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67	<div class="navpath"><b>itpp</b>::<a class="el" href="classitpp_1_1PAM__c.html">PAM_c</a>
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71	<h1>itpp::PAM_c Class Reference<br>
72	<small>
73	[<a class="el" href="group__modulators.html">Digital Modulation</a>]</small>
74	</h1><!-- doxytag: class="itpp::PAM_c" --><!-- doxytag: inherits="Modulator< std::complex< double > >" -->M-ary <a class="el" href="classitpp_1_1PAM.html" title="M-ary PAM modulator with real symbols.">PAM</a> modulator with complex symbols.
75	<a href="#_details">More...</a>
76	<p>
77	<code>#include <<a class="el" href="modulator_8h-source.html">modulator.h</a>></code>
78	<p>
79
80	<p>
81	<a href="classitpp_1_1PAM__c-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 Member Functions</h2></td></tr>
84	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9bf8f8af7de4d55dc96b430179e22615"></a><!-- doxytag: member="itpp::PAM_c::PAM_c" ref="9bf8f8af7de4d55dc96b430179e22615" args="()" -->
85	</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#9bf8f8af7de4d55dc96b430179e22615">PAM_c</a> ()</td></tr>
86
87	<tr><td class="mdescLeft"> </td><td class="mdescRight">Default Constructor. <br></td></tr>
88	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ddf72f5ca262c86fb593c52a83ddd5a3"></a><!-- doxytag: member="itpp::PAM_c::PAM_c" ref="ddf72f5ca262c86fb593c52a83ddd5a3" args="(int M)" -->
89	</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#ddf72f5ca262c86fb593c52a83ddd5a3">PAM_c</a> (int <a class="el" href="classitpp_1_1Modulator.html#a434960c7ff9e5356d832aa53b46930b">M</a>)</td></tr>
90
91	<tr><td class="mdescLeft"> </td><td class="mdescRight">Constructor. <br></td></tr>
92	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e1d8dee85093389be82470086df67797"></a><!-- doxytag: member="itpp::PAM_c::~PAM_c" ref="e1d8dee85093389be82470086df67797" args="()" -->
93	virtual </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#e1d8dee85093389be82470086df67797">~PAM_c</a> ()</td></tr>
94
95	<tr><td class="mdescLeft"> </td><td class="mdescRight">Destructor. <br></td></tr>
96	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5fdc1ce14d29d8d291dd23406904b606"></a><!-- doxytag: member="itpp::PAM_c::set_M" ref="5fdc1ce14d29d8d291dd23406904b606" args="(int M)" -->
97	void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#5fdc1ce14d29d8d291dd23406904b606">set_M</a> (int <a class="el" href="classitpp_1_1Modulator.html#a434960c7ff9e5356d832aa53b46930b">M</a>)</td></tr>
98
99	<tr><td class="mdescLeft"> </td><td class="mdescRight">Set the size of the signal constellation. <br></td></tr>
100	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4254b3f8ca63e0a99fe83b1eeac22d2b"></a><!-- doxytag: member="itpp::PAM_c::demodulate_bits" ref="4254b3f8ca63e0a99fe83b1eeac22d2b" args="(const cvec &signal, bvec &output) const " -->
101	void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#4254b3f8ca63e0a99fe83b1eeac22d2b">demodulate_bits</a> (const cvec &signal, bvec &output) const </td></tr>
102
103	<tr><td class="mdescLeft"> </td><td class="mdescRight">Hard demodulation of <a class="el" href="classitpp_1_1PAM.html" title="M-ary PAM modulator with real symbols.">PAM</a> symbols in complex domain to bits. <br></td></tr>
104	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="95dc1aef180ef59c6140427827f6f076"></a><!-- doxytag: member="itpp::PAM_c::demodulate_bits" ref="95dc1aef180ef59c6140427827f6f076" args="(const cvec &signal) const " -->
105	bvec </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#95dc1aef180ef59c6140427827f6f076">demodulate_bits</a> (const cvec &signal) const </td></tr>
106
107	<tr><td class="mdescLeft"> </td><td class="mdescRight">Hard demodulation of <a class="el" href="classitpp_1_1PAM.html" title="M-ary PAM modulator with real symbols.">PAM</a> symbols in complex domain to bits. <br></td></tr>
108	<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#56e1f1d20bfecdd0e5ef37456a5179ae">demodulate_soft_bits</a> (const cvec &rx_symbols, double N0, vec &soft_bits, <a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> method=LOGMAP) const </td></tr>
109
110	<tr><td class="mdescLeft"> </td><td class="mdescRight">Soft demodulator for AWGN channels. <a href="#56e1f1d20bfecdd0e5ef37456a5179ae"></a><br></td></tr>
111	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c50d75d6d712a6809cab3170dac4cf0f"></a><!-- doxytag: member="itpp::PAM_c::demodulate_soft_bits" ref="c50d75d6d712a6809cab3170dac4cf0f" args="(const cvec &rx_symbols, double N0, Soft_Method method=LOGMAP) const " -->
112	virtual vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#c50d75d6d712a6809cab3170dac4cf0f">demodulate_soft_bits</a> (const cvec &rx_symbols, double N0, <a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> method=LOGMAP) const </td></tr>
113
114	<tr><td class="mdescLeft"> </td><td class="mdescRight">Soft demodulator for AWGN channels. <br></td></tr>
115	<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#6cd8dbe2ce99f63785cc51772e4e586d">demodulate_soft_bits</a> (const cvec &rx_symbols, const cvec &channel, double N0, vec &soft_bits, <a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> method=LOGMAP) const </td></tr>
116
117	<tr><td class="mdescLeft"> </td><td class="mdescRight">Soft demodulator for known fading channels. <a href="#6cd8dbe2ce99f63785cc51772e4e586d"></a><br></td></tr>
118	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ba7ea8361cec966f9a018980f77a2a74"></a><!-- doxytag: member="itpp::PAM_c::demodulate_soft_bits" ref="ba7ea8361cec966f9a018980f77a2a74" args="(const cvec &rx_symbols, const cvec &channel, double N0, Soft_Method method=LOGMAP) const " -->
119	virtual vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#ba7ea8361cec966f9a018980f77a2a74">demodulate_soft_bits</a> (const cvec &rx_symbols, const cvec &channel, double N0, <a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> method=LOGMAP) const </td></tr>
120
121	<tr><td class="mdescLeft"> </td><td class="mdescRight">Soft demodulator for known fading channels. <br></td></tr>
122	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b9722a6826869c6d6e15a9835d76239b"></a><!-- doxytag: member="itpp::PAM_c::set" ref="b9722a6826869c6d6e15a9835d76239b" args="(const Vec< std::complex< double > > &symbols, const ivec &bits2symbols)" -->
123	virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#b9722a6826869c6d6e15a9835d76239b">set</a> (const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &<a class="el" href="classitpp_1_1Modulator.html#3069840e9e7a44180615fb772cf9ae42">symbols</a>, const ivec &<a class="el" href="classitpp_1_1Modulator.html#3ca26614189cb7a66da369bf0c4b9070">bits2symbols</a>)</td></tr>
124
125	<tr><td class="mdescLeft"> </td><td class="mdescRight">Set the constellation to use in the modulator. <br></td></tr>
126	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6e7cfa06570e2a1de515be5222a53a83"></a><!-- doxytag: member="itpp::PAM_c::bits_per_symbol" ref="6e7cfa06570e2a1de515be5222a53a83" args="() const" -->
127	virtual int </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#6e7cfa06570e2a1de515be5222a53a83">bits_per_symbol</a> () const</td></tr>
128
129	<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns number of bits per symbol. <br></td></tr>
130	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="28b1c28bf8f4596e4d5149f1f3c8cd76"></a><!-- doxytag: member="itpp::PAM_c::get_symbols" ref="28b1c28bf8f4596e4d5149f1f3c8cd76" args="() const" -->
131	virtual <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex<br class="typebreak">
132	< double > > </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#28b1c28bf8f4596e4d5149f1f3c8cd76">get_symbols</a> () const</td></tr>
133
134	<tr><td class="mdescLeft"> </td><td class="mdescRight">Get the symbol values used in the modulator. <br></td></tr>
135	<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual ivec </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#a8186f0e837fd3d440a6acb7a0225d35">get_bits2symbols</a> () const</td></tr>
136
137	<tr><td class="mdescLeft"> </td><td class="mdescRight">Get the bitmap, which maps input bits into symbols. <a href="#a8186f0e837fd3d440a6acb7a0225d35"></a><br></td></tr>
138	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4f7bde9d3bfa9e39c06017534e3f6647"></a><!-- doxytag: member="itpp::PAM_c::modulate" ref="4f7bde9d3bfa9e39c06017534e3f6647" args="(const ivec &symbolnumbers, Vec< std::complex< double > > &output) const" -->
139	virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#4f7bde9d3bfa9e39c06017534e3f6647">modulate</a> (const ivec &symbolnumbers, <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &output) const</td></tr>
140
141	<tr><td class="mdescLeft"> </td><td class="mdescRight">Modulation of symbols. <br></td></tr>
142	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e0cb2673987e110920b519c139cdebe1"></a><!-- doxytag: member="itpp::PAM_c::modulate" ref="e0cb2673987e110920b519c139cdebe1" args="(const ivec &symbolnumbers) const" -->
143	virtual <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex<br class="typebreak">
144	< double > > </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#e0cb2673987e110920b519c139cdebe1">modulate</a> (const ivec &symbolnumbers) const</td></tr>
145
146	<tr><td class="mdescLeft"> </td><td class="mdescRight">Modulation of symbols. <br></td></tr>
147	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="845b5fbf4dad59edd3772627250623a1"></a><!-- doxytag: member="itpp::PAM_c::demodulate" ref="845b5fbf4dad59edd3772627250623a1" args="(const Vec< std::complex< double > > &signal, ivec &output) const" -->
148	virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#845b5fbf4dad59edd3772627250623a1">demodulate</a> (const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &signal, ivec &output) const</td></tr>
149
150	<tr><td class="mdescLeft"> </td><td class="mdescRight">Demodulation of symbols. <br></td></tr>
151	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7f2c15efa18d1cb46b8c97723c11ec9d"></a><!-- doxytag: member="itpp::PAM_c::demodulate" ref="7f2c15efa18d1cb46b8c97723c11ec9d" args="(const Vec< std::complex< double > > &signal) const" -->
152	virtual ivec </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#7f2c15efa18d1cb46b8c97723c11ec9d">demodulate</a> (const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &signal) const</td></tr>
153
154	<tr><td class="mdescLeft"> </td><td class="mdescRight">Demodulation of symbols. <br></td></tr>
155	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="53826bf7e0ec83b99592235b0c2f6235"></a><!-- doxytag: member="itpp::PAM_c::modulate_bits" ref="53826bf7e0ec83b99592235b0c2f6235" args="(const bvec &bits, Vec< std::complex< double > > &output) const" -->
156	virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#53826bf7e0ec83b99592235b0c2f6235">modulate_bits</a> (const bvec &bits, <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &output) const</td></tr>
157
158	<tr><td class="mdescLeft"> </td><td class="mdescRight">Modulation of bits. <br></td></tr>
159	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="622fa1ce4243330b7efa0605a9492513"></a><!-- doxytag: member="itpp::PAM_c::modulate_bits" ref="622fa1ce4243330b7efa0605a9492513" args="(const bvec &bits) const" -->
160	virtual <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex<br class="typebreak">
161	< double > > </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#622fa1ce4243330b7efa0605a9492513">modulate_bits</a> (const bvec &bits) const</td></tr>
162
163	<tr><td class="mdescLeft"> </td><td class="mdescRight">Modulation of bits. <br></td></tr>
164	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4d03bbe8bd467898f149d5f134f6f120"></a><!-- doxytag: member="itpp::PAM_c::demodulate_bits" ref="4d03bbe8bd467898f149d5f134f6f120" args="(const Vec< std::complex< double > > &signal, bvec &bits) const" -->
165	virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#4d03bbe8bd467898f149d5f134f6f120">demodulate_bits</a> (const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &signal, bvec &bits) const</td></tr>
166
167	<tr><td class="mdescLeft"> </td><td class="mdescRight">Hard demodulation of bits. <br></td></tr>
168	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9e3432dad687ac0ee102c208e34920f8"></a><!-- doxytag: member="itpp::PAM_c::demodulate_bits" ref="9e3432dad687ac0ee102c208e34920f8" args="(const Vec< std::complex< double > > &signal) const" -->
169	virtual bvec </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#9e3432dad687ac0ee102c208e34920f8">demodulate_bits</a> (const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &signal) const</td></tr>
170
171	<tr><td class="mdescLeft"> </td><td class="mdescRight">Hard demodulation of bits. <br></td></tr>
172	<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#9beffaf8f69378f9c20a85f3023bd9af">demodulate_soft_bits</a> (const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &rx_symbols, double N0, vec &soft_bits, <a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> method=LOGMAP) const</td></tr>
173
174	<tr><td class="mdescLeft"> </td><td class="mdescRight">Soft demodulator for AWGN channels. <a href="#9beffaf8f69378f9c20a85f3023bd9af"></a><br></td></tr>
175	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a9cba88e460e11775fb72d21b543c375"></a><!-- doxytag: member="itpp::PAM_c::demodulate_soft_bits" ref="a9cba88e460e11775fb72d21b543c375" args="(const Vec< std::complex< double > > &rx_symbols, double N0, Soft_Method method=LOGMAP) const" -->
176	virtual vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#a9cba88e460e11775fb72d21b543c375">demodulate_soft_bits</a> (const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &rx_symbols, double N0, <a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> method=LOGMAP) const</td></tr>
177
178	<tr><td class="mdescLeft"> </td><td class="mdescRight">Soft demodulator for AWGN channels. <br></td></tr>
179	<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#bd014d868b4f883712f92a7130401714">demodulate_soft_bits</a> (const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &rx_symbols, const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &channel, double N0, vec &soft_bits, <a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> method=LOGMAP) const</td></tr>
180
181	<tr><td class="mdescLeft"> </td><td class="mdescRight">Soft demodulator for fading channels. <a href="#bd014d868b4f883712f92a7130401714"></a><br></td></tr>
182	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e40b7afd0d38d2d86b561b9dff6f55fd"></a><!-- doxytag: member="itpp::PAM_c::demodulate_soft_bits" ref="e40b7afd0d38d2d86b561b9dff6f55fd" args="(const Vec< std::complex< double > > &rx_symbols, const Vec< std::complex< double > > &channel, double N0, Soft_Method method=LOGMAP) const" -->
183	virtual vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#e40b7afd0d38d2d86b561b9dff6f55fd">demodulate_soft_bits</a> (const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &rx_symbols, const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > &channel, double N0, <a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> method=LOGMAP) const</td></tr>
184
185	<tr><td class="mdescLeft"> </td><td class="mdescRight">Soft demodulator for fading channels. <br></td></tr>
186	<tr><td colspan="2"><br><h2>Protected Member Functions</h2></td></tr>
187	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bb3e654a3fb6d127ee8d266677689233"></a><!-- doxytag: member="itpp::PAM_c::calculate_softbit_matrices" ref="bb3e654a3fb6d127ee8d266677689233" args="()" -->
188	void </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#bb3e654a3fb6d127ee8d266677689233">calculate_softbit_matrices</a> ()</td></tr>
189
190	<tr><td class="mdescLeft"> </td><td class="mdescRight">This function calculates the soft bit mapping matrices S0 and S1. <br></td></tr>
191	<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
192	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d654c2e53ee82b2279ab894b8801b980"></a><!-- doxytag: member="itpp::PAM_c::scaling_factor" ref="d654c2e53ee82b2279ab894b8801b980" args="" -->
193	double </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1PAM__c.html#d654c2e53ee82b2279ab894b8801b980">scaling_factor</a></td></tr>
194
195	<tr><td class="mdescLeft"> </td><td class="mdescRight">Scaling factor used to normalize the average energy to 1. <br></td></tr>
196	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="552cd7add3e998eca485d0ea39808e0d"></a><!-- doxytag: member="itpp::PAM_c::setup_done" ref="552cd7add3e998eca485d0ea39808e0d" args="" -->
197	bool </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#552cd7add3e998eca485d0ea39808e0d">setup_done</a></td></tr>
198
199	<tr><td class="mdescLeft"> </td><td class="mdescRight">Setup indicator. <br></td></tr>
200	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3656edc52486e0551b734b32ab67d3b6"></a><!-- doxytag: member="itpp::PAM_c::k" ref="3656edc52486e0551b734b32ab67d3b6" args="" -->
201	int </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#3656edc52486e0551b734b32ab67d3b6">k</a></td></tr>
202
203	<tr><td class="mdescLeft"> </td><td class="mdescRight">Number of bits per modulation symbol. <br></td></tr>
204	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a434960c7ff9e5356d832aa53b46930b"></a><!-- doxytag: member="itpp::PAM_c::M" ref="a434960c7ff9e5356d832aa53b46930b" args="" -->
205	int </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#a434960c7ff9e5356d832aa53b46930b">M</a></td></tr>
206
207	<tr><td class="mdescLeft"> </td><td class="mdescRight">Number of modulation symbols. <br></td></tr>
208	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1b1a9a706c0736c51966703bea58cf48"></a><!-- doxytag: member="itpp::PAM_c::bitmap" ref="1b1a9a706c0736c51966703bea58cf48" args="" -->
209	<a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#1b1a9a706c0736c51966703bea58cf48">bitmap</a></td></tr>
210
211	<tr><td class="mdescLeft"> </td><td class="mdescRight">Bit to symbol mapping table (size: M x k). <br></td></tr>
212	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3ca26614189cb7a66da369bf0c4b9070"></a><!-- doxytag: member="itpp::PAM_c::bits2symbols" ref="3ca26614189cb7a66da369bf0c4b9070" args="" -->
213	ivec </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#3ca26614189cb7a66da369bf0c4b9070">bits2symbols</a></td></tr>
214
215	<tr><td class="mdescLeft"> </td><td class="mdescRight">Bit to symbol mapping in decimal form (size: M). <br></td></tr>
216	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3069840e9e7a44180615fb772cf9ae42"></a><!-- doxytag: member="itpp::PAM_c::symbols" ref="3069840e9e7a44180615fb772cf9ae42" args="" -->
217	<a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#3069840e9e7a44180615fb772cf9ae42">symbols</a></td></tr>
218
219	<tr><td class="mdescLeft"> </td><td class="mdescRight">Corresponding modulation symbols (size: M). <br></td></tr>
220	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c19c8fe07e95e4eb80e832a633b7c422"></a><!-- doxytag: member="itpp::PAM_c::S0" ref="c19c8fe07e95e4eb80e832a633b7c422" args="" -->
221	imat </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#c19c8fe07e95e4eb80e832a633b7c422">S0</a></td></tr>
222
223	<tr><td class="mdescLeft"> </td><td class="mdescRight">Matrix where row k contains the constellation points with '0' in bit position k. <br></td></tr>
224	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9d4c223ffd96fdc5b26ba5c44956998b"></a><!-- doxytag: member="itpp::PAM_c::S1" ref="9d4c223ffd96fdc5b26ba5c44956998b" args="" -->
225	imat </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#9d4c223ffd96fdc5b26ba5c44956998b">S1</a></td></tr>
226
227	<tr><td class="mdescLeft"> </td><td class="mdescRight">Matrix where row k contains the constellation points with '1' in bit position k. <br></td></tr>
228	<tr><td colspan="2"><br><h2>Related Functions</h2></td></tr>
229	<tr><td colspan="2">(Note that these are not member functions.) <br><br></td></tr>
230	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d47d1377dffb2aed9f21f8f976e80a0a"></a><!-- doxytag: member="itpp::PAM_c::Modulator_1D" ref="d47d1377dffb2aed9f21f8f976e80a0a" args="" -->
231	typedef <a class="el" href="classitpp_1_1Modulator.html">Modulator</a>< double > </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#d47d1377dffb2aed9f21f8f976e80a0a">Modulator_1D</a></td></tr>
232
233	<tr><td class="mdescLeft"> </td><td class="mdescRight">Definition of 1D Modulator (with real symbols). <br></td></tr>
234	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="97dc4e87ae4fa63c4e7dbbeac0ab00b0"></a><!-- doxytag: member="itpp::PAM_c::Modulator_2D" ref="97dc4e87ae4fa63c4e7dbbeac0ab00b0" args="" -->
235	typedef <a class="el" href="classitpp_1_1Modulator.html">Modulator</a><br class="typebreak">
236	< std::complex< double > > </td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Modulator.html#97dc4e87ae4fa63c4e7dbbeac0ab00b0">Modulator_2D</a></td></tr>
237
238	<tr><td class="mdescLeft"> </td><td class="mdescRight">Definition of 2D Modulator (with complex symbols). <br></td></tr>
239	</table>
240	<hr><a name="_details"></a><h2>Detailed Description</h2>
241	M-ary <a class="el" href="classitpp_1_1PAM.html" title="M-ary PAM modulator with real symbols.">PAM</a> modulator with complex symbols.
242	<p>
243	This class implements an M-ary <a class="el" href="classitpp_1_1PAM.html" title="M-ary PAM modulator with real symbols.">PAM</a> modulator with the following signal values: <img class="formulaInl" alt="$\{-(M-1), \ldots, -3, -1, 1, 3, \ldots, (M-1)\}$" src="form_267.png">. Symbol numbering is from right to left in the increasing order. The Gray encoding of bits to symbols is used.<p>
244	The constellation symbols are normalized so that the average energy is equal to 1. That is, normalized with <img class="formulaInl" alt="$ \sqrt{(M^2-1)/3}$" src="form_268.png">.<p>
245	<dl class="note" compact><dt><b>Note:</b></dt><dd>Although the constellation points can be represented in the real domain only, this class uses complex based interface to be compatible with other <a class="el" href="classitpp_1_1PSK.html" title="M-ary PSK modulator.">PSK</a> and <a class="el" href="classitpp_1_1QAM.html" title="M-ary QAM modulator with square lattice.">QAM</a> based modulators.</dd></dl>
246	<dl class="see" compact><dt><b>See also:</b></dt><dd><a class="el" href="classitpp_1_1PAM.html" title="M-ary PAM modulator with real symbols.">PAM</a> </dd></dl>
247	<hr><h2>Member Function Documentation</h2>
248	<a class="anchor" name="bd014d868b4f883712f92a7130401714"></a><!-- doxytag: member="itpp::PAM_c::demodulate_soft_bits" ref="bd014d868b4f883712f92a7130401714" args="(const Vec< std::complex< double > > &rx_symbols, const Vec< std::complex< double > > &channel, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const" -->
249	<div class="memitem">
250	<div class="memproto">
251	<table class="memname">
252	<tr>
253	<td class="memname">virtual void <a class="el" href="classitpp_1_1Modulator.html">itpp::Modulator</a>< std::complex< double > >::demodulate_soft_bits </td>
254	<td>(</td>
255	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > & </td>
256	<td class="paramname"> <em>rx_symbols</em>, </td>
257	</tr>
258	<tr>
259	<td class="paramkey"></td>
260	<td></td>
261	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > & </td>
262	<td class="paramname"> <em>channel</em>, </td>
263	</tr>
264	<tr>
265	<td class="paramkey"></td>
266	<td></td>
267	<td class="paramtype">double </td>
268	<td class="paramname"> <em>N0</em>, </td>
269	</tr>
270	<tr>
271	<td class="paramkey"></td>
272	<td></td>
273	<td class="paramtype">vec & </td>
274	<td class="paramname"> <em>soft_bits</em>, </td>
275	</tr>
276	<tr>
277	<td class="paramkey"></td>
278	<td></td>
279	<td class="paramtype"><a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> </td>
280	<td class="paramname"> <em>method</em> = <code>LOGMAP</code></td><td> </td>
281	</tr>
282	<tr>
283	<td></td>
284	<td>)</td>
285	<td></td><td></td><td> const<code> [virtual, inherited]</code></td>
286	</tr>
287	</table>
288	</div>
289	<div class="memdoc">
290
291	<p>
292	Soft demodulator for fading channels.
293	<p>
294	This function calculates the log-likelihood ratio (LLR) of the received signal from fading channels. Depending on the soft demodulation method chosen, either full log-MAP calculation is performed (default method), according to the following equation: <p class="formulaDsp">
295	<img class="formulaDsp" alt="\[\log \left( \frac{P(b_i=0\|r)}{P(b_i=1\|r)} \right) = \log \left( \frac{\sum_{s_i \in S_0} \exp \left( -\frac{\|r_k - c_k s_i\|^2}{N_0} \right)} {\sum_{s_i \in S_1} \exp \left( -\frac{\|r_k - c_k s_i\|^2}{N_0} \right)} \right) \]" src="form_275.png">
296	<p>
297	or approximate, but faster calculation is performed.<p>
298	The approximate method finds for each bit the closest constellation points that have zero and one in the corresponding position. Let <img class="formulaInl" alt="$d_0 = \|r_k - c_k s_0\|$" src="form_276.png"> denote the distance to the closest zero point and <img class="formulaInl" alt="$d_1 = \|r_k - c_k s_1\|$" src="form_277.png"> denote the distance to the closest one point for the corresponding bit respectively. The approximate algorithm then computes <p class="formulaDsp">
299	<img class="formulaDsp" alt="\[\frac{d_1^2 - d_0^2}{N_0}\]" src="form_272.png">
300	<p>
301	<p>
302	When this function is to be used together with MAP-based turbo decoding algorithms then the channel reliability factor <img class="formulaInl" alt="$L_c$" src="form_274.png"> of the turbo decoder shall be set to 1. The output from this function can also be used by a Viterbi decoder using an AWGN based metric calculation function.<p>
303	<dl compact><dt><b>Parameters:</b></dt><dd>
304	<table border="0" cellspacing="2" cellpadding="0">
305	<tr><td valign="top"></td><td valign="top"><em>rx_symbols</em> </td><td>The received noisy constellation symbols <img class="formulaInl" alt="$r_k$" src="form_278.png"> </td></tr>
306	<tr><td valign="top"></td><td valign="top"><em>channel</em> </td><td>The channel values <img class="formulaInl" alt="$c_k$" src="form_253.png"> </td></tr>
307	<tr><td valign="top"></td><td valign="top"><em>N0</em> </td><td>The spectral density of the AWGN noise </td></tr>
308	<tr><td valign="top"></td><td valign="top"><em>soft_bits</em> </td><td>The soft bits calculated using the expression above </td></tr>
309	<tr><td valign="top"></td><td valign="top"><em>method</em> </td><td>The method used for demodulation (LOGMAP or APPROX)</td></tr>
310	</table>
311	</dl>
312	<dl class="note" compact><dt><b>Note:</b></dt><dd>For soft demodulation it is suggested to use the N-dimensional modulator (Modulator_ND) instead, which is based on the QLLR (quantized) arithmetic and therefore is faster. Please note, however, that mixed use of <code>Modulator_1D/<code>Modulator_2D</code> and</code> <code>Modulator_ND</code> is not advised. </dd></dl>
313
314	</div>
315	</div><p>
316	<a class="anchor" name="9beffaf8f69378f9c20a85f3023bd9af"></a><!-- doxytag: member="itpp::PAM_c::demodulate_soft_bits" ref="9beffaf8f69378f9c20a85f3023bd9af" args="(const Vec< std::complex< double > > &rx_symbols, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const" -->
317	<div class="memitem">
318	<div class="memproto">
319	<table class="memname">
320	<tr>
321	<td class="memname">virtual void <a class="el" href="classitpp_1_1Modulator.html">itpp::Modulator</a>< std::complex< double > >::demodulate_soft_bits </td>
322	<td>(</td>
323	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html">Vec</a>< std::complex< double > > & </td>
324	<td class="paramname"> <em>rx_symbols</em>, </td>
325	</tr>
326	<tr>
327	<td class="paramkey"></td>
328	<td></td>
329	<td class="paramtype">double </td>
330	<td class="paramname"> <em>N0</em>, </td>
331	</tr>
332	<tr>
333	<td class="paramkey"></td>
334	<td></td>
335	<td class="paramtype">vec & </td>
336	<td class="paramname"> <em>soft_bits</em>, </td>
337	</tr>
338	<tr>
339	<td class="paramkey"></td>
340	<td></td>
341	<td class="paramtype"><a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> </td>
342	<td class="paramname"> <em>method</em> = <code>LOGMAP</code></td><td> </td>
343	</tr>
344	<tr>
345	<td></td>
346	<td>)</td>
347	<td></td><td></td><td> const<code> [virtual, inherited]</code></td>
348	</tr>
349	</table>
350	</div>
351	<div class="memdoc">
352
353	<p>
354	Soft demodulator for AWGN channels.
355	<p>
356	This function calculates the log-likelihood ratio (LLR) of the received signal from AWGN channels. Depending on the soft demodulation method chosen, either full log-MAP calculation is performed (default method), according to the following equation: <p class="formulaDsp">
357	<img class="formulaDsp" alt="\[\log \left( \frac{P(b_i=0\|r)}{P(b_i=1\|r)} \right) = \log \left( \frac{\sum_{s_i \in S_0} \exp \left( -\frac{\|r_k - s_i\|^2}{N_0} \right)} {\sum_{s_i \in S_1} \exp \left( -\frac{\|r_k - s_i\|^2}{N_0} \right)} \right) \]" src="form_269.png">
358	<p>
359	or approximate, but faster calculation is performed.<p>
360	The approximate method finds for each bit the closest constellation points that have zero and one in the corresponding position. Let <img class="formulaInl" alt="$d_0 = \|r_k - s_0\|$" src="form_270.png"> denote the distance to the closest zero point and <img class="formulaInl" alt="$d_1 = \|r_k - s_1\|$" src="form_271.png"> denote the distance to the closest one point for the corresponding bit respectively. The approximate algorithm then computes <p class="formulaDsp">
361	<img class="formulaDsp" alt="\[\frac{d_1^2 - d_0^2}{N_0}\]" src="form_272.png">
362	<p>
363	<p>
364	This function can be used on channels where the channel gain <img class="formulaInl" alt="$c_k = 1$" src="form_273.png">.<p>
365	When this function is to be used together with MAP-based turbo decoding algorithms then the channel reliability factor <img class="formulaInl" alt="$L_c$" src="form_274.png"> of the turbo decoder shall be set to 1. The output from this function can also be used by a Viterbi decoder using an AWGN based metric calculation function.<p>
366	<dl compact><dt><b>Parameters:</b></dt><dd>
367	<table border="0" cellspacing="2" cellpadding="0">
368	<tr><td valign="top"></td><td valign="top"><em>rx_symbols</em> </td><td>The received noisy constellation symbols </td></tr>
369	<tr><td valign="top"></td><td valign="top"><em>N0</em> </td><td>The spectral density of the AWGN noise </td></tr>
370	<tr><td valign="top"></td><td valign="top"><em>soft_bits</em> </td><td>The soft bits calculated using the expression above </td></tr>
371	<tr><td valign="top"></td><td valign="top"><em>method</em> </td><td>The method used for demodulation (LOGMAP or APPROX)</td></tr>
372	</table>
373	</dl>
374	<dl class="note" compact><dt><b>Note:</b></dt><dd>For soft demodulation it is suggested to use the N-dimensional modulator (<code>Modulator_ND</code>) instead, which is based on the QLLR (quantized) arithmetic and therefore is faster. Please note, however, that mixed use of <code>Modulator_1D/<code>Modulator_2D</code> and</code> <code>Modulator_ND</code> is not advised. </dd></dl>
375
376	</div>
377	</div><p>
378	<a class="anchor" name="6cd8dbe2ce99f63785cc51772e4e586d"></a><!-- doxytag: member="itpp::PAM_c::demodulate_soft_bits" ref="6cd8dbe2ce99f63785cc51772e4e586d" args="(const cvec &rx_symbols, const cvec &channel, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const " -->
379	<div class="memitem">
380	<div class="memproto">
381	<table class="memname">
382	<tr>
383	<td class="memname">void itpp::PAM_c::demodulate_soft_bits </td>
384	<td>(</td>
385	<td class="paramtype">const cvec & </td>
386	<td class="paramname"> <em>rx_symbols</em>, </td>
387	</tr>
388	<tr>
389	<td class="paramkey"></td>
390	<td></td>
391	<td class="paramtype">const cvec & </td>
392	<td class="paramname"> <em>channel</em>, </td>
393	</tr>
394	<tr>
395	<td class="paramkey"></td>
396	<td></td>
397	<td class="paramtype">double </td>
398	<td class="paramname"> <em>N0</em>, </td>
399	</tr>
400	<tr>
401	<td class="paramkey"></td>
402	<td></td>
403	<td class="paramtype">vec & </td>
404	<td class="paramname"> <em>soft_bits</em>, </td>
405	</tr>
406	<tr>
407	<td class="paramkey"></td>
408	<td></td>
409	<td class="paramtype"><a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> </td>
410	<td class="paramname"> <em>method</em> = <code>LOGMAP</code></td><td> </td>
411	</tr>
412	<tr>
413	<td></td>
414	<td>)</td>
415	<td></td><td></td><td> const<code> [virtual]</code></td>
416	</tr>
417	</table>
418	</div>
419	<div class="memdoc">
420
421	<p>
422	Soft demodulator for known fading channels.
423	<p>
424	This function calculates the log-likelihood ratio (LLR) of the received signal from fading channels. Depending on the soft demodulation method chosen, either full log-MAP calculation is performed (default method), according to the following equation: <p class="formulaDsp">
425	<img class="formulaDsp" alt="\[\log \left( \frac{P(b_i=0\|r)}{P(b_i=1\|r)} \right) = \log \left( \frac{\sum_{s_i \in S_0} \exp \left( -\frac{\|r_k - c_k s_i\|^2}{N_0} \right)} {\sum_{s_i \in S_1} \exp \left( -\frac{\|r_k - c_k s_i\|^2}{N_0} \right)} \right) \]" src="form_275.png">
426	<p>
427	or approximate, but faster calculation is performed.<p>
428	The approximate method finds for each bit the closest constellation points that have zero and one in the corresponding position. Let <img class="formulaInl" alt="$d_0 = \|r_k - c_k s_0\|$" src="form_276.png"> denote the distance to the closest zero point and <img class="formulaInl" alt="$d_1 = \|r_k - c_k s_1\|$" src="form_277.png"> denote the distance to the closest one point for the corresponding bit respectively. The approximate algorithm then computes <p class="formulaDsp">
429	<img class="formulaDsp" alt="\[\frac{d_1^2 - d_0^2}{N_0}\]" src="form_272.png">
430	<p>
431	<p>
432	When this function is to be used together with MAP-based turbo decoding algorithms then the channel reliability factor <img class="formulaInl" alt="$L_c$" src="form_274.png"> of the turbo decoder shall be set to 1. The output from this function can also be used by a Viterbi decoder using an AWGN based metric calculation function.<p>
433	<dl compact><dt><b>Parameters:</b></dt><dd>
434	<table border="0" cellspacing="2" cellpadding="0">
435	<tr><td valign="top"></td><td valign="top"><em>rx_symbols</em> </td><td>The received noisy constellation symbols <img class="formulaInl" alt="$r_k$" src="form_278.png"> (complex) </td></tr>
436	<tr><td valign="top"></td><td valign="top"><em>channel</em> </td><td>The channel values <img class="formulaInl" alt="$c_k$" src="form_253.png"> </td></tr>
437	<tr><td valign="top"></td><td valign="top"><em>N0</em> </td><td>The spectral density of the AWGN noise </td></tr>
438	<tr><td valign="top"></td><td valign="top"><em>soft_bits</em> </td><td>The soft bits calculated using the expression above </td></tr>
439	<tr><td valign="top"></td><td valign="top"><em>method</em> </td><td>The method used for demodulation (LOGMAP or APPROX)</td></tr>
440	</table>
441	</dl>
442	<dl class="note" compact><dt><b>Note:</b></dt><dd>For soft demodulation it is suggested to use the N-dimensional modulator (<a class="el" href="classitpp_1_1Modulator__ND.html" title="Base class for an N-dimensional (ND) vector (MIMO) modulator.">Modulator_ND</a>) instead, which is based on the QLLR (quantized) arithmetic and therefore is faster. Please note, however, that mixed use of <code>Modulator_1D/<code>Modulator_2D</code> and</code> <code><a class="el" href="classitpp_1_1Modulator__ND.html" title="Base class for an N-dimensional (ND) vector (MIMO) modulator.">Modulator_ND</a></code> is not advised. </dd></dl>
443
444	<p>References <a class="el" href="log__exp_8h-source.html#l00172">itpp::exp()</a>, <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, <a class="el" href="modulator_8h-source.html#l00228">itpp::Modulator< std::complex< double > >::k</a>, <a class="el" href="modulator_8h-source.html#l00047">itpp::LOGMAP</a>, <a class="el" href="modulator_8h-source.html#l00230">itpp::Modulator< std::complex< double > >::M</a>, <a class="el" href="tcp_8h-source.html#l00117">itpp::max()</a>, <a class="el" href="fix__functions_8cpp-source.html#l00084">itpp::real()</a>, <a class="el" href="modulator_8h-source.html#l00239">itpp::Modulator< std::complex< double > >::S0</a>, <a class="el" href="modulator_8h-source.html#l00242">itpp::Modulator< std::complex< double > >::S1</a>, <a class="el" href="modulator_8h-source.html#l00226">itpp::Modulator< std::complex< double > >::setup_done</a>, <a class="el" href="elem__math_8h-source.html#l00056">itpp::sqr()</a>, <a class="el" href="modulator_8h-source.html#l00236">itpp::Modulator< std::complex< double > >::symbols</a>, and <a class="el" href="log__exp_8h-source.html#l00105">itpp::trunc_log()</a>.</p>
445
446	</div>
447	</div><p>
448	<a class="anchor" name="56e1f1d20bfecdd0e5ef37456a5179ae"></a><!-- doxytag: member="itpp::PAM_c::demodulate_soft_bits" ref="56e1f1d20bfecdd0e5ef37456a5179ae" args="(const cvec &rx_symbols, double N0, vec &soft_bits, Soft_Method method=LOGMAP) const " -->
449	<div class="memitem">
450	<div class="memproto">
451	<table class="memname">
452	<tr>
453	<td class="memname">void itpp::PAM_c::demodulate_soft_bits </td>
454	<td>(</td>
455	<td class="paramtype">const cvec & </td>
456	<td class="paramname"> <em>rx_symbols</em>, </td>
457	</tr>
458	<tr>
459	<td class="paramkey"></td>
460	<td></td>
461	<td class="paramtype">double </td>
462	<td class="paramname"> <em>N0</em>, </td>
463	</tr>
464	<tr>
465	<td class="paramkey"></td>
466	<td></td>
467	<td class="paramtype">vec & </td>
468	<td class="paramname"> <em>soft_bits</em>, </td>
469	</tr>
470	<tr>
471	<td class="paramkey"></td>
472	<td></td>
473	<td class="paramtype"><a class="el" href="group__modulators.html#g5128af4688e1a1caa84e1fabf051faa7">Soft_Method</a> </td>
474	<td class="paramname"> <em>method</em> = <code>LOGMAP</code></td><td> </td>
475	</tr>
476	<tr>
477	<td></td>
478	<td>)</td>
479	<td></td><td></td><td> const<code> [virtual]</code></td>
480	</tr>
481	</table>
482	</div>
483	<div class="memdoc">
484
485	<p>
486	Soft demodulator for AWGN channels.
487	<p>
488	This function calculates the log-likelihood ratio (LLR) of the received signal from AWGN channels. Depending on the soft demodulation method chosen, either full log-MAP calculation is performed (default method), according to the following equation: <p class="formulaDsp">
489	<img class="formulaDsp" alt="\[\log \left( \frac{P(b_i=0\|r)}{P(b_i=1\|r)} \right) = \log \left( \frac{\sum_{s_i \in S_0} \exp \left( -\frac{\|r_k - s_i\|^2}{N_0} \right)} {\sum_{s_i \in S_1} \exp \left( -\frac{\|r_k - s_i\|^2}{N_0} \right)} \right) \]" src="form_269.png">
490	<p>
491	or approximate, but faster calculation is performed.<p>
492	The approximate method finds for each bit the closest constellation points that have zero and one in the corresponding position. Let <img class="formulaInl" alt="$d_0 = \|r_k - s_0\|$" src="form_270.png"> denote the distance to the closest zero point and <img class="formulaInl" alt="$d_1 = \|r_k - s_1\|$" src="form_271.png"> denote the distance to the closest one point for the corresponding bit respectively. The approximate algorithm then computes <p class="formulaDsp">
493	<img class="formulaDsp" alt="\[\frac{d_1^2 - d_0^2}{N_0}\]" src="form_272.png">
494	<p>
495	<p>
496	This function can be used on channels where the channel gain <img class="formulaInl" alt="$c = 1$" src="form_288.png">.<p>
497	When this function is to be used together with MAP-based turbo decoding algorithms then the channel reliability factor <img class="formulaInl" alt="$L_c$" src="form_274.png"> of the turbo decoder shall be set to 1. The output from this function can also be used by a Viterbi decoder using an AWGN based metric calculation function.<p>
498	<dl compact><dt><b>Parameters:</b></dt><dd>
499	<table border="0" cellspacing="2" cellpadding="0">
500	<tr><td valign="top"></td><td valign="top"><em>rx_symbols</em> </td><td>The received noisy constellation symbols <img class="formulaInl" alt="$r_k$" src="form_278.png"> (complex, but symbols are real) </td></tr>
501	<tr><td valign="top"></td><td valign="top"><em>N0</em> </td><td>The spectral density of the AWGN noise </td></tr>
502	<tr><td valign="top"></td><td valign="top"><em>soft_bits</em> </td><td>The soft bits calculated using the expression above </td></tr>
503	<tr><td valign="top"></td><td valign="top"><em>method</em> </td><td>The method used for demodulation (LOGMAP or APPROX)</td></tr>
504	</table>
505	</dl>
506	<dl class="note" compact><dt><b>Note:</b></dt><dd>For soft demodulation it is suggested to use the N-dimensional modulator (<a class="el" href="classitpp_1_1Modulator__ND.html" title="Base class for an N-dimensional (ND) vector (MIMO) modulator.">Modulator_ND</a>) instead, which is based on the QLLR (quantized) arithmetic and therefore is faster. Please note, however, that mixed use of <code>Modulator_1D/<code>Modulator_2D</code> and</code> <code><a class="el" href="classitpp_1_1Modulator__ND.html" title="Base class for an N-dimensional (ND) vector (MIMO) modulator.">Modulator_ND</a></code> is not advised. </dd></dl>
507
508	<p>References <a class="el" href="log__exp_8h-source.html#l00172">itpp::exp()</a>, <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, <a class="el" href="modulator_8h-source.html#l00228">itpp::Modulator< std::complex< double > >::k</a>, <a class="el" href="modulator_8h-source.html#l00047">itpp::LOGMAP</a>, <a class="el" href="modulator_8h-source.html#l00230">itpp::Modulator< std::complex< double > >::M</a>, <a class="el" href="tcp_8h-source.html#l00117">itpp::max()</a>, <a class="el" href="fix__functions_8cpp-source.html#l00084">itpp::real()</a>, <a class="el" href="modulator_8h-source.html#l00239">itpp::Modulator< std::complex< double > >::S0</a>, <a class="el" href="modulator_8h-source.html#l00242">itpp::Modulator< std::complex< double > >::S1</a>, <a class="el" href="modulator_8h-source.html#l00226">itpp::Modulator< std::complex< double > >::setup_done</a>, <a class="el" href="elem__math_8h-source.html#l00056">itpp::sqr()</a>, <a class="el" href="modulator_8h-source.html#l00236">itpp::Modulator< std::complex< double > >::symbols</a>, and <a class="el" href="log__exp_8h-source.html#l00105">itpp::trunc_log()</a>.</p>
509
510	<p>Referenced by <a class="el" href="modulator_8cpp-source.html#l00474">demodulate_soft_bits()</a>.</p>
511
512	</div>
513	</div><p>
514	<a class="anchor" name="a8186f0e837fd3d440a6acb7a0225d35"></a><!-- doxytag: member="itpp::PAM_c::get_bits2symbols" ref="a8186f0e837fd3d440a6acb7a0225d35" args="() const" -->
515	<div class="memitem">
516	<div class="memproto">
517	<table class="memname">
518	<tr>
519	<td class="memname">virtual ivec <a class="el" href="classitpp_1_1Modulator.html">itpp::Modulator</a>< std::complex< double > >::get_bits2symbols </td>
520	<td>(</td>
521	<td class="paramname"> </td>
522	<td> ) </td>
523	<td> const<code> [inline, virtual, inherited]</code></td>
524	</tr>
525	</table>
526	</div>
527	<div class="memdoc">
528
529	<p>
530	Get the bitmap, which maps input bits into symbols.
531	<p>
532	The mapping is done as follows. An input bit sequence in decimal notation is used for indexing the <code>bits2symbols</code> table. The indexing result denotes the symbol to be used from the <code>symbols</code> table, e.g.:<p>
533	<div class="fragment"><pre class="fragment"> PSK <a class="code" href="group__miscfunc.html#g441f466a2b056fe5f2b05fcd894c472f" title="Calculates the modulus, i.e. the signed reminder after division.">mod</a>(8); <span class="comment">// assume 8-PSK modulator</span>
534	cvec sym = <a class="code" href="group__miscfunc.html#g441f466a2b056fe5f2b05fcd894c472f" title="Calculates the modulus, i.e. the signed reminder after division.">mod</a>.get_symbols();
535	ivec bits2sym = <a class="code" href="group__miscfunc.html#g441f466a2b056fe5f2b05fcd894c472f" title="Calculates the modulus, i.e. the signed reminder after division.">mod</a>.get_bits2symbols();
536	bvec in_bits = <span class="stringliteral">"100"</span> <span class="comment">// input bits</span>
537	<span class="keywordtype">int</span> d = <a class="code" href="group__convertfunc.html#g698adf78bc0f9d36fd5987bc87d543fa" title="Convert a bvec to decimal int with the first bit as MSB if msb_first == true.">bin2dec</a>(in_bits); <span class="comment">// decimal representation of in_bits = 4</span>
538	<span class="comment">// mapping of d into PSK symbol using bits2sym and sym tables</span>
539	std::complex<double> out_symbol = sym(bits2sym(d));
540	</pre></div>
541	</div>
542	</div><p>
543	<hr>The documentation for this class was generated from the following files:<ul>
544	<li><a class="el" href="modulator_8h-source.html">modulator.h</a><li><a class="el" href="modulator_8cpp.html">modulator.cpp</a></ul>
545	</div>
546	<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:19 2009 for mixpp by
547	<a href="http://www.doxygen.org/index.html">
548	<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>
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