{"id":6675,"date":"2022-03-16T15:26:05","date_gmt":"2022-03-16T06:26:05","guid":{"rendered":"https:\/\/www11.ieice.org\/cs\/ap\/wp\/?page_id=6675"},"modified":"2025-12-05T18:50:25","modified_gmt":"2025-12-05T09:50:25","slug":"rayleigh_fading","status":"publish","type":"page","link":"https:\/\/www.ieice.org\/cs\/ap\/misc\/denpan-db\/prop_model_db\/model_list\/rayleigh_fading\/","title":{"rendered":"\u30ec\u30a4\u30ea\u30fc\u30d5\u30a7\u30fc\u30b8\u30f3\u30b0"},"content":{"rendered":"
<\/div>

<\/path><\/svg><\/i> \"Loading\"<\/p>

<\/div>(since 2025\/12\/5)<\/p>\n\n\n\n

\u30e2\u30c7\u30eb\u306e\u6982\u8981<\/h3>\n\n\n\n

\u53d7\u4fe1\u7aef\u672b\u306b\u304a\u3044\u3066\u3001\u632f\u5e45\u304a\u3088\u3073\u4f4d\u76f8\u304c\u4e0d\u898f\u5247\u306b\u5909\u52d5\u3059\u308b\u8907\u6570\u306e\u5230\u6765\u6ce2\u306e\u5408\u6210\u53d7\u4fe1\u4fe1\u53f7\u306f\u5f0f(1)\u3067\u8868\u73fe\u53ef\u80fd\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\\begin{eqnarray}
e(t) &=& {\\rm Re} \\left[\\sum_{i=1}^N r_i (t) \\exp (j\\{2 \\pi f t + \\theta_i (t)\\}) \\right] \\\\
&=& \\sum_{i=1}^N r_i (t) \\cos \\theta_i (t) \\cos\u2061(2 \\pi f t) – \\sum_{i=1}^N r_i (t) \\sin \\theta_i (t) \\sin\u2061(2 \\pi f t) \\\\
&=& x(t) \\cos(2 \\pi f t) – y(t) \\sin(2 \\pi f t) \\\\
&=& r(t) \\cos{2 \\pi f t + \\theta(t)}
\\tag{1}
\\end{eqnarray}<\/p>\n\n\n\n

\u56f31\u306e\u3088\u3046\u306b\u57fa\u5730\u5c40\u3068\u53d7\u4fe1\u7aef\u672b\u306e\u9593\u306b\u898b\u901a\u3057\u304c\u5b58\u5728\u305b\u305a\u3001\u5468\u56f2\u306e\u5efa\u7269\u306a\u3069\u304b\u3089\u306e\u53cd\u5c04\u3084\u56de\u6298\u3092\u53d7\u3051\u305f\u591a\u6570\u306e\u5230\u6765\u6ce2\u304c\u53d7\u4fe1\u7aef\u672b\u306b\u5230\u6765\u3059\u308b\u74b0\u5883\u3092\u8003\u3048\u308b\u3002\u3053\u306e\u3068\u304d\u3001\\(\\theta_i(t)\\)\u304c\u4e92\u3044\u306b\u72ec\u7acb\u3067\\(0\\)\u304b\u3089\\(2\\pi\\)\u306b\u4e00\u69d8\u306b\u5206\u5e03\u3057\u3001\\(x\\)\u304a\u3088\u3073\\(y\\)\u306f\u72ec\u7acb\u3067\u6ce2\u6570\\(N\\)\u304c\u5341\u5206\u306b\u5927\u304d\u3044\u5834\u5408\u3001\\(x\\)\u304a\u3088\u3073\\(y\\)\u306f\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u306b\u3088\u308a\u6b63\u898f\u5206\u5e03\u3068\u306a\u308b\u3002\\(x\\)\u3068\\(y\\)\u306e\u5909\u52d5\u306f\u72ec\u7acb\u3067\u3042\u308b\u305f\u3081\u3001 \\(x\\)\u3068\\(y\\)\u306e\u7d50\u5408\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u305d\u308c\u305e\u308c\u306e\u767a\u751f\u78ba\u7387\u306e\u7a4d\u3068\u306a\u308b\u3002\\(x\\)\u3068\\(y\\)\u306e\u7d50\u5408\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3092\u30e4\u30b3\u30d3\u30a2\u30f3\u3092\u8003\u616e\u3057\u3066\u632f\u5e45\\(r\\)\u3068\u4f4d\u76f8\\(\\theta\\)\u306e\u95a2\u4fc2\u306b\u5909\u63db\u3059\u308b\u3068\u3001\\(r\\)\u3068\\(\\theta\\)\u306e\u7d50\u5408\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u5f0f(2)\u3068\u306a\u308b\u3002<\/p>\n\n\n\n

\\(
f_{r \\theta} (r,\\theta) = \\frac{r}{2 \\pi \\sigma^2} \\exp \\left( \\frac{-r^2}{2 \\sigma^2} \\right)
\\tag{2}
\\)<\/p>\n\n\n\n

\u5f0f(2)\u3092\\(\\theta\\)\u3067\u7a4d\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u53d7\u4fe1\u4fe1\u53f7\u306e\u632f\u5e45r\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u306f\u5f0f(3)\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306f\u5f0f(6)\u3068\u3057\u3066\u6c42\u307e\u308a\u3001\u3053\u306e\u5206\u5e03\u3092\u30ec\u30a4\u30ea\u30fc\u5206\u5e03\u3068\u3044\u3046\u3002\u305d\u3057\u3066\u3001\u3053\u306e\u3088\u3046\u306a\u632f\u5e45\u306e\u77ac\u6642\u5909\u52d5\u7279\u6027\u3092\u6301\u3064\u30d5\u30a7\u30fc\u30b8\u30f3\u30b0\u3092\u30ec\u30a4\u30ea\u30fc\u30d5\u30a7\u30fc\u30b8\u30f3\u30b0\u3068\u547c\u3076[1] \u3002<\/p>\n\n\n\n

\u30ec\u30a4\u30ea\u30fc\u30d5\u30a7\u30fc\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306f\u3001\u57fa\u5730\u5c40\u3068\u53d7\u4fe1\u7aef\u672b\u306e\u9593\u306b\u898b\u901a\u3057\u304c\u5b58\u5728\u3057\u306a\u3044\u5e02\u8857\u5730\u306e\u79fb\u52d5\u901a\u4fe1\u306e\u77ac\u6642\u5909\u52d5\u7279\u6027\u3092\u8868\u73fe\u3059\u308b\u96fb\u6ce2\u4f1d\u642c\u30e2\u30c7\u30eb\u3068\u3057\u3066\u4f7f\u308f\u308c\u308b\u3053\u3068\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u30ec\u30a4\u30ea\u30fc\u30d5\u30a7\u30fc\u30b8\u30f3\u30b0\u306e\u767a\u751f\u65b9\u6cd5\u306e\u4ee3\u8868\u7684\u306a\u3082\u306e\u3068\u3057\u3066\u3001\u56f32\u306b\u793a\u3055\u308c\u308b\u3088\u3046\u306b\u632f\u5e45\u304c\u7b49\u3057\u304f\u30e9\u30f3\u30c0\u30e0\u306a\u521d\u671f\u4f4d\u76f8\u3092\u6301\u3064\u8907\u6570\u306e\u6ce2\u304c\u6c34\u5e73\u9762\u5185\u5168\u65b9\u5411\u304b\u3089\u4e00\u69d8\u306b\u5230\u6765\u3059\u308bJakes\u30e2\u30c7\u30eb[2]\u304c\u6709\u540d\u3067\u3042\u308b\u3002\u56f33\u306f\u8907\u6570\u306e\u5468\u6ce2\u6570\u306b\u3088\u308b\u30ec\u30a4\u30ea\u30fc\u30d5\u30a7\u30fc\u30b8\u30f3\u30b0\u306e\u8a08\u7b97\u4f8b\u3067\u3042\u308b\u3002\u5468\u6ce2\u6570\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u5909\u52d5\u5468\u671f\u304c\u77ed\u304f\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u56f34\u306f\u56f33\u306b\u793a\u3057\u305f\u632f\u5e45\u306e\u7d2f\u7a4d\u78ba\u7387\u3068\u30ec\u30a4\u30ea\u30fc\u5206\u5e03\u306e\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3067\u3042\u308b\u3002\u5909\u52d5\u5468\u671f\u304c\u7570\u306a\u3063\u3066\u3082\u30ec\u30a4\u30ea\u30fc\u5206\u5e03\u306b\u5f93\u3046\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n

\n
\"\"
\u56f31 \u8907\u6570\u5230\u6765\u6ce2\u306e\u5408\u6210\u306b\u3088\u308b\u77ac\u6642\u5909\u52d5\u306e\u767a\u751f<\/figcaption><\/figure><\/div>\n\n
\n
\"\"
\u56f32 \u30ec\u30a4\u30ea\u30fc\u30d5\u30a7\u30fc\u30b8\u30f3\u30b0\u751f\u6210\u30e2\u30c7\u30eb\uff08Jakes\u30e2\u30c7\u30eb\uff09<\/figcaption><\/figure><\/div>\n\n\n

\u6570\u5f0f<\/h3>\n\n\n\n

\u632f\u5e45\u5206\u5e03\uff1a\\(f_r(r)\\)
\\(
f_r(r) = \\frac{r}{\\sigma^2} \\exp \\left(\\frac{-r^2}{2 \\sigma^2} \\right)
\\tag{3}
\\)<\/p>\n\n\n\n

\u4f4d\u76f8\u5206\u5e03\uff1a\\(f_\\theta(r)\\)
\\(
f_\\theta(r) = \\frac{1}{2 \\pi}
\\tag{4}
\\)<\/p>\n\n\n\n

\u5e73\u5747\u96fb\u529b\uff1a
\\(
\\bar{r^2}=2 \\sigma^2
\\tag{5}
\\)<\/p>\n\n\n\n

\u7d2f\u7a4d\u5206\u5e03\uff1a\\(F_r(r)\\)
\\(
F_r(r) = 1-\\exp \\left(\\frac{-r^2}{2\\sigma^2} \\right)
\\tag{6}
\\)<\/p>\n\n\n\n

\u30d1\u30e9\u30e1\u30fc\u30bf<\/h3>\n\n\n\n

\u3007\u30ec\u30d9\u30eb\u5206\u5e03\u30e2\u30c7\u30eb<\/p>\n\n\n\n

\u8a18\u53f7<\/td>\u30d1\u30e9\u30e1\u30fc\u30bf\u8aac\u660e[\u5358\u4f4d]<\/td><\/tr>
\\(r\\)<\/td>\u632f\u5e45 [V\/m]<\/td><\/tr>
\\(\\sigma\\)<\/td>\u6a19\u6e96\u504f\u5dee [V\/m]<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u8a08\u7b97\u4f8b<\/h3>\n\n\n
\n
\"\"
\u56f33 \u30ec\u30a4\u30ea\u30fc\u30d5\u30a7\u30fc\u30b8\u30f3\u30b0\u767a\u751f\u4f8b<\/figcaption><\/figure><\/div>\n\n
\n
\"\"
\u56f34 \u632f\u5e45\u306e\u7d2f\u7a4d\u5206\u5e03<\/figcaption><\/figure><\/div>\n\n\n

\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b<\/h3>\n\n\n\n

\u4ee5\u4e0b\u3001MATLAB\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b\u3092\u8a18\u8f09\u3059\u308b\u3002<\/p>\n\n\n\n

clear all\nfreq=1.0*10^9; % frequency [Hz]\nV=0.5; % velocity of UE [m\/s]\nc=2.99792458*10^8; % speed of light [m\/s]\nN=100; % number of arrival waves\nphai_i=rand(1,N)*2*pi; % arrival angle [rad]\nzeta_i=rand(1,N)*2*pi; % initial phase [rad]\nlambda=c\/freq; % wavelength [m]\ncount=1;\nfor t=0:0.01:100 % time [s]\n    R(count,1)=t;\n    R(count,2)=1\/sqrt(N)*sum(exp(1i*(2*pi*V*t*cos(phai_i)\/lambda+zeta_i))); % amplitude\n    R(count,3)=20*log10(abs(R(count,2))); % amplitude in dB\n    count=count+1;\nend<\/code><\/pre><\/div>\n\n\n\n
\u53c2\u7167<\/h2>\n\n\n\n[1] \u5510\u6ca2\u597d\u7537, \u6539\u8a02 \u30c7\u30a3\u30b8\u30bf\u30eb\u79fb\u52d5\u901a\u4fe1\u306e\u96fb\u6ce2\u4f1d\u642c\u57fa\u790e, \u30b3\u30ed\u30ca\u793e, 2016.<\/p>\n\n\n\n[2] W. C. Jakes (Ed.), Microwave Mobile Communications, IEEE Press, 1993.<\/p>\n","protected":false},"excerpt":{"rendered":"
\u30e2\u30c7\u30eb\u306e\u6982\u8981 \u53d7\u4fe1\u7aef\u672b\u306b\u304a\u3044\u3066\u3001\u632f\u5e45\u304a\u3088\u3073\u4f4d\u76f8\u304c\u4e0d\u898f\u5247\u306b\u5909\u52d5\u3059\u308b\u8907\u6570\u306e\u5230\u6765\u6ce2\u306e\u5408\u6210\u53d7\u4fe1\u4fe1\u53f7\u306f\u5f0f(1)\u3067\u8868\u73fe\u53ef\u80fd\u3067\u3042\u308b\u3002 \\begin{eqnarray}e(t) &=& {\\rm Re} \\left[\\s […]<\/p>\n","protected":false},"author":5,"featured_media":0,"parent":12073,"menu_order":27,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-6675","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages\/6675","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/comments?post=6675"}],"version-history":[{"count":24,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages\/6675\/revisions"}],"predecessor-version":[{"id":14872,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages\/6675\/revisions\/14872"}],"up":[{"embeddable":true,"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/pages\/12073"}],"wp:attachment":[{"href":"https:\/\/www.ieice.org\/cs\/ap\/wp-json\/wp\/v2\/media?parent=6675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}