<< Chapter < Page Chapter >> Page >
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 .

Got questions? Get instant answers now!

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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of electrical engineering i' conversation and receive update notifications?

Ask