{"id":51523,"date":"2025-08-10T23:59:05","date_gmt":"2025-08-10T15:59:05","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/51523.html"},"modified":"2025-08-10T23:59:05","modified_gmt":"2025-08-10T15:59:05","slug":"%e8%bd%a6%e8%bd%bd%e6%af%ab%e7%b1%b3%e6%b3%a2%e9%9b%b7%e8%be%bedml%e7%ae%97%e6%b3%95%e7%90%86%e8%ae%ba%e7%ae%80%e6%9e%90","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/51523.html","title":{"rendered":"\u8f66\u8f7d\u6beb\u7c73\u6ce2\u96f7\u8fbeDML\u7b97\u6cd5\u7406\u8bba\u7b80\u6790"},"content":{"rendered":"

\u8f66\u8f7d\u6beb\u7c73\u6ce2\u96f7\u8fbeDML\u7b97\u6cd5\u7406\u8bba\u7b80\u6790<\/h2>\n

DML\u7b97\u6cd5\u572877GHz\u8f66\u8f7d\u96f7\u8fbe\u4e2d\u7684\u6570\u5b66\u5efa\u6a21<\/h3>\n

\u8f66\u8f7d\u6beb\u7c73\u6ce2\u96f7\u8fbe\u7684\u786e\u5b9a\u6027\u6700\u5927\u4f3c\u7136（DML）\u7b97\u6cd5\u4e3a\u76ee\u6807\u89d2\u5ea6\u4f30\u8ba1\u63d0\u4f9b\u4e86\u4e25\u683c\u7684\u6570\u5b66\u6846\u67b6\u3002\u572877GHz\u9891\u6bb5，\u6ce2\u957f\u03bb\u7ea6\u4e3a3.9mm，\u4f7f\u5f97\u7d27\u51d1\u7684\u5929\u7ebf\u9635\u5217\u8bbe\u8ba1\u6210\u4e3a\u53ef\u80fd，\u540c\u65f6\u4fdd\u6301\u9ad8\u5206\u8fa8\u7387\u7684\u6d4b\u89d2\u80fd\u529b\u3002<\/p>\n

\u9635\u5217\u63a5\u6536\u4fe1\u53f7\u6a21\u578b\u7684\u5efa\u7acb<\/h4>\n

\u8f66\u8f7d\u96f7\u8fbe\u7cfb\u7edf\u91c7\u7528M\u4e2a\u5929\u7ebf\u5355\u5143\u63a5\u6536\u6765\u81eaK\u4e2a\u76ee\u6807\u7684\u4fe1\u53f7，\u63a5\u6536\u4fe1\u53f7\u5411\u91cf\u7684\u6570\u5b66\u8868\u8fbe\u4e3a：<\/p>\n

x(t)=A(\u03b8)s(t)+n(t)x(t) = A(\u03b8)s(t) + n(t)<\/span><\/span>x<\/span>(<\/span>t<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>A<\/span>(<\/span>\u03b8<\/span>)<\/span>s<\/span>(<\/span>t<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>n<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d，x(t)\u4e3aM\u00d71\u7ef4\u63a5\u6536\u4fe1\u53f7\u5411\u91cf，A(\u03b8)\u4e3aM\u00d7K\u7ef4\u9635\u5217\u6d41\u5f62\u77e9\u9635，\u5305\u542b\u6240\u6709\u76ee\u6807\u7684\u5bfc\u5411\u77e2\u91cf，s(t)\u4e3aK\u00d71\u7ef4\u6e90\u4fe1\u53f7\u5411\u91cf，n(t)\u4e3aM\u00d71\u7ef4\u52a0\u6027\u566a\u58f0\u5411\u91cf，\u5047\u8bbe\u4e3a\u7a7a\u95f4\u548c\u65f6\u95f4\u4e0a\u7684\u767d\u590d\u9ad8\u65af\u566a\u58f0：n(t)\u00a0CN(0,\u03c3n2I)n(t) ~ CN(0, \u03c3\u2099\u00b2I)<\/span><\/span>n<\/span>(<\/span>t<\/span>)<\/span>\u00a0<\/span>CN<\/span>(<\/span>0<\/span>,<\/span><\/span>\u03c3<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>I<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u5bf9\u4e8e\u5747\u5300\u7ebf\u9635（ULA）\u914d\u7f6e，\u7b2ck\u4e2a\u76ee\u6807\u7684\u5bfc\u5411\u77e2\u91cf\u5177\u6709\u660e\u786e\u7684\u76f8\u4f4d\u5173\u7cfb：<\/p>\n

aula(\u03b8k)=[1,e(\u2212jkdsin\u03b8k),e(\u2212j2kdsin\u03b8k),…,e(\u2212j(M\u22121)kdsin\u03b8k)]Ta\u1d64\u2097\u2090(\u03b8\u2096) = [1, e^(-jkd sin \u03b8\u2096), e^(-j2kd sin \u03b8\u2096), …, e^(-j(M-1)kd sin \u03b8\u2096)]\u1d40<\/span><\/span>a<\/span><\/span>u<\/span>l<\/span>a<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>1<\/span>,<\/span><\/span>e<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>jk<\/span>d<\/span>s<\/span>in<\/span>\u03b8<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>,<\/span><\/span>e<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>2<\/span>k<\/span>d<\/span>s<\/span>in<\/span>\u03b8<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>,<\/span><\/span>…<\/span>,<\/span><\/span>e<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>j<\/span>(<\/span>M<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>)<\/span>k<\/span>d<\/span>s<\/span>in<\/span>\u03b8<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>]<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2dk = 2\u03c0\/\u03bb\u4e3a\u6ce2\u6570，d\u4e3a\u9635\u5143\u95f4\u8ddd\u3002\u8fd9\u79cd\u7ebf\u6027\u76f8\u4f4d\u8fdb\u5c55\u4f7f\u5f97\u89d2\u5ea6\u4f30\u8ba1\u5177\u6709\u660e\u786e\u7684\u51e0\u4f55\u610f\u4e49\u3002<\/p>\n

\u4f3c\u7136\u51fd\u6570\u6784\u5efa\u4e0e\u786e\u5b9a\u6027\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u63a8\u5bfc<\/h3>\n

\u8054\u5408\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u7684\u6570\u5b66\u6784\u5efa<\/h4>\n

DML\u7b97\u6cd5\u7684\u6838\u5fc3\u5728\u4e8e\u5c06\u76ee\u6807\u4fe1\u53f7\u89c6\u4e3a\u786e\u5b9a\u6027\u4f46\u672a\u77e5\u7684\u53c2\u6570，\u800c\u975e\u968f\u673a\u8fc7\u7a0b\u3002\u5bf9\u4e8e\u590d\u9ad8\u65af\u566a\u58f0\u73af\u5883，N\u6b21\u5feb\u62cd\u4e0b\u63a5\u6536\u6570\u636eX = [x(t\u2081), x(t\u2082), \u2026, x(t\u2099)]\u7684\u8054\u5408\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e3a：<\/p>\n

p(X\u2223\u03b8,S)=(1\/\u03c0(MN)\u03c3n(2MN))exp(\u22121\/\u03c3n2\u2223\u2223X\u2212A(\u03b8)S\u2223\u2223F2)p(X|\u03b8,S) = (1\/\u03c0^(MN)\u03c3\u2099^(2MN)) exp(-1\/\u03c3\u2099\u00b2 ||X – A(\u03b8)S||\u00b2_F)<\/span><\/span>p<\/span>(<\/span>X<\/span>\u2223<\/span>\u03b8<\/span>,<\/span><\/span>S<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>1\/<\/span>\u03c0<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>MN<\/span>)<\/span>\u03c3<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>MN<\/span>))<\/span>e<\/span>x<\/span>p<\/span>(<\/span>\u2212<\/span>1\/<\/span>\u03c3<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223\u2223<\/span>X<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>A<\/span>(<\/span>\u03b8<\/span>)<\/span>S<\/span>\u2223<\/span>\u2223<\/span><\/span>F<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d\u2223\u2223\u22c5\u2223\u2223F2||\u00b7||\u00b2_F<\/span><\/span>\u2223\u2223<\/span>\u22c5<\/span><\/span>\u2223<\/span>\u2223<\/span><\/span>F<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8868\u793aFrobenius\u8303\u6570\u7684\u5e73\u65b9，S = [s(t\u2081), s(t\u2082), \u2026, s(t\u2099)]\u4e3aK\u00d7N\u7684\u4fe1\u53f7\u77e9\u9635\u3002<\/p>\n

\u5bf9\u6570\u4f3c\u7136\u51fd\u6570\u4e0e\u6d53\u7f29\u4f3c\u7136\u51fd\u6570<\/h4>\n

\u5bf9\u6570\u4f3c\u7136\u51fd\u6570\u7684\u63a8\u5bfc\u6d88\u9664\u4e86\u6307\u6570\u9879\u7684\u590d\u6742\u6027：<\/p>\n

L(\u03b8,S)=\u2212MNlog(\u03c0\u03c3n2)\u22121\/\u03c3n2\u2223\u2223X\u2212A(\u03b8)S\u2223\u2223F2L(\u03b8,S) = -MN log(\u03c0\u03c3\u2099\u00b2) – 1\/\u03c3\u2099\u00b2 ||X – A(\u03b8)S||\u00b2_F<\/span><\/span>L<\/span>(<\/span>\u03b8<\/span>,<\/span><\/span>S<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>MNl<\/span>o<\/span>g<\/span>(<\/span>\u03c0<\/span>\u03c3<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1\/<\/span>\u03c3<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223\u2223<\/span>X<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>A<\/span>(<\/span>\u03b8<\/span>)<\/span>S<\/span>\u2223<\/span>\u2223<\/span><\/span>F<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5173\u952e\u7684\u6570\u5b66\u6d1e\u5bdf\u5728\u4e8e，\u5bf9\u4e8e\u56fa\u5b9a\u7684\u03b8，\u901a\u8fc7\u6700\u5c0f\u4e8c\u4e58\u6cd5\u53ef\u4ee5\u83b7\u5f97S\u7684\u6700\u4f18\u4f30\u8ba1：<\/p>\n

S^(\u03b8)=(AH(\u03b8)A(\u03b8))(\u22121)AH(\u03b8)X=A\u2020(\u03b8)X\u015c(\u03b8) = (A^H(\u03b8)A(\u03b8))^(-1)A^H(\u03b8)X = A\u2020(\u03b8)X<\/span><\/span><\/span>S<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>A<\/span>(<\/span>\u03b8<\/span>)<\/span>)<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>)<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>X<\/span><\/span>=<\/span><\/span><\/span><\/span>A<\/span>\u2020<\/span>(<\/span>\u03b8<\/span>)<\/span>X<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5c06\u6b64\u4ee3\u5165\u539f\u59cb\u4f3c\u7136\u51fd\u6570，\u5f97\u5230\u6d53\u7f29\u4f3c\u7136\u51fd\u6570：<\/p>\n

Lc(\u03b8)=\u2212\u2223\u2223PA\u22a5(\u03b8)X\u2223\u2223F2L_c(\u03b8) = -||P_A\u22a5(\u03b8)X||\u00b2_F<\/span><\/span>L<\/span><\/span>c<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>\u2223\u2223<\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22a5<\/span>(<\/span>\u03b8<\/span>)<\/span>X<\/span>\u2223<\/span>\u2223<\/span><\/span>F<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2dPA\u22a5(\u03b8)=I\u2212A(\u03b8)(AH(\u03b8)A(\u03b8))(\u22121)AH(\u03b8)P_A\u22a5(\u03b8) = I – A(\u03b8)(A^H(\u03b8)A(\u03b8))^(-1)A^H(\u03b8)<\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22a5<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>I<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>A<\/span>(<\/span>\u03b8<\/span>)<\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>A<\/span>(<\/span>\u03b8<\/span>)<\/span>)<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>)<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span><\/span><\/span><\/span>\u662f\u6b63\u4ea4\u8865\u6295\u5f71\u77e9\u9635\u3002<\/p>\n

\u5173\u952e\u6570\u5b66\u539f\u7406\u7684\u6df1\u5165\u63a8\u5bfc<\/h3>\n

\u6b63\u4ea4\u6295\u5f71\u7b97\u5b50\u7684\u6570\u5b66\u6027\u8d28\u4e0e\u8bc1\u660e<\/h4>\n

\u6b63\u4ea4\u6295\u5f71\u77e9\u9635PA=A(AHA)(\u22121)AHP_A = A(A^H A)^(-1)A^H<\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>A<\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span>)<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>)<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5177\u6709\u4ee5\u4e0b\u5173\u952e\u6027\u8d28：<\/p>\n

\u5e42\u7b49\u6027\u8bc1\u660e：
\nPA2=A(AHA)\u22121AH\u22c5A(AHA)\u22121AH=A(AHA)\u22121(AHA)(AHA)\u22121AH=A(AHA)\u22121AH=PA
\nP_A\u00b2 = A(A^H A)\u207b\u00b9A^H \u00b7 A(A^H A)\u207b\u00b9A^H
\n = A(A^H A)\u207b\u00b9(A^H A)(A^H A)\u207b\u00b9A^H
\n = A(A^H A)\u207b\u00b9A^H = P_A
\n<\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>A<\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span>)<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span>A<\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span>)<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>A<\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span>)<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span>)<\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span>)<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>A<\/span>(<\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span>)<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6b63\u4ea4\u8865\u6295\u5f71\u7684\u5b8c\u5907\u6027： PA+PA\u22a5=I，\u4e14PA\u22a5PA=0P_A + P_A^\u22a5 = I，\u4e14P_A^\u22a5 P_A = 0<\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u22a5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>I<\/span>，\u4e14<\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u22a5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd9\u4e9b\u6027\u8d28\u4fdd\u8bc1\u4e86\u4fe1\u53f7\u5b50\u7a7a\u95f4\u548c\u566a\u58f0\u5b50\u7a7a\u95f4\u7684\u6b63\u4ea4\u5206\u89e3，\u662fDML\u7b97\u6cd5\u6709\u6548\u6027\u7684\u6570\u5b66\u57fa\u7840\u3002<\/p>\n

\u8c31\u5cf0\u641c\u7d22\u7684\u6570\u5b66\u4f18\u5316<\/h4>\n

DML\u7684\u4ee3\u4ef7\u51fd\u6570\u4f18\u5316\u7b49\u4ef7\u4e8e：<\/p>\n

J(\u03b8)=yHPA\u22a5(\u03b8)y=yHy\u2212yHPA(\u03b8)yJ(\u03b8) = y^H P_A^\u22a5(\u03b8) y = y^H y – y^H P_A(\u03b8) y<\/span><\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>y<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u22a5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>y<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>y<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u56e0\u6b64\u6700\u5c0f\u5316J(\u03b8)\u7b49\u4ef7\u4e8e\u6700\u5927\u5316yHPA(\u03b8)yy^H P_A(\u03b8) y<\/span><\/span>y<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>y<\/span><\/span><\/span><\/span><\/span>，\u8fd9\u8f6c\u5316\u4e3a\u8c31\u5cf0\u641c\u7d22\u95ee\u9898\u3002\u68af\u5ea6\u4fe1\u606f\u4e3a：<\/p>\n

\u2207\u03b8J(\u03b8)=\u22122ReDH(\u03b8)PA\u22a5(\u03b8)y\u2207_\u03b8 J(\u03b8) = -2 Re{D^H(\u03b8) P_A^\u22a5(\u03b8) y}<\/span><\/span>\u2207<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>2<\/span>R<\/span>e<\/span>D<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u22a5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2dD(\u03b8) = \u2202A(\u03b8)\/\u2202\u03b8\u662f\u5bfc\u5411\u77e9\u9635\u7684\u5bfc\u6570\u3002<\/p>\n

\u725b\u987f-\u62c9\u592b\u900a\u4f18\u5316\u7b97\u6cd5\u5e94\u7528<\/h4>\n

\u4e8c\u9636\u4f18\u5316\u65b9\u6cd5\u901a\u8fc7Hessian\u77e9\u9635\u52a0\u901f\u6536\u655b：<\/p>\n

\u03b8(n+1)=\u03b8(n)\u2212\u03b1nH(\u22121)(\u03b8(n))\u2207J(\u03b8(n))\u03b8^(n+1) = \u03b8^(n) – \u03b1_n H^(-1)(\u03b8^(n)) \u2207J(\u03b8^(n))<\/span><\/span>\u03b8<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03b1<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>)<\/span>(<\/span>\u03b8<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span>))<\/span>\u2207<\/span>J<\/span>(<\/span>\u03b8<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span>))<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Hessian\u77e9\u9635\u7684\u8ba1\u7b97\u6d89\u53ca\u4e8c\u9636\u5bfc\u6570：
\nHij=\u22022J(\u03b8)\/\u2202\u03b8i\u2202\u03b8jH_ij = \u2202\u00b2J(\u03b8)\/\u2202\u03b8_i\u2202\u03b8_j<\/span><\/span>H<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>J<\/span>(<\/span>\u03b8<\/span>)<\/span>\/<\/span>\u2202<\/span>\u03b8<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b8<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u51c6\u725b\u987f\u65b9\u6cd5（BFGS）\u901a\u8fc7\u8fed\u4ee3\u66f4\u65b0\u907f\u514d\u76f4\u63a5\u8ba1\u7b97Hessian：
\nBk+1=Bk+(ykykT)\/(ykTsk)\u2212(BkskskTBk)\/(skTBksk)B_{k+1} = B_k + (y_k y_k^T)\/(y_k^T s_k) – (B_k s_k s_k^T B_k)\/(s_k^T B_k s_k)<\/span><\/span>B<\/span><\/span>k<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>B<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>(<\/span>y<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>y<\/span><\/span>k<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\/<\/span>(<\/span>y<\/span><\/span>k<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>(<\/span>B<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\/<\/span>(<\/span>s<\/span><\/span>k<\/span><\/span><\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>s<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6027\u80fd\u5206\u6790\u7684\u7406\u8bba\u6781\u9650<\/h3>\n

\u514b\u62c9\u7f8e\u7f57\u754c\u7684\u7cbe\u786e\u63a8\u5bfc<\/h4>\n

DML\u4f30\u8ba1\u7684\u514b\u62c9\u7f8e\u7f57\u754c（CRB）\u63d0\u4f9b\u4e86\u7406\u8bba\u6027\u80fd\u4e0b\u754c：<\/p>\n

\u6761\u4ef6\u6a21\u578b（\u786e\u5b9a\u6027\u4fe1\u53f7）：
\nCRBc(\u03b8)=\u03c32\/2\u22c5Re(DHPA\u22a5D)\u22121
\nCRB_c(\u03b8) = \u03c3\u00b2\/2 \u00b7 Re{(D^H P_A^\u22a5 D)^-1}
\n<\/span><\/span>CR<\/span>B<\/span><\/span>c<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/2<\/span>\u22c5<\/span><\/span>R<\/span>e<\/span>(<\/span>D<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span><\/span>A<\/span><\/span><\/span><\/span>\u22a5<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>D<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5bf9\u4e8e\u5355\u76ee\u6807\u5747\u5300\u7ebf\u9635：
\nCRB(\u03b8)=(6\u03c32)\/(\u03c02d2sin2\u03b8\u22c5SNR\u22c5M(M2\u22121))
\nCRB(\u03b8) = (6\u03c3\u00b2)\/(\u03c0\u00b2d\u00b2sin\u00b2\u03b8 \u00b7 SNR \u00b7 M(M\u00b2-1))
\n<\/span><\/span>CRB<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>6<\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\/<\/span>(<\/span>\u03c0<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>s<\/span>i<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b8<\/span>\u22c5<\/span><\/span>SNR<\/span>\u22c5<\/span><\/span>M<\/span>(<\/span>M<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>))<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd9\u8868\u660e\u4f30\u8ba1\u7cbe\u5ea6\u4e0e\u4fe1\u566a\u6bd4\u3001\u9635\u5143\u6570\u91cf\u7684\u4e09\u6b21\u65b9\u6210\u6b63\u6bd4，\u4e0e\u76ee\u6807\u89d2\u5ea6\u7684\u6b63\u5f26\u5e73\u65b9\u6210\u53cd\u6bd4\u3002<\/p>\n

\u6e10\u8fd1\u6027\u80fd\u4e0e\u4e00\u81f4\u6027\u5206\u6790<\/h4>\n

DML\u4f30\u8ba1\u5668\u7684\u6e10\u8fd1\u6027\u8d28\u5305\u62ec：<\/p>\n

\u4e00\u81f4\u6027： \u03b8^DML\u2192p\u03b80asN\u2192\u221e\u03b8\u0302_DML \u2192^p \u03b8\u2080 as N \u2192 \u221e<\/span><\/span><\/span>\u03b8<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>M<\/span>L<\/span><\/span>\u2192<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span>s<\/span>N<\/span><\/span>\u2192<\/span><\/span><\/span><\/span>\u221e<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6e10\u8fd1\u6b63\u6001\u6027： \u221aN(\u03b8^DML\u2212\u03b80)\u2192dN(0,CRB\u22121)\u221aN(\u03b8\u0302_DML – \u03b8\u2080) \u2192^d N(0, CRB\u207b\u00b9)<\/span><\/span>\u221a<\/span>N<\/span>(<\/span><\/span>\u03b8<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>M<\/span>L<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2192<\/span><\/span>d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span>(<\/span>0<\/span>,<\/span><\/span>CR<\/span>B<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6709\u9650\u6837\u672c\u4e0b\u7684\u65b9\u5dee\u8868\u8fbe\u5f0f：
\nVar(\u03b8^DML)\u2248CRB(\u03b80)\u22c5(1+2K\/N+O(1\/N2))
\nVar(\u03b8\u0302_DML) \u2248 CRB(\u03b8\u2080) \u00b7 (1 + 2K\/N + O(1\/N\u00b2))
\n<\/span><\/span>Va<\/span>r<\/span>(<\/span><\/span>\u03b8<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>M<\/span>L<\/span>)<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>CRB<\/span>(<\/span>\u03b8<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>\u22c5<\/span><\/span>(<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span>K<\/span>\/<\/span>N<\/span><\/span>+<\/span><\/span><\/span><\/span>O<\/span>(<\/span>1\/<\/span>N<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>))<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5206\u8fa8\u7387\u7406\u8bba\u6781\u9650\u63a8\u5bfc<\/h4>\n

\u7edf\u8ba1\u5206\u8fa8\u7387\u6781\u9650（SRL）\u8d85\u8d8a\u4e86\u7ecf\u5178\u745e\u5229\u51c6\u5219：<\/p>\n

SRL=\u221a(12\/(\u03c02SNR))\u22c5(\u03bb\/D)\u22c5Q\u22121(Pfa\/2)
\nSRL = \u221a(12\/(\u03c0\u00b2SNR)) \u00b7 (\u03bb\/D) \u00b7 Q\u207b\u00b9(P_fa\/2)
\n<\/span><\/span>SR<\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>\u221a<\/span>(<\/span>12\/<\/span>(<\/span>\u03c0<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>SNR<\/span>))<\/span>\u22c5<\/span><\/span>(<\/span>\u03bb<\/span>\/<\/span>D<\/span>)<\/span>\u22c5<\/span><\/span>Q<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>P<\/span><\/span>f<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span>\/2<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5bf9\u4e8e\u7d27\u5bc6\u95f4\u9694\u7684\u76ee\u6807，\u6700\u5c0f\u65b9\u5dee\u754c\u4e3a：
\nCRB(\u03b81,\u03b82)\u2248(\u03c32\/2)\u22c5[1\/(M\u22c5SNR)]\u22c5[1+sinc2(\u03c0d\u22c5\u0394\u03b8\u22c5sin\u03b8\/\u03bb)]
\nCRB(\u03b8\u2081,\u03b8\u2082) \u2248 (\u03c3\u00b2\/2) \u00b7 [1\/(M\u00b7SNR)] \u00b7 [1 + sinc\u00b2(\u03c0d\u00b7\u0394\u03b8\u00b7sin \u03b8\/\u03bb)]
\n<\/span><\/span>CRB<\/span>(<\/span>\u03b8<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u03b8<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>(<\/span>\u03c3<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/2<\/span>)<\/span>\u22c5<\/span><\/span>[<\/span>1\/<\/span>(<\/span>M<\/span>\u22c5<\/span><\/span>SNR<\/span>)]<\/span>\u22c5<\/span><\/span>[<\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>s<\/span>in<\/span>c<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c0<\/span>d<\/span>\u22c5<\/span><\/span>\u0394<\/span>\u03b8<\/span>\u22c5<\/span><\/span>s<\/span>in<\/span>\u03b8<\/span>\/<\/span>\u03bb<\/span>)]<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

MIMO\u96f7\u8fbe\u914d\u7f6e\u4e0b\u7684\u7279\u6b8a\u63a8\u5bfc<\/h3>\n

\u865a\u62df\u9635\u5217\u7684\u6570\u5b66\u6784\u5efa<\/h4>\n

MIMO\u96f7\u8fbe\u901a\u8fc7\u53d1\u5c04\u548c\u63a5\u6536\u5bfc\u5411\u77e2\u91cf\u7684Kronecker\u79ef\u5f62\u6210\u865a\u62df\u9635\u5217：<\/p>\n

avirtual(\u03b8)=at(\u03b8)\u2297ar(\u03b8)a_virtual(\u03b8) = a_t(\u03b8) \u2297 a_r(\u03b8)<\/span><\/span>a<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>r<\/span>t<\/span>u<\/span>a<\/span>l<\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span>\u2297<\/span><\/span><\/span><\/span>a<\/span><\/span>r<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u865a\u62df\u9635\u5217\u63d0\u4f9bM\u00d7N\u4e2a\u865a\u62df\u901a\u9053，\u6709\u6548\u5b54\u5f84\u4e3a：
\nLvirtual=Ltx+LrxL_virtual = L_tx + L_rx<\/span><\/span>L<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>r<\/span>t<\/span>u<\/span>a<\/span>l<\/span><\/span>=<\/span><\/span><\/span><\/span>L<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>L<\/span><\/span>r<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u89d2\u5206\u8fa8\u7387\u6539\u5584\u4e3a：
\n\u0394\u03b8\u2248\u03bb\/(2\u03c0\u22c5Lvirtual)\u0394\u03b8 \u2248 \u03bb\/(2\u03c0\u00b7L_virtual)<\/span><\/span>\u0394<\/span>\u03b8<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>\u03bb<\/span>\/<\/span>(<\/span>2<\/span>\u03c0<\/span>\u22c5<\/span><\/span>L<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>r<\/span>t<\/span>u<\/span>a<\/span>l<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

MIMO\u7279\u5b9a\u7684DML\u4f18\u5316<\/h4>\n

MIMO\u914d\u7f6e\u4e0b\u7684DML\u4f3c\u7136\u51fd\u6570：
\n\u03b8DML=argmax\u03b8\u2223aH(\u03b8)Rx^\u22232
\n\u03b8_DML = arg max_\u03b8 |a^H(\u03b8)Rx\u0302|\u00b2
\n<\/span><\/span>\u03b8<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>M<\/span>L<\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span>r<\/span>g<\/span>ma<\/span>x<\/span><\/span>\u03b8<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>a<\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b8<\/span>)<\/span>R<\/span><\/span>x<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2dR\u4e3a\u91c7\u6837\u534f\u65b9\u5dee\u77e9\u9635\u3002\u5173\u952e\u4f18\u52bf\u5305\u62ec：<\/p>\n