Download presentation

Presentation is loading. Please wait.

Published byRyann Dods Modified over 3 years ago

1
II. Modulation & Coding

2
© Tallal Elshabrawy Design Goals of Communication Systems 1.Maximize transmission bit rate 2.Minimize bit error probability 3.Minimize required transmission power 4.Minimize required system bandwidth 5.Minimize system complexity, computational load & system cost 6.Maximize system utilization 2

3
© Tallal Elshabrawy Some Tradeoffs in M-PSK Modulaion 1Trades off BER and Energy per Bit 2Trades off BER and Normalized Rate in b/s/Hz 3Trades off Normalized Rate in b/s/Hz and Energy per Bit 3 1 2 3 m=4 m=3 m=1, 2

4
© Tallal Elshabrawy Shannon-Hartley Capacity Theorem C:System Capacity (bits/s) W:Bandwidth of Communication (Hz) S:Signal Power (Watt) N:Noise Power (Watt) 4 System Capacity for communication over of an AWGN Channel is given by:

5
© Tallal Elshabrawy Shannon-Hartley Capacity Theorem 5 Practical Systems Unattainable Region

6
© Tallal Elshabrawy Shannon Capacity in terms of E b /N 0 Consider transmission of a symbol over an AWGN channel 6

7
© Tallal Elshabrawy Shannon Limit 7 Let

8
© Tallal Elshabrawy Shannon Limit 8 Shannon Limit=-1.6 dB

9
© Tallal Elshabrawy Shannon Limit No matter how much/how smart you decrease the rate by using channel coding, it is impossible to achieve communications with very low bit error rate if E b /N 0 falls below -1.6 dB

10
© Tallal Elshabrawy Shannon Limit 10 Shannon Limit=-1.6 dB BPSK Uncoded P b = 10 -5 QPSK Uncoded P b = 10 -5 8 PSK Uncoded P b =10 -5 16 PSK Uncoded P b =10 -5 Room for improvement by channel coding Normalized Channel Capacity b/s/Hz E b /N 0

11
© Tallal Elshabrawy 1/3 Repetition Code BPSK Is this really purely a gain? No! We have lost one third of the information transmitted rate 11 Coding Gain= 3.2 dB

12
© Tallal Elshabrawy 012345678910 -6 10 -5 10 -4 10 -3 10 -2 10 E b /N 0 P b BPSK Uncoded 8 PSK 1/3 Repitition Code 1/3 Repetition Code 8 PSK 12 Coding Gain= -0.5 dB When we don’t sacrifice information rate 1/3 repetition codes did not help us

13
© Tallal Elshabrawy The waveform generator converts binary data to voltage levels (1 V., -1 V.) The channel has an effect of altering the voltage that was transmitted Waveform detection performs a HARD DECISION by mapping received voltage back to binary values based on decision zones Channel Encoder Waveform Generator Waveform Detection Channel Decoder Channel v r x y v = [v 1 v 2 … v i … v n ] e = [e 1 e 2 … e i … e n ] r = [r 1 r 2 … r i … r n ] x = [x 1 x 2 … x i … x n ] y = [y 1 y 2 … y i … y n ] 0 T 0 T +1 V. -1 V. vivi v i =1 v i =0 xixi 0 y i >0 y i <0 r i =1 r i =0 riri + zizi ]-∞, ∞[ yiyi Hard Decision Decoding

14
© Tallal Elshabrawy The waveform generator converts binary data to voltage levels (1 V., -1 V.) The channel has an effect of altering the voltage that was transmitted The input to the channel decoder is a vector of voltages rather than a vector of binary values Channel Encoder Waveform Generator Channel Decoder Channel v r x v = [v 1 v 2 … v i … v n ] e = [e 1 e 2 … e i … e n ] r = [r 1 r 2 … r i … r n ] x = [x 1 x 2 … x i … x n ] 0 T 0 T +1 V. -1 V. vivi v i =1 v i =0 xixi + zizi ]-∞, ∞[ riri Soft Decision Decoding

15
© Tallal Elshabrawy Hard Decision -Each received bit is detected individually -If the voltage is greater than 0 detected bit is 1 -If the voltage is smaller than 0 detected bit is 0 -Detection information of neighbor bits within the same codeword is lost Channel Encoder Waveform Generator Waveform Detection Channel Decoder Channel 0 0 0 r y v = [v 1 v 2 … v i … v n ] e = [e 1 e 2 … e i … e n ] r = [r 1 r 2 … r i … r n ] x = [x 1 x 2 … x i … x n ] y = [y 1 y 2 … y i … y n ] 0 -1 -1 -1 0.1 -0.9 0.1 1 0 1 1 Hard Decision: Example 1/3 Repetition Code BPSK

16
© Tallal Elshabrawy Soft Decision -If the accumulated voltage within the codeword is greater than 0 detected bit is 1 -If the accumulated voltage within the codeword is smaller than 0 detected bit is 0 -Information of neighbor bits within the same codeword contributes to the channel decoding process Channel Encoder Waveform Generator Channel Decoder Channel 0 0 0 r v = [v 1 v 2 … v i … v n ] e = [e 1 e 2 … e i … e n ] r = [r 1 r 2 … r i … r n ] x = [x 1 x 2 … x i … x n ] y = [y 1 y 2 … y i … y n ] 0 -1 -1 -1 0.1 -0.9 0.1 0 Accumulated Voltage = 0.1-0.9+0.1=-0.7<0 Soft Decision: Example 1/3 Repetition Code BPSK

17
© Tallal Elshabrawy 1/3 Repetition Code BPSK Soft Decision Channel Coding (1/3 Repetition Code) Waveform Representation Channel Soft Decision Decoding r Important Note

18
© Tallal Elshabrawy BER Performance Soft Decision 1/3 Repetition Code BPSK Select b*=0 if Note that r 0 r 1 and r 2 are independent and identically distributed. In other words Therefore Similarly

19
© Tallal Elshabrawy Select b*=0 if BER Performance Soft Decision 1/3 Repetition Code BPSK

20
© Tallal Elshabrawy where BER Performance Soft Decision 1/3 Repetition Code BPSK n is Gaussian distributed with mean 0 and variance 3N 0 /2

21
© Tallal Elshabrawy Hard Vs Soft Decision: 1/3 Repetition Code BPSK Coding Gain= 4.7 dB

22
© Tallal Elshabrawy 1/3 Repetition Code 8 PSK Hard Decision 22 Coding Gain= 1.5 dB

23
© Tallal Elshabrawy Shannon Limit and BER Performance 23 Shannon Limit=-1.6 dB BPSK Uncoded P b = 10 -5 QPSK Uncoded P b = 10 -5 8 PSK Uncoded P b =10 -5 16 PSK Uncoded P b =10 -5 BPSK 1/3 Rep. Code Hard Decision P b = 10 -5 BPSK 1/3 Rep. Code Sodt Decision P b = 10 -5 Normalized Channel Capacity b/s/Hz E b /N 0 1/3 8PSK 1/3 Rep. Code Hard Decision P b = 10 -5 8PSK 1/3 Rep. Code Soft Decision P b = 10 -5

Similar presentations

OK

1 CSCD 433 Network Programming Fall 2016 Lecture 4 Digital Line Coding and other...

1 CSCD 433 Network Programming Fall 2016 Lecture 4 Digital Line Coding and other...

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on needle stick injury protocol Ppt on p&g products brands Ppt on non conventional sources of energy Ppt on question tags youtube Free ppt on moving coil galvanometer principle Ppt on group development tuckman Ppt on new trends in the field of automobile air conditioning Ppt on motivational quotes Ppt on opera web browser Ppt on differential aptitude test