外文翻譯--基于線性預(yù)測方法的水聲信道最小均方誤差盲均衡（節(jié)選）

1、<p><b>　　中文3775字</b></p><p>　　畢業(yè)設(shè)計(論文)外文資料翻譯</p><p>　　系 別 電子信息系 </p><p>　　專 業(yè) 通信工程 </p><p>　　班 級

2、 </p><p>　　姓 名 </p><p>　　學 號 </p><p>　　外文出處 J. Marine Sci. Appl. (2011) 10: 113-120

3、60;</p><p>　　附 件 1. 原文； 2. 譯文 </p><p><b>　　2013年03月</b></p><p>　　Blind Adaptive MMSE Equalization of Underwater Acoustic</p><p>　　Channels Based

4、on the Linear Prediction Method</p><p>　　R Bragos, R Blanco-Enrich</p><p>　　Abstract: </p><p>　　The problem of blind adaptive equalization of underwater single-input multiple-output

5、 (SIMO)acoustic channels was analyzed by using the linear prediction method. Minimum mean square error (MMSE) blind equalizers with arbitrary delay were described on a basis of channel identification. Two methods forcalc

6、ulating linear MMSE equalizers were proposed. One was based on full channel identification and realizedusing RLS adaptive algorithms, and the other was based on the zero-delay MMSE equalizer and </p><p>　　1

7、Introduction</p><p>　　Time-varying characteristic and multi-path fading of underwater acoustic channels can induce severe inter symbol interference (ISI) in high data rate communication systems. Channel equa

8、lization applying adaptive filters is one of the techniques to mitigate the effects of ISI. Conventionally, the initialization of an adaptive filter is achieved by a known training sequence from a transmitter before data

9、 transmission, so that valuable channel capacity is reduced. Recently, blind equalization techn</p><p>　　Traditionally, symbol rate sampled channel output sequence is stationary and higher order statistics a

10、re used to estimate the channel and to calculate the equalizer. More recently, it has been shown that the channel output sequence is cyclostationary if the sampling rate exceeds the symbol rate, and then second-order sta

11、tistics (SOS) contain sufficient information to estimate most communication channels using cyclostationarity (Tong et al., 1994; Tong et al., 1995; Papadias and Slock, 1999). Bas</p><p>　　However, it turns o

12、ut that these methods have much computational complexity or they are very sensitive to channel order mismatch (Moulines et al., 1995; Meraim et al., 1997; Liu et al., 1994; Alberge et al., 2002), which are major obstacle

13、s for their real-time implementations. The prediction error method offers an alternative to the class of techniques above. It was introduced by Slock (1994), Meraim et al. (1997), Ding (1997), Gesber and Duhamei (1997),

14、Tugnait (1999) and offered great advantag</p><p>　　coefficient of the channel response must be known a priori and noise variance should be estimated correctly. </p><p>　　In order to improve the

15、performance of blind equalizers without the aforementioned limitations, two methods for finding linear MMSE equalizers with arbitrary delay are presented in this paper. One is based on full channel identification and rea

16、lized using RLS adaptive algorithm, the other is based on the zero-delay MMSE equalizer and realized using LMS and RLS adaptive algorithms, respectively. Simulation results show that the proposed methods are robust to ch

17、annel order mismatch and they have b</p><p>　　2 Problem formulation</p><p>　　Consider a linear time-invariant communication channel.The received baseband signal y(t) can be expressed as</p>

18、;<p><b>　　(1)</b></p><p>　　where denotes the symbol emitted by the digital source at time with being the symbol duration; the overall complex baseband equivalent impulse response of the

19、transmitter filter, unknown channel and the receiver filter; the channel output without noise; and the channel noise that is assumed to be stationary as well as uncorrelated with . The following assumptions are held t

20、hroughout this paper:</p><p>　　1) The symbol sequence is stationary sub-Gaussian signal with zero-mean and unit-variance.</p><p>　　2) The noise is Gaussian with variance .</p><p>

21、　　3) is causal and has finite support .</p><p>　　4) The subchannels have no common zeros.</p><p>　　The oversampling factor is assumed to be L and the initial sampling time instant is. The oversa

22、mpled received signal can now be represented as</p><p><b>　　(2)</b></p><p><b>　　Let</b></p><p><b>　　，</b></p><p>　　， (3)

23、</p><p>　　then Eq.(2) becomes</p><p><b>　　(4)</b></p><p><b>　　Define</b></p><p><b>　　，</b></p><p>　　，

24、(5)</p><p>　　where i = 0,…,L ?1 . Then the single-input single-output (SISO) system of Eq.(4) has an equivalent SIMO description as follows,</p><p><b>　　(6)</b></p><p>　

25、　Define the following symbol rate vector,</p><p><b>　　,</b></p><p>　　, (7)</p><p>　　The Eq.(4) can be represented in a vector form</p><p><b&g

26、t;　　(8)</b></p><p>　　Furthermore, it can be represented as the following matrix form,</p><p><b>　　(9)</b></p><p>　　where H is a block Toeplitz matrix, is a vect

27、or and ,，are vctors as follows</p><p><b>　　(10)</b></p><p>　　(11) </p><p>　　3 The proposed methods</p><p>　　3.1 ZF

28、equalizers and MMSE equalizers</p><p>　　Consider the fractionally spaced FIR linear equalizer shownin Fig.1, where for is the equalizer with order of the ith subchannel. In the absence of noise, one natura

29、l choice is to require for some integer delay d with . This type of equalizer is known as zero-forcing. More precisely, a ZF equalizer is described by</p><p><b>　　(12)</b></p><p>　　

30、where superscript (d) refers to the delay d . Choose in Eq.(10), then Eq.(12) can be written as</p><p><b>　　(13)</b></p><p>　　where ector of the equalizer taps corresponding to dela

31、y d and , , vector with an 1 as the (d +1) th element and zeros elsewhere. The existence of ZF equalizers d ,ZF g has been proven (Giannaki and Halford, 1997; Slock and Papadias,1995) if the subchannels have no common z

32、eros and It can be written in the following expression,</p><p><b>　　(14)</b></p><p>　　where is the th column of the matrix H .</p><p>　　As ZF equalizers do not address

33、 noise suppression, another kind of equalizer called blind MMSE equalizers has been proposed to find such that</p><p>　　is minimized, where</p><p><b>　　(15)</b></p><p>　

34、　Take the complex derivative with respect to the unknown equalizer taps and set them to zero, MMSE equalizer with arbitrary delay d is obtained,</p><p><b>　　(16)</b></p><p>　　where

35、. RLS and cyclic LMS algorithms[15] have been proposed to recursively calculate the equalizer taps.</p><p>　　However, they can only be used to calculate zero-delay MMSE equalizer based on the assumption of t

36、he knowledge of h(0). If it is modified to get MMSE equalizers with arbitrary delay, noise variance of the received data must be estimated correctly, which makes it impractical for realization. Fortunately, according to

37、Eq.(16), if the correct estimates of are obtained, then will be available so that RLS algorithm can be used to recursively calculate .Based on this idea, channel identification becom</p><p>　　For the existin

38、g SOS based channel identification methods, most of them are sensitive to channel order mismatch or computationally complicated. The prediction error method offers an alternative to the channel identification. In the fol

39、lowing sections, linear prediction based channel identification and equalization methods will be presented.</p><p>　　3.2 MMSE equalizers with arbitrary delay based on</p><p>　　linear prediction

40、Consider the following one-step-ahead linear prediction problem</p><p><b>　　(17) </b></p><p>　　where is a prediction error vector and is a L × L(N ?1) prediction matrix. Minim

41、izing the prediction error covariance leads to the following optimization problem,</p><p><b>　　(18)</b></p><p>　　The solution of the optimization problem is the optimal predictor. S

42、uppose thatis the optimal linear predictor in the noiseless case and , then the following relationship can be derived (Li and Fan, 2000; Chow et al.,2002)</p><p><b>　　(19)</b></p><p&g

43、t;<b>　　and</b></p><p><b>　　(20) </b></p><p>　　In real application situations, the exact channel order is not known a priori.. Rewrite the matrix PN?1 as</p><p&

44、gt;<b>　　(21)</b></p><p>　　Eq.(20) shows that the prediction error covariance is a rank-one matrix. Any column of this matrix can be used as the estimate of h(0). Then according to Eq.(22), the wh

45、ole channel response can be calculated recursively so that the estimate of is obtained. Notice that hn should be satisfied to ensure good estimation result.</p><p>　　Through the analysis above and combining

46、Eq.(16), Eq.(17),Eq.(20) and Eq.(21), the following linear prediction based RLS algorithm, namely MMSE-RLS-1 for simplicity, is given for computing blind MMSE equalizer with arbitrary delay.</p><p>　　Step 1:

47、 Initialization where is a small positive constant.</p><p><b>　　,,</b></p><p><b>　　,,</b></p><p>　　where is a small positive constant.</p><p>

48、　　For each time instant n = 1, 2, ..., perform Step 2 to Step 5.</p><p>　　Step 2: Get the optimal linear predictor PN?1 ,</p><p>　　Step 3: Estimate.The column of E(n) with the largest norm is ta

49、ken as the estimate of h(0).</p><p>　　Step 4: Calculate the estimates of using Eq.(22).</p><p>　　Step 5: Form vector and calculate </p><p>　　In fact, the algorithm can be modified

50、as cyclic LMS. Though cyclic LMS algorithm has extremely low computational complexity, it has slower convergence rate than RLS algorithm and it is rather sensitive to amplitude error of the channel response estimation. T

51、herefore, this algorithm will not be considered here but another modified MMSE equalizer will be realized using LMS and RLS adaptation.</p><p>　　3.3 MMSE equalizers with arbitrary delay based on zero-delay M

52、MSE equalizer</p><p>　　In order to enhance the performance of blind equalizers, MMSE equalizers are proposed here and LMS and RLS algorithms are developed to recursively calculate the equalizer taps. In the

53、noise case, let the derivative of Eq.(18) with respect to PN?1 equal to zero, the following equation can be obtained,</p><p>　　(23) (24)</p><p>　　Combining Eq.(23

54、) with Eq.(16), it shows that</p><p><b>　　(25)</b></p><p>　　Compare it with Eq.(24), there is only a difference of computing the inversion of the first prediction error covariance, w

55、hich makes the performance of zero-delay MMSE equalizer better than that of zero-delay ZF equalizer.</p><p>　　ZF equalizer with arbitrary delay can be deduced by a second linear prediction model</p>&

56、lt;p><b>　　(26)</b></p><p>　　where is the optimal linear predictor and is prediction error. Then there exists the following relationship:</p><p><b>　　(27)</b></p&

57、gt;<p>　　While for the MMSE equalizer, there isn’t this kind of compact expression. Li and Fan (2000) has shown thatcan be realized by the following minimization problem:</p><p><b>　　(28)</b&

58、gt;</p><p>　　received data filtered by a d-delay ZF equalizer is equivalent to that the received data delayed by d filtered by a zero-delay ZF equalizer. Hence, the expression can be modified to get a d-dela

59、y MMSE equalizer based on the zero-delay MMSE equalizer using the similar minimization problem.</p><p><b>　　(29)</b></p><p>　　Eq.(29) can be adaptively optimized using an LMS algorit

60、hm or RLS algorithm. Firstly, is estimated in section 3.2, and then the zero-delay MMSE equalizer is calculated by Eq.(24). After that,can be updated recursively by an LMS algorithm to minimize</p><p>　　or s

61、implifywhich results in the following tap adaptation equations:</p><p><b>　　(30)</b></p><p><b>　　(31)</b></p><p>　　4 Simulation results</p><p>　

62、　In this section, simulation results are presented for the proposed algorithms MMSE-RLS-1, MMSE-LMS-2 and MMSE-RLS-3 described in the previous sections. The performance of the proposed algorithms is compared with the two

63、 existing algorithms (Li and Fan, 2000), which are both ZF algorithms and called Li-ZF-RLS and Li-ZF-LMS respectively for notational convenience. The two ZF algorithms have been proven to have faster convergence rate and

64、 lower ISI than many other existing algorithms. As a performa</p><p>　　(32) (33)</p><p>　　4.1 Experiment 1: performance of the proposed algorithms

65、 in noise</p><p>　　The performance of the proposed algorithms is considered in the presence of additive noise firstly. The channel used is a shallow sea channel (Zielinski et al., 1995) with carrier frequenc

66、y of 10 kHz, bandwidth of 2 kHz and baud rate of 1000 bit/s. The wind speed is assumed to be 20 kn. The transmitter and receiver are both put 10 m under the surface and 5 000 m far from each other. The oversampling facto

67、r L is 4. The estimated channel order and the real channel order are both 9. Let the predict</p><p>　　Fig.2 shows the ISI curves of the three proposed algorithms under SNR of 15 dB and 25 dB, respectively. I

68、t is clear that MMSE-RLS-1 converges and achieves sufficiently low ISI after as few as 1 000 symbols, while MMSE-RLS-3 has almost the same performance as MMSE-RLS-1 under low SNR and converges slower than MMSE-RLS-1 unde

69、r high SNR. Thus, it can be concluded from the simulation that</p><p>　　MMSE-RLS-1 is much more robust to channel noise. Meanwhile, it can be noticed that the two RLS algorithms, MMSE-RLS-1 and MMSE-RLS-3, p

70、erform much better</p><p>　　than MMSE-LMS-2 in both convergence rate and residual ISI.</p><p>　　4.2 Experiment 2: comparison with existing algorithms</p><p>　　In this experiment, th

71、e channel used is a channel (Zhang,2005) with a carrier frequency of 15 kHz and baud rate of1000 bit/s. The oversampling factor L is 2. The transmitterand the receiver are put 18.30 m and 15.2 m under the water,respectiv

72、ely. The distance between them is about 5 000 m and the depth of water is 54.9 m.</p><p>　　4.2.1 Convergence rate and residual ISI</p><p>　　Convergence rate and residual ISI are main performan c

73、ecriteria for adaptive algorithms. In this simulation, the estimated channel orderand the real channel order are both assumed to be 9. Let the predictor order be N = 10 and the delay be d= 4 . For MMSE-RLS-1 and Li-ZF-RL

74、S ,. The step</p><p>　　sizes of MMSE-LMS-2 and Li-ZF-LMS are both 0.003. For MMSE-RLS-3, , . Fig.3 shows the residual ISI comparison of different algorithms versus number of iterations under SNR of 15 dB and

75、 25 dB, respectively.</p><p>　　基于線性預(yù)測方法的水聲信道最小均方誤差盲均衡</p><p>　　R Bragos, R Blanco-Enrich</p><p><b>　　摘要</b></p><p>　　線性預(yù)測方法是對自適應(yīng)盲均衡水下單輸入多輸出(SIMO)聲信道的問題進行分析。

76、最小均方誤差(MMSE)盲均衡器是在與任意延遲的信道識別的基礎(chǔ)上，對描述計算線性MMSE均衡器的兩種方法提出建議。一個完整的信道識別的基礎(chǔ)，應(yīng)當實現(xiàn)使用RLS自適應(yīng)算法的基礎(chǔ)上，并含有其他基于零延遲的MMSE均衡器，并實現(xiàn)LMS和RLS自適應(yīng)算法。通過對兩個現(xiàn)有均衡算法和性能的比較，利用水聲信道進行模擬研究。結(jié)果表明，該算法強大到足以調(diào)整信道的順序不匹配。它們具有幾乎在相同的條件下，獲得比相應(yīng)的ZF算法高的信號噪聲比(SNR)和低SNR

77、下的更好的性能。</p><p><b>　　1 導(dǎo)言</b></p><p>　　在高速數(shù)據(jù)通信中，隨時間變化和多路徑衰落的特性可以引起水聲信道嚴重的符號干擾。自適應(yīng)濾波器是信道均衡的技術(shù)之一，用來減輕符號間的干擾。自適應(yīng)濾波器的初始化是通過發(fā)射機已知的訓(xùn)練序列中取得的，并且是在數(shù)據(jù)傳輸之前，使寶貴的信道容量減小。最近，盲均衡技術(shù)（斯托亞諾維奇，1996年）已經(jīng)吸引

78、了越來越多的關(guān)注。相比自適應(yīng)均衡技術(shù)，盲均衡技術(shù)的優(yōu)點主要是，無論何時何地通訊設(shè)備發(fā)生故障，都無需使用訓(xùn)練序列重新啟動系統(tǒng)。</p><p>　　在傳統(tǒng)觀念上，碼元速率采樣通道輸出序列是固定的，其是使用高階統(tǒng)計估計信道和均衡器。最近，新的研究已經(jīng)表明，如果采樣速率超過碼元速率，并且二階統(tǒng)計量(SOS)中包含了足夠的信息，該通道的輸出序列是周期平穩(wěn)的。通過tong(1994)等人在研討會上的工作，許多有效的盲方法已

79、經(jīng)被提出，并用于估計二階輸出的統(tǒng)計量信道。然而，事實證明，這些方法有很多的計算復(fù)雜性，因為它們對信道階數(shù)的不匹配非常敏感(Moulines.1995；Meraim.1997；Liu.1994年；Alberge.2002年)，這是主要阻礙它們實現(xiàn)實時的原因。預(yù)測誤差方法則提供了一個可以替代上述技術(shù)的方法。這是Slock(1994)，Meraim(1997年)，ding(1997)Gesber和Duhamei(1997年)，Tugnait(

80、1999)技術(shù)，它提供了巨大的優(yōu)勢，雖然頻道順序不匹配，但卻具有穩(wěn)固性和低計算復(fù)雜度?；诙嗦肪€性預(yù)測，迫零均衡(ZF)最小均方誤差(MMSE)均衡器可以進行任意延遲，這是源自Papadias和Slock(1999年)。然而，計算迫零均衡均衡器不是在第(n +1)步超前線性預(yù)測的無噪聲估計</p><p>　　為了提高盲均衡器的性能，使其沒有上述的限制，本文提出兩種方法用來找到任意延遲線性MMSE均衡器。一種是基

81、于全通道識別和利用RLS自適應(yīng)算法，另一種是基于零延遲的MMSE均衡器和分別利用LMS和RLS自適應(yīng)算法的均衡器。仿真結(jié)果表明，兩種方法是可靠的，信道階數(shù)不匹配，他們相應(yīng)的ZF算法的性能優(yōu)于低SNR性能。對于整份文件，向量和矩陣粗體小型大寫字母。 符號數(shù)，，,代表的含義，轉(zhuǎn)置，共軛，轉(zhuǎn)置，偽逆。是的矩陣和是矩陣的的零矩陣。 表示統(tǒng)計期望。</p><p><b>　　2問題描述</b><

82、;/p><p>　　考慮一個線性時不變的通信信道的接收基帶信號可以表示為</p><p><b>　　(1)</b></p><p>　　其中，表示符號所發(fā)出的數(shù)字信號源,的符號的持續(xù)時間， 整體的復(fù)基帶等效脈沖響應(yīng)發(fā)射機濾波器，未知的信道和接收機過濾器，無噪音的通道輸出，信道噪聲，被假定為固定的，以及無關(guān)。以下是整篇文章的假設(shè)：</p>

83、;<p>　　1) 是碼元序列高斯信號與零均值的單位方差。</p><p>　　2) 噪聲是高斯分布，方差為。</p><p>　　3) 是因果序列，并具有有限的支持的。</p><p>　　4) 子信道沒有共同的零。</p><p>　　過采樣系數(shù)被假定為L，初始采樣時刻為。過采樣的接收信號現(xiàn)在可以被表示為</p>

84、<p><b>　　(2) </b></p><p><b>　　，</b></p><p>　　， (3) </p><p><b>　　則方程(2)變?yōu)?lt;/b></p><p><b>　　(4)</b><

85、/p><p><b>　　定義</b></p><p><b>　　，</b></p><p>　　， (5) </p><p>　　其中i = 0,1，...，L-1。然后，單輸入單輸出(SISO)系統(tǒng)的公式(4)具有等效的SIM

86、O描述，如下所示</p><p><b>　　(6)</b></p><p>　　定義以下符號速率矢量</p><p><b>　　,</b></p><p>　　, (7) 方程(4)可以直接表示成向量形式</p&

87、gt;<p><b>　　(8)</b></p><p>　　此外，它還可以表示成以下矩陣形式</p><p>　　(9) 其中H是的矩陣，是一個的矩陣，,，是的矩陣</p><p><b>　　(10)</b></p><p>　　(11)

88、 </p><p><b>　　3 建議方法</b></p><p>　　3.1 ZF均衡和MMSE均衡器</p><p>　　考慮FIR線性均衡器如圖1，中的，是均衡器中的第i個子信道，在沒有噪聲時，一個普通的聲音中的d是整數(shù)延遲,這種形式相當于一個迫零均衡。更準確的說迫

89、零均衡可以表示</p><p><b>　　(12)</b></p><p>　　其中上標d表示延遲，在方程式（10）里，則方程式（12）可以寫成</p><p><b>　　(13)</b></p><p>　　其中是一個的向量均衡器抽頭，,是一個中的1作為第d+1元素和其他地方的值。如果不存在共

90、同的0和，可以表示如下</p><p><b>　　(14)</b></p><p>　　其中,是矩陣的第d+1列。</p><p>　　圖1 MMSE均衡器模型</p><p>　　由于ZF均衡不解決噪聲抑制，另一個種均衡器稱為盲MMSE均衡器可以找到使得取到最小，可以表示成</p><p>&

91、lt;b>　　(15)</b></p><p>　　以高階的導(dǎo)數(shù)相對于未知均衡器的抽頭，將其設(shè)置為0，對于MMSE盲均衡器，可以獲得任意延遲d使得</p><p><b>　　(16)</b></p><p>　　其中，RLS和循環(huán)LMS]已經(jīng)被提出來遞歸地計算均衡器的抽頭。然而，它們只能被用于計算零延遲的MMSE均衡器，并滿

92、足。如果改變MMSE均衡器與任意延遲，所接收的數(shù)據(jù)的噪聲方差，必須正確地估計，這是不現(xiàn)實的。幸運的是，根據(jù)方程(16)，可以正確的估計，獲得，然后實現(xiàn)RLS算法，可用于遞歸地計算。這就成為信道識別主要的問題。</p><p>　　對于現(xiàn)有的SOS基于信道的識別方法，他們大多敏感的信道階數(shù)不匹配或計算復(fù)雜。預(yù)測誤差的方法提供了一種替代信道識別的方法。在以下章節(jié)中，基于線性預(yù)測的通道將提交??為盲均衡方法</p

93、><p>　　3.2 MMSE均衡器的基礎(chǔ)上任意延遲的線性預(yù)測</p><p>　　考慮以下的1步的預(yù)線性預(yù)測的問題</p><p><b>　　(17) </b></p><p>　　其中，是一個的預(yù)測誤差矢量，是的預(yù)測矩陣。最大限度地減少并優(yōu)化預(yù)測誤差的協(xié)方差</p><p><b>　

94、　(18) </b></p><p>　　最優(yōu)化問題的解決方案是最佳的。假設(shè)是最佳的線性預(yù)測,在無噪聲的情況下和，那么下面的關(guān)系可以推導(dǎo)出（Li和Fan，2000年Chow等）。</p><p><b>　　(19)</b></p><p><b>　　和</b></p><p>&

95、lt;b>　　(20)</b></p><p><b>　　重寫矩陣</b></p><p><b>　　(21)</b></p><p>　　其中中的是一個的矩陣。H可以表示成</p><p><b>　　(22)</b></p><p&

96、gt;　　方程式(20)表示的預(yù)測誤差的協(xié)方差是一個秩1矩陣。在任何列此矩陣可以被用作的估計的h(0)。然后根據(jù)式(22)，全信道響應(yīng)可以遞歸計算，以便估計的得到。請注意，壽命應(yīng)滿足確保良好的估計結(jié)果。</p><p>　　經(jīng)過上面的分析，結(jié)合方程(16)，方程(17)，方程(20)和式(21)，下面的基于線性預(yù)測的RLS算法，即MMSE-RLS-1為簡單起見，是計算盲MMSE均衡器與任意延遲的。</p&g

97、t;<p>　　步驟1初始化,其中是一個很小的數(shù)。</p><p><b>　　,,</b></p><p><b>　　,,</b></p><p>　　其中是一個很小的數(shù)。</p><p>　　第2步：獲得最佳線性預(yù)測</p><p><b>　　

98、第3步，假設(shè)</b></p><p><b>　　第4步，建立</b></p><p><b>　　第5步，通過計算</b></p><p>　　實際上，該算法可以被修改成循環(huán)的LMS。雖然循環(huán)LMS算法具有極低的計算復(fù)雜性，但它的收斂速度比RLS算法慢，這是對估計信道響應(yīng)時相當敏感的。因此，MMSE均衡器將實

99、現(xiàn)使用LMS和RLS，這是對其的一種改進。</p><p>　　3.3在 MMSE均衡器的基礎(chǔ)上的任意延遲與零延遲的MMSE均衡器</p><p>　　為了提高盲均衡器的性能，在這里建議對MMSE均衡器的LMS和RLS算法的改進，以遞歸計算均衡器的抽頭。在的噪聲的情況下，讓衍生物的式(18)。相對于等于零，下面的等式可以得到</p><p><b>　　(

100、23)</b></p><p>　　結(jié)合等式(23)和等式(16)表示如下</p><p><b>　　(24)</b></p><p>　　結(jié)果，由零延遲的MMSE均衡器得式(14)和式(19)可以寫成</p><p><b>　　(25)</b></p><p&g

101、t;　　比較它與方程(24)，有只相差計算第一預(yù)測的反轉(zhuǎn),協(xié)方差，這使得,零延遲的MMSE均衡器的性能優(yōu)于ZF均衡器。</p><p>　　ZF均衡器可以推斷，一個任意延遲的第二線性預(yù)測模型。</p><p><b>　　(26)</b></p><p>　　其中是最佳線性預(yù)測和是預(yù)測誤差。則存在以下關(guān)系：</p><p&g

102、t;<b>　　(27)</b></p><p>　　而對于MMSE均衡器，沒有這表達。LI和FAN(2000)表明，由下面的最小化，可以實現(xiàn)問題：</p><p><b>　　(28)</b></p><p>　　這最小化的基本思想是，原先由延遲的均衡器過濾接收到的數(shù)據(jù)相當于零延遲ZF均衡器所接收的數(shù)據(jù)延遲。因此，該表達

103、式可以是改進，以獲得的d延遲是在MMSE均衡器的基礎(chǔ)上的零延遲的MMSE均衡器，是最小化問題。</p><p><b>　　(29)</b></p><p>　　方程(29)可以使用一個LMS自適應(yīng)地優(yōu)化算法RLS算法。首先，從第3.2節(jié)中估算，然后計算零延遲的MMSE均衡。之后遞歸更新的LMS算法，以盡量簡化</p><p><b>

104、;　　Alpha</b></p><p><b>　　生成等式如下</b></p><p><b>　　(30)</b></p><p>　　為簡單起見，該算法被稱為MMSE-LMS-2?？梢詫崿F(xiàn)均衡器的計算使用RLS，形成以下MMSE-RLS-3的算法：</p><p><b&g

105、t;　　(31)</b></p><p><b>　　4仿真結(jié)果</b></p><p>　　MMSE-RLS-1-LMS-2提出的算法，和在前面的章節(jié)中描述的MMSE-RLS-3。 算法的性能較好，現(xiàn)有的兩個算法(FAN，2000年)，這是ZF算法和LI-ZF-RLS和Li-ZF-LMS分別在符號上的便利。這兩個ZF算法已被證明具有較快的收斂速度，低IS

106、I比其他許多現(xiàn)有的算法。作為一個性能考核，殘余ISI估計過50個獨立的蒙地卡羅運行，并把它定義為</p><p><b>　　(32)</b></p><p><b>　　其中的可以表示成</b></p><p><b>　　(33)</b></p><p>　　4.1實驗1：

107、性能的建議噪聲算法</p><p>　　本文提出的算法的性能，被認為是在加性噪聲的存在下，首先。使用的信道是與運營商的一個淺海信道(思霖懇等人，1995)頻率為10 kHz，2 kHz的帶寬和波特率1000比特/秒。假設(shè)風速為20海里?！鞍l(fā)射器和接收器都在表面下把10米，5 000米，遠離彼此。過采樣系數(shù)L為4。估計信道階H美國東部時間L和真正的通道順序。我們的預(yù)測令N = 10，和延遲是d= 10。對于MMSE

108、-RLS-1，，MMSE-LMS-2步長大小為0.025。對于MMSE-RLS-3，，</p><p>　　圖2 ISI曲線算法</p><p>　　圖2顯示了ISI曲線的三個建議算法在SNR為15 dB和25 dB。很顯然， MMSE-RLS-1收斂，并達到足夠低的ISI后數(shù)為1 000，而MMSE-RLS-3幾乎相同的性能下的MMSE-RLS-1低SNR和收斂速度等于MMSE-RLS-

109、1在高SNR的情況下。因此，它可以從模擬中，完成MMSE-RLS-1信道噪聲更強大。同時，它可以注意到，兩個RLS算法，MMSE-RLS-1和MMSE-RLS-3，更好地執(zhí)行MMSE-LMS-2的收斂速度和殘余ISI。</p><p>　　4.2實驗2：與現(xiàn)有算法相比</p><p>　　在這個實驗中，使用的信道是一個信道用的載波頻率為15 kHz和波特率1000比特/秒。過采樣因子L是2

110、。發(fā)射器與接收器分別在18.30米和15.2 m，。他們之間的距離大約是5 000米，并且水深度是54.9米。</p><p>　　4.2.1收斂速度和剩余ISI</p><p>　　收斂率和殘留ISI的主要性能是自適應(yīng)算法的標準。在該仿真中，估計信道階真正的信道階假定為9。我們的預(yù)測令N = 10，和延遲是d= 4。用于MMSE-RLS-1和LI-ZF-RLS，,。MMSE-LMS-2和