\u672c\u6587\u9488\u5bf9\u5355\u8f7d\u6ce2\u591a\u5f84\u4fe1\u9053\u4e0b\u7684\u4e09\u79cd\u524d\u7f00\u6548\u679c\u8fdb\u884c\u63a8\u5bfc.<\/p>\n
\u8003\u8651\u51c6\u9759\u6001\u591a\u5f84\u4fe1\u9053\u7684\u5b58\u5728\uff0c\u5373\u4fe1\u9053\u5b58\u5728\u591a\u5f84\u65f6\u5ef6\uff0c\u4f46\u5176\u54cd\u5e94\u5728\u4e00\u6bb5\u65f6\u95f4\u5185\u4fdd\u6301\u4e0d\u53d8\uff0c\u5373${\\bf h}=[h_0,h_1, \\cdots,h_{L-1}]^T$. \u4e14\u4fe1\u53f7\u7531\u4e09\u90e8\u5206\u7ec4\u6210\uff0c\u5bfc\u9891\uff0c\u6570\u636e\u548c\u4fdd\u62a4\u95f4\u9694(\u53ef\u4ee5\u662fCP\uff0cZP). \u8003\u8651\u65f6\u57df\u4fe1\u53f7\u6210\u5757\u72b6\u5206\u5e03\uff0c\u603b\u5757\u6570\u4e3a$K$, \u6bcf\u5757\u5927\u5c0f\u4e3a$M$. \u4ece\u524d\u81f3\u540e\u4f9d\u6b21\u4e3a\u5bfc\u9891,\u6570\u636e\u548cCP, \u5176\u4e2dCP\u957f\u5ea6\u4e3a$N_P$, \u6570\u636e\u957f\u5ea6\u4e3a$N_D$\uff0c\u4fdd\u62a4\u95f4\u9694\u957f\u5ea6\u4e3a$N_G$. \u4ee4${\\bf x}[k]=[x_0[k],x_1[k],\\cdots, x_{M-1}[k]]^T$\u8868\u793a\u7b2c$k$\u5757\u7684\u6570\u636e\uff0c\u56e0\u6b64\u5b9e\u9645\u6570\u636e\u7ec4\u7ec7\u5f62\u5f0f\u4e3a${\\bf x}=[{\\bf x}[0]^T,{\\bf x}[1]^T,\\cdots, {\\bf x}[K-1]^T]^T$. \u56e0\u6b64\uff0c\u7ecf\u8fc7\u4fe1\u9053\u7684\u5927\u81f4\u8868\u8fbe\u5f0f\u4e3a\n$${y_n} = \\sum\\limits_{l = 0}^{L - 1} {{x_{n - l}}} h[l]$$<\/p>\n
\u6b64\u5904\u7684\u4e0b\u6807$n$\u4e3a$\\bf y$\u7684\u7edf\u4e00\u4e0b\u6807\uff0c\u5bf9\u5e94\u7684$x$\u7684\u4e0b\u6807\u4e3a\u5c06$\\bf x$\u8fdb\u884c\u7edf\u4e00\u6807\u5b9a\u540e\u7684\u7ed3\u679c. <\/p>\n
\u4ee5\u4e0b\u8ba8\u8bba\u8db3\u591f\u957f\u7684\u4e09\u79cd\u4fdd\u62a4\u524d\u7f00\u4e0b\uff0c\u5c06\u4e0a\u8ff0\u7b49\u5f0f\u6309\u5217\u8fdb\u884c\u5c55\u5f00\u7684\u7ed3\u679c.<\/p>\n
\u6b64\u65f6\u5c55\u5f00\u4e3a\n$$\\bf Y=\\bf H\\bf X$$<\/p>\n
\u5176\u4e2d${\\bf{X}} = [ {{\\bf{x}}[0]}, {{\\bf{x}}[1]},\\cdots, {{\\bf{x}}[K-1]} ]\\in {\\mathbb C}^{M\\times K}$; ${\\bf{Y}} = [ {{\\bf{y}}[0]}, {{\\bf{y}}[1]},\\cdots, {{\\bf{y}}[K-1]} ]\\in {\\mathbb C}^{M\\times K}$. \u800c\u5728\u4fe1\u53f7\u8db3\u591f\u957f\u7684\u60c5\u51b5\u4e0b\uff0c\u4fe1\u9053\u77e9\u9635$\\bf H$\u4e3a\n$${\\bf{H}} = \\left[ {\\begin{matrix}\n{{h_0}}&0& \\cdots &0\\\\\n{{h_1}}&{{h_0}}& \\cdots &0\\\\\n \\vdots & \\vdots & \\ddots &0\\\\\n0& \\cdots &{{h_1}}&{{h_0}}\n\\end{matrix}} \\right]\\in {\\mathbb C}^{M\\times M}$$<\/p>\n
\u89c2\u5bdf\u5230\uff0c\u7531\u4e8e\u96f6\u524d\u7f00\u7684\u5b58\u5728\uff0c$y_0[k]$\u4ec5\u4ec5\u4e0e$x_0[k]$\u6709\u5173, \u524d\u6570\u4e2a\u5143\u7d20\u540c\u7406. \u6b64\u65f6\uff0c\u4e0a\u4e00\u5b50\u5757\u7684ISI\u6d88\u5931. \u5e76\u4e14\u7531\u4e8e${\\bf X}_{M-N_G+1:M,:}$\u4e3a\u96f6\u5143\uff0c\u6539\u53d8\u77e9\u9635\u7684\u5bf9\u5e94\u4f4d\u7f6e\u7684\u5143\u7d20\u4e0d\u5f71\u54cd\u7ed3\u679c\uff0c\u56e0\u6b64\u53ef\u4ee5\u5c06\u4fe1\u9053\u77e9\u9635\u53d8\u4e3a\n$${\\bf{H_1}} = \\left[ {\\begin{matrix}\n{{h_0}}&0& \\cdots &h_1\\\\\n{{h_1}}&{{h_0}}& \\cdots &h_2\\\\\n \\vdots & \\vdots & \\ddots &0\\\\\n0& \\cdots &{{h_1}}&{{h_0}}\n\\end{matrix}} \\right]\\in {\\mathbb C}^{M\\times M}$$\n\u6b64\u65f6$\\bf H_1$\u4e3a\u5faa\u73af\u77e9\u9635\uff0c\u53ef\u8fdb\u884c\u5085\u91cc\u53f6\u5bf9\u89d2\u5316. \u5373${{\\bf{H}}_1} = {\\bf{F}}^H\\Lambda{{\\bf{F}}}$. \u540c\u65f6\u5b58\u5728$diag(\\Lambda)=FT(\\bf h)$, \u5176\u4e2d$FT$\u4e3a\u5085\u91cc\u53f6\u53d8\u6362. \u6b64\u65f6\uff0c\u5bf9\u4e8e\u5bf9\u89d2\u9635\u53ef\u4ee5\u4f7f\u7528\u8f83\u4e3a\u7b80\u4fbf\u7684\u65b9\u5f0f\u8fdb\u884c\u5747\u8861.<\/p>\n
\u6b64\u65f6\u9700\u8981\u5728\u6700\u524d\u65b9\u589e\u52a0\u76f8\u540c\u7684\u5e38\u6570\uff0c\u4e4b\u540e\u7684\u63a8\u5bfc\u8fc7\u7a0b\u4e0e\u96f6\u524d\u7f00\u57fa\u672c\u76f8\u540c\u3002<\/p>\n
\u6ce8\u610f\u6b64\u65f6\u672c\u5757\u5185\u90e8\u7684\u6570\u636e\u52a0\u7684\u662f\u540e\u9762\u4e00\u5757\u6570\u636e\u7684\u4e00\u90e8\u5206\uff0c\u4e3e\u4f8b\uff0c${\\bf x}[0]$\u540e\u4fa7\u5faa\u73af\u524d\u7f00\u4e3a${\\bf x}[1]$\u7684\u5012\u6570$N_G$\u4e2a\u6570\u636e\uff0c\u8fd9\u6837\u624d\u80fd\u4fdd\u8bc1\u540e\u6587\u7684\u5faa\u73af\u6027. \u540c\u65f6 \u6700\u5f00\u59cb\u6570\u636e\u7684\u6700\u524d\u65b9\u4e5f\u5e94\u589e\u52a0\u5faa\u73af\u524d\u7f00.<\/p>\n
\u5728\u53bb\u9664CP\u540e\uff0c\u6b64\u65f6\u6570\u636e\u4e5f\u53ef\u5c55\u5f00\u4e3a\n$$\\bf Y'=\\bf H_1\\bf X'$$\n\u4f46\u6b64\u65f6${\\bf{X'}} = [ {{\\bf{x'}}[0]}, {{\\bf{x'}}[1]},\\cdots, {{\\bf{x'}}[K-1]} ]\\in {\\mathbb C}^{(M-N_G)\\times K}$; ${\\bf{Y'}} = [ {{\\bf{y'}}[0]}, {{\\bf{y'}}[1]},\\cdots, {{\\bf{y'}}[K-1]} ]\\in {\\mathbb C}^{(M-N_G)\\times K}$, \u5176\u4e2d${{\\bf{x'}}[k]}$\u548c${{\\bf{y'}}[k]}$\u4e3a\u53bb\u9664CP\u7684\u6570\u636e\u3002\n\u800c\u6b64\u65f6\n$${\\bf{H_1}} = \\left[ {\\begin{matrix}\n{{h_0}}&0& \\cdots &h_1\\\\\n{{h_1}}&{{h_0}}& \\cdots &h_2\\\\\n \\vdots & \\vdots & \\ddots &0\\\\\n0& \\cdots &{{h_1}}&{{h_0}}\n\\end{matrix}} \\right]\\in {\\mathbb C}^{{(M-N_G)}\\times {(M-N_G)}}$$\n\u6ce8\u610f\u5230\u6b64\u65f6\u77e9\u9635\u7ef4\u5ea6\u51cf\u5c0f\uff0c\u540c\u65f6\u77e9\u9635\u76f4\u63a5\u662f\u6807\u51c6\u7684\u5faa\u73af\u77e9\u9635\uff0c\u53ef\u4ee5\u76f4\u63a5\u8fdb\u884c\u5085\u91cc\u53f6\u5bf9\u89d2\u5316.<\/p>\n
\u4e09\u79cd\u524d\u7f00\u4e0b\uff0c\u5747\u53ef\u4ee5\u8fdb\u884c\u5355\u8f7d\u6ce2\u9891\u57df\u5747\u8861\u3002\u4f46\u4e09\u79cd\u524d\u7f00\u7684\u52a0\u7684\u65b9\u5f0f\u4e0d\u540c\uff0c\u4e14\u4e0d\u540c\u7684\u524d\u7f00\u5177\u6709\u4e0d\u540c\u7684\u7279\u6027(PAPR\u7b49)\uff0c\u9700\u8981\u914c\u60c5\u9009\u62e9.<\/p>\n","protected":false},"excerpt":{"rendered":"
\u672c\u6587\u9488\u5bf9\u5355\u8f7d\u6ce2\u591a\u5f84\u4fe1\u9053\u4e0b\u7684\u4e09\u79cd\u524d\u7f00\u6548\u679c\u8fdb\u884c\u63a8\u5bfc. \u7cfb\u7edf\u6a21\u578b \u8003\u8651\u51c6\u9759\u6001\u591a\u5f84\u4fe1\u9053\u7684\u5b58\u5728\uff0c\u5373\u4fe1\u9053\u5b58\u5728\u591a\u5f84\u65f6\u5ef6\uff0c\u4f46\u5176\u54cd\u5e94\u5728\u4e00\u6bb5\u65f6\u95f4\u5185\u4fdd\u6301\u4e0d\u53d8\uff0c\u5373${\\bf h}=[h_0,h_1, \\cdots,h_{L-1}]^T$. \u4e14\u4fe1\u53f7\u7531\u4e09\u90e8\u5206\u7ec4\u6210\uff0c\u5bfc\u9891\uff0c\u6570\u636e\u548c\u4fdd\u62a4\u95f4\u9694(\u53ef\u4ee5\u662fCP\uff0cZP). \u8003\u8651\u65f6\u57df\u4fe1\u53f7\u6210\u5757\u72b6\u5206\u5e03\uff0c\u603b\u5757\u6570\u4e3a$K$, \u6bcf\u5757\u5927\u5c0f\u4e3a$M$. \u4ece\u524d\u81f3\u540e\u4f9d\u6b21\u4e3a\u5bfc\u9891,\u6570\u636e\u548cCP, \u5176\u4e2dCP\u957f\u5ea6\u4e3a$N_P$, \u6570\u636e\u957f\u5ea6\u4e3a$N_D$\uff0c\u4fdd\u62a4\u95f4\u9694\u957f\u5ea6\u4e3a$N_G$. \u4ee4${\\bf x}[k]=[x_0[k],x_1[k],\\cdots, x_{M-1}[k]]^T$\u8868\u793a\u7b2c$k$\u5757\u7684\u6570\u636e\uff0c\u56e0\u6b64\u5b9e\u9645\u6570\u636e\u7ec4\u7ec7\u5f62\u5f0f\u4e3a$…… <\/p>\n \u7ee7\u7eed\u9605\u8bfb»»»<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[11,9,10],"_links":{"self":[{"href":"https:\/\/etc.lmdewz.xyz\/index.php?rest_route=\/wp\/v2\/posts\/101"}],"collection":[{"href":"https:\/\/etc.lmdewz.xyz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/etc.lmdewz.xyz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/etc.lmdewz.xyz\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/etc.lmdewz.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=101"}],"version-history":[{"count":0,"href":"https:\/\/etc.lmdewz.xyz\/index.php?rest_route=\/wp\/v2\/posts\/101\/revisions"}],"wp:attachment":[{"href":"https:\/\/etc.lmdewz.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/etc.lmdewz.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/etc.lmdewz.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}