ber vs ebno
17
BER ( TEORICO) = ( ( 4 k ) ( 1− 1 √ M ) ( 1 2 ) ) ( erfc ( √ 3∗k∗EbN 0 M−1 √ 2 ) ) Donde: M=Indicede Modulacion k=Numero de Bits por simbolo EbN 0=Ruido enunidadesLineales ( Watt ) M=2 k porloque k=log 2 M EbN 0 ( watt )=10 ( EbN0 (db) 10 )
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Ejercicios acerca del BER calculado con el Simulado
Transcript of ber vs ebno
BER (TEORICO )=(( 4k )(1− 1
√M )( 12 ))(erfc(√ 3∗k∗EbN 0M−1√2 ))
Donde:
M=Indicede Modulacion
k=Numerode Bits por simbolo
EbN 0=Ruido enunidades Lineales (Watt )
M=2k porlo quek=log2M
EbN 0 (watt )=10(EbN 0 (db)10 )
Ejemplo: Reducción a la Formula para 4 – QAM
4 – QAM
M = 4
K = ?
k=log2M
k=log24
k=2
BER (TEORICO )=(( 4k )(1− 1
√M )( 12 ))(erfc(√ 3∗k∗EbN 0M−1√2 ))
BER (TEORICO )=(( 42 )(1− 1
√4 )(12 ))(erfc(√ 3∗2∗EbN 04−1√2 ))
BER (TEORICO )=(( 42 )(1−12 )( 12 ))(erfc (√ 3∗2∗EbN 04−1√2 ))
BER (TEORICO )=(( 21 )( 2−12 )( 12 ))(erfc (√ 6∗EbN 032 ))
BER (TEORICO )=(( 12 )) (erfc (√EbN 0 ) )
Ejemplo: Reducción a la Formula para 8 -QAM
8 – QAM
M = 8
K = ?
k=log2M
k=log28
k=3
BER (TEORICO )=(( 4k )(1− 1
√M )( 12 ))(erfc(√ 3∗k∗EbN 0M−1√2 ))
BER (TEORICO )=(( 43 )(1− 1
√8 )( 12 ))(erfc (√ 3∗3∗EbN 08−1√2 ))
BER (TEORICO )=(( 43 )(√8−1√8 )( 12 ))(erfc (√ 9∗EbN 072 ))
BER (TEORICO )=(( 4√8−46√8 ))(erfc(√ 9∗EbN 014 ))
Ejemplo: Reducción a la Formula para 16 -QAM
16 – QAM
M = 16
K = ?
k=log2M
k=log216
k=4
BER (TEORICO )=(( 4k )(1− 1
√M )( 12 ))(erfc(√ 3∗k∗EbN 0M−1√2 ))
BER (TEORICO )=(( 44 )(1− 1
√16 )( 12 ))(erfc (√ 3∗k∗EbN 0M−1√2 ))
BER (TEORICO )=((1 )(1− 14 )( 12 ))(erfc(√ 3∗4∗EbN 016−12 ))
BER (TEORICO )=(( 4−14 )( 12 ))(erfc (√ 12∗EbN 0152 ))
BER (TEORICO )=(( 38 ))(erfc(√ 6∗EbN 015 ))
Ejemplo: Reducción a la Formula para 64 -QAM
64 – QAM
M = 64
K = ?
k=log2M
k=log264
k=6
BER (TEORICO )=(( 4k )(1− 1
√M )( 12 ))(erfc(√ 3∗k∗EbN 0M−1√2 ))
BER (TEORICO )=(( 46 )(1− 1
√64 )( 12 ))(erfc (√ 3∗6∗EbN 064−1√2 ))
BER (TEORICO )=(( 43 )( 8−18 )( 12 ))(erfc (√ 18∗EbN 0632 ))
BER (TEORICO )=(( 2842 ))(erfc(√ 9∗EbN 063 ))BER (TEORICO )=(( 23 ))(erfc(√ 9∗EbN 063 ))
Ejemplo: Reducción a la Formula para 128 -QAM
128 – QAM
M = 128
K = ?
k=log2M
k=log2128
k=7
BER (TEORICO )=(( 4k )(1− 1
√M )( 12 ))(erfc(√ 3∗k∗EbN 0M−1√2 ))
BER (TEORICO )=(( 47 )(1− 1
√128 )( 12 ))(erfc (√ 3∗7∗EbN 0128−1√2 ))
BER (TEORICO )=(( 47 )(√128−1√128 )( 12 ))(erfc (√ 21∗EbN 01272 ))
BER (TEORICO )=(( 4√128−414 √128 ))(erfc (√ 9∗EbN 063 ))
Ejemplo: Reducción a la Formula para 256 – QAM
256 – QAM
M = 256
K = ?
k=log2M
k=log2256
k=8
BER (TEORICO )=(( 4k )(1− 1
√M )( 12 ))(erfc(√ 3∗k∗EbN 0M−1√2 ))
BER (TEORICO )=(( 48 )(1− 1
√256 )( 12 ))(erfc (√ 3∗8∗Eb N 0256−1√2 ))
BER (TEORICO )=(( 48 )(1− 116 )( 12 ))(erfc (√ 3∗8∗EbN 0256−1
√2 ))
BER (TEORICO )=(( 12 )( 16−116 )( 12 ))(erfc (√ 24∗EbN 02552 ))
BER (TEORICO )=(( 156 4 ))(erfc(√ 12∗EbN 0255 ))
Cuadro BER teorico
M 2dB 4dB 6 dB 8 dB 10 dB 12 dB 14 dB 16 dB 18 Db 20 dB 22 dB 24 dB 26 dB
4 – QAM 5,63E-02 2,29E-02 5,95E-03 7,73E-04 3,36E-05 2,61E-07 1,33E-10 9,12E-16 6,76E-24 1,00E-36 5,30E-57 4,43E-89 7,31E-140
8 – QAM 8,76E-02 4,71E-02 1,89E-02 4,80E-03 6,01E-04 2,47E-05 1,76E-07 7,82E-11 4,29E-16 2,24E-24 1,91E-37 4,21E-58 8,78E-91
16 – QAM 1,18E-01 7,74E-02 4,19E-02 1,70E-02 4,39E-03 5,65E-04 2,42E-05 1,84E-07 9,07E-11 5,87E-16 3,99E-24 5,13E-37 2,18E-57
64 – QAM 1,60E-01 1,31E-01 9,97E-02 6,75E-02 3,85E-02 1,69E-02 4,95E-03 7,72E-04 4,50E-05 5,54E-07 5,85E-10 1,27E-14 5,82E-22
128 – QAM 1,69E-01 1,47E-01 1,22E-01 9,45E-02 6,56E-02 3,88E-02 1,81E-02 5,79E-03 1,04E-03 7,55E-05 1,32E-06 2,41E-09 1,25E-13
256 – QAM 1,71E-01 1,56E-01 1,37E-01 1,15E-01 9,08E-02 6,48E-02 4,00E-02 1,98E-02 7,00E-03 1,47E-03 1,35E-04 3,44E-06 1,14E-08
Valor para establecer una Buena comunicación
Cuadro BER simulado
2dB 4dB 6 dB 8 dB 10 dB 12 dB 14 dB 16 dB 18 Db 20 dB 22 dB 24 dB 26 dB
4 – QAM 5,65E-02 2,29E-02 5,99E-03 7,92E-04 3,50E-05 0 0 0 0 0 0 0 08 – QAM 1,31E-01 7,89E-02 3,76E-02 1,26E-02 2,39E-03 1,90E-04 4,33E-06 0 0 0 0 0 016 – QAM 1,58E-01 1,03E-01 5,60E-02 2,25E-02 5,91E-03 7,64E-04 3,43E-05 7,50E-07 0 0 0 0 064 – QAM 2,46E-01 2,04E-01 1,56E-01 1,06E-01 6,05E-02 2,66E-02 7,75E-03 1,24E-03 6,72E-05 6,67E-07 0 0 0128 – QAM 2,78E-01 2,41E-01 2,01E-01 1,56E-01 1,08E-01 6,34E-02 2,91E-02 9,09E-03 1,52E-03 1,10E-04 1,29E-06 0 0256 – QAM 2,94E-01 2,66E-01 2,34E-01 1,98E-01 1,57E-01 1,12E-01 6,93E-02 3,44E-02 1,21E-02 2,59E-03 2,37E-04 5,25E-06 0
http://www.noticias.in.rs/ultimas/%C2%BFque-es-el-ber-bit-error-ratio-y-el-bert-bit-error-ratio-probador/
