1、一仿真要求：f= （0.0000+1i*0.0000,0.0485+1i*0.0194,0.0573+1i*0.0253, 0.0786+1i*0.0282,0.0874+1i*0.0447,0.9222+1i*0.0301,0.1427+1i*0.0349,0.0835+1i*0.0157,0.0621+1i*0.0078,0.0359+1i*0.0049,0.0214+1i*0.0019）1. 研究信道的幅度譜(單位dB)，畫出頻譜圖。2. 設計K=1(2k+1=3)及K=10(2K+1=21)的MMSE均衡器。3. 設計K=1(2k+1=3)及K=10(2K+1=21)的ZF均衡器(迫零

2、均衡器)。4. 畫出以上均衡器的頻譜圖及等效信道頻譜。5. 分析總結。二實驗原理：均衡器通信系統中，是用來校正傳輸信道幅度頻率特性和相位頻率特性的部件。將頻率為f的正弦波放入傳輸信道，輸出電壓與輸入電壓的幅度比隨f變化的特性稱為頻率特性，簡稱幅頻特性；輸出電壓與輸入電壓的相位差隨f變化的特性稱為相位頻率特性，簡稱相頻特性。各種傳輸信道所傳輸的信號，一般有一些不同頻率的分量組成。在信號頻帶范圍內，若信道的幅頻特性是恒定值；相位；隨f變化的特性是直線。可寫成C(f)=2ft+，t為常數；(稱為相截)等于n，n=0，±2，±4，則信號波形經傳輸不產生畸變。條件使不同頻率分量經傳輸

3、后有相同的輸出輸入幅度比，條件、使其有相同的時間延遲。但實際通信常不符合上訴條件，因而信號產生畸變。若畸變超過允許量，則要用均衡器對信號特性進行校正。由于實際的限帶信道的傳遞函數往往是非理想的，且經常是時變的、未知的，因而系統特性不符合奈窐斯特準則，導致在接受端抽樣時刻存在碼間干擾，使得系統誤碼性能下降。為此，要考慮在信道傳遞函數是非理想情況，且信號在信道傳輸中受到加性白高斯噪聲干擾條件下的接收機的設計問題。在限帶數字通信系統中所采取的技術之一是在收端抽樣、判決之前加一均衡器，此均衡器是用來補償信道特性的不完善，從而減小在收端抽樣時刻的碼間干擾。圖2.1 具有均衡器的數字基帶傳輸系統均衡器通常

4、是用濾波器來實現的，使用濾波器來補償失真的脈沖，判決器得到的解調輸出樣本，是經過均衡器修正過的或者清除了碼間干擾之后的樣本。自適應均衡器直接從傳輸的實際數字信號中根據某種算法不斷調整增益，因而能適應信號的隨機變化，使均衡器總是保持最佳的狀態，從而有更好的失真補償性能。信道均衡技術大致分為兩大類：線性均衡和非線性均衡。在信道頻率響應特性比較平坦、所引起的碼間干擾不太嚴重的情況下，可采用線性均衡。線性均衡器可用橫向濾波器實現，圖示如下：圖2.2 橫向濾波器結構三仿真結果：1.研究信道的幅度譜(單位dB)，畫出頻譜圖。clcf=0.0000+1i*0.0000,0.0485+1i*0.0194,0.

5、0573+1i*0.0253, 0.0786+1i*0.0282,0.0874+1i*0.0447,0.9222+1i*0.0301,0.1427+1i*0.0349,0.0835+1i*0.0157,0.0621+1i*0.0078,0.0359+1i*0.0049,0.0214+1i*0.0019;N=64;y1=fft(f,N);y2=abs(y1);x=(0:N-1)*(10/(N-1); % w/(2*pi)y=10*log10(y2);plot(x,y);xlabel('k');ylabel('F(e(jwT)| (dB)');title('

6、幅度譜F(e(jwT)');grid on 圖3.1 幅度譜2. 設計K=1(2k+1=3)及K=10(2K+1=21)的MMSE均衡器(迫零均衡器)。2.1 K=1(2K+1=3)的MMSE均衡器：f=0.0000+j*0.0000,0.0485+j*0.0194,0.0573+j*0.0253,0.0786+j*0.0282,0.0874+j*0.0447,0.9222+j*0.0301,0.1427+j*0.0349,0.0835+j*0.0157,0.0621+j*0.0078,0.0359+j*0.0049,0.0214+j*0.0019;N0=0;f2=N0*eye(3);

7、f3=N0*eye(21);m=conv(conj(f),fliplr(f);f1=m(11), m(12), m(13); m(12) ,m(11), m(12) ;m(13) m(12) m(11) ;r=m(11:21) zeros(1,10);c=m(11:-1:1) zeros(1,10);f4=toeplitz(r,c);F1=f1+f2;q1=f(7),f(6),f(5);Cop3=F1*q1'Cop3 Cop3 = 0.3776 + 0.0592i 0.8955 + 0.0499i 0.3379 + 0.0672i2.2 K=10(2K+1=21)的MMSE均衡器：f=

8、0.0000+j*0.0000,0.0485+j*0.0194,0.0573+j*0.0253,0.0786+j*0.0282,0.0874+j*0.0447,0.9222+j*0.0301,0.1427+j*0.0349,0.0835+j*0.0157,0.0621+j*0.0078,0.0359+j*0.0049,0.0214+j*0.0019;N0=0;f2=N0*eye(3);f3=N0*eye(21);m=conv(conj(f),fliplr(f);f1=m(11), m(12), m(13); m(12) ,m(11), m(12) ;m(13) m(12) m(11) ;r=m

9、(11:21) zeros(1,10);c=m(11:-1:1) zeros(1,10);f4=toeplitz(r,c);F21=f3+f4;q2=0,0,0,0,0,conj(f(11),conj(f(10),conj(f(9),conj(f(8),conj(f(7),conj(f(6),conj(f(5),conj(f(4),conj(f(3),conj(f(2),conj(f(1),0,0,0,0,0;Cop21=F21*q2'Cop21 Cop21 = 0.0023 - 0.0002i 0.0067 - 0.0006i 0.0147 - 0.0010i 0.0283 - 0.

10、0015i 0.0494 - 0.0011i 0.1082 + 0.0030i 0.1925 - 0.0018i 0.2656 + 0.0066i 0.3375 + 0.0243i 0.4397 + 0.0503i 0.9547 + 0.0637i 0.3963 + 0.0854i 0.3222 + 0.0788i 0.2502 + 0.0757i 0.1865 + 0.0620i 0.0816 + 0.0287i 0.0408 + 0.0199i 0.0231 + 0.0120i 0.0114 + 0.0063i 0.0043 + 0.0024i 0.0012 + 0.0009iclccle

11、ar allclose allf=0.0000+j*0.0000,0.0485+j*0.0194,0.0573+j*0.0253,0.0786+j*0.0282,0.0874+j*0.0447,0.9222+j*0.0301,0.1427+j*0.0349,0.0835+j*0.0157,0.0621+j*0.0078,0.0359+j*0.0049,0.0214+j*0.0019;N0=0;f2=N0*eye(3);f3=N0*eye(21);m=conv(conj(f),fliplr(f);f1=m(11), m(10), m(9); m(12) ,m(11), m(10) ;m(13)

12、m(12) m(11) ;r=m(11:21) zeros(1,10);c=m(11:-1:1) zeros(1,10);f4=toeplitz(r,c);F1=f1+f2;F2=f3+f4;q1=f(7),f(6),f(5);q2=0,0,0,0,0,conj(f(11),conj(f(10),conj(f(9),conj(f(8),conj(f(7),conj(f(6),conj(f(5),conj(f(4),conj(f(3),conj(f(2),conj(f(1),0,0,0,0,0;a1=F1q1'a2=F2q2'N=64;fs=10;x=(0:N-1)*fs/N;A

13、1=fft(a1,N);A2=fft(a2,N);B1=abs(A1);B2=abs(A2);C1=10*log10(B1);C2=10*log10(B2);plot(x,C1,'or');text(6,2.5,'三抽頭MMSE均衡器');xlabel('wT');ylabel('10log10|F(ejwT)| (dB)');hold onplot(x,C2,'dg');text(3,0.8,'二十一抽頭MMSE均衡器');title('MMSE均衡器');圖3.2 MMSE均衡器

14、3.設計K=1(2k+1=3)及K=10(2K+1=21)的ZF均衡器。3.1 K=1的ZF均衡器：f=0.0000+1i*0.0000,0.0485+1i*0.0194,0.0573+1i*0.0253, 0.0786+1i*0.0282,0.0874+1i*0.0447,0.9222+1i*0.0301,0.1427+1i*0.0349,0.0835+1i*0.0157,0.0621+1i*0.0078,0.0359+1i*0.0049,0.0214+1i*0.0019;q3=0;1;0;A=f(6),f(5),f(4);f(7),f(6),f(5);f(8),f(7),f(6);F=in

15、v(A);Cop3=F*q3;Cop3首先得到：F = 1.1043 - 0.0227i -0.0942 - 0.0418i -0.0886 - 0.0204i -0.1656 - 0.0289i 1.1112 - 0.0155i -0.0942 - 0.0418i -0.0759 - 0.0035i -0.1656 - 0.0289i 1.1043 - 0.0227i然后得到：Cop3 = -0.0942 - 0.0418i 1.1112 - 0.0155i -0.1656 - 0.0289i得出：3.2 K=10的ZF均衡器：f=0.0000+1i*0.0000,0.0485+1i*0.0

16、194,0.0573+1i*0.0253, 0.0786+1i*0.0282,0.0874+1i*0.0447,0.9222+1i*0.0301,0.1427+1i*0.0349,0.0835+1i*0.0157,0.0621+1i*0.0078,0.0359+1i*0.0049,0.0214+1i*0.0019;q21=zeros(1,10);1;zeros(1,10);r=f(6:end) zeros(1,15); %r列c=f(6:-1:1) zeros(1,15); %c行A=toeplitz(r,c);F=inv(A);Cop21=F*q21;Cop21首先得到F= 0.0000 +

17、 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i 0.0000 + 0.0000i 0.0001 + 0.0001i 0.0000 + 0.0002i -0.0001 + 0.0000i -0.0006 - 0.0004i -0.0013 - 0.0016i 0.0009 - 0.0003i 0.0035 + 0.0015i 0.0091 + 0.0049i 0.0150 + 0.0116i -0.0471 - 0.0110i -0.0519 - 0

18、.0141i -0.0789 - 0.0165i -0.0890 - 0.0405i 1.1076 - 0.0219i然后得到：Cop21 = -0.0006 - 0.0004i -0.0012 - 0.0015i 0.0011 + 0.0000i 0.0035 + 0.0017i 0.0087 + 0.0046i 0.0136 + 0.0106i -0.0496 - 0.0135i -0.0468 - 0.0122i -0.0697 - 0.0128i -0.0730 - 0.0347i 1.1273 - 0.0116i -0.1501 - 0.0240i -0.0653 - 0.0000i

19、 -0.0465 + 0.0027i -0.0194 + 0.0012i -0.0102 + 0.0009i 0.0122 + 0.0014i 0.0037 - 0.0003i 0.0009 - 0.0003i -0.0004 - 0.0001i -0.0005 - 0.0001iclcclear allclose allf=0.0000+j*0.0000,0.0485+j*0.0194,0.0573+j*0.0253,0.0786+j*0.0282,0.0874+j*0.0447,0.9222+j*0.0301,0.1427+j*0.0349,0.0835+j*0.0157,0.0621+j

20、*0.0078,0.0359+j*0.0049,0.0214+j*0.0019;F1=f(6),f(5),f(4);f(7),f(6),f(5);f(8),f(7),f(6);r=f(6:11) zeros(1,15);c=f(6:-1:1) zeros(1,15);F2=toeplitz(r,c);q1=0,1,0;q2=0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0;a1=F1q1'a2=F2q2'N=64;fs=10;x=(0:N-1)*fs/N;A1=fft(a1,N);A2=fft(a2,N);B1=abs(A1);B2=abs(A

21、2);C1=10*log10(B1);C2=10*log10(B2);plot(x,C1,'og');text(4.8,1.4,'三抽頭ZF均衡器');xlabel('wT');ylabel('10log10|F(ejwT)| (dB)');hold onplot(x,C2);text(1.5,1,'二十一抽頭ZF均衡器');title('ZF均衡器');圖3.3 ZF均衡器4.畫出以上均衡器的頻譜圖及等效信道頻譜。4.1 MMSE的等效信道clcclear allclose allf=0.0000

22、+j*0.0000,0.0485+j*0.0194,0.0573+j*0.0253,0.0786+j*0.0282,0.0874+j*0.0447,0.9222+j*0.0301,0.1427+j*0.0349,0.0835+j*0.0157,0.0621+j*0.0078,0.0359+j*0.0049,0.0214+j*0.0019;N0=0;f2=N0*eye(3);f3=N0*eye(21);m=conv(conj(f),fliplr(f);f1=m(11), m(10), m(9); m(12) ,m(11), m(10) ;m(13) m(12) m(11) ;r=m(11:21)

23、 zeros(1,10);c=m(11:-1:1) zeros(1,10);f4=toeplitz(r,c);F1=f1+f2;F2=f3+f4;q1=f(7),f(6),f(5);q2=0,0,0,0,0,conj(f(11),conj(f(10),conj(f(9),conj(f(8),conj(f(7),conj(f(6),conj(f(5),conj(f(4),conj(f(3),conj(f(2),conj(f(1),0,0,0,0,0;a1=F1q1'a2=F2q2'c3=conv(a1,f);c21=conv(a2,f); N=64;fs=10;x=(0:N-1)

24、*fs/N;h3=10*log10(abs(fft(c3,N);h21=10*log10(abs(fft(c21,N);figure(1); plot(x,h3,'-b',x,h21,'ob'); legend('抽頭為3的等效信道','³抽頭為21的等效信道'); xlabel('omegaT');ylabel('10log10|F(ejomega)*C(ejomega)| (dB)');title('MMSE的抽頭為3和抽頭為21的等效信道');4.2 ZF的等效信道：

25、clcclear allclose allf=0.0000+j*0.0000,0.0485+j*0.0194,0.0573+j*0.0253,0.0786+j*0.0282,0.0874+j*0.0447,0.9222+j*0.0301,0.1427+j*0.0349,0.0835+j*0.0157,0.0621+j*0.0078,0.0359+j*0.0049,0.0214+j*0.0019;F1=f(6),f(5),f(4);f(7),f(6),f(5);f(8),f(7),f(6);r=f(6:11) zeros(1,15);c=f(6:-1:1) zeros(1,15);F2=toepli