Examples of Communication Systems/xDSL as Transmission Technology - Revision history

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@@ Line 364: / Line 364: @@
 [[File:EN_Bei_T_2_3_S9d_ganz_neuV8.png|right|frame|Discrete multitone transmission system]]
-[[File:P_ID1951__Bei_T_2_3_S9b_v3.png|right|frame|DMT transmitter and receiver '''Korrektur''' das Bild muss ich noch machen]]
+[[File:EN_Bei_T_2_3_S9d_60Prozent.png|right|frame|DMT transmitter and receiver ]]
 *To perform a DMT modulation,&nbsp; the transmitter accumulates a block of input bits in a data buffer to be transmitted as one frame.

@@ Line 236: / Line 236: @@
 #The symbol error probability $p$&nbsp; depends on the Euclidean distance of the two points and the AWGN noise power density&nbsp; $N_0$.
 #A distortion to the more distant blue point instead of one of the two neighboring brown points is rather unlikely with Gaussian noise.
-[[File:EN Bei T 2 3 S6b neu.png|right|frame|Signal space constellation:&nbsp; "$\rm 16\hspace{0.05cm}&ndash;\hspace{-0.02cm}QAM$";&nbsp; left: ITU propsal,&nbsp; right:&nbsp; Gray encoding. '''KORREKTUR: Symbolfehler, Bitfehler''']]
+[[File:EN_Bei_T_2_3_S6b_neu_v2.png|right|frame|Signal space constellation:&nbsp; "$\rm 16\hspace{0.05cm}&ndash;\hspace{-0.02cm}QAM$";&nbsp; left: ITU propsal,&nbsp; right:&nbsp; Gray encoding]]
 An analysis shows:

@@ Line 273: / Line 273: @@
 [[File:EN_Bei_T_2_3_S7d_neu.png|right|frame|Reference model for&nbsp; ADSL&ndash;CAP]]
-*Digital filtering is used instead of multiplication by cosine and minus sine.&nbsp; $g_{\rm I}(t)$&nbsp; and&nbsp; $g_{\rm Q}(t)$&nbsp; are impulse responses of two transversal bandpass '''KORREKTUR: band-pass''' filters with same amplitude characteristic,&nbsp;  phase-shifted  by&nbsp; $π/2$.
+*Digital filtering is used instead of multiplication by cosine and minus sine.&nbsp; $g_{\rm I}(t)$&nbsp; and&nbsp; $g_{\rm Q}(t)$&nbsp; are impulse responses of two transversal band-pass filters with same amplitude characteristic,&nbsp;  phase-shifted  by&nbsp; $π/2$.
 *Both are orthogonal to each other,&nbsp; which means that the integral of the product&nbsp; $g_{\rm I}(t) · g_{\rm Q}(t)$&nbsp; over a symbol duration gives zero.

@@ Line 183: / Line 183: @@
 $\text{Example 1:}$&nbsp;
 An important QAM parameter is the bit number&nbsp; $b$&nbsp; processed to the amplitude coefficient pair&nbsp; $(a_{\rm I}, a_{\rm Q})$.&nbsp; Here&nbsp; $b$&nbsp; is always an even number.
-[[File:EN_Bei_T_2_3_S6a_v2.png|right|frame|Signal space constellations&nbsp; "$\rm 4\hspace{0.05cm}&ndash;\hspace{-0.02cm}QAM$"&nbsp; $($left$)$&nbsp; and&nbsp; "$\rm 16\hspace{0.05cm}&ndash;\hspace{-0.02cm}QAM$"&nbsp; $($right$)$
+[[File:EN_Bei_T_2_3_S6a_v2.png|right|frame|Signal space constellations&nbsp; "$\rm 4\hspace{0.05cm}&ndash;\hspace{-0.02cm}QAM$"&nbsp; $($left$)$&nbsp; and&nbsp; "$\rm 16\hspace{0.05cm}&ndash;\hspace{-0.02cm}QAM$"&nbsp; $($right$)$]]
 *If&nbsp; $b = 2$,&nbsp; both&nbsp; $a_{\rm I}$&nbsp; and&nbsp; $a_{\rm Q}$&nbsp; can only take the values&nbsp; $±1$&nbsp; resulting in the&nbsp; $\rm 4\hspace{0.05cm}&ndash;\hspace{-0.02cm}QAM$&nbsp; corresponding to the left constellation.

@@ Line 116: / Line 116: @@
 *QAM is a&nbsp; "single carrier modulation method"&nbsp; around the carrier frequency&nbsp; $f_{\rm T}$.&nbsp; First,&nbsp; a blockwise serial/parallel conversion of the bit stream and signal space assignment is performed.
-*From each&nbsp; $b$&nbsp; binary symbols,&nbsp; two multilevel '''KORREKTUR: multi-level''' amplitude coefficients&nbsp; $a_{{\rm I}n}$&nbsp; and&nbsp; $a_{{\rm Q}n}$&nbsp; are derived&nbsp; $($"in-phase component"&nbsp; and&nbsp; "quadrature component"$)$.&nbsp; Both coefficients can each take one of&nbsp; $M = 2^{b/2}$&nbsp; possible amplitude values.
+*From each&nbsp; $b$&nbsp; binary symbols,&nbsp; two multi-level  amplitude coefficients&nbsp; $a_{{\rm I}n}$&nbsp; and&nbsp; $a_{{\rm Q}n}$&nbsp; are derived&nbsp; $($"in-phase component"&nbsp; and&nbsp; "quadrature component"$)$.&nbsp; Both coefficients can each take one of&nbsp; $M = 2^{b/2}$&nbsp; possible amplitude values.
 *The example considered here applies to the&nbsp; $\text{16-QAM}$&nbsp; with&nbsp; $b = M = 4$&nbsp; and correspondingly sixteen&nbsp; signal space points. For a &nbsp; $\text{256-QAM}$&nbsp; would hold: &nbsp; $b = 8$&nbsp; and&nbsp; $M = 16$&nbsp; $(2^b = M^2 = 256)$.

@@ Line 309: / Line 309: @@
 *After&nbsp; $68$&nbsp; data frames,&nbsp; one synchronization frame is inserted each.
-*Due to the&nbsp; "cyclic prefix"&nbsp; $($see chapter&nbsp; [[Examples_of_Communication_Systems/Methods_to_Reduce_the_Bit_Error_Rate_in_DSL#Insert.C3.BCgen_of_Guard.E2.80.93Interval_and_cyclic_Pr. C3.A4fix|"Insertion of Guard&ndash;Interval and Cyclic Prefix"]]$)$&nbsp; the symbol duration&nbsp; $T = 1/f_0$&nbsp; must still be shortened by the factor&nbsp; $16/17$.
+*Due to the&nbsp; "cyclic prefix"&nbsp; $($see chapter&nbsp; [[Examples_of_Communication_Systems/Methods_to_Reduce_the_Bit_Error_Rate_in_DSL#Inserting_guard_interval_and_cyclic_prefix|"Insertion of Guard&ndash;Interval and Cyclic Prefix"]]$)$&nbsp; the symbol duration&nbsp; $T = 1/f_0$&nbsp; must still be shortened by the factor&nbsp; $16/17$.
 *Thus,&nbsp; the&nbsp; &raquo;'''basic frequency'''&laquo;&nbsp; of DMT is&nbsp;

@@ Line 47: / Line 47: @@
 *[[Modulation_Methods/Quadrature_Amplitude_Modulation|$\rm QAM$]]&nbsp; $($"Quadrature Amplitude Modulation"$)$&nbsp; and
-*[[Examples_of_Communication_Systems/xDSL_as_Transmission_Technology#Carrierless_Amplitude_Phase_Modulation_.28CAP.29|$\rm CAP$]]&nbsp; $($"Carrierless Amplitude Phase Modulation$)$.
+*[[Examples_of_Communication_Systems/xDSL_as_Transmission_Technology#Carrierless_Amplitude_Phase_Modulation|$\rm CAP$]]&nbsp; $($"Carrierless Amplitude Phase Modulation$)$.
@@ Line 59: / Line 59: @@
 #After this occupancy gap follows the ADSL upstream band from&nbsp; $\text{138 kHz}$&nbsp; to&nbsp;$\text{276 kHz}$.&nbsp; This allows the transmission of&nbsp; $N_{\rm Up} = 32$&nbsp; subcarriers with bandwidth &nbsp;$\text{4.3125 kHz}$&nbsp; each.&nbsp; This value is derived from the frame transmission rate.
 #The subsequent downstream range extends to&nbsp; $\text{1104 kHz}$&nbsp; for ADSL,&nbsp; with which&nbsp; $N_{\rm Down} = 256$&nbsp; subcarriers can be realized.&nbsp; The separation of the upstream and the downstream channel in xDSL is done by a band-pass filter in the modem.
-#However,&nbsp; the first&nbsp; $64$&nbsp; subcarriers&nbsp; $($this corresponds to $\text{276 kHz)}$&nbsp; must not be occupied.&nbsp; With the&nbsp; [[Examples_of_Communication_Systems/xDSL_as_Transmission_Technology#Possible_bandwidth_allocation_for_xDSL|"frequency uniform position method"]]&nbsp; only&nbsp; $32$&nbsp; subcarriers would have to be left out,&nbsp; taking into account that the separation of uplink and downlink requires a more complex implementation.
+#However,&nbsp; the first&nbsp; $64$&nbsp; subcarriers&nbsp; $($this corresponds to $\text{276 kHz)}$&nbsp; must not be occupied.&nbsp; With the&nbsp; [[Examples_of_Communication_Systems/xDSL_as_Transmission_Technology#Possible_bandwidth_allocations_for_xDSL|"frequency uniform position method"]]&nbsp; only&nbsp; $32$&nbsp; subcarriers would have to be left out,&nbsp; taking into account that the separation of uplink and downlink requires a more complex implementation.
 #For&nbsp; ADSL2+,&nbsp; the system bandwidth is&nbsp; $\text{2208 kHz}$ &nbsp; ⇒ &nbsp; $N_{\rm Down} = 512$&nbsp; subcarriers.&nbsp; The number of bins to be spared remains unchanged compared to ADSL.&nbsp; Taking into account that two bins are occupied by control functions&nbsp; $($e.g. for synchronization$)$,&nbsp; $190$&nbsp; $($ADSL$)$&nbsp; or&nbsp; $446$&nbsp; $($ADSL2+$)$ downstream channels remain for users.
 #The ISDN reservation prescribed in Germany,&nbsp; however,&nbsp; has the consequence for xDSL that the low frequencies,&nbsp; which are by far the least attenuated in a copper line and would therefore actually be the most suitable,&nbsp; cannot be used.