-1时刻的后验方差，v
n-1为符号x
n-1先验方差；h
n-1为信道矩阵的第n-1列向量，
为n-1时刻的信道协方差矩阵的逆矩阵，
为n-1时刻的滤波系数；特别地，本发明的n时刻是指处理符号x
n的时刻，n-1时刻是指处理符号x
n-1的时刻。
进一步的，每次利用未估计符号对应的先验判决和已估计符号的后验判决来获取估计符号时，计算预处理向量均值，预处理向量均值表示为：
其中，
为预处理向量均值；
为符号x
n的后验均值，
为符号x
n的先验均值， Δx
n-1为
和
之差。
进一步的，在利用未估计符号对应的先验判决和已估计符号的后验判决来获取估计符号的过程中，计算每个未知符号时使用固定的协方差矩阵。
本发明还提出另一种基于混合软信息的双向块迭代均衡器，包括前述的任意一种均衡器，其中一个均衡器为前向均衡器，用于按顺序计算符号序列的外验信息；另一个为反向均衡器，用于反向计算符号序列的外验信息，通过设置的权重组合这两个均衡器获得外验信息，获得最终结果。
进一步的，获取最优的权重组合过程包括：若前向均衡器的权重为λ
j、反向均衡器的权重为(1-λ
j)，则前向均衡器的权重λ
j表示为：
λ
j＝arg min(E{|L
e(c
n,j)-L
c(c
n,j)|
2}).
λ
j＝arg min(E{|L
e(c
n,j)-L
c(c
n,j)|
2}).
其中，L
e(c
n,j)为前向均衡器获得的外验信息；L
c(c
n,j)为反向均衡器获得的外验信息；E{*}表示求期望。
本发明在传统BLE均衡器基础上，提出了同时使用先验和后验信息的HBLE均衡器，并提供两种快速递推方法，用来降低HBLE均衡器的计算复杂度；为了进一步降低计算复杂度，在HBLE均衡器的基础上提出了使用固定协方差矩阵的LC-HBLE均衡器；另外，在现有均衡器的基础上，添加一个反向均衡器，用来获得分集增益并进一步提高系统性能；EXIT图和仿真结果都表明本文提出的各种均衡器性能优于传统BLE均衡器，但是它们的复杂度和BLE是同一量级，且当未知符号较大时，可以使用LC-HBLE和Bi-LC-HBLE均衡器，避免较大的计算复杂度；当未知符号较小时，使用Bi-HBLE和HBLE均衡器能够获得更好的性能。
图1为现有发射端和ISI信道结构示意图；
图2为现有块传输系统结构示意图；
图3为本发明提出的HBLE均衡器结构示意图；
图4为本发明提出的Bi-HBLE/Bi-LC-HBLE均衡器结构示意图；
图5为本发明Bi-HBLE/Bi-LC-HBLE均衡器符号检测顺序示意图；
图6为本发明中各种均衡器以及传统BLE均衡器的BPSK误码率曲线示意图；
图7为本发明中各种均衡器以及传统BLE均衡器BPSK调制下EXIT图。
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实 施例，都属于本发明保护的范围。
本发明提供一种快时变信道下基于混合软信息的块迭代均衡器，利用未估计符号对应的先验判决和已估计符号的后验判决来获取估计符号。
实施例1
在本实施例中，提供一种现有技术的均衡器。
现有技术发射端和ISI信道的示意图如图1所示，若有M个未知符号个数，一个符号序列对应的比特数为Q，则一个由M个未知符号构成的序列长度为M·Q比特，该序列表示为c＝[c
1,…,c
n,…,c
M]，将该序列通过ISI信道传输到接收端，接收端接收源数据之后输入编码器进行编码，编码完成后进行交织，令
表示未知符号n的子序列，其中c
n,j∈0,1，符号映射器将c
n映射为符号x
n，x
n从调制集合
取值，每个α
i对应一个比特模式s
n＝[s
i,1,…,s
i,Q]，其中s
i,j∈0,1。
如图2，对于块传输系统来说，检测块有三个子块构成。其中一块由与前一个检测块相邻的N个训练数据组成，第二块由M个未知符号构成，第三块也是由N个训练符号组成。
具有L个抽头的ISI信道冲激响应可表示为：
其中，h
k为第k个抽头系数，δ[n-k]为表示冲激函数在n-k时刻的值；独立同分布噪声抽样表示为w
n，其实部和虚部的方差为
为噪声功率。因此，接收符号记为：
接收符号矩阵形式可表示为：
r＝Hx+H
1t
1+H
2t
2+w
其中，H表示为
为矩阵的值域，K表示信道矩阵的列，其值为M+L-1，h表示为h＝[h
L-1 h
L-2 … h
0]
H，h
L-1为信道第L-1个抽头系数； H
1表示为
H
2表示为
φ为表示这些位置全部元素为0；t
1、t
2表示靠近未知符号x的训练符号，w为噪声向量。
从接收信号中消除训练符号对未知符号的影响，可以得到：
r-H
1t
1-H
2t
2＝Hx+w＝z；
其中，z表示预处理符号。
利用一个线性滤波器来估计未知符号，即发射符号x，估计的值
表示为：
其中，
和d＝[d
1,d
2,…,d
M]
T分别表示滤波矩阵和误差向量。
因此，根据MMSE准则，G、d和
的值可表示为：
G＝cov(z,z)
-1cov(z,x)；
d＝E(x)-G
HE(z)；
其中
xcov(·)和E(·)分别表示求协方差和期望。
通过信道译码器的先验信息L(c
n,j)，符号x
n的先验均值和方差可表示为：
其中，
为符号x
n的先验均值，α
i为相移键控符号；v
n为符号x
n的方差。
P(x
n＝α
i)为x
n的值为α
i的概率，表示为：
其中，P(c
n,j＝s
i,j)为c
n,j＝s
i,j的概率，
为符号，表示为：
其中，s
i,j为比特值。
此时可以将估计的发射符号
表示为：
其中，Λ表示为
Σ表示为
I
K为K×K的单位矩阵。
当逐符号执行检测过程时，估计的发射符号
中第n个估计符号
可表示为：
其中，s
n是一个长度为M，并且第n个元素为1，其余元素全为零的列向量，表示为s
n＝[0
1×(n-1) 1 0
1×(M-n)]
T，0
i×j表示元素全为0的i×j矩阵；h
n为信道矩阵第n列的列向量，表示为h
n＝Hs
n；
为符号x
n的先验均值，v
n为符号x
n的先验方差。
为了叙述简单，定义滤波器的滤波系数为f
n，表示为：f
n＝Σ
-1h
n，因此，估计符号
可表示为
从上式可知，估计符号
依赖于先验信息L(c
n,j)，为了让估计符号
独立于符号x
n的先验信息，令
v
n＝1，滤波器的滤波系数f
n和估计符号
可表示为：
基于矩阵求逆准则，进一步将f′
n转换为：
最终的估计符号
可表示为：
其中，
为了得到发射符号xn对应的外验信息，假设估计符号
服从是加性高斯信道输出，信道输入为发射符号x
n，则估计符号表示为：
其中，A是等效幅度，η
n表示加性高斯白噪声，均值为零，方差为
结合前述估计符号的表达式，等效幅度A和方差
可表示为：
估计符号
近似符号高斯分布，即
发射符号x
n对应的外验信息可表示为：
其中，ρ
n,i为估计噪声功率与真实噪声功率比值，表示为
实施例2
本实施例在实施例1的基础上提供一种应用于块传输系统的基于最小均方误差(minimum mean square error，MMSE)准则的混合软信息辅助的块线性均衡器(hybrid soft information aided block linear equalizer，HBLE)，该HBLE均衡器同时利用估计符号的后验信息和未估计符号的先验信息计算滤波器系数和消除码间干扰(inter-symbol interference,ISI)。
本实施例的均衡器结构如图3所示，均衡器内包括滤波单元、软信息计算单元和统计信息计算单元，预处理符号z输入滤波单元，滤波单元进行滤波获得估计的值
软信息计算单元根据估计的值
计算得到当前迭代中发射符号x
n的外验信息L
e(c
n,j)和当前迭代中发射符号x
n的后验信息L
p(c
n,j)，并将当前迭代中发射符号x
n的后验信息L
p(c
n,j)反馈给统计信息计算单元，统计信息计算单元根据当前迭代中发射符号x
n的后验信息L
p(c
n,j)和从上次迭代中获取的先验信息L(c
n-1,j)获取估计符号
和n时刻的方差矩阵Λ
n，作为第n+1时刻滤波单元的相关参数。以下进行具体说明。
当完成发射符号x
n-1的处理后，其后验信息可表示为：
L
p(c
n-1,j)＝L
e(c
n-1,j)+L(c
n-1,j)；
其中，L
e(c
n-1,j)表示当前迭代中发射符号x
n-1的外验信息，L(c
n-1,j)表示从上次迭代中获取的先验信息，发射符号x
n-1的后验均值和方差可表示为：
其中，
为n-1时刻的后验均值符号。
P′(x
n-1＝α
i)为x
n-1＝α
i概率，表示为：
当已估计符号对应的先验均值和方差被后验均值和方差替换以后，估计符号
可表示为：
其中，
为，表示为
Λ
n为n时刻的方差矩阵， 表示为
为n-1时刻的后验方差，v
n为n时刻的先验方差；
为n时刻滤波器系数，表示为
Σ
n为n时刻的信道协方差矩阵；
为n时刻滤波器标量，表示为
与传统BLE均衡器相似，发射符号x
n对应的外验信息与实施例1中外验信息表达式得到，唯一的区别是将k
n和f
n替换为
和
本实施例HBLE均衡器的结构如图3所示，L
e(c
n,j)为比特c
n,j对应的外验信息，L
p(c
n,j)为比特c
n,j对应的后验信息。
实施例3
实施例2中由于HBLE均衡器需要为每个未知符号重新计算逆矩阵，所以其计算复杂度远远高于传统BLE均衡器，因此为了避免大量的直接矩阵求逆运算，本实施例利用矩阵求逆准则提出一种快速递推方法来获取滤波器向量。
Σ
n为n时刻的信道协方差矩阵，矩阵Σ
n和Σ
n-1可表示为：
因此，矩阵Σ
n和Σ
n-1之间的关系可表示为：
其中，
当得到逆矩阵
后，逆矩阵
可表示为：
其中，
得到逆矩阵
后，HBLE均衡器的滤波器向量为
实施例4
在实施例2中，对于每个未知符号都需要重新计算预处理向量均值
计算复杂度远远高于传统BLE均衡器。因此，提出了另一个快速递推算法来进一步降低HBLE均衡器 的计算复杂度。
其中，
实施例5
在实施例2～4的基础上，HBLE均衡器的协方差矩阵Λ
n会随着时间n不断变化，导致对于每个未知符号都需要重新计算逆矩阵。因此，HBLE均衡器计算复杂度远远高于传统BLE均衡器。为了进一步降低计算复杂度，提出了使用固定协方差矩阵Λ＝diag(v
1,…,v
M)的低复杂度HBLE(low-complexity HBEL，LC-HBLE)均衡器。这样，在处理全部未知符号过程中，只需要执行一次矩阵求逆运算。对于LC-HBLE均衡器来说，估计符号
可表示为：
其中：
可以的得到
可以利用Σ来近似表示Σ
n，因此，ρ
n,i可简化为：
外验信息和后验软判决符号的计算和HBLE均衡器一样，此处不再赘述。
实施例6
对于HBLE/LC-HBLE均衡器来说，后验判决符号会随着检测顺序的变化而变化，从而检测顺序会影响均衡器的输出。基于最近提出的双向软判决反馈均衡器结构和本发明中的 HBLE/LC-HBLE均衡器，本实施例提出了基于混合软信息的双向块迭代(bidirectional-HBLE，Bi-HBLE)均衡器，可将HBLE均衡器替换为LC-HBLE均衡器，即基于混合软信息的双向块迭代均衡器包括Bi-HBLE/Bi-LC-HBLE均衡器，从而进一步改善均衡器性能。本实施例的均衡器结构如图4所示，该均衡器包括前向HBLE/LC-HBLE、反向HBLE/LC-HBLE以及软信息合并器，预处理符号z分别输入前向HBLE/LC-HBLE、反向HBLE/LC-HBLE，前向HBLE/LC-HBLE得到前向均衡器输出的外验信息
反向HBLE/LC-HBLE得到反向均衡器输出的外验信息
软信息合并器为
分配权重，得到最终双向结构均衡器输出的外验信息L
e(c
n,j)。Bi-HBLE/Bi-LC-HBLE由一个前向HBLE/LC-HBLE均衡器和一个反向HBLE/LC-HBLE均衡器组成。前向均衡器从符号x
1一直处理达到x
M为止，而反向均衡器的处理顺序恰恰相反，即反向均衡器从符号x
M一直处理达到x
1为止。如图5所示，虚线的线表示了均衡器的检测顺序。
利用因果符号的后验软判决，前向均衡器能够有效消除因果干扰。另一方面，利用非因果符号的后验软判决，反向均衡器能够消除非因果干扰。因此，Bi-HBLE/Bi-LC-HBLE均衡器能够同时消除因果和非因果干扰。
假设前向和反向均衡器的外验信息是高斯信道的输出，符号x
n的正确外验信息L
c(c
n,j)为输入：
其中，
和
分别表示前向和反向均衡器输出的外验信息；
和
分别表示均值为零方差为
的高斯白噪声，并且和L
c(c
n,j)相互独立；β
j表示
和
之间的相关系数，则双向结构均衡器的输出可表示为：
其中，λ
j表示加权系数。基于MMSE准则，λ
j可表示为：
λ
j＝arg min(E{|L
e(c
n,j)-L
c(c
n,j)|
2}).
根据最优化理论有：
因此，加权因子可表示为：
当
时，加权因子λ
j＝0.5，合并方式是均值合并。
对于传统BLE均衡器来说，前向和反向均衡器输出的外验信息是相同的，因此，基于BLE的双向均衡器会失效，不能获得分集增益。
实施例7
本实施例就复数乘法(complex multiplication,CM)而言，比较了提出各种均衡器和传统BLE均衡器的复杂度。计算复杂度的主要来源包括计算滤波器系数、后验矩和符号估计，结果如表1所示。
表1
比较了所提出的均衡器和传统BLE均衡器之间的BER性能；在仿真中，使用长度为576码率为1/3的LDPC编码器对发射二进制比特进行编码；映射后的符号通过一个三阶信道，其冲激响应为
未知符号和训练符号的长度分别设置为M＝32和N＝16；信道译码器采用归一化BP算法。
图6展示了BPSK调制下各种均衡器的BER性曲线，其中横坐标为信噪比Eb/No，纵坐标为误比特率(biterrorrate，BER)，迭代次数为4。由于利用了后验判决符号，HBLE(即实施例1～4所提任一均衡器)和LC-HBLE(即实施例5所提均衡器)均衡器的性能高于传统BLE均衡器。然而，Bi-HBLE和Bi-LC-HBLE(即实施例6中所提均衡器)可以得到最好的性能。与HBLE和LC-HBLE相比，Bi-HBLE和Bi-LC-HBLE使用了额外的反向均衡器，因此可以获得时间分集增益。
图7展现了均衡器的收敛性能。其中，
和
分别表示均衡器的输入和输出互信息(mutual information,MI)；
和
分别表示译码器的输入和输出互信息。可以发现，在给定输入MI时，Bi-HBLE产生最大的输出MI，接着是HBLE或者Bi-LC-HBLE、LC-HBLE以及BLE。因此，Bi-HBLE具有最快的收敛速率以及最佳的性能。
尽管已经示出和描述了本发明的实施例，对于本领域的普通技术人员而言，可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由所附权利要求及其等同物限定。
Claims (8)
- 基于混合软信息的块迭代均衡器，其特征在于，所述均衡器利用符号序列中未估计符号对应的先验信息和已估计符号对应的后验信息计算滤波器向量，获取最终估计的符号序列。
- 根据权利要求1所述的基于混合软信息的块迭代均衡器，其特征在于，估计符号表示为：
其中，为滤波器标量；
为均衡器的滤波器的滤波系数；z为预处理序列；H为信道矩阵；
为均值向量，表示为
为符号x n-1的后验均值，
为符号x n的先验均值；h n为信道矩阵的第n列向量。
- 根据权利要求2所述的基于混合软信息的块迭代均衡器，其特征在于，均衡器的滤波器的滤波系数表示为：
其中，为信道协方差矩阵的逆矩阵。
- 根据权利要求3所述的基于混合软信息的块迭代均衡器，其特征在于，信道协方差矩阵的逆矩阵表示为：
其中，Σ n-1为n-1时刻的信道协方差矩阵；为n-1时刻的后验方差，v n-1为n-1时刻先验方差；h n-1为信道矩阵的第n-1列向量，
为n-1时刻的信道协方差矩阵的逆矩阵，
为n-1时刻的滤波系数。
- 根据权利要求2所述的基于混合软信息的块迭代均衡器，其特征在于，每次利用未估计符号对应的先验判决和已估计符号的后验判决来获取估计符号时，计算预处理序列z的均值，预处理向量均值表示为：
其中，为预处理向量均值，H为信道矩阵，Δx n-1为
和
之差；h n-1为信道矩阵的第n-1列向量。
- 根据权利要求1～5所述的任一一种基于混合软信息的块迭代均衡器，其特征在于，在利用未估计符号对应的先验判决和已估计符号的后验判决来获取估计符号的过程中，计算每个未知符号时使用固定的协方差矩阵。
- 基于混合软信息的双向块迭代均衡器，其特征在于，包括权利要求1～6所述的任意一种均衡器，其中一个均衡器为前向均衡器，用于按顺序计算符号序列的外验信息；另一个为反向均衡器，用于反向计算符号序列的外验信息，通过设置的权重组合这两个均衡器获得外验信息，获得最终结果。
- 根据权利要求7所述的基于混合软信息的双向块迭代均衡器，其特征在于，获取最优的权重组合过程包括：若前向均衡器的权重为λ j、反向均衡器的权重为(1-λ j)，则前向均衡器的权重λ j表示为：λ j＝argmin(E{|L e(c n,j)-L c(c n,j)| 2}).其中，L e(c n,j)为前向均衡器获得的外验信息；L c(c n,j)为反向均衡器获得的外验信息；E{*}表示求期望。
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| US20150381392A1 (en) * | 2014-06-30 | 2015-12-31 | Hughes Network Systems, Llc | Optimized receivers for faster than nyquist (ftn) transmission rates in high spectral efficiency satellite systems |
| CN105656823A (zh) * | 2016-01-27 | 2016-06-08 | 华南理工大学 | 基于最小误码率准则的水下通信Turbo接收系统及方法 |
| CN109246039A (zh) * | 2018-08-09 | 2019-01-18 | 华南理工大学 | 一种基于双向时域均衡的软信息迭代接收方法 |
| CN112039809A (zh) * | 2020-08-20 | 2020-12-04 | 重庆邮电大学 | 基于混合软信息的块迭代均衡器及双向块迭代均衡器 |
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| US20150381392A1 (en) * | 2014-06-30 | 2015-12-31 | Hughes Network Systems, Llc | Optimized receivers for faster than nyquist (ftn) transmission rates in high spectral efficiency satellite systems |
| CN105656823A (zh) * | 2016-01-27 | 2016-06-08 | 华南理工大学 | 基于最小误码率准则的水下通信Turbo接收系统及方法 |
| CN109246039A (zh) * | 2018-08-09 | 2019-01-18 | 华南理工大学 | 一种基于双向时域均衡的软信息迭代接收方法 |
| CN112039809A (zh) * | 2020-08-20 | 2020-12-04 | 重庆邮电大学 | 基于混合软信息的块迭代均衡器及双向块迭代均衡器 |
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