EE450 Discussion #5 Shannon’s Theorem  Modulations MultiplexingShannon’s Theorem C = B log2(1 + SNR) Theoretical Maximum Capacity that can be obtained on a line Sets an Upper Bound on the capacity given the conditions Used for Calculating the Signal to Noise Ratio – Given the Bandwidth and capacity of the channel Bandwidth - Given the SNR and Channel Capacity Capacity - Given the SNR and the BandwidthProblem #1 What SNR is needed to put a T-1 carrier on a 50 khz line? What do we know? T-1 Capacity = 1.544 Mbps Bandwidth = 50 KHz Move them around and Solve: 1,544,000 = 50,000 log 2 (1+SNR) 2^30.88 –1 = SNRContinued So SNR = 1976087931 SNR is typically measured in DB Use SNR dB = 10 log 10(SNR) In this case  SNR dB = 10 log 10(1976087931) SNR aprox. 92.9 dB However you must NOT plug SNR into Shannon’s theorem in dB formatProblem #2 Calculate the maximum rate supported by a telephone line with BW of 4 KHz. When the signal is 10 volts, the noise is 5 milivolts. SNR=Signal power/Noise Power Power is proportional to square of the voltage S/N = (10^2)/(0.005^2) = 4000000 B = 4000 Hz C = B log 2 (1+S/N) Reminder: log 2 x = ln x / ln 2 C = 4000 log 2 (1+4000000)= 87726 bpsReview on Modems Modem Stands for  MOdulator / DEModulator Uses Sine wave As the carrier SignalWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998Digital to Analog EncodingModulation  Need to Encode Digital Data in an Analog Signal In modem transmission we use different techniques for modulation Amplitude Modulation Frequency Modulation Phase ShiftAmplitude Modulation Varies the Amplitude of the SignalAmplitude Modulation Same Signal Greater AmplitudeAmplitude = 2Amplitude = 1Amplitude Modulation Amplitude 2 = 1 Amplitude 1 = 0 This signal Represents: 0011010WCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998ASKFSKWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998Phase-Shift Modulation Start with our normal sine wave The sine wave has a period of P  P may be denoted as T instead in the equationsPhase-Shift Modulation Shift the Phase of the Sine Wave Shifted diagram shows that the cycle starting at 1 vs. starting at 0PSKWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998PSKConstellationWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 19984-PSKWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 19984-PSKConstellationWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 19988-PSKConstellationWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998PSKWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998Combining Both Modulation used in Modern Modems Uses: Amplitude Modulation Phase Shift Keying QAM Quadrature Amplitude Modulation Big Name – Simple Concept4-QAM and 8-QAMConstellationWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 19988-QAM SignalWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 199816-QAMConstellationWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998Bit Rate and Baud RateWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998Problem #3 A modem uses an 8-PSK modulation scheme supporting data rate of 4800 bps. What is the signaling rate (aka baud rate)? 8 PSK – (Phase Shift Keying) 8 different encoding levels  Each encoding has log2 8 = 3 bits 4800 / 3 = 1600 Baud RateWays of Multiplexing/Demultiplexing Time Division Multiplexing (TDM) You have n input lines coming in The same # of lines going out.. Only one line interconnecting. How?Packing the Data In Multiplexing – A way of aggregating data onto a single line without compromising the rate at which original data is sent. We are not limiting anyone's channel capacity We are simply sending there signal through a shared lineSharing – by time slots Sample the Line 1 – Place its value in slot 1 Sampling the Line – and Send its value on its waySlot1Line1Line2Line3Line4More Time Slots Line 2 Places its Sample on the Line And it goes on…Slot2|Slot1Line1Line2Line3Line4Other Side - Demultiplexing Similar to Multiplexing just the reverseSlot2|Slot1Line1Line2Line3Line4Slot2Line1Line2Line3Line4TDMWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998Synchronous TDMWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998WCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998TDM, MultiplexingWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998TDM, DemultiplexingData RateWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998TDM - Example T-1 Lines Carries the equivalent of 24 voice lines Each analog voice line is sampled at 8000 times a second Digital Sample is thrown on the Digital Carrier Line On the other side Digital samples are used to reconstruct Analog Signal.STDM (Asynchronous TDM) How does it Work? Checks to see if there is data to transmit on input line If there is transmit data If not move on to next input lineAsynchronous TDMWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998Frames and AddressesWCB/McGraw-HillThe McGraw-Hill Companies, Inc., 1998a. Only three lines sending dataTDM vs. STDM Synchronous TDM – Gray Slots are actually carrying dataSlot 1 Slot 2 Slot 4Slot 3 Slot 1 Slot 3Slot 2 Statistical TDM – Uses empty time slots but does add some overhead Slot 1 Slot 2 Slot 1 Slot 2 Slot 3 Slot 1Notes on TDM- Sampling Occurs very quickly- Applicable to fixed number of flows- Requires Precise Timing- Resources are guaranteedSTDM Statistical Time Division Multiplexing Similar to regular TDM but different in this: Traffic is sent on demand – Only if there is data on line 1, will slot 1 be occupied by line 1 Resources are not guaranteed If we are no longer guaranteed a time slot why use it? We (the carrier) can take advantage of one of the input lines not being busy Important distinction – STDM is used mainly for Digital LinesTDM vs. STDM1. Traffic is sent on demand utilizing unused time slots so it benefits the Carrier 2. Resources are not guaranteed so when time slots are busy the users suffer3. In real life there is some overhead4. Speedup isn’t as obvious1. Resources are guaranteed to the users 2. Sampling Occurs very quickly 3. Applicable to fixed number of flows4. Requires Precise Timing5. Wastes valuable carrier spaceStatistical TDM Parameters I = Number of Input Sources R = Data rate