How ADSL Modems Work Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin

1-2 Signals Continuous-time signals are functions of a real argument, e.g. x(t) Discrete-time signals are functions of an integer argument, e.g. x[n] t x(t)x(t) n x[n]x[n]

1-3 Systems A system generates an output signal from an input signal Continuous-time systems with input signal x and output signal y (a.k.a. the response): y(t) = x(t) + x(t-1) y(t) = x 2 (t) Discrete-time system examples y[n] = x[n] + x[n-1] y[n] = x 2 [n] x(t)x(t) y(t)y(t) x[n]x[n] y[n]y[n]

1-4 Communication Systems Voiceband modems (56k) Digital subscriber line (DSL) modems –ISDN: 144 kilobits per second (kbps) –Business/symmetric: HDSL and HDSL2 –Home/asymmetric: ADSL and VDSL Cable modems Cell phones –First generation (1G): AMPS –Second generation (2G): GSM, IS-95 (CDMA) –Third generation (3G): cdma2000, WCDMA

1-5 Digital Subscriber Line (DSL) Broadband Access Customer Premises downstream upstream Voice Switch Central Office DSLAM DSL modem LPF Telephone Network Interne t DSLAM - Digital Subscriber Line Access Multiplexer LPF – Low Pass Filter

1-6 ADSL Standards Maximum data rates supported (ideal case) –13.38 Mbps downstream –1.56 Mbps upstream Widespread deployment in US, Canada, Western Europe, Hong Kong ADSL:cable modem market 1:2 in US & 5:1 worldwide

1-7 Multicarrier Modulation Divide channel into narrowband subchannels –Based on the Fourier series –Standardized for ADSL subchannel frequency magnitude carrier channel Subchannels are 4.3 kHz wide in ADSL

1-8 Amplitude Modulation (AM) Radio station frequency f c AM stations are spaced 10 kHz apart from 550 kHz to 1700 kHz Input is an audio signal x(t) with frequencies from 0 to 5 kHz Output is the transmitted signal: y(t) = x(t) cos(2  f c t) What if x(t) were a single musical tone? x(t) = cos(2  f m t) y(t) = x(t) cos(2  f c t) = cos(2  f m t) cos(2  f c t) y(t) = ½ cos(2  f c – f m ) t) + ½ cos(2  f c + f m ) t) x(t)x(t) cos(2  f c t) y(t)y(t)

1-9 Corporate Technical Ladder Test Engineer BS degree Test other people’s designs Starting salary: $55,000 Design Engineer MS degree, or BS degree plus 2 years experience and design short courses Design new products Starting salary: $70,000 What about the Ph.D.? ¾ of Ph.D.’s to industry ¼ of Ph.D.’s to academia BSEE Tech. BSEE MSEE PhDEE 1 PhDEE 2 Technician Test Eng. Design Eng. Project Management Technical Staff (R&D) VP, Eng. CTO Director Eng. (1)Ph.D. based on system prototyping (2)Ph.D. with significant theoretical results