WO2015165261A1 - 一种自适应rls判决反馈均衡系统及其实现方法 - Google Patents

一种自适应rls判决反馈均衡系统及其实现方法 Download PDF

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WO2015165261A1
WO2015165261A1 PCT/CN2014/092650 CN2014092650W WO2015165261A1 WO 2015165261 A1 WO2015165261 A1 WO 2015165261A1 CN 2014092650 W CN2014092650 W CN 2014092650W WO 2015165261 A1 WO2015165261 A1 WO 2015165261A1
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equalizer
sequence
input signal
result
signal
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陈芳炯
郑倍雄
林少娥
罗梦娜
季飞
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South China University of Technology SCUT
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B11/00—Transmission systems employing ultrasonic, sonic or infrasonic waves
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B13/00—Transmission systems characterised by the medium used for transmission, not provided for in groups H04B3/00 - H04B11/00
    • H04B13/02—Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy

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  • the invention relates to a digital wireless communication technology, in particular to an adaptive RLS decision feedback equalization system and an implementation method thereof.
  • the invention is a channel adaptive equalization technology of an underwater receiving end, which is mainly applied to complex long channel response underwater sounds.
  • the reliable transmission of the receiving end in the system and the fast adaptive equalization in the time domain or the frequency domain in the underwater acoustic system are used to eliminate inter-code interference or inter-subcarrier interference of the signal.
  • the ocean is a vast and rich world.
  • the exploration of marine science has attracted great attention from many scientists.
  • underwater acoustic communication and related information science and technology have played an important role in promoting the development of the marine industry.
  • the underwater acoustic communication channel has relatively high time selectivity and frequency selectivity, so the underwater acoustic channel is generally considered to be one of the most challenging communication media.
  • typical shallow seawater acoustic channels exhibit strong temporal dispersion effects, and inter-symbol interference is very severe.
  • an effective fast equalization algorithm is needed to eliminate the severe inter-symbol interference of the underwater acoustic channel or the orthogonal selective frequency division multiple access technique is used to make the frequency selective fading channel into a flat fading channel.
  • the response length of a channel can generally be considered to be several symbol periods, which is relatively easy to equalize.
  • the response of the channel is up to several hundred symbol periods, and the resulting intersymbol interference is very serious.
  • the background noise power of the underwater acoustic channel is also relatively large, and the signal-to-noise ratio tends to be low.
  • the background noise of the underwater acoustic channel mainly includes the marine environmental noise and ship self-noise, such as interference noise caused by wind and rain and tide, ship noise, seabed biological noise, etc., thus causing the complexity of the underwater acoustic channel noise.
  • the transmission rate of the underwater acoustic communication system is much lower than that of the terrestrial communication system, and the real-time requirements are not high.
  • the interference absorption of the underwater sound medium by the seawater medium and the complex and variable seabed channel environment, the received water acoustic signal is severely distorted. Therefore, the problem that underwater acoustic communication needs to solve is to reduce the bit error rate as much as possible to ensure reliable communication.
  • the main problem is the inter-symbol interference (ISI) problem, which can be used to perform symbol equalization in the time domain to reduce inter-symbol interference.
  • ISI inter-symbol interference
  • the main problem is the inter-subcarrier interference caused by the inaccurate frequency timing.
  • the subcarriers are equalized in the rate domain to reduce interference between subcarriers. Both of these solutions can be carried out under the minimum bit error rate criterion.
  • This patent mainly aims at realizing the minimum bit error rate equalization of symbols in the time domain of the underwater acoustic communication system, and its implementation can be similarly applied to the underwater acoustic communication system. In the frequency domain.
  • An adaptive channel equalizer based on minimum error rate criterion provided by South China University of Technology and its implementation method (Chinese invention patent number: CN102916916A), the main feature of this patent is that it is different from the traditional adaptive equalization algorithm, directly Derived from the minimum error rate criterion, the filtered output signal is mapped to a parameter that measures the degree of error as the basis for the next filter coefficient modification.
  • the patent is mainly applied to wireless channels with less channel response, the convergence speed is faster than the minimum mean square criterion adaptive method, the calculation amount is small, the equalizer structure is simple and easy to implement, but for the long channel response underwater acoustic communication channel Not very suitable.
  • a dual-mode adaptive decision feedback equalization module provided by South China University of Technology and its implementation method (Chinese Invention Application No.: 20140041987.1) propose a method of decision feedback based on minimum error rate criterion.
  • the equalization module adopts a decision feedback structure and can switch jobs in two modes.
  • This patent is applicable to underwater acoustic channels that are invariant or extremely slow, and the convergence speed is faster than that of the equalizer without feedback. However, it is difficult to converge to the ideal result for the underwater acoustic channel with relatively fast channel variation.
  • the evaluation adaptive equalization module can measure the reliability of the communication system transmission according to the error performance, convergence speed and algorithm complexity of the equalization algorithm, which is mainly based on the bit error rate.
  • the patent implementation method mentioned above can meet the requirement of minimizing the bit error rate.
  • the adaptive RLS decision feedback equalization system of the criterion has the ability to quickly converge to a very low bit error rate, and is more suitable for the application of underwater acoustic communication systems.
  • the primary object of the present invention is to overcome the shortcomings and shortcomings of the prior art, and provide an adaptive RLS decision feedback equalization system, which can achieve a minimum error rate result. It effectively eliminates inter-symbol interference and converges to the optimal value at a fast speed, occupies less bandwidth; and can achieve the minimum error rate result, effectively eliminate inter-symbol interference, and achieve fast convergence speed.
  • Another object of the present invention is to overcome the shortcomings and deficiencies of the prior art, and to provide an implementation method of an adaptive RLS decision feedback equalization system, which requires only a small number of training symbols to achieve considerable system performance and flexibility. High, can overcome the shortcomings of most related adaptive equalization algorithms that are difficult to apply directly in complex underwater environments.
  • an adaptive RLS decision feedback equalization system comprising: an error cross-correlation module, an equalization module, a decision feedback unit, a coefficient update unit, and an autocorrelation estimation module, the error code
  • the result of the cross-correlation module processing is to map the previous filtered output signal y k into the multiplication result of the error indication signal e k and the equalizer input signal sequence r k as an indication vector for the equalizer parameter adjustment, and the correspondence is as follows:
  • the subscript k indicates the current time
  • the subscript D is the time delay of the equalizer output signal relative to the transmitting end signal
  • s kD is the expected signal in the transmitting terminal pilot signal
  • ⁇ is a constant factor for controlling the mapping relationship
  • r k represents an equalizer input signal sequence, which is composed of a received symbol sequence and a decision feedback symbol sequence;
  • the equalization module includes a filter and a coefficient updating unit, and the filter performs filter equalization on the current time input signal sequence r k to obtain an output signal y k
  • c k-1 is the pre - updated filter coefficient, including the feedforward filter f k-1 and the feedback filter b k-1
  • the superscript T represents the transposition of the matrix
  • the input signal sequence r k is the received symbol sequence ⁇ k and decision feedback symbol sequence composition
  • the decision feedback unit directly performs the decision according to the equalized output signal, and the decision result is used as a feedback input signal of the equalizer, and the realization is as follows:
  • the equalizer coefficient update unit based on the input signal sequence r k, the cross-correlation module error processing result of the current I k to update the filter coefficients c k-1 to c k, to achieve the following:
  • ⁇ is an adjustment step constant
  • w is a forgetting constant factor
  • the filter coefficient c k and the equalizer input signal sequence r k are column vectors
  • P k-1 is an autocorrelation inverse matrix before updating
  • the autocorrelation inverse matrix estimation module comprises a memory coefficient unit and an autocorrelation inverse matrix register, and the autocorrelation inverse matrix estimation is updated by using the current time received symbol sequence r k result, and the updated autocorrelation inverse matrix estimation is implemented as follows:
  • w is a forgetting constant factor
  • the received signal r k is a column vector
  • P k-1 is an autocorrelation inverse matrix before updating.
  • an implementation method of an adaptive RLS decision feedback equalization system including the following steps:
  • step size u the forgetting constant factor w, the error cross-correlation result I k , the equalizer input signal sequence r k and the autocorrelation inverse matrix estimation result P k-1 before updating, the filter coefficient c k-1 Updated to c k ;
  • FIG. 1 is a schematic structural diagram of a general adaptive decision feedback equalization system.
  • FIG. 2 is a schematic diagram of a channel acting on a transmission sequence.
  • FIG. 3 is a schematic diagram of an adaptive RLS decision feedback equalization system implementing a minimum error rate criterion according to the present invention.
  • FIG. 4 is a schematic diagram of a filter structure in an equalization module.
  • Figure 5 is a schematic illustration of the impact response of a hydroacoustic channel tested in an experiment.
  • an adaptive decision feedback recursive equalizer based on a minimum error rate criterion includes: an error cross-correlation module, an equalization module, a decision feedback unit, a coefficient update unit, and an autocorrelation estimation module are implemented by using DSP. .
  • the function of the error cross-correlation module is to map the current filter output signal into a parameter for measuring the degree of error, as the basis for the next filter parameter modification, and the specific mapping relationship is as follows:
  • k time slot subscript, representing the current time
  • s k a desired signal in the pilot signal of the transmitting end
  • D a delay of the output signal of the filter relative to the pilot signal at the transmitting end
  • ⁇ is a sufficiently large constant for controlling the mapping relationship.
  • r k represents a sequence of received symbols
  • the function of the equalization module is: filtering the received signal sequence r k to obtain a filter output signal y k , and according to the input signal sequence r k , the autocorrelation inverse matrix P k-1 before unupdated , and the error cross correlation
  • the module processing result I k updates the filter coefficients.
  • the specific operation method is as follows:
  • f k-1 a column vector consisting of filter coefficients of the feedforward equalizer before updating
  • b k-1 a column vector consisting of filter coefficients of the feedback equalizer before updating
  • ⁇ k a column vector consisting of received signals whose elements are sorted by time from the current time
  • C k-1 a column vector consisting of a feedforward and feedback equalizer filter coefficients before being updated
  • r k a column vector consisting of an input signal sequence, a sequence consisting of a received signal and a decision feedback signal, the vector length being equal to c k-1 ;
  • I k a column vector composed of the result of the error cross-correlation module processing, the element of which is the product of the number of errors and the sequence of the received signal, and the vector length is equal to r k ;
  • P k-1 an autocorrelation inverse matrix of the received sequence before updating, updated according to the input signal sequence r k , the dimension of the matrix being equal to the length of the column vector r k ;
  • ⁇ the range of values is The adjustment step size for controlling the filter coefficient is usually 1 for convenience;
  • w The forgetting constant factor, the value is usually close to 1.
  • the autocorrelation inverse matrix estimation module comprises a memory coefficient unit and an autocorrelation inverse matrix register, and the autocorrelation inverse matrix estimation result is updated by using the current time input signal sequence r k result, and the updated autocorrelation inverse matrix estimation is implemented as follows:
  • r k a column vector consisting of an input signal sequence, a sequence consisting of a received signal and a decision feedback signal;
  • P k-1 The autocorrelation inverse matrix of the received sequence before updating is updated according to the received received sequence, and the dimension of the matrix is equal to the length of the column vector r k .
  • the adaptive RLS decision feedback equalizer implementing the minimum error rate criterion is balanced by the error cross-correlation module, the equalization module and the autocorrelation inverse matrix estimation module, and the specific steps are as follows:
  • Step 2 filtering the input signal sequence r k by using the currently unupdated filter coefficient c k-1 to generate a filtered output signal y k ;
  • Step 3 Using the filtered output signal y k to make a decision, and the decision output is an estimation result of the desired signal.
  • Step 4 y k from the filtered output signal, a desired pilot sequence signal s kD received sequence r k and the bit error calculated cross correlation result I k;
  • Step 5 According to the step size u, the forgetting constant factor w, the error cross-correlation result I k , the equalizer input signal sequence r k and the autocorrelation inverse matrix estimation result P k-1 before updating, the filter coefficient c k- 1 updated to c k ;
  • Step 6 The constant forgetting factor w and the equalizer input signal autocorrelation sequence r k inverse estimation result P k-1 is updated to P k;
  • Step 7 Repeat steps 2 through 6 until the equalizer coefficients converge, ie, satisfy the convergence condition:
  • the transmission signal s k is a binary pilot signal input to the channel
  • s kD is a desired signal in the pilot signal
  • h k is a channel impulse response
  • the memory length is L
  • n k is a power spectral density ⁇ . 2 white Gaussian noise.
  • the convolution of the channel to the signal is shown in Figure 2.
  • the channel output signal is:
  • the equalization module input signal can be expressed as:
  • the backward equalization module has a filter coefficient of The equalization module decision feedback signal can be expressed as:
  • the equalization module performs weighted diversity processing on the received signal and the decision feedback signal, respectively, and then adds them. As shown in FIG. 4, the output signal is:
  • This method is not based directly on the minimum bit error rate criterion and does not guarantee optimal bit error rate performance.
  • the algorithm is based on gradient descent, instead of directly pointing to the optimal convergence result, the convergence speed is slow, and it is difficult to use in underwater communication environment.
  • the invention provides a new adaptive decision feedback recursive equalizer algorithm based on minimum error rate criterion, and the derivation process is as follows:
  • bit error rate of the above equalization method can be expressed as
  • w is the forgetting constant factor
  • w k+i means that there is a decay process for the missymbol result
  • ⁇ is the Langeland multiplier.
  • tanh( ⁇ x) approximation instead of sgn(x), where ⁇ is a sufficiently large constant, which is derived as follows:
  • equation (16) can be expressed as:
  • the algorithm is named as an adaptive RLS decision feedback equalization (RLS-DFE) that implements a minimum error rate criterion (minimum-BER).
  • RLS-DFE adaptive RLS decision feedback equalization
  • minimum-BER minimum error rate criterion
  • the present invention is an adaptive RLS decision feedback equalization that implements a minimum error rate criterion, which is significantly better than a least mean square algorithm in terms of bit error rate performance; in the above embodiment, a decision feedback module is introduced based on a minimum error rate criterion.
  • a decision feedback module is introduced based on a minimum error rate criterion.
  • the input of the equalizer adds an estimation module of the autocorrelation inverse matrix, and uses the autocorrelation information of the signal to accelerate the convergence speed.
  • the simulation platform of the underwater acoustic channel is built by matlab, and the modulation mode of BPSK is selected.
  • Three other algorithms and the present invention are selected.

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  • Computer Networks & Wireless Communication (AREA)
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Abstract

本发明公开了一种自适应RLS判决反馈均衡系统，其特征在于，包括:误码互相关模块、均衡模块、判决反馈单元、系数更新单元和自相关估计模块；本发明还公开了一种自适应RLS判决反馈均衡系统的实现方法，包括以下步骤：1）设置滤波系数的初始值c0；2）产生滤波输出信号yk；3）计算误码互相关结果Ik；4）将滤波系数ck-1更新为ck；5）根据遗忘常数因子w和均衡器输入信号序列rk将自相关逆矩阵估计结果Pk-1更新为Pk；6）重复步骤2）至5），直至均衡器系数收敛为止。具有只需要少量的训练信号便可达到可观的系统性能以及适用于复杂水声环境下接收端的可靠传输和快速自适应均衡等优点。

Description

一种自适应RLS判决反馈均衡系统及其实现方法 技术领域
本发明涉及一种数字无线通信技术，特别涉及一种自适应RLS判决反馈均衡系统及其实现方法，本发明是一种水下接收端的信道自适应均衡技术，主要应用在复杂长信道响应水声系统中接收端的可靠传输，并实现在水声系统中时域或者频域的快速自适应均衡，用于消除信号的码间干扰或者子载波间干扰。
背景技术
海洋是一个广阔而丰富的世界，对海洋科学的探索引起众多科学工作者的极大关注，而其中水声通信及相关信息科学技术对海洋产业的发展有重要推动作用。但是，水声通信信道具有比较高的时间选择性和频率选择性，所以水声信道被普遍认为是最具挑战性的通信媒介之一。相比于陆地无线信道来说，典型的浅海水声信道表现出很强的时间色散效应，码间干扰非常严重。这时候就需要一种有效快速的均衡算法来消除水声信道严重的码间干扰或者采用正交频分多址技术使频率选择性衰落信道变为平坦性衰落信道。
由于水底环境复杂多变，海面的随机起伏变化使水声信号强度和相位不太稳定，由此造成的多径时延是比较严重的。对于陆地无线通信，信道的响应长度一般可认为是几个符号周期，比较容易均衡。但对于水声通信，信道的响应长达数百个符号周期，由此带来的码间干扰是很严重的。同时，水声信道的背景噪声功率也比较大，信噪比往往较低。水声信道的背景噪声主要包括海洋环境噪声和船舰自噪声，如风雨和潮汐引起的干扰噪声、船舶噪声、海底生物噪声等等，从而造成了水声信道噪声的复杂性。
水声通信系统的传输速率要比陆地通信系统的传输速率低很多，实时性要求不高。但是海水介质对水声信号的干扰吸收和海底信道环境的复杂多变，接收到的水声信号畸变严重。所以水声通信亟须解决的问题就是尽可能降低误码率，以保证可靠的通信。对于单载波水声系统而言，主要问题是码间干扰(ISI)问题，可以采用在时域上进行符号均衡，减少码间干扰。对于多载波水声系统而言，存在的主要问题是频率定时不准造成的子载波间干扰，则此时可以在频 率域上对子载波进行均衡，减少子载波间干扰。这两种解决方式都可以在最小误码率准则下进行，本专利主要是针对水声通信系统时域上实现对符号的最小误码率均衡，其实现也可以类似地运用到水声通信系统的频率域中。
一种由华南理工大学提供的基于最小误码率准则的自适应信道均衡器及其实现方法(中国发明专利号：CN102916916A)，该专利主要特点是它有别于传统的自适应均衡算法，直接由最小误码率准则推导而来，将滤波输出信号映射成衡量误码程度的参量，作为下一次滤波系数修改的依据。该专利主要应用在信道响应比较少的无线信道，收敛速度比最小均方准则的自适应方法要快，运算量小，均衡器结构简单且易于实现，但是对于长信道响应的水声通信信道则不太适用。
另外由华南理工大学提供的一种双模自适应判决反馈均衡模块及其实现方法(中国发明申请号：20140041987.1)，提出了一种基于最小误码率准则的判决反馈实现方法。该均衡模块采用了判决反馈结构，并且可以在两种模式下切换工作。该专利适用在时不变或者变化极其缓慢的水声信道，收敛速度较无反馈结果的均衡器要快，但是对于信道变化变化比较快的水声信道，则难以收敛到理想的结果。
在实际水声通信通信系统中，评价自适应均衡模块可以根据均衡算法的误码性能、收敛速度和算法复杂度，而衡量通信系统传输的可靠性最主要是根据误码率。前面提到的专利实现方法能够满足尽量降低误码率的要求，但在实际的水声通信应用中，不希望迭代次数过多，即均衡模块收敛速度要求非常快，才能满足水声通信的实时性要求。同时，在时变的水声信道中，当收敛速度高于信道响应变化速度时，才有可能收敛到比较理想的结果，所以只有快速收敛的均衡模块才能适用于变化的水声信道。
现有的大部分自适应均衡算法存在很多的不足，无法同时兼顾极低误码率和极高收敛速度两个方面，难以直接应用在复杂的水下环境中，所以本发明实现最小误码率准则的自适应RLS判决反馈均衡系统具有快速收敛到极低的误码率的能力，更适合水声通信系统的应用。
发明内容
本发明的首要目的在于克服现有技术的缺点与不足，提供一种自适应RLS判决反馈均衡系统，该自适应RLS判决反馈均衡系统能够实现最小误码率结果， 有效地消除码间干扰，并且以很快的速度收敛到最优值，占用带宽少；并且能够实现最小误码率结果，有效地消除码间干扰，自适应收敛速度快。
本发明的另一目的在于克服现有技术的缺点与不足，提供一种自适应RLS判决反馈均衡系统的实现方法，该实现方法只需要极少的训练符号便可达到可观的系统性能，灵活性高，能够克服了大部分相关自适应均衡算法难以直接应用在复杂的水下环境中的不足。
本发明的首要目的通过下述技术方案实现：一种自适应RLS判决反馈均衡系统，包括：误码互相关模块、均衡模块、判决反馈单元、系数更新单元和自相关估计模块，所述误码互相关模块处理结果为将前一次滤波输出信号yk映射成误码指示信号ek和均衡器输入信号序列rk的数乘结果，作为均衡器参数调整的指示向量，对应关系如下所述：
Ik＝(tanh(βyk)-sk-D)·rk＝ekrk，
其中，下标k表示当前时刻，下标D为均衡器输出信号相对于发送端信号的时延；sk-D为发送端导频信号中的期望信号；β为用于控制映射关系的常数因子；ek＝tanh(βyk)-sk-D为误码指示符号；rk表示均衡器输入信号序列，由接收符号序列和判决反馈符号序列共同组成；
所述均衡模块包含滤波器和系数更新单元，滤波器对当前时刻输入信号序列rk进行滤波均衡，得到输出信号yk
Figure PCTCN2014092650-appb-000001
其中，ck-1为未更新前滤波系数，包含前馈滤波fk-1和反馈滤波bk-1两部分，上标T表示矩阵的转置；输入信号序列rk由接收符号序列γk和判决反馈符号序
Figure PCTCN2014092650-appb-000002
组成；
所述判决反馈单元依据均衡后的输出信号直接进行判决，判决结果将作为均衡器的反馈输入信号，实现如下：
Figure PCTCN2014092650-appb-000003
其中，||||表示模值计算，通过取最小模值结果来表示判决过程；
Figure PCTCN2014092650-appb-000004
为输出的判决结果，是对发送端导频信号中的期望信号sk-D的估计，将用于均衡器反馈部分的输入信号；
所述系数更新单元依据均衡器输入信号序列rk、误码互相关模块处理结果Ik将当前滤波系数ck-1更新为ck，实现如下：
Figure PCTCN2014092650-appb-000005
其中，μ为调整步长常数；w为遗忘常数因子；滤波系数ck和均衡器输入信号序列rk为列矢量；Pk-1为未更新前的自相关逆矩阵；
所述自相关逆矩阵估计模块包含记忆系数单元和自相关逆矩阵寄存器，利用当前时刻接收符号序列rk结果对自相关逆矩阵估计进行更新，更新自相关逆矩阵估计实现如下：
Figure PCTCN2014092650-appb-000006
其中，w为遗忘常数因子；接收信号rk为列矢量；Pk-1为未更新前的自相关逆矩阵。
本发明的另一目的通过以下技术方案实现：一种自适应RLS判决反馈均衡系统的实现方法，包括以下步骤：
1)设置滤波系数的初始值c0，可设定任意非零值；设置自相关逆矩阵的初始值P0，尽量选择接近实际的输入序列的自相关逆矩阵，如果难以估计，可以令P0＝σE，其中E为单位矩阵，σ可选为一个较大的常数，比如取10以上；设置控制参数D、β、μ、w、ε的值；
2)利用当前未更新的滤波系数ck-1对输入信号序列rk进行滤波产生滤波输出信号yk；
3)由滤波输出信号yk、导频序列中的期望信号sk-D和输入信号序列rk计算出误码互相关结果Ik；
4)根据步长u、遗忘常数因子w、误码互相关结果Ik、均衡器输入信号序列rk以及未更新前的自相关逆矩阵估计结果Pk-1，将滤波系数ck-1更新为ck；
5)根据遗忘常数因子w和均衡器输入信号序列rk将自相关逆矩阵估计结果Pk-1更新为Pk
6)重复步骤2)～5)，直至均衡器系数收敛即||ck+1-ck||≤ε为止。
本发明相对于现有技术具有如下的优点及效果：
1)均衡器滤波系数的调整直接基于最小误码率准则，可实现最小误码率信道均衡结果；
2)均衡器滤波中引入反馈部分，利用反馈信息，可实现更优的收敛效果；
3)在每次滤波系数的调整中引入自相关逆矩阵的估计，可显著加快自适应 算法的收敛速度。
附图说明
图1为一般的自适应判决反馈均衡系统结构示意图。
图2为信道作用于发送序列的示意图。
图3为本发明实现最小误码率准则的自适应RLS判决反馈均衡系统示意图。
图4为均衡模块中的滤波器结构的示意图。
图5为在实验所测试水声信道的冲击响应的示意图。
图6为在实验水声信道下几种自适应均衡与本发明的基于最小误码率准则的自适应判决反馈递归均衡收敛性能的比较结果。
具体实施方式
下面结合实施例及附图对本发明作进一步详细的描述，但本发明的实施方式不限于此。
实施例
如图3所示，一种基于最小误码率准则的自适应判决反馈递归均衡器，包括：误码互相关模块、均衡模块、判决反馈单元、系数更新单元和自相关估计模块均采用DSP实现。
所述误码互相关模块的作用是：将当前次的滤波器输出信号映射成衡量误码程度的参量，作为下一次滤波参数修改的依据，具体映射关系如下：
Ik＝(tanh(βyk)-sk-D)·rk＝ekrk，  (1)
其中各标号的含义如下：
k：时隙下标，代表当前时刻；
yk：滤波器当前时刻输出信号；
sk：发送端的导频信号中的期望信号；
D：为滤波器输出信号相对于发送端导频信号的延时；
β：为充分大的常数，用于控制映射关系。
ek＝tanh(βyk)-sk-D为误码指示符号；
rk表示接收符号序列；
所述均衡模块的作用是：对接收信号序列rk进行滤波，得到滤波器输出信号 yk，并依据输入信号序列rk、未更新前的自相关逆矩阵Pk-1以及误码互相关模块处理结果Ik更新滤波系数。具体运算方式如下：
Figure PCTCN2014092650-appb-000007
Figure PCTCN2014092650-appb-000008
其中各标号的含义如下：
fk-1：由未更新前前馈均衡器滤波系数组成的列矢量；
bk-1：由未更新前反馈均衡器滤波系数组成的列矢量；
γk：由接收信号组成的列矢量，其元素从当前时刻起按时间递减排序；
Figure PCTCN2014092650-appb-000009
判决反馈信号组成的列矢量，其元素按时间递减排序；
ck-1：由未更新前由前馈和反馈均衡器滤波系数共同组成的列矢量；
rk：由输入信号序列组成的列矢量，由接收信号和判决反馈信号共同组成的序列，矢量长度与ck-1相等；
Ik：误码互相关模块处理结果组成的列矢量，其元素为误码与接收信号序列的的数量乘积，矢量长度与rk相等；
Pk-1：未更新前接收序列的自相关逆矩阵，根据输入信号序列rk进行更新，矩阵的维数等于列矢量rk长度；
μ：取值范围为
Figure PCTCN2014092650-appb-000010
用于控制滤波系数的调整步长，出于方便考虑，通常可取为1；
w：遗忘常数因子，取值通常取接近1。
所述自相关逆矩阵估计模块包含记忆系数单元和自相关逆矩阵寄存器，利用当前时刻输入信号序列rk结果对自相关逆矩阵估计结果进行更新，更新自相关逆矩阵估计实现如下：
Figure PCTCN2014092650-appb-000011
其中各标号的含义如下：
w：遗忘常数因子；
rk：由输入信号序列组成的列矢量，由接收信号和判决反馈信号共同组成的序列；
Pk-1：未更新前接收序列的自相关逆矩阵，根据接收到的接收序列进行更新，矩阵的维数等于列矢量rk长度。
所述实现最小误码率准则的自适应RLS判决反馈均衡器由误码互相关模块、均衡模块和自相关逆矩阵估计模块按顺序循环工作完成均衡，具体步骤如下：
步骤1：设置滤波系数的初始值c0，可设定任意非零值；设置自相关逆矩阵的初始值P0，尽量选择接近实际的输入信号序列的自相关逆矩阵，如果难以估计，可以令P0＝σE，其中E为单位矩阵，σ可选为一个较大的常数，比如取10以上；设置控制参数D、β、μ、w、ε的值；
步骤2：利用当前未更新的滤波系数ck-1对输入信号序列rk进行滤波产生滤波输出信号yk；
步骤3：利用滤波输出信号yk进行判决，判决输出对期望信号的估计结果
Figure PCTCN2014092650-appb-000012
步骤4：由滤波输出信号yk、导频序列中的期望信号sk-D和接收序列rk计算出误码互相关结果Ik；
步骤5：根据步长u、遗忘常数因子w、误码互相关结果Ik、均衡器输入信号序列rk以及未更新前的自相关逆矩阵估计结果Pk-1，将滤波系数ck-1更新为ck；
步骤6：根据遗忘常数因子w和均衡器输入信号序列rk将自相关逆矩阵估计结果Pk-1更新为Pk；
步骤7：重复步骤2到步骤6，直至均衡器系数收敛，即满足收敛条件：||ck+1-ck||≤ε。
如图1所示，发送信号sk为信道输入的二进制导频信号，sk-D为导频信号中的期望信号，hk为信道冲击响应，记忆长度为L，nk是功率谱密度为σ2的白高斯噪声。
信道对信号的卷积作用如图2所示，可得到信道输出信号为：
Figure PCTCN2014092650-appb-000013
均衡模块输入信号可以表示成：
Figure PCTCN2014092650-appb-000014
其中，rk为接收信号，nk为加性噪声，H为托普利兹矩阵，sk＝[sk…sk-M-N+1]T，前向均衡模块滤波系数为
Figure PCTCN2014092650-appb-000015
后向均衡模块滤波系数为
Figure PCTCN2014092650-appb-000016
均衡模块判决反馈信号可以表示成：
Figure PCTCN2014092650-appb-000017
均衡模块对接收信号和判决反馈信号分别作加权分集处理然后相加，如图4所示，输出信号为：
Figure PCTCN2014092650-appb-000018
对于二进制信号对均衡结果作判决反馈：
Figure PCTCN2014092650-appb-000019
基于最小均方误差准则，目标函数为：
Figure PCTCN2014092650-appb-000020
对目标函数求导：
Figure PCTCN2014092650-appb-000021
根据梯度算法得出：
ck+1＝ck-uekrk，
这就是著名的最小均方(least mean-squares)的自适应判决反馈算法，简称LMS-DFE算法。这种方法不是直接基于最小误码率准则，不能保证最优误码率性能。并且该算法是基于梯度下降的，而不是直接指向最优收敛结果，收敛速度较慢，难以用于水下通信环境。
本发明提供一种新的基于最小误码率准则的自适应判决反馈递归均衡器算法，推导过程如下：
上述均衡方法的误码率可以表示成
Figure PCTCN2014092650-appb-000022
考虑下面的约束最优化问题min||ck-ck-1||2约束条件为
Figure PCTCN2014092650-appb-000023
其中j＝D，D+1，…，k，表示同时对多个符号结果进行约束。使用lagrange乘数法求解，定义目标函数为：
Figure PCTCN2014092650-appb-000024
其中，w表示遗忘常数因子，wk+i表示对误符号结果有一个衰退过程，λ为朗格朗日乘数。为了方便求导，这里用tanh(βx)近似代替sgn(x)，β为充分大的常数，求导如下：
Figure PCTCN2014092650-appb-000025
令
Figure PCTCN2014092650-appb-000026
即偏导结果为零，可以得到：
Figure PCTCN2014092650-appb-000027
转置得：
Figure PCTCN2014092650-appb-000028
将其代入约束条件，并进行加权叠加
Figure PCTCN2014092650-appb-000029
得到：
Figure PCTCN2014092650-appb-000030
上式进一步可以化为：
Figure PCTCN2014092650-appb-000031
将上式中tanh(x)近似为一阶泰勒展开式tanh(x+△)≈tanh(x)+tanh′(x)Δ，即：
Figure PCTCN2014092650-appb-000032
假定在间隔k这时候均衡器已经补偿了信道的失真，理论上可以得到等式左边
Figure PCTCN2014092650-appb-000033
此时可以认为该项的值为一个常数。则可以得到：
Figure PCTCN2014092650-appb-000034
等式两边加上
Figure PCTCN2014092650-appb-000035
得到：
Figure PCTCN2014092650-appb-000036
将(9)式
Figure PCTCN2014092650-appb-000037
代入上式，得到：
Figure PCTCN2014092650-appb-000038
对式(15)进行变换，得到：
Figure PCTCN2014092650-appb-000039
定义列矢量
Figure PCTCN2014092650-appb-000040
定义自相关矩阵的估计结果为
Figure PCTCN2014092650-appb-000041
步长
Figure PCTCN2014092650-appb-000042
则式(16)可以表示为：
Figure PCTCN2014092650-appb-000043
直接求解计算自相关逆矩阵
Figure PCTCN2014092650-appb-000044
的结果比较繁琐，可以由下面的公式进行迭代计算：
Figure PCTCN2014092650-appb-000045
上式通过矩阵的线性变换，可以得到：
Figure PCTCN2014092650-appb-000046
令
Figure PCTCN2014092650-appb-000047
则可以得到基于最小误码率的自适应判决反馈递归均衡器：
Figure PCTCN2014092650-appb-000048
该算法命名为实现最小误码率准则(minimum-BER)的自适应RLS判决反馈均衡(RLS-DFE)，具体实施方式如图3所示。
本发明是实现最小误码率准则的自适应RLS判决反馈均衡，在误码率性能方面显著优于最小均方算法；在上述实施例中，在基于最小误码率准则下引入了判决反馈模块，使均衡器的收敛性能提高了很多。与梯度估计算法不同，均衡器的输入增加了自相关逆矩阵的估计模块，利用信号的自相关信息来加快收敛速度。
如图5和图6所示，通过matlab搭建水声信道的仿真平台，选择了BPSK的调制方式，在实际测试水声信道进行实验，信噪比SNR＝16dB，选择三种其他算法与本发明的基于最小误码率准则的自适应RLS判决反馈均衡(RLS-DFE)比较收敛结果，其中w取值为0.99，β取值为1，自适应步长u为1，初始自相关逆矩阵P0＝σE中σ＝50。从图中可以看到看出RLS-DFE算法无论是是误码性能还是收敛速度，都显著优于其他三种算法。
上述实施例为本发明较佳的实施方式，但本发明的实施方式并不受上述实施例的限制，其他的任何未背离本发明的精神实质与原理下所作的改变、修饰、替代、组合、简化，均应为等效的置换方式，都包含在本发明的保护范围之内。

Claims (3)

  1. 一种自适应RLS判决反馈均衡系统，其特征在于，包括：误码互相关模块、均衡模块、判决反馈单元、系数更新单元和自相关估计模块，所述误码互相关模块处理结果为将前一次滤波输出信号yk映射成误码指示信号ek和均衡器输入信号序列rk的数乘结果，作为均衡器参数调整的指示向量，对应关系如下：
    Ik＝(tanh(βyk)-sk-D)·rk＝ekrk，
    其中，下标k表示当前时刻，下标D为均衡器输出信号相对于发送端信号的时延；sk-D为发送端导频信号中的期望信号；β为用于控制映射关系的常数因子；ek＝tanh(βyk)-sk-D为误码指示符号；rk表示均衡器输入信号序列，由接收符号序列和判决反馈符号序列共同组成；
    所述均衡模块包含滤波器和系数更新单元，滤波器对当前时刻输入信号序列rk进行滤波均衡，得到输出信号yk：
    Figure PCTCN2014092650-appb-100001
    其中，ck-1为未更新前滤波系数，包含前馈滤波fk-1和反馈滤波bk-1两部分，上标T表示矩阵的转置；输入信号序列rk由接收符号序列γk和判决反馈符号序
    Figure PCTCN2014092650-appb-100002
    组成；
    所述判决反馈单元依据均衡后的输出信号yk直接进行判决，判决结果将作为均衡器的反馈输入信号，实现如下：
    Figure PCTCN2014092650-appb-100003
    其中，||||表示模值计算，通过取最小模值结果来表示判决过程；
    Figure PCTCN2014092650-appb-100004
    为输出的判决结果，是对发送端导频信号中的期望信号sk-D的估计，将用于均衡器反馈部分的输入信号；
    所述系数更新单元依据均衡器输入信号序列rk、误码互相关模块处理结果Ik将当前滤波系数ck-1更新为ck，实现如下：
    Figure PCTCN2014092650-appb-100005
    其中，μ为调整步长常数；w为遗忘常数因子；滤波系数ck和均衡器输入信号序列rk为列矢量；Pk-1为未更新前的自相关逆矩阵；
    所述自相关逆矩阵估计模块包含记忆系数单元和自相关逆矩阵寄存器，利 用当前时刻接收符号序列rk结果对自相关逆矩阵估计进行更新，更新自相关逆矩阵估计如下：
    Figure PCTCN2014092650-appb-100006
    其中，w为遗忘常数因子；接收信号rk为列矢量；Pk-1为未更新前的自相关逆矩阵。
  2. 根据权利要求1所述的自适应RLS判决反馈均衡系统，其特征在于，所述均衡器接收信号rk的元素从当前时刻开始，按时间递减排列。
  3. 根据权利要求1所述自适应RLS判决反馈均衡系统的实现方法，包括如下步骤：
    1)设置滤波系数的初始值c0，所述c0为任意非零值；设置自相关逆矩阵的初始值P0，令P0＝σE，其中，E为单位矩阵，σ可选为常数，设置控制参数D、β、μ、w和ε的值；
    2)利用当前未更新的滤波系数ck-1对输入信号序列rk进行滤波，产生滤波输出信号yk；
    3)由滤波输出信号yk、导频序列中的期望信号sk-D和输入信号序列rk，计算出误码互相关结果Ik；
    4)根据步长u、遗忘常数因子w、误码互相关结果Ik、均衡器输入信号序列rk以及未更新前的自相关逆矩阵估计结果Pk-1，将滤波系数ck-1更新为ck；
    5)根据遗忘常数因子w和均衡器输入信号序列rk将自相关逆矩阵估计结果Pk-1更新为Pk；
    6)重复步骤2)至5)，直至均衡器系数收敛即：||ck+1-ck||≤ε为止。
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