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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 is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
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Akash Reply
it is a goid question and i want to know the answer as well
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Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Answers please
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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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