QUIZ. Explain in your own words the two types of changes that a signal experiences while propagating. Give examples!

QUIZ Explain in your own words the two types of changes that a signal experiences while propagating. Give examples!

QUIZ Explain why it s bad for technical standards to be developed: too early too late

QUIZ Explain: The two elephants How ISO-OSI got crushed

QUIZ List the layers of the 5-layer network model used in our text. Mention one or two characteristics for each layer.

PHYSICAL: voltages, durations, duplexing, cables, pins DATA LINK: frames, error detection/correction, flow ctrl., medium access NETWORK: addressing, routing, congestion, QoS TRANSPORT: fragmenting/reassembly, end-to-end APPLICATION: programs the user interacts with, e.g. FTP, HTTP, SMTP

QUIZ The Saint Bernard network described in P.1 at the end of Ch.1 has: High / Low (choose one) throughput High / Low (choose one) latency

2.1 Bandwidth-Limited Signals In most design problems, we already have a given transmission channel, with a fixed bandwidth. The question then is how many harmonics will pass through.

Actually, received Relation between data rate and harmonics for a telephone channel (approx. 0-3100 Hz).

Sampling a bandwidth-limited signal In order to convert the received analog signal to digital, we need to sample the output. Sampling rate = # of samples collected per second. Question: How much information is lost in the sampling process?

Nyquist Theorem A binary signal (2 levels) whose max freq. is B can be perfectly reconstructed (w/o loss of information) by sampling it 2B times a second Max data rate = 2B [bps] Generalization: A signal with V levels Max data rate = 2B log 2 V [bps]

Nyquist Theorem Max data rate = 2B [bps] Max data rate = 2B log 2 V [bps] Example p.94 of text: We send binary signals on a noiseless 3-kHz channel. What is the maximum data rate? What if now we send 4 levels on the same channel? 8 levels?

Nyquist Theorem Max data rate = 2B [bps] Max data rate = 2B log 2 V [bps] The previous example seems to indicate that the data rate can increase indefinitely by simply increasing the number of levels! Problem 2: A noiseless 4-kHz channel is sampled every 1 ms. What is the maximum data rate? Can you figure out what happens in real-life?

Noiseless vs. noisy All previous discussion was for perfect or noiseless communication channels, i.e. channels that distort signals only through attenuation (and different propagation speeds of the harmonics). In real-life, there is a third source of distortion: noise. In computer/telecoms networks, the effects of noise are dealt with mostly in L2 and L3, but we can also use it in L1 to obtain an upper bound on the channel s data rate.

Signal-to-noise ratio SNR = signal-to-noise ratio = S/N Adimensional! Power of noise Decibels 10 log 10 S/N [db] Power of signal Refers in general to the ratio of any quantity to a baseline level of that quantity (e.g amplification in a sound system).

QUIZ 10 log 10 S/N [db] The signal in a transmission line has a power of 0.1W. The the noise (due to a nearby refrigerator) has 1mW of power. What is the SNR? As a ratio: In db:

Trick QUIZ 10 log 10 S/N [db] The signal in a transmission line has a voltage amplitude of 0.1V. The amplitude of the noise (due to a nearby refrigerator) is 1mV. What is the SNR? As a ratio: In db:

QUIZ 10 log 10 S/N [db] The noise in a transmission line was measured as having a power of 0.1mW. The SNR must be 40 db. What is the power needed for the signal?

Background information: Signal-to-noise ratio Why logarithmic? B/c of very large range, e.g. Sound pressure compare 100 db to the plain ratio. Why is the decibel sometimes defined as 20 log 10 S/N? Hint: this is sometimes called the power db which is misleading, b/c all decibel measurements refer to power!

Shannon s Theorem Max data rate = B log 2 (1+S/N) [bps] Irrespective of how many signal levels V. S/N must be plugged in as a ratio (of powers!), not in db! Note the base 2 of the logarithm! It is at theoretical limit, rarely approached in practice. Problem 2, continued: A 4-kHz channel has a SNR of 30 db? What is the maximum data rate over the channel?

Shannon s Theorem Max data rate = B log 2 (1+S/N) [bps] Irrespective of how many signal levels V. S/N must be plugged in as a ratio (of powers!), not in db! Note the base 2 of the logarithm! It is at theoretical limit, rarely approached in practice. Problem 2, continued: A 4-kHz channel has a SNR of 30 db? What is the maximum data rate over the channel?

Shannon Theorem Max data rate = B log 2 (1+S/N) [bps] Caveat: In the proof of Shannon s Theorem, the noise spectral distribution is assumed uniform, i.e. white noise. In industrial environments, noise can be far from white

QUIZ on Theoretical Basis TV channels are 6MHz wide. How many bps can be sent if 4-level signals are being used? (assuming a noiseless channel).

QUIZ on Theoretical Basis TV channels are 6MHz wide. How many bps can be sent if 4-level signals are being used? (assuming a noiseless channel). What if the signal-to-noise ratio is 20 db? End of Section 2.1

A twist on the decibel: Not in text dbm (decibel-milli) dbm is used in the telecomms industry as a convenient measure for signal power The noise N in 10 log 10 S/N is assumed to equal 1mW What is the power of a 0 dbm signal?

Not in text dbm (decibel-milli) The noise N in 10 log 10 S/N is assumed to equal 1mW What is the power of a 0 dbm signal? Solution: 0 = 10 log 10 S/(1mW) S/1mW = 1 S = 1 mw This is the power used in Bluetooth Class 3 (short range 1m)

QUIZ: dbm (decibel-milli) Not in text The noise N in 10 log 10 S/N is assumed to equal 1mW What is the power of a: 3 dbm signal? -3 dbm signal?

QUIZ: dbm (decibel-milli) The noise N in 10 log 10 S/N is assumed to equal 1mW What is the power of a: 3 dbm signal? -3 dbm signal? Not in text Solution: 3 = 10 log 10 S/(1mW) S/1mW = 10 0.3 2 S 2 mw -3 = 10 log 10 S/(1mW) S/1mW = 10-0.3 0.5 S 0.5 mw Conclusion: Every 3 db is approx. a factor of 2

QUIZ: dbm (decibel-milli) The noise N in 10 log 10 S/N is assumed to equal 1mW What is the power of a: 4 dbm signal? 20 dbm signal? Not in text

QUIZ: dbm (decibel-milli) Not in text The noise N in 10 log 10 S/N is assumed to equal 1mW What is the power of a: 4 dbm signal? 20 dbm signal? Answer: 4 dbm S 2.5 mw 20 dbm S = 100 mw Bluetooth Class 2 (medium range 10m) Bluetooth Class 1 (long range 100m)

To do for next time: Read section 2.1 carefully, practice all examples in text and notes!