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3<title>mixpp: Miscellaneous Communications Functions</title>
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61<h1>Miscellaneous Communications Functions<br>
62<small>
63[<a class="el" href="group__comm.html">Communications Module</a>]</small>
64</h1><table border="0" cellpadding="0" cellspacing="0">
65<tr><td></td></tr>
66<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
67<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g568738607726089989baf278058899fd"></a><!-- doxytag: member="misccommfunc::graycode" ref="g568738607726089989baf278058899fd" args="(int m)" -->
68<a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__misccommfunc.html#g568738607726089989baf278058899fd">itpp::graycode</a> (int m)</td></tr>
69
70<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Generate Gray code of blocklength m.<p>
71The codes are contained as binary codewords {0,1} in the rows of the returned matrix. See also the <code>gray()</code> function in <code>math/scalfunc.h</code>. <br></td></tr>
72<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g3815994ee069b1911dec1fc6afc350c8"></a><!-- doxytag: member="misccommfunc::hamming_distance" ref="g3815994ee069b1911dec1fc6afc350c8" args="(const bvec &amp;a, const bvec &amp;b)" -->
73int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__misccommfunc.html#g3815994ee069b1911dec1fc6afc350c8">itpp::hamming_distance</a> (const <a class="el" href="classitpp_1_1Vec.html#e10151f44bbabf17b670a9493d8088cf">bvec</a> &amp;a, const <a class="el" href="classitpp_1_1Vec.html#e10151f44bbabf17b670a9493d8088cf">bvec</a> &amp;b)</td></tr>
74
75<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Calculate the Hamming distance between <em>a</em> and <em>b</em>. <br></td></tr>
76<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g1661dfd39dc7327de562d3eca3d113aa"></a><!-- doxytag: member="misccommfunc::weight" ref="g1661dfd39dc7327de562d3eca3d113aa" args="(const bvec &amp;a)" -->
77int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__misccommfunc.html#g1661dfd39dc7327de562d3eca3d113aa">itpp::weight</a> (const <a class="el" href="classitpp_1_1Vec.html#e10151f44bbabf17b670a9493d8088cf">bvec</a> &amp;a)</td></tr>
78
79<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Calculate the Hamming weight of <em>a</em>. <br></td></tr>
80<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__misccommfunc.html#gc2ed3971292517906bb3fa47e9bfb061">itpp::waterfilling</a> (const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;alpha, double P)</td></tr>
81
82<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Compute the water-filling solution<p>
83This function computes the solution of the water-filling problem <p class="formulaDsp">
84<img class="formulaDsp" alt="\[ \max_{p_0,...,p_{n-1}} \sum_{i=0}^{n-1} \log\left(1+p_i\alpha_i\right) \]" src="form_237.png">
85<p>
86 subject to <p class="formulaDsp">
87<img class="formulaDsp" alt="\[ \sum_{i=0}^{n-1} p_i \le P \]" src="form_238.png">
88<p>
89.  <a href="#gc2ed3971292517906bb3fa47e9bfb061"></a><br></td></tr>
90</table>
91<hr><h2>Function Documentation</h2>
92<a class="anchor" name="gc2ed3971292517906bb3fa47e9bfb061"></a><!-- doxytag: member="itpp::waterfilling" ref="gc2ed3971292517906bb3fa47e9bfb061" args="(const vec &amp;alpha, double P)" -->
93<div class="memitem">
94<div class="memproto">
95      <table class="memname">
96        <tr>
97          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::waterfilling           </td>
98          <td>(</td>
99          <td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;&nbsp;</td>
100          <td class="paramname"> <em>alpha</em>, </td>
101        </tr>
102        <tr>
103          <td class="paramkey"></td>
104          <td></td>
105          <td class="paramtype">double&nbsp;</td>
106          <td class="paramname"> <em>P</em></td><td>&nbsp;</td>
107        </tr>
108        <tr>
109          <td></td>
110          <td>)</td>
111          <td></td><td></td><td></td>
112        </tr>
113      </table>
114</div>
115<div class="memdoc">
116
117<p>
118Compute the water-filling solution<p>
119This function computes the solution of the water-filling problem <p class="formulaDsp">
120<img class="formulaDsp" alt="\[ \max_{p_0,...,p_{n-1}} \sum_{i=0}^{n-1} \log\left(1+p_i\alpha_i\right) \]" src="form_237.png">
121<p>
122 subject to <p class="formulaDsp">
123<img class="formulaDsp" alt="\[ \sum_{i=0}^{n-1} p_i \le P \]" src="form_238.png">
124<p>
125.
126<p>
127<dl compact><dt><b>Parameters:</b></dt><dd>
128  <table border="0" cellspacing="2" cellpadding="0">
129    <tr><td valign="top"></td><td valign="top"><em>alpha</em>&nbsp;</td><td>vector of <img class="formulaInl" alt="$\alpha_0,...,\alpha_{n-1}$" src="form_239.png"> gains (must have strictly positive elements) </td></tr>
130    <tr><td valign="top"></td><td valign="top"><em>P</em>&nbsp;</td><td>power constraint </td></tr>
131  </table>
132</dl>
133<dl class="return" compact><dt><b>Returns:</b></dt><dd>vector of power allocations <img class="formulaInl" alt="$p_0,...,p_{n-1}$" src="form_240.png"></dd></dl>
134The computational complexity of the method is <img class="formulaInl" alt="$O(n^2)$" src="form_241.png"> at most
135<p>References <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, and <a class="el" href="matfunc_8h-source.html#l00051">itpp::length()</a>.</p>
136
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