Digital Signal Transmission/Carrier Frequency Systems with Coherent Demodulation - Revision history

Hwang at 10:04, 17 November 2022

2022-11-17T10:04:53Z

Guenter at 15:17, 6 September 2022

2022-09-06T15:17:20Z

Guenter at 12:05, 3 September 2022

2022-09-03T12:05:17Z

Hwang at 18:19, 1 September 2022

2022-09-01T18:19:35Z

Hwang at 12:54, 1 September 2022

2022-09-01T12:54:39Z

Hwang at 12:53, 1 September 2022

2022-09-01T12:53:21Z

Guenter at 14:49, 24 August 2022

2022-08-24T14:49:47Z

Guenter at 08:05, 23 August 2022

2022-08-23T08:05:24Z

Guenter at 08:03, 23 August 2022

2022-08-23T08:03:16Z

Guenter at 15:21, 22 August 2022

2022-08-22T15:21:58Z

@@ Line 38: / Line 38: @@
   \hspace{0.05cm}.$$
-*While the coefficients &nbsp; $a_{{\rm I}i}$ &nbsp; and &nbsp; $a_{{\rm Q}i}$ &nbsp; are dimensionless,&nbsp; the new coefficients &nbsp; $s_{{\rm I}i}$ &nbsp; and &nbsp; $s_{{\rm Q}i}$ &nbsp; have the unit&nbsp; "root of energy" &nbsp; &rArr; &nbsp; see page&nbsp; [[Digital_Signal_Transmission/Signals,_Basis_Functions_and_Vector_Spaces#Nomenclature_in_the_fourth_chapter|"Nomenclature in the fourth main chapter"]]:
+*While the coefficients &nbsp; $a_{{\rm I}i}$ &nbsp; and &nbsp; $a_{{\rm Q}i}$ &nbsp; are dimensionless,&nbsp; the new coefficients &nbsp; $s_{{\rm I}i}$ &nbsp; and &nbsp; $s_{{\rm Q}i}$ &nbsp; have the unit&nbsp; "root of energy" &nbsp; &rArr; &nbsp; see section&nbsp; [[Digital_Signal_Transmission/Signals,_Basis_Functions_and_Vector_Spaces#Nomenclature_in_the_fourth_chapter|"Nomenclature in the fourth main chapter"]]:
 :$$s_{{\rm I}i} = {\sqrt{E_{gs}}} \cdot a_{{\rm I}i}\hspace{0.05cm}, $$

@@ Line 53: / Line 53: @@
 <br>
 In the following,&nbsp; we always assume the equivalent low-pass signal unless explicitly stated otherwise.&nbsp; In particular,&nbsp; the signals&nbsp;
-[[File:EN_Dig_T_4_4_S2.png|right|frame|AWGN channel model for complex signals '''KORREKTUR: optimal '''|class=fit]]
+[[File:EN_Dig_T_4_4_S2_v2.png|right|frame|AWGN channel model for complex signals|class=fit]]
 *$s(t) = s_{\rm TP}(t)$&nbsp; and&nbsp;

← Older revision		Revision as of 12:05, 3 September 2022
Line 60:		Line 60:


−	in the graph are  "low-pass signals"  and thus generally complex.  The suffix  "TP"  is omitted in the remainder of this paper ~~'''KORREKTUR: in the following'''~~.<br>	+	in the graph are  "low-pass signals"  and thus generally complex.  The suffix  "TP"  is omitted in the remainder of this paper .<br>

	To this figure is to be noted:		To this figure is to be noted:

@@ Line 225: / Line 225: @@
 ::<math>\Rightarrow\hspace{0.3cm} M = 4\hspace{-0.1cm}:\hspace{0.1cm}d_{\rm min}/E^{1/2}  =  \sqrt{2} \approx 1.414  \hspace{0.05cm}, \hspace{0.8cm} M = 8\hspace{-0.1cm}:\hspace{0.1cm}d_{\rm min}/E^{1/2}   \approx 0.765  \hspace{0.05cm},\hspace{0.8cm} M = 16\hspace{-0.1cm}:\hspace{0.1cm}d_{\rm min}/E^{1/2}   \approx 0.390  \hspace{0.05cm}.</math>
-*The upper bound&nbsp; $p_{\rm UB}$&nbsp; for the AWGN symbol error probability&nbsp; $p_{\rm S}$&nbsp; after the&nbsp; [[Digitalsignal%C3%BCbertragung/Approximation_der_Fehlerwahrscheinlichkeit#Union_Bound_-_Obere_Schranke_f.C3.BCr_die_Fehlerwahrscheinlichkeit|"Union Bound"]]&nbsp; yields:
+*The upper bound&nbsp; $p_{\rm UB}$&nbsp; for the AWGN symbol error probability&nbsp; $p_{\rm S}$&nbsp; after the&nbsp; [[Digital_Signal_Transmission/Approximation_of_the_Error_Probability#Union_Bound_-_Upper_bound_for_the_error_probability|"Union Bound"]]&nbsp; yields:
 ::<math>p_{\rm UB} =  2 \cdot {\rm Q} \left ( \sin ({ \pi}/{ M}) \cdot \sqrt{ { {2E_{\rm S}}}/{ N_0} }\right )  \ge  p_{\rm S}

← Older revision		Revision as of 12:54, 1 September 2022
Line 60:		Line 60:


−	in the graph are  "low-pass signals"  and thus generally complex.  The suffix  "TP"  is omitted in the remainder of this paper.<br>	+	in the graph are  "low-pass signals"  and thus generally complex.  The suffix  "TP"  is omitted in the remainder of this paper '''KORREKTUR: in the following'''.<br>

	To this figure is to be noted:		To this figure is to be noted:

@@ Line 10: / Line 10: @@
 In the first three chapters of this&nbsp; [[Digital_Signal_Transmission|fourth main chapter:]] &nbsp; "Generalized Description of Digital Modulation Methods",&nbsp; the structure of the optimal receiver and the signal representation by means of basis functions were treated by the example of baseband transmission.
-[[File:EN_Dig_T_4_4_S1.png|right|frame|Equivalent low-pass model of carrier-modulated transmission methods '''Korrektur''' hinten etwas verschieben|class=fit]]
+[[File:EN_Dig_T_4_4_S1_v2.png|right|frame|Equivalent low-pass model of carrier-modulated transmission methods|class=fit]]
 With the same systematics and the same uniformity,&nbsp; band&ndash;pass systems will now also be considered which have already been described in earlier books or chapters,&nbsp; namely
@@ Line 118: / Line 118: @@
 *with sinusoidal carrier: &nbsp; $s_{{\rm I}i} \equiv 0$&nbsp; and&nbsp; $s_{{\rm Q}i} = \{\pm E^{1/2}\}$.
-[[File:EN_Dig_T_4_4_S3.png|right|frame|Signal space constellations of the BPSK '''Korrektur''' BPSK statt OOK|class=fit]]
+[[File:EN_Dig_T_4_4_S4_v2.png|right|frame|Signal space constellations of the BPSK|class=fit]]
 The improvements compared to on&ndash;off keying can be seen from the equations given in the graphic&nbsp; $($in the field with green background$)$:
@@ Line 140: / Line 140: @@
 *the two innermost signal space points&nbsp; $(\pm 1)$&nbsp; do not differ in terms of amplitude&nbsp; ("envelope"),
 *but only in terms of phase&nbsp; $(0^\circ$ or $180^\circ)$.
-[[File:EN_Dig_T_4_4_S5.png|right|frame|Signal room constellation of the 8-ASK'''Korrektur'''|class=fit]]
+[[File:EN_Dig_T_4_4_S5.png|right|frame|Signal room constellation of the 8-ASK|class=fit]]

@@ Line 10: / Line 10: @@
 In the first three chapters of this&nbsp; [[Digital_Signal_Transmission|fourth main chapter:]] &nbsp; "Generalized Description of Digital Modulation Methods",&nbsp; the structure of the optimal receiver and the signal representation by means of basis functions were treated by the example of baseband transmission.
-[[File:EN_Dig_T_4_4_S1.png|right|frame|Equivalent low-pass model of carrier-modulated transmission methods '''Korrektur'''|class=fit]]
+[[File:EN_Dig_T_4_4_S1.png|right|frame|Equivalent low-pass model of carrier-modulated transmission methods '''Korrektur''' hinten etwas verschieben|class=fit]]
 With the same systematics and the same uniformity,&nbsp; band&ndash;pass systems will now also be considered which have already been described in earlier books or chapters,&nbsp; namely
@@ Line 53: / Line 53: @@
 <br>
 In the following,&nbsp; we always assume the equivalent low-pass signal unless explicitly stated otherwise.&nbsp; In particular,&nbsp; the signals&nbsp;
-[[File:EN_Dig_T_4_4_S2.png|right|frame|AWGN channel model for complex signals '''Korrektur'''|class=fit]]
+[[File:EN_Dig_T_4_4_S2.png|right|frame|AWGN channel model for complex signals|class=fit]]
 *$s(t) = s_{\rm TP}(t)$&nbsp; and&nbsp;
@@ Line 84: / Line 84: @@
 The simplest digital modulation method is&nbsp; "On&ndash;off keying"&nbsp; $\rm (OOK)$,&nbsp; which has already been described in detail in the book&nbsp; [[Modulation_Methods/Linear_Digital_Modulation#ASK_.E2.80.93_Amplitude_Shift_Keying|"Modulation Methods"]]&nbsp; on the basis of its band-pass signals.&nbsp; There,&nbsp; this method was partly also called&nbsp; "Amplitude Shift Keying"&nbsp; $\rm (2&ndash;ASK)$.<br>
-[[File:EN_Dig_T_4_4_S3.png|right|frame|Signal space constellations for on-off keying '''Korrektur'''|class=fit]]
+[[File:EN_Dig_T_4_4_S3.png|right|frame|Signal space constellations for on-off keying|class=fit]]
 This method can be characterized as follows: