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8/16/20021 Modems Key Learning Points Fundamentals of modulation and demodulation Frequency Domain Representation Time Domain Representation M-ary Modulation and Bandwidth Efficiency BER vs bit/second
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8/16/20022 2.5 Public Carrier Circuits for Limited Geographic Span: use privately owned resources e.g. Local Area Network, Routers, Hubs for Larger Geographic Span: Line of Sight (LOS) uwave satellite links public carriers (e.g. Sprint, MCI, …) - analog PSTN using modems - digital leased lines: T1, T3, ISDN
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8/16/20023 2.5.1: Analog PSTN Circuit designed for analog voice transmission (mixed audio frequencies ) Bandwidth ranges 400-3000Hz - DC power supply will not pass low frequency signals (1111… or 0000…) - 2 voltage levels for different signals won’t work (0 output for 1111… or 0000…)
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8/16/20024 Binary Data Transmission over PSTN Requires Modem Modulator: Convert binary data into from compatible with PSTN at transmitter Demodulator: Convert signal back, recover data at receiver 2 options for conventional PSTN modem connection: 1. short-term switched path: dialing & setting up ~ phone call 2. leased line: bypass normal switching equipment (switch exchanges) - set-up on long-term basis - economical only if utilization is high - operating characteristics accurately quantified higher signal rates
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8/16/20025 Modulation: three general types which can be combined (i) Amplitude Shift Key, (ii) Frequency Shift Key, (iii) Phase Shift Key binary data requires at least 2 signal levels as binary data keys between 1 and 0 signal shifts between 2 levels different methods require different amounts of BW
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8/16/20026 (1) carrier signal: v c (t) = cos w c t (assume unity amplitude) carrier frequency, f c : (Hz) or w c = 2 f c (rads) f c selected within PSTN Bandwidth (1000Hz-2000Hz) (2) binary data signal, v d (t) fundamental frequency of data signal: w 0 = 2 f 0 mathematically modulation is v c (t) v d (t)
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8/16/20027 1. Amplitude Shift Key (ASK) Principal of Operation: - amplitude of audio tone (f c ) switched between 2 levels - bit rate of transmitted binary signal determines switching rate & bandwidth - binary data is effectively carried by carrier signal unipolar periodic data signal given by: v d (t) = v ASK (t) = v c (t) v d (t) modulated signal given by
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8/16/20028 = v ASK (t) = v c (t) v d (t) = *2cosA cosB = cos(A-B) + cos(A+B)
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8/16/20029 v ASK (t) = v ASK (t) consists of original data signal v d (t) translated in frequency by w c (w c ± w 0, w c ± 3w 0, w c ± 5w 0 ) … DC component translated to sinusoidal component at w c 2 frequency components for fundamental & each harmonic - frequency components are equally space on either side of f c - spectral components are known as sidebands - each bandpass component at ½ power of original baseband sidebands
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8/16/200210 f c –3f 0 f c –f 0 f c f c +f 0 f c +3f 0 f signal power 6f 0 2f 0 ASK – frequency domain digital signal carrier signal 1 0 1 0 1 0 +V 0 ASK – time domain
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8/16/200211 Recall from discussion of Limited Bandwidth: higher channel bandwidth received signal is closer to transmitted given data rate = R, minimum channel bandwidth for satisfactory performance in the worst case - f 0 of “101010…” (shortest period highest f 0 ) - f 0 = ½ R
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8/16/200212 minimum channel bandwidth for ASK - to receive only f 0 bandwidth, B = 2f 0 = R - to receive f 0 and 3rd Harmonic bandwitdh = 6f 0 = 3R, component at carrier frequency is present in received signal, contains no information (inefficient) - Nyquist: maximum achievable data rate for ideal channel C = 2 B Alternatively, let B = 2f 0 max data rate R = B =2 2f 0 both primary sidebands used to compute minimum BW either contains required signal, f 0
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8/16/200213 Single Side Band (SSB) use band pass filter on transmitter lower required bandwidth to B = f 0 (Nyquist rate) - limit pass band - remove lower sidebands: (fc - f0) e.g. limit pass band to f c + (f c + 5f 0 ) primary sideband signal power cut in ½ relative to v c (t ) - reduces Signal to Noise Ration increases BER SSB-ASK f c –5f 0 … f c –f 0 f c f c +f 0 …. f c +5f 0 f filter power passband filter
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8/16/200214 Demodulation: Recover transmitted Signal – at receiver assume ideal channel - no noise, distortion, attenuation practically, problem is more difficult received signal = v ASK (t) v ASK (t) = receiver multiplies v ASK (t) by v c (t) v d (t) v 2 c (t)
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8/16/200215 Produces 2 versions of received signal each at ½ original power both with data contained in sidebands one is centered at 2f c (high frequency component ) other is at baseband (f c - f c ) = 0 collecting terms yields:
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8/16/200216 Select baseband signal with Low Pass filter: Low pass filter output = bandwidth limited version of v d (t) pass only 0, f 0 3f 0, (assume 3rd harmonic used ) filter all components < 3f 0 hi frequency components completely filtered Recovered Signal =
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8/16/200217 Recovered Signal after low pass filtering, f cutoff = 3f n Original Data Signal v d (t) = Modulated Signal v ASK (t) = Demodulated Signal
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8/16/200218 v d (t) f 0 3f 0 f f c –3f 0 f c –f 0 f c f c +f 0 f c +3f 0 f v ASK (t) 2 f c –3f 0 2f c –f 0 2f c 2f c +f 0 2 f c +3f 0 f 0 3f 0 demodulated f 0 3f 0 filtered and recovered Ideal ASK Modulation – Frequency Domain
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8/16/200219 v d ‘(t) PSTN cos(w c t) v d (t) cos(w ’ c t) v ASK (t) More Practically if attenuation is included 10-30dB attenuation common if noise is included received power > noise floor (SNR) if distortion is included must use equalizers, match filter, etc if carriers aren’t synchronized phase noise w c (t)-w ’ c (t) = (t) receiver must synchronize sampling interval to recover signal Fantasy: Received Signal = ½ power of Transmitted Signal
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8/16/200220 ASK is simple to implement, not used in early, low rate modems - PSTN long haul switching & transmission systems were analog - voice & data signals transmitted & switched as analog signals - ASK sensitive to resulting variable signal attenuation More recently PSTN long haul switching & transmission systems are digital - source signal is analog only to local exchange - converted digital signal retains form thru-out network - significant improvement in electrical characteristics of PSTN ckts ASK & PSK used to in higher rate modems
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8/16/200221 data-rate300bps1200bps4800bps component f0f0 150Hz600Hz2400Hz 3f 0 450Hz1800Hz7200Hz ie: Estimate BW to transmit f 0 & 3f 0 using ASK for data rates: (without SSB) baseband 14400Hz3600Hz900Hz 6f06f0 4800Hz1200Hz300Hz 2 f 0 Required BW 4800bps1200bps300bpsdata-rate bandpass
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8/16/200222 2. Frequency Shift Key (FSK): used in early low rate modems Principal of Operation use 2 fixed amplitude carrier signals, v c1 (t), v c2 (t) to avoid reliance on amplitude variance modulation is equivalent to summing 2 ASK modulators - one carrier uses original data signal, v d (t) - other carrier uses compliment of data signal, v’ d (t) - 2 data signals: v d (t) and v d ’(t) = 1- v d (t) 2 carrier frequencies f c1, f c2 frequency shift: f s = f c2 - f c1 v FSK (t) = v c1 (t) v d (t) + v c2 (t) v d ’(t) = cos(w c1 t) v d (t) + cos(w c2 t) v d ’(t)
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8/16/200223 1 0 1 0 1 0 data v d (t) carrier v c1 (t) +V -V +V -V 0 1 0 1 0 1 inverted data v’ d (t) carrier v c2 (t)
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8/16/200224 FSK – time domain v FSK (t) = cos w c1 t + cos w c2 t
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8/16/200225 signal power FSK – frequency domain f c1 –3f 01 f c1 –f 01 f c1 f c1 +f 01 f c1 +3f 01 6f 01 2f 01 f c2 –3f 02 f c2 –f 02 f c2 f c2 +f 02 f c2 +3f 02 frequency shift: f s = f c2 – f c1 6f 02 2f 02 v FSK (t)
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8/16/200226 FSK bandwidth requirements f c1 modulates ‘1’ and f c2 modulates ‘0’ - minimum bandwidth for each carrier is ½ R - highest fundamental freq component of each carrier ½ of ASK assume just f 0 component received (no harmonics) - let f s = f c2 -f c1 total bandwidth for FSK is 2f 0-FSK + f s - since f 0-FSK ½ f 0-ASK total BW f 0-ASK + f s - with 3rd harmonic: 6f 0 ASK + f s
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8/16/200227 f c1 f c2 -3 -2 -1 0 1 2 3 frequency = 1/T b Sunde FSK MSK Attn (dB) 0 -10 -20 -30 -40 choice of f s is significant - naïve choice vs efficient choice spectrum of simple FSK vs CPFSK techniques - Sunde FSK - MSK
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8/16/200228 simple FSK system with phase jumps switch cos w 2 t cos w 1 t input data phase jumps VCO cos w c t input data continuous phase FSK (CPFSK) with VCO based oscillator Implementation of FSK
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8/16/200229 ie: EIA for Bell 103, ITU-T for V.21 - FSK modems, full-duplex links f 0 = 75 Hz R = 150 bps 2f 0 = 150 Hz R = 300 bps f s = 200Hz, separation between primary sidebands = 50Hz space = binary 0, mark = binary 1 DTE modem modulator ‘0’ = 1070 Hz ‘1’ = 1270 Hz demodulator ’0’ = 2025 Hz ‘1’= 2225 Hz modem demodulator ‘0’ = 1070 Hz ‘1’ = 1270 Hz modulator ’0’ = 2025 Hz ’1’ = 2225 Hz
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8/16/200230 3. PSK: phase shifts in carrier encode bits in data stream carrier frequency & amplitude are constant (constant envelope) phase coherent ‘1’ ‘0’ i. phase coherent PSK: 2 fixed carriers 180° phase shift represents ‘1’ or ‘0’ One signal is simply inverse of other Disadvantage: requires reference carrier signal at receiver - received phase signal is compared to local reference carrier - more complex demodulation circuitry
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8/16/200231 differential 90° = ‘0’ 270° = ‘1’’ 270° phase shift relative to current signal next bit = ‘1’ ii. differential PSK: phase shift at each bit transition irrespective of whether ‘111…’ or ‘000…’ transmitted 90° phase shift relative to current signal next bit = ‘0’ demodulation: determine magnitude of each phase shift (not absolute value)
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8/16/200232 PSK Bandwidth requirement: represent data in bi-polar form negative signal level results in 180° phase change in carrier assume unity amplitude, fundamental freq = w 0 v d (t) = v c (t) = cos w c t v PSK (t) = v d (t)v c (t) v PSK (t) = ...)5cos( 5 1 )3 3 1 ) 2 000 twwtwwtww ccc
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8/16/200233 f c –3f 0 f c –f 0 f c f c +f 0 f c +3f 0 f signal power 6f 0 2f 0
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8/16/200234 PSK BW Requirements - same bandwidth as ASK, no carrier component, cosw c t at w c - assume 10101… w/ only f 0 to be received min BW = 2 f 0 -absence of carrier component means more power to sidebands - sidebands contain data more resilient to noise than FSK, ASK with band pass filter on transmitter band limit transmitted signal to f c achieve nyquist rate for minimum bandwidth required ½ R = f 0 (~ ASK) no component at w c all received power in data carrying signal, f c ± f 0, …
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8/16/200235 Phase Diagram 2 axis: in-phase, I & quadrature, Q represents carrier as vector, length = amplitude vector rotates CCW around axis angular frequency, w - ‘1’ represented as vector in phase with carrier - ‘0’ represented as vector 180° out of phase with carrier Q (quadrature) 180 = 00 =1 I (in-phase)
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8/16/200236 4. Multilevel Modulation Advanced modulation techniques higher bit rates - multi-level signaling - mix of basic schemes (PSK, ASK) - more complex (cost), higher bit error rate Used in all digital PSTN (switching & transmission) Multi-Level Signal (use amplitude, phase, or frequency) use n signal levels each signal represents log 2 n data bits - 4 signal levels 2 bits/signal element - 8 signal levels 3 bits/signal element - 16 signal levels 4 bits/signal element
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8/16/200237 Q (quadrature) 180 o = 00 0 o = 11 I (in-phase) 90 o = 00 270 o = 10 QPSK (4-PSK): 4 signals (0°, 90°, 180°, 270°) 2 bits/signal
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8/16/200238 QAM – (quad amplitude modulation) Combine ASK & PSK QAM-16 levels per signal element 4-bits per symbol - 12 phase levels - 4 amplitudes levels - different amplitude associated with adjacent phases - 48 total signal levels possible bits/symbol = 5 2 (t) 1 (t)
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8/16/200239 using 16 of 48 possible signals makes recovery less prone to errors - same amplitude levels have large phase variation - same phase angles have large amplitude variation - extra bit can be used for forward error correction practical limits to M-level signalling: more phase/amplitude levels difference between unique signal symbols is reduced increases impact of channel impairments (noise distortion, attenuation scheme’s robustness depends on proximity of adjacent points in constellation complexity rises cost, risk, rate of failures rise
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8/16/200240 received signal region bit error unlikely 8 signals 3 bits/signal Q (quadrature) 0 o = 010 270 o = 111 I (in-phase) 180 o = 100 90 o = 001 45 o = 011 225 o =101 300 o = 110 135 o = 111 received signal region bit error likely reduce error rate: maximize distance between adjacent points grey coding – adjacent symbols differ by 1 bit offset phase angles for adjacent amplitude
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8/16/200241 All modulation schemes scramble & descramble reduces probability that consecutive bits in sequence are in adjacent bit positions - at transmitter: bit stream scrambled using pseudo random sequence - at receiver: bit stream descrambled restore bit stream - used in V.29 modems (fax machines @ 9600 bps)
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8/16/200242 trellis–code modulation (TCM) - another redundancy scheme - use all 32 amplitude –phase alternatives - resulting 5 bit symbols contain only 4 data bits - 5 th bit generated using convolutional encoder, used for error correction at transmitter: each 4-bit set in source stream converted to 5 bits at receiver: most likely 4 data bits determined - with no bit errors correct 4 bit set collected - with bit errors some probability that correct 4 bits selected used in V.32 for rates up to 14.4kbps V.34 fast modems rates up to 19.2k, 24k, & 28k
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8/16/200243 different types of PSTN Modems
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8/16/200244 2.5.1a. Cable Modems (CM) Connection speed 3-50 Mbit/s Distance can be 100 km or more Master-Slave Topology (CATV is traditionally simplex) CATV networks are Hybrid Fibre-Coax (HFC) networks - fiber-optic cables from the Head-End to locations near the subscriber - the signal is converted to coaxial cables to subscriber premises. CMTS: Cable Modem Termination System - connects cable TV network to data network - CMTS can drive 1-2000 simultaneous CMs on 1 TV channel
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8/16/200245 Cable Modem 4 Cable Modem 3 Cable Modem 2 CMTS (head) Upstream Demodulator QPSK/16-QAM carrier freq. 5-65MHz BW: 2MHz Data Rate: 3Mbps Downstream Modulator 64 QAM/256QAM carrier freq: 65-850MHz BW: 6-8MHz Data Rate: 27-56Mbps Cable Modem 1 Upstream Modulator QPSK/16-QAM carrier freq: 5-65ZMHz BW: 2MHz Data Rate: 3Mbps Downstream Demodulator 64 QAM/256QAM carrier freq: 65-850MHz BW: 6-8MHz Data Rate: 27-56Mbps
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8/16/200246 OSI DOCSIS (Data Over Cable Service Interface Specification) Higher LayersApplications DOCSIS Control Messages Transport LayerTCP/UDP Network LayerIP Data Link LayerIEEE 802.2 Physical Layer UpstreamDownstream TDMA 5 - 42 MHz QPSK/16-QAM TDMA 42 - 850 MHz 64/256-QAM ITU-T J.83 Annex B
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8/16/200247 2.5.1.b Digital Subscriber Line (DSL) – up to 52Mbps over traditional phone lines uses carrier frequencies between 25KHz.. 1MHz always on – no need to dial Internet Service Provider (ISP) dedicated connections (not shared with your neighbors) voice & data over a single line more expensive, additional hardware required special DSL modem at your computer DSL Multiplexer (DSLAM) at central office - separates voice/data streams - sends voice stream to phone company & data stream to ISP limited availability connection speed is dependent on distance from phone company data rate is lowered to reduce distortion DSL link must be within 2 miles of central office
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