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67  <div class="navpath"><b>itpp</b>::<a class="el" href="classitpp_1_1ND__UPAM.html">ND_UPAM</a>
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70<div class="contents">
71<h1>itpp::ND_UPAM Class Reference<br>
72<small>
73[<a class="el" href="group__modulators.html">Digital Modulation</a>]</small>
74</h1><!-- doxytag: class="itpp::ND_UPAM" --><!-- doxytag: inherits="itpp::Modulator_NRD" -->Real-valued MIMO channel with uniform <a class="el" href="classitpp_1_1PAM.html" title="M-ary PAM modulator with real symbols.">PAM</a> along each dimension. 
75<a href="#_details">More...</a>
76<p>
77<code>#include &lt;<a class="el" href="modulator__nd_8h-source.html">modulator_nd.h</a>&gt;</code>
78<p>
79
80<p>
81<a href="classitpp_1_1ND__UPAM-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
82<tr><td></td></tr>
83<tr><td colspan="2"><br><h2>Public Types</h2></td></tr>
84<tr><td class="memItemLeft" nowrap align="right" valign="top">enum &nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#6e3b4c745f904cdb34301aeb4cc03035">Soft_Demod_Method</a> { <a class="el" href="classitpp_1_1Modulator__ND.html#6e3b4c745f904cdb34301aeb4cc03035c743f79c2dbf90c34fd03075b7648058">FULL_ENUM_LOGMAP</a>,
85<a class="el" href="classitpp_1_1Modulator__ND.html#6e3b4c745f904cdb34301aeb4cc03035d5798fd18f93f399475392b8aee09cba">ZF_LOGMAP</a>
86 }</td></tr>
87
88<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Soft demodulation method.  <a href="classitpp_1_1Modulator__ND.html#6e3b4c745f904cdb34301aeb4cc03035">More...</a><br></td></tr>
89<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
90<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5b440db5066286247a0177272c1176be"></a><!-- doxytag: member="itpp::ND_UPAM::ND_UPAM" ref="5b440db5066286247a0177272c1176be" args="(int nt=1, int Mary=2)" -->
91&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1ND__UPAM.html#5b440db5066286247a0177272c1176be">ND_UPAM</a> (int <a class="el" href="classitpp_1_1Modulator__ND.html#18f0f81646514aa7210415f83fc62c1b">nt</a>=1, int Mary=2)</td></tr>
92
93<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructor. <br></td></tr>
94<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b26eff798737d05ee27b45b904385cf8"></a><!-- doxytag: member="itpp::ND_UPAM::~ND_UPAM" ref="b26eff798737d05ee27b45b904385cf8" args="()" -->
95&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1ND__UPAM.html#b26eff798737d05ee27b45b904385cf8">~ND_UPAM</a> ()</td></tr>
96
97<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Destructor. <br></td></tr>
98<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="83dd565c60cd49a332eb780a7a9b21a3"></a><!-- doxytag: member="itpp::ND_UPAM::set_M" ref="83dd565c60cd49a332eb780a7a9b21a3" args="(int nt=1, int Mary=2)" -->
99void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1ND__UPAM.html#83dd565c60cd49a332eb780a7a9b21a3">set_M</a> (int <a class="el" href="classitpp_1_1Modulator__ND.html#18f0f81646514aa7210415f83fc62c1b">nt</a>=1, int Mary=2)</td></tr>
100
101<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set component modulators to M-PAM with Gray mapping. <br></td></tr>
102<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="82146d878368029d8499e909cdc95d10"></a><!-- doxytag: member="itpp::ND_UPAM::set_M" ref="82146d878368029d8499e909cdc95d10" args="(int nt=1, ivec Mary=&quot;2&quot;)" -->
103void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1ND__UPAM.html#82146d878368029d8499e909cdc95d10">set_M</a> (int <a class="el" href="classitpp_1_1Modulator__ND.html#18f0f81646514aa7210415f83fc62c1b">nt</a>=1, ivec Mary=&quot;2&quot;)</td></tr>
104
105<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set component modulators to M-PAM with Gray mapping, different M per component. <br></td></tr>
106<tr><td class="memItemLeft" nowrap align="right" valign="top">int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1ND__UPAM.html#7f53ad7f4de6b0e7f6260905ed522cd2">sphere_decoding</a> (const vec &amp;y, const mat &amp;H, double rmin, double rmax, double stepup, QLLRvec &amp;detected_bits)</td></tr>
107
108<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Sphere decoding.  <a href="#7f53ad7f4de6b0e7f6260905ed522cd2"></a><br></td></tr>
109<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="85019d35a647571786af4eedce111544"></a><!-- doxytag: member="itpp::ND_UPAM::get_symbols" ref="85019d35a647571786af4eedce111544" args="() const " -->
110<a class="el" href="classitpp_1_1Array.html">Array</a>&lt; vec &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#85019d35a647571786af4eedce111544">get_symbols</a> () const </td></tr>
111
112<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Get modulation symbols per dimension. <br></td></tr>
113<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f8993b9fc18d5a8ca4564ea3b928f22c"></a><!-- doxytag: member="itpp::ND_UPAM::modulate_bits" ref="f8993b9fc18d5a8ca4564ea3b928f22c" args="(const bvec &amp;bits, vec &amp;symbols) const " -->
114void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#f8993b9fc18d5a8ca4564ea3b928f22c">modulate_bits</a> (const bvec &amp;bits, vec &amp;<a class="el" href="classitpp_1_1Modulator__NRD.html#a5a276d6745c7a38dd4ae6b5eb70147e">symbols</a>) const </td></tr>
115
116<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Modulate <code>bits</code> into <code>symbols</code>. <br></td></tr>
117<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e5f4bd15dcb3615845c97bd0c64ffe0b"></a><!-- doxytag: member="itpp::ND_UPAM::modulate_bits" ref="e5f4bd15dcb3615845c97bd0c64ffe0b" args="(const bvec &amp;bits) const " -->
118vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#e5f4bd15dcb3615845c97bd0c64ffe0b">modulate_bits</a> (const bvec &amp;bits) const </td></tr>
119
120<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Modulate <code>bits</code> vector. Symbols are returned. <br></td></tr>
121<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#42d28853cead832c7e7644366023601b">demodulate_soft_bits</a> (const vec &amp;y, const mat &amp;H, double sigma2, const QLLRvec &amp;LLR_apriori, QLLRvec &amp;LLR_aposteriori, <a class="el" href="classitpp_1_1Modulator__ND.html#6e3b4c745f904cdb34301aeb4cc03035">Soft_Demod_Method</a> method)</td></tr>
122
123<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Soft demodulation wrapper function for various methods.  <a href="#42d28853cead832c7e7644366023601b"></a><br></td></tr>
124<tr><td class="memItemLeft" nowrap align="right" valign="top">QLLRvec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#e1bdcbd5307ac1ab0e368f33fee5f149">demodulate_soft_bits</a> (const vec &amp;y, const mat &amp;H, double sigma2, const QLLRvec &amp;LLR_apriori, <a class="el" href="classitpp_1_1Modulator__ND.html#6e3b4c745f904cdb34301aeb4cc03035">Soft_Demod_Method</a> method)</td></tr>
125
126<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Soft demodulation wrapper function for various methods.  <a href="#e1bdcbd5307ac1ab0e368f33fee5f149"></a><br></td></tr>
127<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#5de17b14ee11626e8323b50cf29fd047">demodulate_soft_bits</a> (const vec &amp;y, const mat &amp;H, double sigma2, const QLLRvec &amp;LLR_apriori, QLLRvec &amp;LLR_aposteriori)</td></tr>
128
129<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Soft MAP demodulation for multidimensional channel, by "brute-force" enumeration of all constellation points.  <a href="#5de17b14ee11626e8323b50cf29fd047"></a><br></td></tr>
130<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#249e4cf64c7106d559e1589f200ccbc7">demodulate_soft_bits</a> (const vec &amp;y, const vec &amp;h, double sigma2, const QLLRvec &amp;LLR_apriori, QLLRvec &amp;LLR_aposteriori)</td></tr>
131
132<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Soft MAP demodulation for parallelchannels without crosstalk.  <a href="#249e4cf64c7106d559e1589f200ccbc7"></a><br></td></tr>
133<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e5a2e50b1bf055d6db9f56bd4fe83105"></a><!-- doxytag: member="itpp::ND_UPAM::set_llrcalc" ref="e5a2e50b1bf055d6db9f56bd4fe83105" args="(LLR_calc_unit llrcalc_in)" -->
134void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#e5a2e50b1bf055d6db9f56bd4fe83105">set_llrcalc</a> (<a class="el" href="classitpp_1_1LLR__calc__unit.html">LLR_calc_unit</a> llrcalc_in)</td></tr>
135
136<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set LLR calculation unit. <br></td></tr>
137<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b68aa9155f305d9fb4e8d3cab45d5c9d"></a><!-- doxytag: member="itpp::ND_UPAM::get_llrcalc" ref="b68aa9155f305d9fb4e8d3cab45d5c9d" args="() const " -->
138<a class="el" href="classitpp_1_1LLR__calc__unit.html">LLR_calc_unit</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#b68aa9155f305d9fb4e8d3cab45d5c9d">get_llrcalc</a> () const </td></tr>
139
140<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Get LLR calculation unit. <br></td></tr>
141<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="64691da50e1a9f604c41bdda141d477a"></a><!-- doxytag: member="itpp::ND_UPAM::get_dim" ref="64691da50e1a9f604c41bdda141d477a" args="() const " -->
142int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#64691da50e1a9f604c41bdda141d477a">get_dim</a> () const </td></tr>
143
144<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Get number of dimensions. <br></td></tr>
145<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="aa89b07529c5c5bbe75d4c6b45f9264c"></a><!-- doxytag: member="itpp::ND_UPAM::get_k" ref="aa89b07529c5c5bbe75d4c6b45f9264c" args="() const " -->
146ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#aa89b07529c5c5bbe75d4c6b45f9264c">get_k</a> () const </td></tr>
147
148<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Get number of bits per modulation symbol per dimension. <br></td></tr>
149<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a9f88563e5de7dd446f0c61c86976c76"></a><!-- doxytag: member="itpp::ND_UPAM::get_M" ref="a9f88563e5de7dd446f0c61c86976c76" args="() const " -->
150ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#a9f88563e5de7dd446f0c61c86976c76">get_M</a> () const </td></tr>
151
152<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Get number of modulation symbols per dimension. <br></td></tr>
153<tr><td colspan="2"><br><h2>Protected Member Functions</h2></td></tr>
154<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#37363ba319fa9230cce3b969dbcf6f1a">update_norm</a> (double &amp;norm, int <a class="el" href="classitpp_1_1Modulator__ND.html#5545e8651244ffca103252926fb18a1c">k</a>, int sold, int snew, const vec &amp;ytH, const mat &amp;HtH, const ivec &amp;s)</td></tr>
155
156<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Update residual norm (for internal use).  <a href="#37363ba319fa9230cce3b969dbcf6f1a"></a><br></td></tr>
157<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a7eaacc702e0564b3388b9fb9413d301"></a><!-- doxytag: member="itpp::ND_UPAM::probabilities" ref="a7eaacc702e0564b3388b9fb9413d301" args="(QLLR l)" -->
158QLLRvec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#a7eaacc702e0564b3388b9fb9413d301">probabilities</a> (QLLR l)</td></tr>
159
160<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Convert LLR to log-probabilities. <br></td></tr>
161<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6278bfead2080abfd50998067336eb12"></a><!-- doxytag: member="itpp::ND_UPAM::probabilities" ref="6278bfead2080abfd50998067336eb12" args="(const QLLRvec &amp;l)" -->
162<a class="el" href="classitpp_1_1Array.html">Array</a>&lt; QLLRvec &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#6278bfead2080abfd50998067336eb12">probabilities</a> (const QLLRvec &amp;l)</td></tr>
163
164<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Convert LLR to log-probabilities, vector version. <br></td></tr>
165<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#48975e0d26dac075e1f448bdca15ca87">update_LLR</a> (const <a class="el" href="classitpp_1_1Array.html">Array</a>&lt; QLLRvec &gt; &amp;logP_apriori, const ivec &amp;s, QLLR scaled_norm, QLLRvec &amp;num, QLLRvec &amp;denom)</td></tr>
166
167<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Update LLR (for internal use).  <a href="#48975e0d26dac075e1f448bdca15ca87"></a><br></td></tr>
168<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#6bb417318b8105a78db7ad2c618283ce">update_LLR</a> (const <a class="el" href="classitpp_1_1Array.html">Array</a>&lt; QLLRvec &gt; &amp;logP_apriori, int s, QLLR scaled_norm, int j, QLLRvec &amp;num, QLLRvec &amp;denom)</td></tr>
169
170<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Update LLR, for scalar channel (for internal use).  <a href="#6bb417318b8105a78db7ad2c618283ce"></a><br></td></tr>
171<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
172<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a5a276d6745c7a38dd4ae6b5eb70147e"></a><!-- doxytag: member="itpp::ND_UPAM::symbols" ref="a5a276d6745c7a38dd4ae6b5eb70147e" args="" -->
173<a class="el" href="classitpp_1_1Array.html">Array</a>&lt; vec &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#a5a276d6745c7a38dd4ae6b5eb70147e">symbols</a></td></tr>
174
175<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Vectors of modulation symbols (along each dimension). <br></td></tr>
176<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="18f0f81646514aa7210415f83fc62c1b"></a><!-- doxytag: member="itpp::ND_UPAM::nt" ref="18f0f81646514aa7210415f83fc62c1b" args="" -->
177int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#18f0f81646514aa7210415f83fc62c1b">nt</a></td></tr>
178
179<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Number of dimensions. <br></td></tr>
180<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8690246ff99fd198a5e7d179954ac5a9"></a><!-- doxytag: member="itpp::ND_UPAM::llrcalc" ref="8690246ff99fd198a5e7d179954ac5a9" args="" -->
181<a class="el" href="classitpp_1_1LLR__calc__unit.html">LLR_calc_unit</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#8690246ff99fd198a5e7d179954ac5a9">llrcalc</a></td></tr>
182
183<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">LLR calculation unit. <br></td></tr>
184<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5545e8651244ffca103252926fb18a1c"></a><!-- doxytag: member="itpp::ND_UPAM::k" ref="5545e8651244ffca103252926fb18a1c" args="" -->
185ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#5545e8651244ffca103252926fb18a1c">k</a></td></tr>
186
187<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Number of bits per modulation symbol. <br></td></tr>
188<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="45916df32ce60b4c286367501482b441"></a><!-- doxytag: member="itpp::ND_UPAM::M" ref="45916df32ce60b4c286367501482b441" args="" -->
189ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#45916df32ce60b4c286367501482b441">M</a></td></tr>
190
191<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Number of modulation symbols along each dimension. <br></td></tr>
192<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cf19a4c13454739dfa68d0b9f6a85211"></a><!-- doxytag: member="itpp::ND_UPAM::bitmap" ref="cf19a4c13454739dfa68d0b9f6a85211" args="" -->
193<a class="el" href="classitpp_1_1Array.html">Array</a>&lt; <a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a> &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#cf19a4c13454739dfa68d0b9f6a85211">bitmap</a></td></tr>
194
195<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Bit mapping table (one table per dimension). <br></td></tr>
196<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="123a047e221467e2f63b4e353963b1a7"></a><!-- doxytag: member="itpp::ND_UPAM::bits2symbols" ref="123a047e221467e2f63b4e353963b1a7" args="" -->
197<a class="el" href="classitpp_1_1Array.html">Array</a>&lt; ivec &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__ND.html#123a047e221467e2f63b4e353963b1a7">bits2symbols</a></td></tr>
198
199<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Bit pattern in decimal form ordered and the corresponding symbols (one pattern per dimension). <br></td></tr>
200<tr><td colspan="2"><br><h2>Friends</h2></td></tr>
201<tr><td class="memItemLeft" nowrap align="right" valign="top">std::ostream &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator__NRD.html#f82a88fab3e6f7a1e6c0a4a7e17fb678">operator&lt;&lt;</a> (std::ostream &amp;os, const <a class="el" href="classitpp_1_1Modulator__NRD.html">Modulator_NRD</a> &amp;m)</td></tr>
202
203<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Output some properties of the MIMO modulator (mainly to aid debugging).  <a href="#f82a88fab3e6f7a1e6c0a4a7e17fb678"></a><br></td></tr>
204</table>
205<hr><a name="_details"></a><h2>Detailed Description</h2>
206Real-valued MIMO channel with uniform <a class="el" href="classitpp_1_1PAM.html" title="M-ary PAM modulator with real symbols.">PAM</a> along each dimension.
207<p>
208<b>Example: (4 x 3 matrix channel with 4-PAM)</b> <div class="fragment"><pre class="fragment"> <a class="code" href="classitpp_1_1ND__UPAM.html#5b440db5066286247a0177272c1176be" title="Constructor.">ND_UPAM</a> chan; <span class="comment">// multidimensional channel with uniform PAM</span>
209 chan.set_M(3, 4); <span class="comment">// 3-dimensional matrix channel, 4-PAM per dimension</span>
210 cout &lt;&lt; chan &lt;&lt; endl;
211 bvec b = <a class="code" href="group__randgen.html#g5aa06887cf1fd3301b040987924068f0" title="Generates a random bit (equally likely 0s and 1s).">randb</a>(3*2); <span class="comment">// 3*2 bits in total</span>
212 vec x = chan.modulate_bits(b);
213 mat H = <a class="code" href="group__randgen.html#g9ecf5af23567f51abc9af737fdbd872a" title="Generates a random Gaussian (0,1) variable.">randn</a>(4,3); <span class="comment">// 4 x 3 real matrix channel</span>
214 <span class="keywordtype">double</span> sigma2 = 0.01; <span class="comment">// noise variance per real dimension</span>
215 vec y = H*x + <a class="code" href="group__miscfunc.html#gf559d29ca56ad3396a4284964b01a9b0" title="Square root of the elements.">sqrt</a>(sigma2)*<a class="code" href="group__randgen.html#g9ecf5af23567f51abc9af737fdbd872a" title="Generates a random Gaussian (0,1) variable.">randn</a>(4); <span class="comment">// transmit vector x</span>
216 QLLRvec llr; <span class="comment">// log-likelihood ratios</span>
217 QLLRvec llr_ap = <a class="code" href="group__specmat.html#g9c37bc66992f8d3d29d8c3aef6a5a514" title="A Int vector of zeros.">zeros_i</a>(3*2);  <span class="comment">// a priori equiprobable bits</span>
218 chan.demodulate_soft_bits(y, H, sigma2, llr_ap, llr);
219 cout &lt;&lt; <span class="stringliteral">"True bits:"</span> &lt;&lt; b &lt;&lt; endl;
220 cout &lt;&lt; <span class="stringliteral">"LLRs:"</span> &lt;&lt; chan.get_llrcalc().to_double(llr) &lt;&lt; endl;
221</pre></div><p>
222<b>Example: (scalar channel with 8-PAM)</b> <div class="fragment"><pre class="fragment"> <a class="code" href="classitpp_1_1ND__UPAM.html#5b440db5066286247a0177272c1176be" title="Constructor.">ND_UPAM</a> chan;
223 chan.set_M(1, 8); <span class="comment">// scalar channel, 8-PAM (3 bits per symbol)</span>
224 cout &lt;&lt; chan &lt;&lt; endl;
225 bvec b = <a class="code" href="group__randgen.html#g5aa06887cf1fd3301b040987924068f0" title="Generates a random bit (equally likely 0s and 1s).">randb</a>(3);
226 vec x = chan.modulate_bits(b);
227 mat H = <span class="stringliteral">"1.0"</span>;      <span class="comment">// scalar channel</span>
228 <span class="keywordtype">double</span> sigma2 = 0.01;
229 vec y= H*x + <a class="code" href="group__miscfunc.html#gf559d29ca56ad3396a4284964b01a9b0" title="Square root of the elements.">sqrt</a>(sigma2)*<a class="code" href="group__randgen.html#g9ecf5af23567f51abc9af737fdbd872a" title="Generates a random Gaussian (0,1) variable.">randn</a>(); <span class="comment">// transmit vector x</span>
230 QLLRvec llr;
231 QLLRvec llr_ap = <a class="code" href="group__specmat.html#g9c37bc66992f8d3d29d8c3aef6a5a514" title="A Int vector of zeros.">zeros_i</a>(3);
232 chan.demodulate_soft_bits(y, H, sigma2, llr_ap, llr);
233 cout &lt;&lt; <span class="stringliteral">"True bits:"</span> &lt;&lt; b &lt;&lt; endl;
234 cout &lt;&lt; <span class="stringliteral">"LLRs:"</span> &lt;&lt; chan.get_llrcalc().to_double(llr) &lt;&lt; endl;
235</pre></div> <hr><h2>Member Enumeration Documentation</h2>
236<a class="anchor" name="6e3b4c745f904cdb34301aeb4cc03035"></a><!-- doxytag: member="itpp::ND_UPAM::Soft_Demod_Method" ref="6e3b4c745f904cdb34301aeb4cc03035" args="" -->
237<div class="memitem">
238<div class="memproto">
239      <table class="memname">
240        <tr>
241          <td class="memname">enum <a class="el" href="classitpp_1_1Modulator__ND.html#6e3b4c745f904cdb34301aeb4cc03035">itpp::Modulator_ND::Soft_Demod_Method</a><code> [inherited]</code>          </td>
242        </tr>
243      </table>
244</div>
245<div class="memdoc">
246
247<p>
248Soft demodulation method.
249<p>
250<dl compact><dt><b>Enumerator: </b></dt><dd>
251<table border="0" cellspacing="2" cellpadding="0">
252<tr><td valign="top"><em><a class="anchor" name="6e3b4c745f904cdb34301aeb4cc03035c743f79c2dbf90c34fd03075b7648058"></a><!-- doxytag: member="FULL_ENUM_LOGMAP" ref="6e3b4c745f904cdb34301aeb4cc03035c743f79c2dbf90c34fd03075b7648058" args="" -->FULL_ENUM_LOGMAP</em>&nbsp;</td><td>
253Log-MAP demodulation by "brute-force" enumeration of all points. </td></tr>
254<tr><td valign="top"><em><a class="anchor" name="6e3b4c745f904cdb34301aeb4cc03035d5798fd18f93f399475392b8aee09cba"></a><!-- doxytag: member="ZF_LOGMAP" ref="6e3b4c745f904cdb34301aeb4cc03035d5798fd18f93f399475392b8aee09cba" args="" -->ZF_LOGMAP</em>&nbsp;</td><td>
255Zero-Forcing Log-MAP approximated demodulation. </td></tr>
256</table>
257</dl>
258
259</div>
260</div><p>
261<hr><h2>Member Function Documentation</h2>
262<a class="anchor" name="249e4cf64c7106d559e1589f200ccbc7"></a><!-- doxytag: member="itpp::ND_UPAM::demodulate_soft_bits" ref="249e4cf64c7106d559e1589f200ccbc7" args="(const vec &amp;y, const vec &amp;h, double sigma2, const QLLRvec &amp;LLR_apriori, QLLRvec &amp;LLR_aposteriori)" -->
263<div class="memitem">
264<div class="memproto">
265      <table class="memname">
266        <tr>
267          <td class="memname">void itpp::Modulator_NRD::demodulate_soft_bits           </td>
268          <td>(</td>
269          <td class="paramtype">const vec &amp;&nbsp;</td>
270          <td class="paramname"> <em>y</em>, </td>
271        </tr>
272        <tr>
273          <td class="paramkey"></td>
274          <td></td>
275          <td class="paramtype">const vec &amp;&nbsp;</td>
276          <td class="paramname"> <em>h</em>, </td>
277        </tr>
278        <tr>
279          <td class="paramkey"></td>
280          <td></td>
281          <td class="paramtype">double&nbsp;</td>
282          <td class="paramname"> <em>sigma2</em>, </td>
283        </tr>
284        <tr>
285          <td class="paramkey"></td>
286          <td></td>
287          <td class="paramtype">const QLLRvec &amp;&nbsp;</td>
288          <td class="paramname"> <em>LLR_apriori</em>, </td>
289        </tr>
290        <tr>
291          <td class="paramkey"></td>
292          <td></td>
293          <td class="paramtype">QLLRvec &amp;&nbsp;</td>
294          <td class="paramname"> <em>LLR_aposteriori</em></td><td>&nbsp;</td>
295        </tr>
296        <tr>
297          <td></td>
298          <td>)</td>
299          <td></td><td></td><td><code> [inherited]</code></td>
300        </tr>
301      </table>
302</div>
303<div class="memdoc">
304
305<p>
306Soft MAP demodulation for parallelchannels without crosstalk.
307<p>
308This function is a much faster equivalent to <code>demodulate_soft_bits</code> with <img class="formulaInl" alt="$H = \mbox{diag}(h)$" src="form_299.png">. Its complexity is linear in the number of subchannels.
309<p>References <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, <a class="el" href="modulator__nd_8h-source.html#l00096">itpp::Modulator_ND::k</a>, <a class="el" href="matfunc_8h-source.html#l00051">itpp::length()</a>, <a class="el" href="modulator__nd_8h-source.html#l00094">itpp::Modulator_ND::llrcalc</a>, <a class="el" href="modulator__nd_8h-source.html#l00098">itpp::Modulator_ND::M</a>, <a class="el" href="modulator__nd_8h-source.html#l00092">itpp::Modulator_ND::nt</a>, <a class="el" href="group__specmat.html#g7c2c02190b4aa222cc692641cc3a73c7">itpp::ones_i()</a>, <a class="el" href="modulator__nd_8cpp-source.html#l00043">itpp::Modulator_ND::probabilities()</a>, <a class="el" href="elem__math_8h-source.html#l00056">itpp::sqr()</a>, <a class="el" href="matfunc_8h-source.html#l00077">itpp::sum()</a>, <a class="el" href="modulator__nd_8h-source.html#l00294">itpp::Modulator_NRD::symbols</a>, <a class="el" href="llr_8h-source.html#l00235">itpp::LLR_calc_unit::to_qllr()</a>, and <a class="el" href="modulator__nd_8cpp-source.html#l00093">itpp::Modulator_ND::update_LLR()</a>.</p>
310
311</div>
312</div><p>
313<a class="anchor" name="5de17b14ee11626e8323b50cf29fd047"></a><!-- doxytag: member="itpp::ND_UPAM::demodulate_soft_bits" ref="5de17b14ee11626e8323b50cf29fd047" args="(const vec &amp;y, const mat &amp;H, double sigma2, const QLLRvec &amp;LLR_apriori, QLLRvec &amp;LLR_aposteriori)" -->
314<div class="memitem">
315<div class="memproto">
316      <table class="memname">
317        <tr>
318          <td class="memname">void itpp::Modulator_NRD::demodulate_soft_bits           </td>
319          <td>(</td>
320          <td class="paramtype">const vec &amp;&nbsp;</td>
321          <td class="paramname"> <em>y</em>, </td>
322        </tr>
323        <tr>
324          <td class="paramkey"></td>
325          <td></td>
326          <td class="paramtype">const mat &amp;&nbsp;</td>
327          <td class="paramname"> <em>H</em>, </td>
328        </tr>
329        <tr>
330          <td class="paramkey"></td>
331          <td></td>
332          <td class="paramtype">double&nbsp;</td>
333          <td class="paramname"> <em>sigma2</em>, </td>
334        </tr>
335        <tr>
336          <td class="paramkey"></td>
337          <td></td>
338          <td class="paramtype">const QLLRvec &amp;&nbsp;</td>
339          <td class="paramname"> <em>LLR_apriori</em>, </td>
340        </tr>
341        <tr>
342          <td class="paramkey"></td>
343          <td></td>
344          <td class="paramtype">QLLRvec &amp;&nbsp;</td>
345          <td class="paramname"> <em>LLR_aposteriori</em></td><td>&nbsp;</td>
346        </tr>
347        <tr>
348          <td></td>
349          <td>)</td>
350          <td></td><td></td><td><code> [inherited]</code></td>
351        </tr>
352      </table>
353</div>
354<div class="memdoc">
355
356<p>
357Soft MAP demodulation for multidimensional channel, by "brute-force" enumeration of all constellation points.
358<p>
359This function computes the LLR values <p class="formulaDsp">
360<img class="formulaDsp" alt="\[ LLR(k) = \log \left( \frac {\sum_{s:b_k=0} \exp \left( -\frac{|y - Hs|^2}{2\sigma^2} \right) P(s)} {\sum_{s:b_k=1} \exp \left( -\frac{|y - Hs|^2}{2\sigma^2} \right) P(s)} \right) \]" src="form_298.png">
361<p>
362<p>
363without approximations. It is assumed that H, y and s are real-valued. Complex-valued channels can be handled using the <code><a class="el" href="classitpp_1_1Modulator__NCD.html" title="Base class for vector (MIMO) channel modulator/demodulators with complex valued components...">Modulator_NCD</a></code> class.<p>
364<dl compact><dt><b>Parameters:</b></dt><dd>
365  <table border="0" cellspacing="2" cellpadding="0">
366    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>y</em>&nbsp;</td><td>Received vector </td></tr>
367    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>H</em>&nbsp;</td><td>Channel matrix </td></tr>
368    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>sigma2</em>&nbsp;</td><td>Noise variance per real dimension (typically <img class="formulaInl" alt="$N_0/2$" src="form_232.png">) </td></tr>
369    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>LLR_apriori</em>&nbsp;</td><td>Vector of a priori LLR values per bit </td></tr>
370    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>LLR_aposteriori</em>&nbsp;</td><td>Vector of a posteriori LLR values</td></tr>
371  </table>
372</dl>
373The function performs an exhaustive search over all possible points <code>s</code> in the n-dimensional constellation. This is only feasible for relatively small constellations. The Jacobian logarithm is used to compute the sum-exp expression.
374<p>References <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, <a class="el" href="modulator__nd_8h-source.html#l00096">itpp::Modulator_ND::k</a>, <a class="el" href="matfunc_8h-source.html#l00051">itpp::length()</a>, <a class="el" href="modulator__nd_8h-source.html#l00094">itpp::Modulator_ND::llrcalc</a>, <a class="el" href="modulator__nd_8h-source.html#l00098">itpp::Modulator_ND::M</a>, <a class="el" href="misc__stat_8h-source.html#l00193">itpp::norm()</a>, <a class="el" href="modulator__nd_8h-source.html#l00092">itpp::Modulator_ND::nt</a>, <a class="el" href="group__specmat.html#g7c2c02190b4aa222cc692641cc3a73c7">itpp::ones_i()</a>, <a class="el" href="modulator__nd_8cpp-source.html#l00043">itpp::Modulator_ND::probabilities()</a>, <a class="el" href="elem__math_8h-source.html#l00056">itpp::sqr()</a>, <a class="el" href="matfunc_8h-source.html#l00077">itpp::sum()</a>, <a class="el" href="modulator__nd_8h-source.html#l00294">itpp::Modulator_NRD::symbols</a>, <a class="el" href="llr_8h-source.html#l00235">itpp::LLR_calc_unit::to_qllr()</a>, <a class="el" href="modulator__nd_8cpp-source.html#l00093">itpp::Modulator_ND::update_LLR()</a>, <a class="el" href="modulator__nd_8cpp-source.html#l00311">itpp::Modulator_NRD::update_norm()</a>, and <a class="el" href="group__specmat.html#g9df9aa3553b6a5c07924954b85466cec">itpp::zeros_i()</a>.</p>
375
376</div>
377</div><p>
378<a class="anchor" name="e1bdcbd5307ac1ab0e368f33fee5f149"></a><!-- doxytag: member="itpp::ND_UPAM::demodulate_soft_bits" ref="e1bdcbd5307ac1ab0e368f33fee5f149" args="(const vec &amp;y, const mat &amp;H, double sigma2, const QLLRvec &amp;LLR_apriori, Soft_Demod_Method method)" -->
379<div class="memitem">
380<div class="memproto">
381      <table class="memname">
382        <tr>
383          <td class="memname">QLLRvec itpp::Modulator_NRD::demodulate_soft_bits           </td>
384          <td>(</td>
385          <td class="paramtype">const vec &amp;&nbsp;</td>
386          <td class="paramname"> <em>y</em>, </td>
387        </tr>
388        <tr>
389          <td class="paramkey"></td>
390          <td></td>
391          <td class="paramtype">const mat &amp;&nbsp;</td>
392          <td class="paramname"> <em>H</em>, </td>
393        </tr>
394        <tr>
395          <td class="paramkey"></td>
396          <td></td>
397          <td class="paramtype">double&nbsp;</td>
398          <td class="paramname"> <em>sigma2</em>, </td>
399        </tr>
400        <tr>
401          <td class="paramkey"></td>
402          <td></td>
403          <td class="paramtype">const QLLRvec &amp;&nbsp;</td>
404          <td class="paramname"> <em>LLR_apriori</em>, </td>
405        </tr>
406        <tr>
407          <td class="paramkey"></td>
408          <td></td>
409          <td class="paramtype"><a class="el" href="classitpp_1_1Modulator__ND.html#6e3b4c745f904cdb34301aeb4cc03035">Soft_Demod_Method</a>&nbsp;</td>
410          <td class="paramname"> <em>method</em></td><td>&nbsp;</td>
411        </tr>
412        <tr>
413          <td></td>
414          <td>)</td>
415          <td></td><td></td><td><code> [inherited]</code></td>
416        </tr>
417      </table>
418</div>
419<div class="memdoc">
420
421<p>
422Soft demodulation wrapper function for various methods.
423<p>
424Currently the following two demodulation methods are supported:<ul>
425<li>FULL_ENUM_LOGMAP - exact demodulation, which use "brute-force" enumeration of all constellation points</li><li>ZF_LOGMAP - approximated methods with Zero-Forcing preprocessing, which sometimes tends to perform poorly, especially for poorly conditioned H</li></ul>
426<p>
427<dl compact><dt><b>Parameters:</b></dt><dd>
428  <table border="0" cellspacing="2" cellpadding="0">
429    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>y</em>&nbsp;</td><td>Received vector </td></tr>
430    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>H</em>&nbsp;</td><td>Channel matrix </td></tr>
431    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>sigma2</em>&nbsp;</td><td>Noise variance per real dimension (typically <img class="formulaInl" alt="$N_0/2$" src="form_232.png">) </td></tr>
432    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>LLR_apriori</em>&nbsp;</td><td>Vector of a priori LLR values per bit </td></tr>
433    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>method</em>&nbsp;</td><td>Soft demodulation method </td></tr>
434  </table>
435</dl>
436<dl class="return" compact><dt><b>Returns:</b></dt><dd>Vector of a posteriori LLR values </dd></dl>
437
438<p>References <a class="el" href="modulator__nd_8cpp-source.html#l00150">itpp::Modulator_NRD::demodulate_soft_bits()</a>.</p>
439
440</div>
441</div><p>
442<a class="anchor" name="42d28853cead832c7e7644366023601b"></a><!-- doxytag: member="itpp::ND_UPAM::demodulate_soft_bits" ref="42d28853cead832c7e7644366023601b" args="(const vec &amp;y, const mat &amp;H, double sigma2, const QLLRvec &amp;LLR_apriori, QLLRvec &amp;LLR_aposteriori, Soft_Demod_Method method)" -->
443<div class="memitem">
444<div class="memproto">
445      <table class="memname">
446        <tr>
447          <td class="memname">void itpp::Modulator_NRD::demodulate_soft_bits           </td>
448          <td>(</td>
449          <td class="paramtype">const vec &amp;&nbsp;</td>
450          <td class="paramname"> <em>y</em>, </td>
451        </tr>
452        <tr>
453          <td class="paramkey"></td>
454          <td></td>
455          <td class="paramtype">const mat &amp;&nbsp;</td>
456          <td class="paramname"> <em>H</em>, </td>
457        </tr>
458        <tr>
459          <td class="paramkey"></td>
460          <td></td>
461          <td class="paramtype">double&nbsp;</td>
462          <td class="paramname"> <em>sigma2</em>, </td>
463        </tr>
464        <tr>
465          <td class="paramkey"></td>
466          <td></td>
467          <td class="paramtype">const QLLRvec &amp;&nbsp;</td>
468          <td class="paramname"> <em>LLR_apriori</em>, </td>
469        </tr>
470        <tr>
471          <td class="paramkey"></td>
472          <td></td>
473          <td class="paramtype">QLLRvec &amp;&nbsp;</td>
474          <td class="paramname"> <em>LLR_aposteriori</em>, </td>
475        </tr>
476        <tr>
477          <td class="paramkey"></td>
478          <td></td>
479          <td class="paramtype"><a class="el" href="classitpp_1_1Modulator__ND.html#6e3b4c745f904cdb34301aeb4cc03035">Soft_Demod_Method</a>&nbsp;</td>
480          <td class="paramname"> <em>method</em></td><td>&nbsp;</td>
481        </tr>
482        <tr>
483          <td></td>
484          <td>)</td>
485          <td></td><td></td><td><code> [inherited]</code></td>
486        </tr>
487      </table>
488</div>
489<div class="memdoc">
490
491<p>
492Soft demodulation wrapper function for various methods.
493<p>
494Currently the following two demodulation methods are supported:<ul>
495<li>FULL_ENUM_LOGMAP - exact demodulation, which use "brute-force" enumeration of all constellation points</li><li>ZF_LOGMAP - approximated methods with Zero-Forcing preprocessing, which sometimes tends to perform poorly, especially for poorly conditioned H</li></ul>
496<p>
497<dl compact><dt><b>Parameters:</b></dt><dd>
498  <table border="0" cellspacing="2" cellpadding="0">
499    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>y</em>&nbsp;</td><td>Received vector </td></tr>
500    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>H</em>&nbsp;</td><td>Channel matrix </td></tr>
501    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>sigma2</em>&nbsp;</td><td>Noise variance per real dimension (typically <img class="formulaInl" alt="$N_0/2$" src="form_232.png">) </td></tr>
502    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>LLR_apriori</em>&nbsp;</td><td>Vector of a priori LLR values per bit </td></tr>
503    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>LLR_aposteriori</em>&nbsp;</td><td>Vector of a posteriori LLR values </td></tr>
504    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>method</em>&nbsp;</td><td>Soft demodulation method </td></tr>
505  </table>
506</dl>
507
508<p>References <a class="el" href="modulator__nd_8h-source.html#l00064">itpp::Modulator_ND::FULL_ENUM_LOGMAP</a>, <a class="el" href="inv_8cpp-source.html#l00109">itpp::inv()</a>, <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, <a class="el" href="itassert_8h-source.html#l00126">it_error</a>, <a class="el" href="modulator__nd_8h-source.html#l00096">itpp::Modulator_ND::k</a>, <a class="el" href="group__specmat.html#gdc0f3edbf58bced9e82d8b260d395cac">itpp::ones()</a>, <a class="el" href="elem__math_8h-source.html#l00126">itpp::sqrt()</a>, <a class="el" href="matfunc_8h-source.html#l00077">itpp::sum()</a>, <a class="el" href="group__specmat.html#g9df9aa3553b6a5c07924954b85466cec">itpp::zeros_i()</a>, and <a class="el" href="modulator__nd_8h-source.html#l00066">itpp::Modulator_ND::ZF_LOGMAP</a>.</p>
509
510<p>Referenced by <a class="el" href="modulator__nd_8cpp-source.html#l00183">itpp::Modulator_NRD::demodulate_soft_bits()</a>.</p>
511
512</div>
513</div><p>
514<a class="anchor" name="7f53ad7f4de6b0e7f6260905ed522cd2"></a><!-- doxytag: member="itpp::ND_UPAM::sphere_decoding" ref="7f53ad7f4de6b0e7f6260905ed522cd2" args="(const vec &amp;y, const mat &amp;H, double rmin, double rmax, double stepup, QLLRvec &amp;detected_bits)" -->
515<div class="memitem">
516<div class="memproto">
517      <table class="memname">
518        <tr>
519          <td class="memname">int itpp::ND_UPAM::sphere_decoding           </td>
520          <td>(</td>
521          <td class="paramtype">const vec &amp;&nbsp;</td>
522          <td class="paramname"> <em>y</em>, </td>
523        </tr>
524        <tr>
525          <td class="paramkey"></td>
526          <td></td>
527          <td class="paramtype">const mat &amp;&nbsp;</td>
528          <td class="paramname"> <em>H</em>, </td>
529        </tr>
530        <tr>
531          <td class="paramkey"></td>
532          <td></td>
533          <td class="paramtype">double&nbsp;</td>
534          <td class="paramname"> <em>rmin</em>, </td>
535        </tr>
536        <tr>
537          <td class="paramkey"></td>
538          <td></td>
539          <td class="paramtype">double&nbsp;</td>
540          <td class="paramname"> <em>rmax</em>, </td>
541        </tr>
542        <tr>
543          <td class="paramkey"></td>
544          <td></td>
545          <td class="paramtype">double&nbsp;</td>
546          <td class="paramname"> <em>stepup</em>, </td>
547        </tr>
548        <tr>
549          <td class="paramkey"></td>
550          <td></td>
551          <td class="paramtype">QLLRvec &amp;&nbsp;</td>
552          <td class="paramname"> <em>detected_bits</em></td><td>&nbsp;</td>
553        </tr>
554        <tr>
555          <td></td>
556          <td>)</td>
557          <td></td><td></td><td></td>
558        </tr>
559      </table>
560</div>
561<div class="memdoc">
562
563<p>
564Sphere decoding.
565<p>
566This function solves the integer-constrained minimization problem <p class="formulaDsp">
567<img class="formulaDsp" alt="\[ \mbox{min} |y - Hs| \]" src="form_302.png">
568<p>
569 with respect to <img class="formulaInl" alt="$s$" src="form_163.png"> using a sphere decoding algorithm and the Schnorr-Eucner search strategy (see the source code for further implementation notes). The function starts with an initial search radius and increases it with a factor (<code>stepup</code>) until the search succeeds.<p>
570<dl compact><dt><b>Parameters:</b></dt><dd>
571  <table border="0" cellspacing="2" cellpadding="0">
572    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>y</em>&nbsp;</td><td>received data vector (<img class="formulaInl" alt="$n_r\times 1$" src="form_303.png">) </td></tr>
573    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>H</em>&nbsp;</td><td>channel matrix (<img class="formulaInl" alt="$n_r\times n_t$" src="form_290.png">) </td></tr>
574    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>rmax</em>&nbsp;</td><td>maximum possible sphere radius to try </td></tr>
575    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>rmin</em>&nbsp;</td><td>sphere radius in the first try </td></tr>
576    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>stepup</em>&nbsp;</td><td>factor with which the sphere radius is increased if the search fails </td></tr>
577    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>detected_bits</em>&nbsp;</td><td>result of the search (hard decisions only, QLLR for a sure "1" is set to 1000) </td></tr>
578  </table>
579</dl>
580<dl class="return" compact><dt><b>Returns:</b></dt><dd>status of the decoding: 0 if the search suceeds, -1 otherwise </dd></dl>
581
582<p>References <a class="el" href="modulator__nd_8h-source.html#l00100">itpp::Modulator_ND::bitmap</a>, <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, <a class="el" href="modulator__nd_8h-source.html#l00096">itpp::Modulator_ND::k</a>, <a class="el" href="matfunc_8h-source.html#l00051">itpp::length()</a>, <a class="el" href="modulator__nd_8h-source.html#l00098">itpp::Modulator_ND::M</a>, <a class="el" href="modulator__nd_8h-source.html#l00092">itpp::Modulator_ND::nt</a>, and <a class="el" href="matfunc_8h-source.html#l00077">itpp::sum()</a>.</p>
583
584</div>
585</div><p>
586<a class="anchor" name="6bb417318b8105a78db7ad2c618283ce"></a><!-- doxytag: member="itpp::ND_UPAM::update_LLR" ref="6bb417318b8105a78db7ad2c618283ce" args="(const Array&lt; QLLRvec &gt; &amp;logP_apriori, int s, QLLR scaled_norm, int j, QLLRvec &amp;num, QLLRvec &amp;denom)" -->
587<div class="memitem">
588<div class="memproto">
589      <table class="memname">
590        <tr>
591          <td class="memname">void itpp::Modulator_ND::update_LLR           </td>
592          <td>(</td>
593          <td class="paramtype">const <a class="el" href="classitpp_1_1Array.html">Array</a>&lt; QLLRvec &gt; &amp;&nbsp;</td>
594          <td class="paramname"> <em>logP_apriori</em>, </td>
595        </tr>
596        <tr>
597          <td class="paramkey"></td>
598          <td></td>
599          <td class="paramtype">int&nbsp;</td>
600          <td class="paramname"> <em>s</em>, </td>
601        </tr>
602        <tr>
603          <td class="paramkey"></td>
604          <td></td>
605          <td class="paramtype">QLLR&nbsp;</td>
606          <td class="paramname"> <em>scaled_norm</em>, </td>
607        </tr>
608        <tr>
609          <td class="paramkey"></td>
610          <td></td>
611          <td class="paramtype">int&nbsp;</td>
612          <td class="paramname"> <em>j</em>, </td>
613        </tr>
614        <tr>
615          <td class="paramkey"></td>
616          <td></td>
617          <td class="paramtype">QLLRvec &amp;&nbsp;</td>
618          <td class="paramname"> <em>num</em>, </td>
619        </tr>
620        <tr>
621          <td class="paramkey"></td>
622          <td></td>
623          <td class="paramtype">QLLRvec &amp;&nbsp;</td>
624          <td class="paramname"> <em>denom</em></td><td>&nbsp;</td>
625        </tr>
626        <tr>
627          <td></td>
628          <td>)</td>
629          <td></td><td></td><td><code> [protected, inherited]</code></td>
630        </tr>
631      </table>
632</div>
633<div class="memdoc">
634
635<p>
636Update LLR, for scalar channel (for internal use).
637<p>
638This function updates the numerator and denominator in the expression <p class="formulaDsp">
639<img class="formulaDsp" alt="\[ \log \left( \frac {\sum_{s:b_k=0} \exp (-x^2) P(s)} {\sum_{s:b_k=1} \exp (-x^2) P(s)} \right) \]" src="form_297.png">
640<p>
641<p>
642<dl compact><dt><b>Parameters:</b></dt><dd>
643  <table border="0" cellspacing="2" cellpadding="0">
644    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>logP_apriori</em>&nbsp;</td><td>Vector of a priori probabilities per bit </td></tr>
645    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>s</em>&nbsp;</td><td>Symbol </td></tr>
646    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>scaled_norm</em>&nbsp;</td><td>Argument of the exponents in the above equation </td></tr>
647    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>j</em>&nbsp;</td><td>Channel index (dimension) </td></tr>
648    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>num</em>&nbsp;</td><td>Logarithm of the numerator in the above expression </td></tr>
649    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>denom</em>&nbsp;</td><td>Logarithm of the denominator in the above expression </td></tr>
650  </table>
651</dl>
652
653<p>References <a class="el" href="modulator__nd_8h-source.html#l00100">itpp::Modulator_ND::bitmap</a>, <a class="el" href="llr_8h-source.html#l00270">itpp::LLR_calc_unit::jaclog()</a>, <a class="el" href="modulator__nd_8h-source.html#l00096">itpp::Modulator_ND::k</a>, and <a class="el" href="modulator__nd_8h-source.html#l00094">itpp::Modulator_ND::llrcalc</a>.</p>
654
655</div>
656</div><p>
657<a class="anchor" name="48975e0d26dac075e1f448bdca15ca87"></a><!-- doxytag: member="itpp::ND_UPAM::update_LLR" ref="48975e0d26dac075e1f448bdca15ca87" args="(const Array&lt; QLLRvec &gt; &amp;logP_apriori, const ivec &amp;s, QLLR scaled_norm, QLLRvec &amp;num, QLLRvec &amp;denom)" -->
658<div class="memitem">
659<div class="memproto">
660      <table class="memname">
661        <tr>
662          <td class="memname">void itpp::Modulator_ND::update_LLR           </td>
663          <td>(</td>
664          <td class="paramtype">const <a class="el" href="classitpp_1_1Array.html">Array</a>&lt; QLLRvec &gt; &amp;&nbsp;</td>
665          <td class="paramname"> <em>logP_apriori</em>, </td>
666        </tr>
667        <tr>
668          <td class="paramkey"></td>
669          <td></td>
670          <td class="paramtype">const ivec &amp;&nbsp;</td>
671          <td class="paramname"> <em>s</em>, </td>
672        </tr>
673        <tr>
674          <td class="paramkey"></td>
675          <td></td>
676          <td class="paramtype">QLLR&nbsp;</td>
677          <td class="paramname"> <em>scaled_norm</em>, </td>
678        </tr>
679        <tr>
680          <td class="paramkey"></td>
681          <td></td>
682          <td class="paramtype">QLLRvec &amp;&nbsp;</td>
683          <td class="paramname"> <em>num</em>, </td>
684        </tr>
685        <tr>
686          <td class="paramkey"></td>
687          <td></td>
688          <td class="paramtype">QLLRvec &amp;&nbsp;</td>
689          <td class="paramname"> <em>denom</em></td><td>&nbsp;</td>
690        </tr>
691        <tr>
692          <td></td>
693          <td>)</td>
694          <td></td><td></td><td><code> [protected, inherited]</code></td>
695        </tr>
696      </table>
697</div>
698<div class="memdoc">
699
700<p>
701Update LLR (for internal use).
702<p>
703This function updates the numerator and denominator in the expression <p class="formulaDsp">
704<img class="formulaDsp" alt="\[ \log \left( \frac {\sum_{s:b_k=0} \exp(-x^2) P(s)} {\sum_{s:b_k=1} \exp(-x^2) P(s)} \right) \]" src="form_296.png">
705<p>
706<p>
707<dl compact><dt><b>Parameters:</b></dt><dd>
708  <table border="0" cellspacing="2" cellpadding="0">
709    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>logP_apriori</em>&nbsp;</td><td>Vector of a priori probabilities per bit </td></tr>
710    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>s</em>&nbsp;</td><td>Symbol vector </td></tr>
711    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>scaled_norm</em>&nbsp;</td><td>Argument of the exponents in the above equation </td></tr>
712    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>num</em>&nbsp;</td><td>Logarithm of the numerator in the above expression </td></tr>
713    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>denom</em>&nbsp;</td><td>Logarithm of the denominator in the above expression </td></tr>
714  </table>
715</dl>
716
717<p>References <a class="el" href="modulator__nd_8h-source.html#l00100">itpp::Modulator_ND::bitmap</a>, <a class="el" href="llr_8h-source.html#l00270">itpp::LLR_calc_unit::jaclog()</a>, <a class="el" href="modulator__nd_8h-source.html#l00096">itpp::Modulator_ND::k</a>, <a class="el" href="modulator__nd_8h-source.html#l00094">itpp::Modulator_ND::llrcalc</a>, and <a class="el" href="modulator__nd_8h-source.html#l00092">itpp::Modulator_ND::nt</a>.</p>
718
719<p>Referenced by <a class="el" href="modulator__nd_8cpp-source.html#l00413">itpp::Modulator_NCD::demodulate_soft_bits()</a>, and <a class="el" href="modulator__nd_8cpp-source.html#l00193">itpp::Modulator_NRD::demodulate_soft_bits()</a>.</p>
720
721</div>
722</div><p>
723<a class="anchor" name="37363ba319fa9230cce3b969dbcf6f1a"></a><!-- doxytag: member="itpp::ND_UPAM::update_norm" ref="37363ba319fa9230cce3b969dbcf6f1a" args="(double &amp;norm, int k, int sold, int snew, const vec &amp;ytH, const mat &amp;HtH, const ivec &amp;s)" -->
724<div class="memitem">
725<div class="memproto">
726      <table class="memname">
727        <tr>
728          <td class="memname">void itpp::Modulator_NRD::update_norm           </td>
729          <td>(</td>
730          <td class="paramtype">double &amp;&nbsp;</td>
731          <td class="paramname"> <em>norm</em>, </td>
732        </tr>
733        <tr>
734          <td class="paramkey"></td>
735          <td></td>
736          <td class="paramtype">int&nbsp;</td>
737          <td class="paramname"> <em>k</em>, </td>
738        </tr>
739        <tr>
740          <td class="paramkey"></td>
741          <td></td>
742          <td class="paramtype">int&nbsp;</td>
743          <td class="paramname"> <em>sold</em>, </td>
744        </tr>
745        <tr>
746          <td class="paramkey"></td>
747          <td></td>
748          <td class="paramtype">int&nbsp;</td>
749          <td class="paramname"> <em>snew</em>, </td>
750        </tr>
751        <tr>
752          <td class="paramkey"></td>
753          <td></td>
754          <td class="paramtype">const vec &amp;&nbsp;</td>
755          <td class="paramname"> <em>ytH</em>, </td>
756        </tr>
757        <tr>
758          <td class="paramkey"></td>
759          <td></td>
760          <td class="paramtype">const mat &amp;&nbsp;</td>
761          <td class="paramname"> <em>HtH</em>, </td>
762        </tr>
763        <tr>
764          <td class="paramkey"></td>
765          <td></td>
766          <td class="paramtype">const ivec &amp;&nbsp;</td>
767          <td class="paramname"> <em>s</em></td><td>&nbsp;</td>
768        </tr>
769        <tr>
770          <td></td>
771          <td>)</td>
772          <td></td><td></td><td><code> [protected, inherited]</code></td>
773        </tr>
774      </table>
775</div>
776<div class="memdoc">
777
778<p>
779Update residual norm (for internal use).
780<p>
781Update the residual norm <img class="formulaInl" alt="$|y-Hs|$" src="form_300.png"> when moving from one constellation point to an adjacent point.<p>
782<dl compact><dt><b>Parameters:</b></dt><dd>
783  <table border="0" cellspacing="2" cellpadding="0">
784    <tr><td valign="top"><tt>[in,out]</tt>&nbsp;</td><td valign="top"><em>norm</em>&nbsp;</td><td>Norm to be updated </td></tr>
785    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>k</em>&nbsp;</td><td>Position where s changed </td></tr>
786    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>sold</em>&nbsp;</td><td>Old value of s[k] </td></tr>
787    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>snew</em>&nbsp;</td><td>New value of s[k] </td></tr>
788    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>ytH</em>&nbsp;</td><td>y'H vector </td></tr>
789    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>HtH</em>&nbsp;</td><td>Grammian matrix H'H </td></tr>
790    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>s</em>&nbsp;</td><td>Symbol vector </td></tr>
791  </table>
792</dl>
793
794<p>References <a class="el" href="matfunc_8h-source.html#l00051">itpp::length()</a>, <a class="el" href="elem__math_8h-source.html#l00056">itpp::sqr()</a>, and <a class="el" href="modulator__nd_8h-source.html#l00294">itpp::Modulator_NRD::symbols</a>.</p>
795
796<p>Referenced by <a class="el" href="modulator__nd_8cpp-source.html#l00224">itpp::Modulator_NRD::demodulate_soft_bits()</a>.</p>
797
798</div>
799</div><p>
800<hr><h2>Friends And Related Function Documentation</h2>
801<a class="anchor" name="f82a88fab3e6f7a1e6c0a4a7e17fb678"></a><!-- doxytag: member="itpp::ND_UPAM::operator&lt;&lt;" ref="f82a88fab3e6f7a1e6c0a4a7e17fb678" args="(std::ostream &amp;os, const Modulator_NRD &amp;m)" -->
802<div class="memitem">
803<div class="memproto">
804      <table class="memname">
805        <tr>
806          <td class="memname">std::ostream &amp; operator&lt;&lt;           </td>
807          <td>(</td>
808          <td class="paramtype">std::ostream &amp;&nbsp;</td>
809          <td class="paramname"> <em>os</em>, </td>
810        </tr>
811        <tr>
812          <td class="paramkey"></td>
813          <td></td>
814          <td class="paramtype">const <a class="el" href="classitpp_1_1Modulator__NRD.html">Modulator_NRD</a> &amp;&nbsp;</td>
815          <td class="paramname"> <em>m</em></td><td>&nbsp;</td>
816        </tr>
817        <tr>
818          <td></td>
819          <td>)</td>
820          <td></td><td></td><td><code> [friend, inherited]</code></td>
821        </tr>
822      </table>
823</div>
824<div class="memdoc">
825
826<p>
827Output some properties of the MIMO modulator (mainly to aid debugging).
828<p>
829Print some properties of the MIMO modulator (mainly to aid debugging).
830</div>
831</div><p>
832<hr>The documentation for this class was generated from the following files:<ul>
833<li><a class="el" href="modulator__nd_8h-source.html">modulator_nd.h</a><li><a class="el" href="modulator__nd_8cpp.html">modulator_nd.cpp</a></ul>
834</div>
835<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:19 2009 for mixpp by&nbsp;
836<a href="http://www.doxygen.org/index.html">
837<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>
838</body>
839</html>
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