Computer Networks - Xarxes de Computadors Outline Course Syllabus - PowerPoint PPT Presentation

Xarxes de Computadors – Computer Networks Computer Networks - Xarxes de Computadors Outline Course Syllabus Unit 1: Introduction Unit 2. IP Networks Unit 3. Point to Point Protocols -TCP Unit 4. Local Area Networks, LANs Unit 5. Data Transmission 1 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Outline Introduction Attenuation Spectral Analysis Modulation (or Symbol) Rate Noise Baseband Digital Transmission Bandpass Digital Transmission Error Detection 2 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Introduction The received signal, r ( t ), differs from the transmitted signal s ( t ) ( r ( t ) and s ( t ) are measured in Volts): r ( t ) = f[ s ( t )] + n ( t ) f[ s ( t )] represent the modifications introduced by the transmission media: Attenuation Distortion n ( t ) represent the interference and noise. NRZ signal r ( t ) V s ( t ) V Amplitude Amplitude Transmission channel 0 0 Transmitter Receiver t b s ( t ) r ( t ) -V -V 0 1 2 3 4 5 0 1 2 3 4 5 time ( t b ) time ( t b ) 3 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Outline Introduction Attenuation Spectral Analysis Modulation (or Symbol) Rate Noise Baseband Digital Transmission Bandpass Digital Transmission Error Detection 4 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Attenuation Every channel introduces some transmission loss , so the power of the signal progressively decreases with increasing distance. We measure the “quantity of signal” in terms of average power (Watts). The power of a signal is proportional to the square of the voltage (Volts), or to the square of the current intensity (Amperes): P = 1 / T ∫ p  t  dt ∝ 1 / T ∫ 2 dt s  t  T T Transmission channel Transmitter Receiver s ( t ) r ( t ) P Tx P Rx The attenuation is defined as the rate of the average power of the transmitted signal ( P Tx ), to the average power of the received signal ( P Rx ). P rx does not include interference or noise: Attenuation, A = P Tx P Rx 5 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Attenuation - deciBels (dBs) Typically relation between powers is given in deciBels (in honor of Alexander Graham Bell, inventor of the telephone): Power relation expressed in dBs = 10 log 10 {Power relation} For instance, the attenuation expressed in dBs is: P Tx Attenuation (dBs), A (dBs) = 10 log 10 P Rx Properties of logarithms dBs, numerical example 6 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Attenuation – why deciBels (dBs)? α α P 1 P 2 P 3 Assume a cable with attenuation: 1 km 1 km = P 1 = P 2 , P 1 = P 1 P 2 2 = P 2 P 3 P 3 P 2 P 3 Thus, the attenuation for n km is α n . In dBs: Atteunation of n km = 10 log(α n ) = n 10 log(α) = n α ( dBs/km ) The manufacturer gives the parameter α ( dBs/km ). Commercial coaxial cable RG-62 7 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Attenuation – Amplifiers and Repeaters Transfer energy from a power supply to the signal. Repeaters: “regenerate” and amplify the signal. P in G 1 P out We define the gain: P out Gain (dBs), G (dBs) = 10log 10 P in If we operate in dBs, attenuation and gain add with opposite sign: A 1 A 2 A 3 P in P out G 1 G 2 8 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Outline Introduction Attenuation Spectral Analysis Modulation (or Symbol) Rate Noise Baseband Digital Transmission Bandpass Digital Transmission Error Detection 9 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Spectral Analysis At the beginning of XIX Fourier showed that any signal can be decomposed in a series (periodic signal) or integral (aperiodic signal) of sinusoidal signals. E.g. for a periodic signal of period T : Jean Baptiste Joseph Fourier f 0 =1/ T is the fundamental period. Each sinusoid is called harmonic, with amplitude v n , frequency n f o and phase Φ n The function F ( f ) that gives the amplitude and phase of each harmonic for every frequency is called the Fourier Transform or Frequency Spectra of the signal. F ( f ) is in general a complex function, where the module and phase of each complex value are the amplitude and phase of the harmonic. | F ( f )| 2 is called the Power Spectral Density of the signal, and it is also defined for random signals (is the Fourier transform of the autocorrelation function ). 10 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Spectral Analysis 1.0 The Fourier series of a rectangular signal is: 0.5 0.0 s ( t ) -0.5 -1.0 T /2 T /2 T 0 T t 1 harmonic 2 harmonics 1.0 1.0 0.5 0.5 0.0 0.0 s ( t ) s(t) -0.5 -0.5 -1.0 -1.0 − T /2 0 T /2 T/2 T/2 − T T T T 0 t t 3 harmonics 10 harmonics 1.0 1.0 0.5 0.5 0.0 0.0 s(t) s(t) -0.5 -0.5 -1.0 -1.0 T/2 T/2 T T T/2 T/2 0 T T 0 t t 11 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Spectral Analysis – Signal Bandwidth Band of frequencies where most of the signal power is concentrated. Typically, where the Power Spectral Density, | F ( f )| 2 , is attenuated less than 3 dBs. 2 T b   f T b  2 sin  f T b  s ( t ) 1.2 2 = A ∣ F  f  ∣ 1.0 bits 1 0 0 1 0 1 1 A 0.8 0.6 t 0 0.4 Tb 2 Tb 3 Tb 4 Tb 5 Tb 6 Tb Tb 0.2 -A f 0.0 1/ T b 2/ T b 3/ T b 0 NRZ signal and its Power Spectral Density 2 ∣ F  f  ∣ 2 ∣ F  f  ∣ 2 ∣ F  f  ∣ Bw Bw Bw f f f 0.0 0.0 0.0 fp 0.0 0.0 0.0 Baseband signal Baseband signal, no Modulated signal direct current. 12 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Spectral Analysis – Time-Frequency Duality A main Fourier Transform property is: s(t) ↔ F(t), then s(α t) ↔ 1/α F(t/α). In other words: If a signal is time-scaled by α, the spectra is scaled by 1/α. Consequence: Increasing the transmission rate α times by reducing the duration of the symbols α times, increases the signal bandwidth by α times: 2 s ( t ) ∣ F  f  ∣ A t 0 Bw T b f 0.0 -A 0.0 ∣  F  f / ∣ s ( α t ) 2 1 A t 0 α Bw T b / α f 0.0 -A 0.0 13 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Spectral Analysis – Transfer Function We will consider linear systems: multiply the signal by a factor, and derivate and integrated the signal (resistors, capacitors and coils). We characterize the transmission media by the Transfer Function : 2 2 = B i ∣ H  f  ∣ B i sin  2  f i t  i  A i sin  2  f i t  H  f  2 A i Transmission Channel 2 2 2 ∣ H  f  ∣ ∣ H  f  ∣ ∣ H  f  ∣ Bw channel Bw channel Bw channel f f f 0.0 0.0 0.0 0.0 0.0 0.0 f p Lowpass Channel Lowpass Channel, no Bandpass Channel direct current. 14 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Spectral Analysis – Distortion In a linear system the following relation holds: s  t = ∑ A i sin  2  f i t  r  t = ∑ B i sin  2  f i t  i = ∑ A i ∣ H  f ∣ sin  2  f i t  i  2 2 = B i ∣ H  f  ∣ 2 A i R  f = S  f  H  f  Transmission Channel 2 2 2 = ∣ S  f  ∣ 2 ∣ H  f  ∣ 2 ∣ S  f  ∣ ∣ H  f  ∣ ∣ R  f  ∣ (a) Bw channel Bw signal Bw signal f f f 0.0 0.0 0.0 0.0 0.0 0.0 2 2 2 = ∣ S  f  ∣ 2 ∣ H  f  ∣ 2 ∣ S  f  ∣ ∣ H  f  ∣ ∣ R  f  ∣ (b) Bw channel Bw signal Bw signal f f f 0.0 0.0 0.0 0.0 0.0 0.0 (a) R ( f ) = S ( f ) → No distortion, (b): R ( f ) ≠ S ( f ) → distortion. 15 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Spectral Analysis – Inter-Symbol Interference (ISI) If the harmonics are reduced, by the time-frequency duality, the duration of the received signal will increase. This provokes Inter-Symbol Interference (ISI). s  t  r  t  H  f  R  f = S  f  H  f  Transmission Channel s ( t ) r ( t ) t 16 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Outline Introduction Attenuation Spectral Analysis Modulation (or Symbol) Rate Noise Baseband Digital Transmission Bandpass Digital Transmission Error Detection 17 Llorenç Cerdà-Alabern

Xarxes de Computadors – Computer Networks Unit 5. Data Transmission Modulation (or Symbol) Rate How can we increase the line bitrate if the channel bandwidth is limited? s ( t ) bits 10 00 00 11 01 10 11 2 V V t 0 Ts 2 Ts 3 Ts 4 Ts 5 Ts 6 Ts Ts -V -2 V NRZ-4 Signal Define the Modulation (or Symbol) Rate as: v m = 1 , symbols per second or bauds T s Clearly, with N symbols we can send at most log 2 ( N ) bits, thus: v t [ bps ]= bits symbol × symbol second = log 2  N × v m [ bauds ] 18 Llorenç Cerdà-Alabern