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

8/16/ 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

8/16/ : Analog PSTN Circuit designed for analog voice transmission (mixed audio frequencies ) Bandwidth ranges  Hz - 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…)

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

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

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)

8/16/ 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

8/16/20028 = v ASK (t) = v c (t)  v d (t) = *2cosA cosB = cos(A-B) + cos(A+B)

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

8/16/ 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 V 0 ASK – time domain

8/16/ 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

8/16/ 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

8/16/ 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

8/16/ 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)

8/16/ 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:

8/16/ 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 =

8/16/ Recovered Signal after low pass filtering, f cutoff = 3f n Original Data Signal v d (t) = Modulated Signal v ASK (t) = Demodulated Signal

8/16/ 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

8/16/ 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

8/16/ 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

8/16/ 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 6f06f0 4800Hz1200Hz300Hz 2  f 0 Required BW 4800bps1200bps300bpsdata-rate bandpass

8/16/ 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)

8/16/ data v d (t) carrier v c1 (t) +V -V +V -V inverted data v’ d (t) carrier v c2 (t)

8/16/ FSK – time domain v FSK (t) = cos w c1 t + cos w c2 t

8/16/ 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)

8/16/ 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

8/16/ f c1 f c frequency = 1/T b Sunde FSK MSK Attn (dB) choice of f s is significant - naïve choice vs efficient choice spectrum of simple FSK vs CPFSK techniques - Sunde FSK - MSK

8/16/ 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

8/16/ 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

8/16/ 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

8/16/ 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)

8/16/ 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 ) twwtwwtww ccc 

8/16/ 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

8/16/ 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, …

8/16/ 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)

8/16/ 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

8/16/ Q (quadrature) 180 o = 00 0 o = 11 I (in-phase) 90 o = o = 10 QPSK (4-PSK): 4 signals (0°, 90°, 180°, 270°)  2 bits/signal

8/16/ 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)

8/16/ 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

8/16/ received signal region  bit error unlikely 8 signals  3 bits/signal Q (quadrature) 0 o = o = 111 I (in-phase) 180 o = o = o = o = o = 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

8/16/ 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 9600 bps)

8/16/ 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

8/16/ different types of PSTN Modems

8/16/ a. 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  simultaneous CMs on 1 TV channel

8/16/ 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: MHz 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: MHz BW: 6-8MHz Data Rate: 27-56Mbps

8/16/ OSI DOCSIS (Data Over Cable Service Interface Specification) Higher LayersApplications DOCSIS Control Messages Transport LayerTCP/UDP Network LayerIP Data Link LayerIEEE Physical Layer UpstreamDownstream TDMA MHz QPSK/16-QAM TDMA MHz 64/256-QAM ITU-T J.83 Annex B

8/16/ 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