in this course we will study modern advanced digital ...digital communications - advanced course:...
TRANSCRIPT
![Page 1: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/1.jpg)
Digital communications - Advanced
course: Introduction - week 1
1
• In this course we will study modern advanced digital communication methods and systems.
• Stationary as well as mobile communication system solutions.
• This course gives a breath and a depth so that you can understand today's advanced communication system, and also many future systems.
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Digital communications - Advanced
course: Introduction - week 1
2
Project work in this course
• 2 students/group.
• A communication application/technical problem/problem area, relevant for the course, is investigated.
• The choice of project is mainly done by the project group.
• Articles and conference papers from IEEE´s database ”IEEE Xplore” http://ieeexplore.ieee.org/Xplore/DynWel.jsp
is recommended to get additional technical information.
• Written report, oral presentation, and be opponent to another group.
• 1-2 hours of discussion/feedback on report/project by a (top) student of MWIR-year 2
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Digital communications - Advanced
course: Introduction - week 1
3
Some examples of applications/systems studied in
previous projects:
• Mobile telephony/broadband (GSM, EDGE, LTE, 4G, 5G,...)
• Internet
• Modem (e.g., ADSL)
• WLAN (Wireless Local Area Network)
• Digital TV
• MIMO
• Massive MIMO
• OFDM+MIMO
• GPS (Global Positioning System)
• Bluetooth
• mmWave
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4
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Digital communications - Advanced
course: Introduction - week 1
6
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Digital communications - Advanced
course: Introduction - week 1
7
![Page 8: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/8.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
In this course we study the MAP receiver in detail
![Page 9: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/9.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
In this course we study the MAP receiver in detail
MAP is defined as
![Page 10: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/10.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
In this course we study the MAP receiver in detail
MAP is defined as
![Page 11: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/11.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
In this course we study the MAP receiver in detail
MAP is defined as
ML is defined as
![Page 12: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/12.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
In this course we study the MAP receiver in detail
MAP is defined as
ML is defined as
Which one is more logical?
![Page 13: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/13.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up
![Page 14: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/14.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here”
![Page 15: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/15.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here?
![Page 16: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/16.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here? Explanation m = ”Fredrik is……”
![Page 17: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/17.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here? Explanation m = ”Fredrik is……”
ML-rule p(r(t)|m1) = 0.9 m1 = ”Fredrik is sick”
![Page 18: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/18.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here? Explanation m = ”Fredrik is……”
ML-rule p(r(t)|m1) = 0.9 m1 = ”Fredrik is sick” p(r(t)|m2) = ? m2 = ”Fredrik is dead”
![Page 19: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/19.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here? Explanation m = ”Fredrik is……”
ML-rule p(r(t)|m1) = 0.9 m1 = ”Fredrik is sick” p(r(t)|m2) = 1 m2 = ”Fredrik is dead”
![Page 20: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/20.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here? Explanation m = ”Fredrik is……”
ML-rule p(r(t)|m1) = 0.9 m1 = ”Fredrik is sick” p(r(t)|m2) = 1 m2 = ”Fredrik is dead”
![Page 21: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/21.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here? Explanation m = ”Fredrik is……”
MAP-rule
![Page 22: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/22.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here? Explanation m = ”Fredrik is……”
MAP-rule
![Page 23: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/23.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here? Explanation m = ”Fredrik is……”
MAP-rule
![Page 24: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/24.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Suppose that on the next lecture, I will not show up Observation r(t) = ”fredrik is not here” Why am I not here? Explanation m = ”Fredrik is……”
MAP-rule
![Page 25: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/25.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
MAP-rule
![Page 26: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/26.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
The ML rule is, in general, totally crazy
![Page 27: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/27.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
The ML rule is, in general, totally crazy • According to what rule do we do everyday decisions?
• According to which rule should a court make their decisions?
![Page 28: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/28.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
The ML rule is, in general, totally crazy • According to what rule do we do everyday decisions? MAP • According to which rule should a court make their decisions? MAP
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MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998
![Page 30: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/30.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy
![Page 31: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/31.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths
![Page 32: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/32.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense
![Page 33: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/33.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense
Implication (to us):
![Page 34: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/34.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense
Implication (to us): NONE
![Page 35: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/35.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense
Implication (to us): NONE Implication to court:
![Page 36: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/36.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense
Implication (to us): NONE Implication to court: Lifetime jail sentence
![Page 37: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/37.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense
Implication (to us): NONE Implication to court: Lifetime jail sentence
CLEARLY ML
![Page 38: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/38.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense
MAP ?
![Page 39: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/39.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense P(mother is murderer) = 1/1000…000 P(mother is not murderer) = 0.9999…999
MAP ?
![Page 40: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/40.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense P(mother is murderer) = 1/1000…000 P(mother is not murderer) = 0.9999…999
MAP ?
![Page 41: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/41.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense P(mother is murderer) = 1/1000…000 P(mother is not murderer) = 0.9999…999
MAP ?
![Page 42: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/42.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998 Observation: Sally Clark, mother of two, had two babies that died in infancy P(observation|natural causes) = 1/10000 according to expert in child deaths P(observation|murder) = 1 according to common sense P(mother is murderer) = 1/1000…000 P(mother is not murderer) = 0.9999…999
MAP: NOT GUILTY
![Page 43: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/43.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
True court case: Sally clark case, England 1998
MAP: NOT GUILTY
Aftermath: Released in 2003, after some math professors took a look at the case. Sally died from alhcolism somewhat later
![Page 44: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/44.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Hypotetical case: Lottery with 1000000 tickets
![Page 45: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/45.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Hypotetical case: Lottery with 1000000 tickets
P(someone presents the winning ticket|person bought a ticket) = 1/1000000
![Page 46: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/46.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Hypotetical case: Lottery with 1000000 tickets
P(someone presents the winning ticket|person bought a ticket) = 1/1000000 P(someone presents the winning ticket|person printed the winning ticket at home on a printer) = 1
![Page 47: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/47.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Hypotetical case: Lottery with 1000000 tickets
P(someone presents the winning ticket|person bought a ticket) = 1/1000000 P(someone presents the winning ticket|person printed the winning ticket at home on a printer) = 1
ML: ??
MAP: ??
![Page 48: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/48.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Hypotetical case: Lottery with 1000000 tickets
P(someone presents the winning ticket|person bought a ticket) = 1/1000000 P(someone presents the winning ticket|person printed the winning ticket at home on a printer) = 1
ML: Jail
MAP: ??
![Page 49: In this course we will study modern advanced digital ...Digital communications - Advanced course: Introduction - week 1 1 • In this course we will study modern advanced digital communication](https://reader035.vdocuments.us/reader035/viewer/2022071502/6122242f4bd43670682927dc/html5/thumbnails/49.jpg)
MAP receiver
Lecture 1: MAP receiver and signal space
MAP is defined as
ML is defined as
Which one is more logical?
Hypotetical case: Lottery with 1000000 tickets
P(someone presents the winning ticket|person bought a ticket) = 1/1000000 P(someone presents the winning ticket|person printed the winning ticket at home on a printer) = 1
ML: Jail
MAP: Prior probability of fraud must be evaluated
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MAP receiver
Lecture 1: MAP receiver and signal space
To analyze a digital communications system, it is difficult to work with a continuous time signal It is hard to evaluate a probability of the form p(r(t)|m)
r(t) m=+1
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MAP receiver
Lecture 1: MAP receiver and signal space
To analyze a digital communications system, it is difficult to work with a continuous time signal It is hard to evaluate a probability of the form p(r(t)|m) We are used to evaluate probabilites of the form p(r|m)
r(t) m=+1
m=+1 r=1.4312
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MAP receiver
Lecture 1: MAP receiver and signal space
To analyze a digital communications system, it is difficult to work with a continuous time signal
Concept of signal space: • Transfer all continuous signals into discrete vectors
• Transformation should be such that no information is lost
• Transformation is done via a set of basis functions
• For two systems with identical signal spaces, all properties (Eb, BER, etc) are idetincal
• However, bandwidth – properties are not. They depend on the basis functions
• Allows for a simpler description and analysis of the system.