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Notes for EECS 120, Sp 2002

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Notes for EECS 120, Sp 2002 Notes for EECS 120, Sp 2002 Pravin Varaiya January 27, 2002 Chapter 1 Communication system Transmitter Receiver m x x y m power T R ym y modulator channel amplifier demodulator amplifier received source carrier modulated transmitted received baseband baseband signal, signal signal signal signal signal 2πω t e c channel ω |M(ω)| |XT( )| ω ω −ω ω c c Figure 1.1: Basic components of a communication system. Figure 1.1 indicates the basic components of a communication system. The source signal m ∈ ContSignals is a baseband signal. The modulator transforms this signal into the signal xm ∈ ContSignals whose frequency spectrum is centered around the carrier frequency ωc rad/sec. The power amplifier boosts the amplitude of xm to a level sufficient for transmission. The transmitted signal xT propagates through the channel. The output of the channel is the received signal yR. The receiver amplifies this signal to ym. The demodulator processes it and the final received signal is y. A well-designed communication system should have y ≈ m. The FCC assigns a particular part of the electromagnetic spectrum—called a channel—to each station. The modulator transforms the baseband signal x into the signal xm whose spectrum Xm fits inside the station’s channel, as shown in the lower part of the figure. For example, the AM station KCBS is assigned the 10 kHz-wide channel, 740 ± 5 kHz, while the FM station KQED is assigned the 200 kHz-wide channel 88.5 ± 0.1 MHz. KRON TV is assigned the 6 MHz-wide channel, 66-72 MHz, called channel # 4. 3 4 CHAPTER 1. COMMUNICATION SYSTEM The FCC also assigns a portion of the spectrum to each cellphone company, e.g., Cingular, Verizon, ATT wireless. That spectrum is shared by the carrier’s subscribers when they make a call. 1.1 Radio, TV and cellular phones The FCC imposes standards on AM and FM broadcast radio, and broadcast TV. AM channels are 10 kHz wide, FM channels are 200 kHz wide, broadcast TV channels are 6 MHz wide. Some features of the standards are shown in Tables 1.1 and 1.2. The oldest cellular telephone system is AMPS, described in Table 1.3. In the AMPS system, the carrier uses a modulation scheme to divide its assigned spectrum among a number of 30 kHz-wide channels. A voice connection between a mobile and the base station occupies two 30 kHz channels, one for uplink, the other for downlink. The voice signal is modulated at the mobile and at the base station so that the modulated signal fits in the assigned channel. Digital control channels are used by the mobile to request the base station for a voice channel and by the base station to assign a voice channel. The voice signal in AMPS is analog. Newer cellular systems digitize voice, and the voice channels are narrower than 30 kHz. As a result, newer systems can carry a larger number of voice calls in the same spectrum as the AMPS system. One says that the newer systems have greater spectral efficiency than AMPS. Appendix 1 is a chart that shows the FCC’s allocation of the radio spectrum (3 kHz–300 GHz) to different uses. The chart in Appendix 2 focuses on wireless radio. Appendix 3 is a primer on the electromagnetic spectrum. Appendix 4 is a brief history of the telegraph and broadcast media. 1.1. RADIO, TV AND CELLULAR PHONES 5 Item Description Assigned frequency, fc In 10-kHz increments from 540 to 1700 kHz Channel bandwidth 10 kHz Carrier frequency stability ±20 Hz % modulation Maintain 85-95%; max: 100% neg; 125% pos Noise and carrier hum At least 45 db below 100% modulation in the band 30 Hz to 20 Hz Max power licensed 50 kW Table 1.1: FCC restrictions on AM broadcast radio. Item Description Assigned frequency, fc In 200-kHz increments from 88.1 MHz to 107.9 MHz Channel bandwidth 200 kHz Carrier frequency stability ±200 Hz 100% modulation ∆F =75kHz Modulation index 5 (∆F =75kHz,B = 200kHz) FM noise At least 60 db below 100% modulation at 400 Hz Max power licensed 100 kW Table 1.2: FCC restrictions on FM broadcast radio. Item Description Channel bandwidth 6 MHz Visual carrier frequency 1.25 MHz ±1000 Hz above lower boundary of channel Aural carrier frequency 4.5 MHz ±1000 Hz above visual carrier Chrominance subcarrier fre- 3.579545 MHz ±10 Hz quency Aspect ratio (width-to-height) 4:3 Modulation visual AM with negative polarity, i.e. decrease in light level causes increases in amplitude Aural modulation FM with 100% modulation being ∆F =25kHz. Table 1.3: FCC restrictions on broadcast TV. 6 CHAPTER 1. COMMUNICATION SYSTEM Item Description Base station transmit bands 869–896 MHz Mobile transmit bands 824–851 Mobile max power 3 Watts Channel bandwidth 30 kHz Voice modulation FM, 12-kHz peak deviation Control channel FSK, 8-kHz peak deviation, 10 kbps Table 1.4: AMPS cellular telephone. 1.2 Channel models The transmitted signal xT is an electromagnetic wave, which propagates or travels through the channel at the speed of light. The received signal is xR. See figure 1.1. A channel has three forms of propagation media, free space, copper, and optical fiber (glass): • Broadcast signals (radio, TV, cellphone) are transmitted freely through space; • Point-to-point transmission is over copper (twisted pair local loop or CATV coax cable) or optical fiber (high-speed Ethernet or long-distance telephony) As the signal propagates through a channel, it degrades through attenuation, dispersion, noise. Attenuation xT yR channel transmit receive power power p pT R Figure 1.2: The signal is attenuated as it propagates through the channel In free space the attenuation is PR c 2 = GT ( ) GR, (1.1) PT 4πfd 5 where GT ,GR are the transmit and receive antenna gains, c =3× 10 km/s is the speed of light, d km is the distance between transmitter and receiver, and f Hz is the carrier frequency. It is standard in communications and control to express power and attenuation in db (decibels). (P Watts equals 10 log10 P db.) So, taking GT = GR =1for illustration, the free space attenuation is 5 PR 3 × 10 10 log10 =20log10 . (1.2) PT 4πfd 1.2. CHANNEL MODELS 7 Thus attenuation gets worse as f and d increase. A ten-fold increase in f or d decreases attenuation by 20 db. Example 1.1: At a distance of 10 km, the attenuation for KCBS-AM with f = 740 kHz is 3 × 105 20 log10 ≈−50 db. 4π × 740 × 103 × 10 For KQED-FM, also at d =10km, but f =88.5 MHz, nearly 100 times the carrier frequency of KCBS, the attenuation will be 1002 or 40 db worse, 3 × 105 20 log10 ≈−90 db. 4π × 88.5 × 106 × 10 For a PCS cellphone in the 2 GHz band, if the distance between the base station and mobile is 1 km, the attenuation is 3 × 105 20 log10 ≈−100 db. 4π × 2 × 109 When the signal is transferred over a waveguide, like coax cable or optical fiber, the signal is con- fined to the waveguide, and attenuation is caused by power dissipation in the medium. So attenuation is expressed in db/km. Example 1.2: For one coax cable (LMR-195), the attenuation is given in the following table. Frequency (MHz) 1 10 100 1000 Attenuation (db/km) -12 -37 -118 -385 By contrast, the attenuation of light in single-mode optical fiber is -0.2 db/km for wave- lengths near 1.55 µm. To explore the consequences of attenuation, refer again to figure1.1. The received power PR must exceed a minimum level so that the demodulated signal y is close to the original signal x. This minimum level is called the receiver sensitivity. For illustration suppose your FM radio receiver sensitivity is -50 db or 10 µW. The transmit power of KQED-FM is 100,000 W or 50 db. Thus your radio can receive the KQED broadcast at a distance of d km if PR 10 log10 = −100 = −70 − 20 log10 d, PT or d ≈ 14 km. For optical receivers the sensitivity is -75 db (0.03 µW). The laser transmit power is small, PT = −30 db (1 mW). So the maximum distance d of the optical fiber (with attenuation of -0.2 db/km) is 10 log10 PR − 10 log10 PT = −0.2d, so −75 + 30 = −0.2d or d = 225 km. Thus signals can travel through optical fiber for 225 km before they need to be amplified. 8 CHAPTER 1. COMMUNICATION SYSTEM Dispersion Σ δ y Σ xT = a(n) (t-nT) R = a(n)h(t-nT) nT channel Figure 1.3: The sequence of impulses xT is spread out by the channel. If T is too small, the responses of the impulses overlap and lead to errors. Dispersion is best appreciated in the context of digital communication. Suppose a binary signal a : Integers →{0, 1} is encoded into a sequence of very narrow pulses T seconds apart. Ideally these pulses are δ functions, so ∞ ∀t ∈ Reals,xT (t)= a(n)δ(t − nT ). n=−∞ Thus a ‘1’ is encoded into the presence of an impulse and a ‘0’ into the absence of an impulse. The channel is an LTI system with impulse response h so the received signal is ∞ ∀t ∈ Reals,yT (t)= a(n)h(t − nT ). n=−∞ Typically, h is spread out or dispersed as shown in figure1.3, and the response to adjacent δ func- tions will overlap if T is very small.
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