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Several properties of digital communication systems make them preferable to analog systems.

Results from the Receiver Error module reveals several properties about digital communication systems.

  • As the received signal becomes increasingly noisy, whether due to increased distance from the transmitter (smaller ) or to increased noise in the channel (larger N 0 ), the probability the receiver makes an error approaches 1 2 . In such situations, the receiver performs only slightly better thanthe "receiver" that ignores what was transmitted and merely guesses what bit was transmitted. Consequently, it becomesalmost impossible to communicate information when digital channels become noisy.
  • As the signal-to-noise ratio increases, performance gains--smaller probability of error p e -- can be easily obtained. At a signal-to-noise ratio of 12 dB, the probability the receiver makes an errorequals 10 -8 . In words, one out of one hundred million bits will, on the average, be in error.
  • Once the signal-to-noise ratio exceeds about 5 dB, the error probability decreases dramatically. Adding 1 dBimprovement in signal-to-noise ratio can result in a factor of 10 smaller p e .
  • Signal set choice can make a significant difference in performance. All BPSK signal sets, baseband or modulated,yield the same performance for the same bit energy. The BPSK signal set does perform much better than the FSK signalset once the signal-to-noise ratio exceeds about 5 dB.

Derive the expression for the probability of error that would result if the FSK signal set were used.

The noise-free integrator output difference now equals A 2 T E b 2 . The noise power remains the same as in the BPSK case, which from the probability of error equation yields p e Q 2 E b N 0 .

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The matched-filter receiver provides impressive performance once adequate signal-to-noise ratios occur. You might wonder whetheranother receiver might be better. The answer is that the matched-filter receiver is optimal: No other receiver can provide a smaller probability of error than the matchedfilter regardless of the SNR . Furthermore, no signal set can provide better performance than the BPSK signal set,where the signal representing a bit is the negative of the signal representing the other bit. The reason for this resultrests in the dependence of probability of error p e on the difference between the noise-free integrator outputs: For a given E b , no other signal set provides a greater difference.

How small should the error probability be? Out of N transmitted bits, on the average N p e bits will be received in error. Do note the phrase "on the average" here: Errors occur randomly because of the noiseintroduced by the channel, and we can only predict the probability of occurrence. Since bits are transmitted at a rate R , errors occur at an average frequency of R p e . Suppose the error probability is an impressively small number like 10 -6 . Data on a computer network like Ethernet is transmitted at a rate R 100 Mbps , which means that errors would occur roughly 100 per second. This error rate is very high, requiring a much smaller p e to achieve a more acceptable average occurrence rate for errors occurring. Because Ethernet is a wireline channel, which meansthe channel noise is small and the attenuation low, obtaining very small error probabilities is not difficult. We do have sometricks up our sleeves, however, that can essentially reduce theerror rate to zero without resorting to expending a large amount of energy at the transmitter. We needto understand digital channels and Shannon's Noisy Channel Coding Theorem .

Questions & Answers

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Answers please
Nikki Reply

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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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