Modulation Methods/Direct-Sequence Spread Spectrum Modulation - Revision history

Guenter at 15:13, 19 January 2023

2023-01-19T15:13:49Z

Hwang at 14:52, 11 January 2023

2023-01-11T14:52:01Z

Hwang at 14:49, 11 January 2023

2023-01-11T14:49:53Z

Hwang at 14:42, 11 January 2023

2023-01-11T14:42:58Z

Hwang at 14:40, 11 January 2023

2023-01-11T14:40:58Z

Hwang at 14:38, 11 January 2023

2023-01-11T14:38:51Z

Hwang at 14:38, 11 January 2023

2023-01-11T14:38:03Z

Hwang at 14:36, 11 January 2023

2023-01-11T14:36:40Z

Hwang at 14:34, 11 January 2023

2023-01-11T14:34:49Z

Reed at 13:59, 9 April 2022

2022-04-09T13:59:23Z

@@ Line 21: / Line 21: @@
 $\text{This system can be characterized as follows:}$
 *If the multiplication with the spreading signal &nbsp;$c(t)$&nbsp; at transmitter and receiver is omitted,&nbsp; the result is a conventional &nbsp;[[Modulation_Methods/Lineare_digitale_Modulation#BPSK_.E2.80.93_Binary_Phase_Shift_Keying|$\text{BPSK system}$]]&nbsp; with the carrier &nbsp;$z(t)$&nbsp; and AWGN noise, characterized by the additive Gaussian noise signal &nbsp;$n(t)$.&nbsp; The second interference component&nbsp; (interference from other participants)&nbsp; is omitted: &nbsp; $i(t) = 0$.
-*For the following it is assumed&nbsp; $($this is essential for direct-sequence spread spectrum!$)$ that the source signal &nbsp;$q(t)$&nbsp; has a rectangular NRZ curve.&nbsp; Then the matched filter can be replaced by an integrator over a symbol duration &nbsp;$T$&nbsp; &nbsp; ⇒ &nbsp; &nbsp;[[Digital_Signal_Transmission/Error_Probability_for_Baseband_Transmission#Optimal_binary_receiver_.E2.80.93_.22Integrate_.26_Dump.22_realization|$\text{Integrate & Dump}$]].&nbsp; This is followed by the threshold decider '''KORREKTUR: decision'''.}}
+*For the following it is assumed&nbsp; $($this is essential for direct-sequence spread spectrum!$)$ that the source signal &nbsp;$q(t)$&nbsp; has a rectangular NRZ curve.&nbsp; Then the matched filter can be replaced by an integrator over a symbol duration &nbsp;$T$&nbsp; &nbsp; ⇒ &nbsp; &nbsp;[[Digital_Signal_Transmission/Error_Probability_for_Baseband_Transmission#Optimal_binary_receiver_.E2.80.93_.22Integrate_.26_Dump.22_realization|$\text{Integrate & Dump}$]].&nbsp; This is followed by the threshold decision.}}
 ==Principle and properties of band spreading methods==
@@ Line 60: / Line 60: @@
 *above the source signal &nbsp;$q(t)$&nbsp; &ndash; marked by blue background &ndash; and the band spread signal &nbsp;$s(t)$&nbsp; as solid black line,
 *at the bottom left the signal &nbsp;$b(t)$&nbsp; after band compression,
-*bottom right the detection signal &nbsp;$d(t)$&nbsp; after the integrator, directly before the decision maker '''KORREKTUR: decision'''.
+*bottom right the detection signal &nbsp;$d(t)$&nbsp; after the integrator, directly before the decision.

@@ Line 125: / Line 125: @@
 {{BlaueBox|TEXT=
 $\text{Conclusions:}$&nbsp;
-*&raquo;'''With AWGN noise'''&laquo;&nbsp; (and also many other channels),&nbsp; '''the bit error probability cannot be reduced by band spreading'''.
+*'''With AWGN noise'''&nbsp; (and also many other channels),&nbsp; '''the bit error probability cannot be reduced by band spreading'''.
 *In the best case,&nbsp; band spreading results in the same bit error probability as BPSK&nbsp; (without spreading).
 *For our purposes,&nbsp; '''band spreading is a necessary measure to be able to supply several subscribers simultaneously in the same frequency band'''.

@@ Line 91: / Line 91: @@
 After thresholding the samples &nbsp;$d(νT)$,&nbsp; one nevertheless obtains mostly the sought amplitude coefficients.&nbsp; The vague statement "mostly" is quantifiable by the bit error probability &nbsp;$p_{\rm B}$.&nbsp;&nbsp; As
 :$$b(t) =  \big [ s(t) + n(t) \big ] \cdot c(t) = q(t) + n(t) \cdot c(t)$$
-and due to the fact that the statistical properties of white noise &nbsp;$n(t)$&nbsp; are not changed by the multiplication with the &nbsp;$±1$ signal &nbsp;$c(t)$,&nbsp; the same result is obtained again as for the&nbsp; [[Modulation_Methods/Lineare_digitale_Modulation#Fehlerwahrscheinlichkeiten_-_ein_kurzer_.C3.9Cberblick|$\text{conventional BPSK}$]]&nbsp; without band spreading/band compression, independent of the spreading degree &nbsp;$J$&nbsp;:
+and due to the fact that the statistical properties of white noise &nbsp;$n(t)$&nbsp; are not changed by the multiplication with the &nbsp;$±1$ signal &nbsp;$c(t)$,&nbsp; the same result is obtained again as for the&nbsp; [[Modulation_Methods/Linear_Digital_Modulation#Error_probabilities_-_a_brief_overview|$\text{conventional BPSK}$]]&nbsp; without band spreading/band compression, independent of the spreading degree &nbsp;$J$&nbsp;:
 :$$p_{\rm B} =  {\rm Q} \left( \hspace{-0.05cm} \sqrt { {2 \cdot E_{\rm B} }/{N_{\rm 0} } } \hspace{0.05cm} \right )  \hspace{0.05cm}.$$ }}

@@ Line 60: / Line 60: @@
 *above the source signal &nbsp;$q(t)$&nbsp; &ndash; marked by blue background &ndash; and the band spread signal &nbsp;$s(t)$&nbsp; as solid black line,
 *at the bottom left the signal &nbsp;$b(t)$&nbsp; after band compression,
-*bottom right the detection signal &nbsp;$d(t)$&nbsp; after the integrator, directly before the decision maker.
+*bottom right the detection signal &nbsp;$d(t)$&nbsp; after the integrator, directly before the decision maker '''KORREKTUR: decision'''.

@@ Line 66: / Line 66: @@
 #&nbsp; Discrete-time and normalized signal representation with rectangles spaced by the chip duration &nbsp;$T_c$&nbsp; is chosen.
 #&nbsp; The spreading factor is &nbsp;$J = 8$.
-#&nbsp; As spreading sequence the &nbsp;[[Modulation_Methods/Spreizfolgen_für_CDMA#Walsh.E2.80.93Funktionen|$\text{Walsh function no. 7}$]]&nbsp; is used.
+#&nbsp; As spreading sequence the &nbsp;[[Modulation_Methods/Spreading_Sequences_for_CDMA#Walsh_functions|$\text{Walsh function no. 7}$]]&nbsp; is used.
 #&nbsp; All images show the noise-free case &nbsp; ⇒ &nbsp; $n(t) = 0$.
 <br clear=all>

@@ Line 16: / Line 16: @@
 Note:
-In in the equivalent low-pass model the multiplications with the transmitter-side carrier signal &nbsp;$z(t)$&nbsp; and the receiverer-side carrier signal &nbsp;&nbsp;$z_{\rm E}(t) =2\cdot z(t)$&nbsp; are omitted.
+In in the equivalent low-pass model the multiplications with the transmitter-side carrier signal &nbsp;$z(t)$&nbsp; and the receiver-side carrier signal &nbsp;&nbsp;$z_{\rm E}(t) =2\cdot z(t)$&nbsp; are omitted.
 <br clear=all>
 {{BlaueBox|TEXT=

@@ Line 11: / Line 11: @@
 [[File:EN_Mod_T_5_2_S1_neu2.png|right|frame| Block diagram and equivalent low-pass model of direct-sequence spread spectrum]]
 In both models,&nbsp;
-*the distortion-free channel&nbsp; $($AWGN and possibly interference from other users,&nbsp; but no &nbsp;[[Digital_Signal_Transmission/Ursachen_und_Auswirkungen_von_Impulsinterferenzen#Definition_des_Begriffs_.E2.80.9EImpulsinterferenz.E2.80.9D|$\text{intersymbol interference}$]]$)$&nbsp; is highlighted in yellow,
+*the distortion-free channel&nbsp; $($AWGN and possibly interference from other users,&nbsp; but no &nbsp;[[Digital_Signal_Transmission/Causes_and_Effects_of_Intersymbol_Interference#Definition_of_the_term_.22Intersymbol_Interference.22|$\text{intersymbol interference}$]]$)$&nbsp; is highlighted in yellow,
-*the &nbsp;[[Digital_Signal_Transmission/Fehlerwahrscheinlichkeit_bei_Basisbandübertragung#Optimaler_Bin.C3.A4rempf.C3.A4nger_-_Realisierung_mit_Matched-Filter|$\text{optimal receiver}$]]&nbsp; $($matched filter plus threshold decider$)$ is highlighted in green.
+*the &nbsp;[[Digital_Signal_Transmission/Error_Probability_for_Baseband_Transmission#Optimal_binary_receiver_.E2.80.93_.22Matched_Filter.22_realization|$\text{optimal receiver}$]]&nbsp; $($matched filter plus threshold decider$)$ is highlighted in green.
 <br><br><br>
 Note:
@@ Line 21: / Line 21: @@
 $\text{This system can be characterized as follows:}$
 *If the multiplication with the spreading signal &nbsp;$c(t)$&nbsp; at transmitter and receiver is omitted,&nbsp; the result is a conventional &nbsp;[[Modulation_Methods/Lineare_digitale_Modulation#BPSK_.E2.80.93_Binary_Phase_Shift_Keying|$\text{BPSK system}$]]&nbsp; with the carrier &nbsp;$z(t)$&nbsp; and AWGN noise, characterized by the additive Gaussian noise signal &nbsp;$n(t)$.&nbsp; The second interference component&nbsp; (interference from other participants)&nbsp; is omitted: &nbsp; $i(t) = 0$.
-*For the following it is assumed&nbsp; $($this is essential for direct-sequence spread spectrum!$)$ that the source signal &nbsp;$q(t)$&nbsp; has a rectangular NRZ curve.&nbsp; Then the matched filter can be replaced by an integrator over a symbol duration &nbsp;$T$&nbsp; &nbsp; ⇒ &nbsp; &nbsp;[[Digital_Signal_Transmission/Fehlerwahrscheinlichkeit_bei_Basisbandübertragung#Optimaler_Bin.C3.A4rempf.C3.A4nger_.E2.80.93_Realisierungsform_.E2.80.9EIntegrate_.26_Dump.E2.80.9D|$\text{Integrate & Dump}$]].&nbsp; This is followed by the threshold decider.}}
+*For the following it is assumed&nbsp; $($this is essential for direct-sequence spread spectrum!$)$ that the source signal &nbsp;$q(t)$&nbsp; has a rectangular NRZ curve.&nbsp; Then the matched filter can be replaced by an integrator over a symbol duration &nbsp;$T$&nbsp; &nbsp; ⇒ &nbsp; &nbsp;[[Digital_Signal_Transmission/Error_Probability_for_Baseband_Transmission#Optimal_binary_receiver_.E2.80.93_.22Integrate_.26_Dump.22_realization|$\text{Integrate & Dump}$]].&nbsp; This is followed by the threshold decider.}}
 ==Principle and properties of band spreading methods==

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 {{Header
 |Untermenü= Multiple Access Methods
-|Vorherige Seite=Aufgaben und Klassifizierung
+|Vorherige Seite=Tasks and Classification
-|Nächste Seite=Spreizfolgen für CDMA
+|Nächste Seite=Spreading Sequences for CDMA
 }}
 ==Block diagram and equivalent low-pass model==