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3 MO R E MO R E MO R E MO R E MO R E MORE MORE MORE MORE MORE MORE MORE S LESS S LESS S EVEN LESS MO RE MO R E MORE MORE MORE MORE MORE MORE MORE MORE MORE MORE MORE MORE MORE MORE MORE MORE M M O R E O R E MO R E MO R E MO R E MO R E MORE MORE MORE MORE MORE O M MORE R E MORE MORE MORE 5 6 3

4 1866 Trans Atlantic Telegraph Cable 1887 Marconi Developed Wireless 1901 Marconi Transmitted Radio Across Atlantic 1923 Television Invented 1948 Electronic Computer & Transistor 1969 Invented Internet 1986 Mobile Telephones A Timeline 1837 Telegraph Invented 1877 Telephone Invented 1906 Radio Transmission of Speech 1936 BBC Transmission of TV 1971 Microprocessor Invented 1988 World Wide Web 7 8 4

5 9 Samuel Thomas von Sömmering s ( ) "Space Multiplexed" Electrochemical Telegraph A B C D A B C D Lines 11 5

6 A B D E F G H I K L 1 M N O P 0 2 R S T 9 3 V W 8 4 Y

7 Alexander Graham Bell invents the Telephone. He offers the patent to Western Union for $100,

8 Cooke and Wheatstone patent telegraph in England Morse's Electro-Magnetic Telegraph patent approved First telegraph message sent between Washington and Baltimore First commercial telegraph line completed. Lines ran from New York to Washington New York and Mississippi Valley Printing Telegraph Company. Became Western Union Telegraph first used to coordinate train departures Transatlantic cable is laid from Newfoundland to Ireland. Fails after 23 days Transcontinental telegraph completed. Pony Express Disbanded 2-days Later! 1867 Stock ticker tape service inaugurated Western Union introduces the money order service Alexander Graham Bell patents the telephone. Upcoming Competition for Telegraph 1924 AT&T offers Teletype system Inauguration of direct stock ticker circuit from New York to San Francisco High-speed ticker tape can print 500 words per minute Western Union offers Telex for international teleprinting (Teleprinter Exchange) Western Union places Westar satellite in operation Western Union discontinues all Telegram and Commercial Messaging services. 17 8

9 1,966-mile-long Central Route between St.Joseph, Missouri, and Sacramento, California 18 Date Messages Handled Date Messages Handled ,158, ,971, ,216, ,645, ,879, ,169, ,168, ,904, ,135, ,319, ,884, ,679,

10 Heaviside Distortionless Condition Pupin Loading Coils Ideal Transmission Line: R = G = 0 Lossy Line: (G/C) = (R/L) Pupin Loading Coils: Spaced every 1.6 kilometers (Manhole Spacing) 21 Smearing Of Telegraph Pulses Due to Impulse Response of Distributed RC Cable Channel 22 10

11 Smearing Of Telegraph Pulses Due to Impulse Response of Distributed RC Cable Channel Compensated by Pupin Loading Coils 23 Modems grew out of the need to connect teletype machines over ordinary phone lines instead of more expensive leased lines which had previously been used for current loop-based teleprinters and automated telegraphs. Mass-produced modems in the United States began as part of NORAD s SAGE air-defense system in 1958, connecting terminals at various airbases, radar sites, and command-and-control centers in the U.S. and Canada. SAGE modems were essentially commercial acoustically coupled Bell 101, 110 baud modems. Modem: Acronym formed from two words. Modulator and Demodulator Modulator and Demodulator Mod Dem Modem Norad: North American Aerospace Defense Command SAGE: Semi-Automatic Ground Environment 24 11

12 Bit Rate 4/16/2012 Digital Signal Analog Signal Terminal MODEM Analog Signal MODEM Computer Digital Signal Modems are the interface between a computer and the telephone line Mechanical Modems Dial Up Modems Teletype Teletype Sounding Telegraph Telgraph Printing Ticker Ticket tape Tape Cook-Wheatstone Telegraph Year 26 12

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14 Information Source Data Waveforms Waveforms Data Bits RF RF Modulator Channel Demodulator Bits Information Destination BANDLIMITED AWGN Amplitude Distribution x Spectral Distribution f 29 Modulator Wireless Channel Demodulator 30 14

15 In Channel Out In G( ) C( ) fixed frequency offset interefernce Out Gain Phase Distortion Fading Freq Dep Flat Non Uniform Gain Amplitudeto-Phase doppler noise f f f f t f 31 DSP Genie-1 DSP Genie-2 DSP Genie-3 DSP Genie-4 DSP Genie

16 33 r(n) e j (n) Matched Filter Equalizer Filter r(n) Detector (Slicer) ^s(n) (n) -j (n) e ^ DDS Loop Filter SNR ATAN d(n) 34 16

17 SNR tanh( ) may be replaced by abs( ) or by gain of 1 Poly- Matched Filter -1 Z Poly- D-Match Filter Loop Filter DDS 2-to-1 Tanh -1 Z - Tanh Poly- Matched Filter -1 Z -sin( n) cos( n) Loop Filter DDS SNR

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19 39 R/W (Bits/Sec/Hz) Region for which R>C Capacity Boundary for which R=C M=16 M=256 M=64 P B1 Region for which R<C Bandwidth Limited Region M=8 P B1 Shannon Limit 2 M=4 P B3 Note: Scale Change Direction of Improving P B 1 M=2 E b/n 0 (db) /2 M=4 M=2 M=8 1/4 M=16 Power Limited Region Legend Coherent MPSK, P =10 B -5 Noncoherent Orthogonal MFSK, P B = Coherent QAM, P B =10 Complements of Bernard 40 Sklar 19

20 Capacity R/W (Bits/Sec/Hz) 4/16/ M=64 M=256 4 M=8 M=16 2 M=4 1 M= E /N (db) b 0 41 Equalizer Inverts Channel Direct Path Reflected Path Transmitted Pulse Received Pulse 42 20

21 Equalizer can Exactly Cancel Channel Channel Equalizer Recursive (IIR) Equalized Channel H ( Z) 1 Z E( Z) H ( Z) 1 1 Z E( Z) 1 Z Z Z Z R Z H Z E Z Z 1 Z 1 ( ) ( ) ( ) [1 ] E Z 1 1( ) 1 Z, ( ) 1, 2 FIR Approximation To IIR Equalizer R ( Z) [1 Z ][1 Z ] 1 Z E Z Z Z R ( Z) [1 Z ][1 Z Z ] 1 Z h(n) r (n) 1 r (n) n n E Z Z Z Z ( ) 1, ( ) [1 ][1 ] 1 r 3(n) 1 R Z Z Z Z Z Z 3 n n 44 21

22 Equalizer Task x(n) c(n) d(n) Channel Filter Equalizer Filter Impulse Impulse Desired Response h(n) Response c c c d c c c d h c c c c d h h h3 c5 c4 c3 c2 c1 d6 h4 c5 c4 c3 c2 d7 h5 c5 c4 c3 d8 c c c c c d c c c c c c d d c c d c d Least Mean Square Solution T T h d h d T T E{ } R E{ d} r d 1 R h r h R r d d T 1 T h [ C C] C d 46 22

23 Impulse Response Matrix [CC T CC] -1 CC T [CC T CC] -1 CC T = d = hh={[cc T CC] -1 CC T d} T hh=

24 Channel, Equalizer, and Equalized Impulse Responses Constellation and Eye Diagrams without and with Equalizer 50 24

25 Channel Probe Delivers Impulse or Frequency Response to Receiver MMS Algorithm x(n) Channel Filter Impulse Impulse Response c(n) Equalizer Filter h(n) d(n) Desired Response 51 x(n) Bandwidth Limited Non-Distorting N(t) Modulator Channel Demodulator s(t) r(t) ^ x(n) 52 25

26 x(n) Shaping Filter Bandwidth Limited N(t) Non-Distorting T Matched Channel Detector Filter s(t) r(t) y(t) y(n) ^ x(n) 53 x(n) Shaping Filter ~ Bandwidth Adaptive x(n) Limited N(t) Algorithm Distorting T Matched Equalizer Channel Detector s(t) r(t) Filter Filter ^ ^ v(t) y(t) y(n) ^ x(n) 54 26

27 Adaptive Equalizer N(n) Algorithm to Adapt Weights x(n) s(n) Channel Delay r(n) d(n) Adaptive Filter y(n) - e(n) y(n) w(n)

28 Whitening Filter (Autoregressive Filter Analyzer) Convert Colored Noise Back to White Noise u(n) u(n-1) u(n-2) u(n-3) u(n-4) b 1 b 2.. b N. u(n-n) b 3 b 4 - ^ u(n) e(n) v( n) e( n) u( n) u( n) [ a u( n 1 [ b u( n 1 1) 1) a u( n 2 b u( n 2 2) 2) a u( n b u( n 3 3 3) 3) a u( n N b u( n N N)] N)] When e(n) is a white Noise Sequence v(n), then b the vector b is a model of the input Signal Generator that formed the signal k a k u(n) 57 Mean Square Error J w E e n e n ( ) ( ) ( ) E d n w u n d n u w H H [ ( ) ( )][ ( ) ] E d n d n ( ) ( ) H w E u ( n) d ( n) H E d ( n) u ( n) w H H w E u ( n) u ( n) w 2 d H H H w r r w w R w ud ud uu 58 28

29 Minimize Error wrt Filter Weights Normal Equations d H d H d H r w 0 w r 2r w R w 2 R w dw ud dw ud ud dw uu uu d J ( w ) 2 r 2 R w J dw ud uu set gradient to 0 1 R w r w R r uu ud uu ud 59 Yule-Walker Equations r (0) r uu ( 1) r uu ( 2) uu r ( N uu r ( N uu r ( N uu 3) 2) 1) r (1) r uu (0) r uu ( 1) uu r ( N uu r ( N uu r ( N uu 4) 3) 2) r (2) r uu (1) r uu (0) uu r ( N uu r ( N uu r ( N uu 5) 4) 3) r ( N uu r ( N uu r ( N uu r (2) r uu (1) r uu (0) uu 1) 2) 3) w w w w N 1 w N r ( 1) r uu ( 2) r uu ( 3) uu r ( N 1) uu r ( N) uu R w uu r uu 60 29

30 Orthogonality Theorem: Error is Orthogonal to Data R UU W r Ud E UU W E Ud T { } { } E UU W T { Ud } 0 E U U W T { [ d ]} 0 T [ UW d ] e E { Ue } 0 61 Performance Surface: Quadratic in Weights u(n) u(n-1) u(n-2) J(w,w ) 1 2 w 1 w 2 e(n) w 1 w 2 2 {[ ( ) 1 ( 1) 2 ( 2)] J = E d n - w u n - - w u n

31 Life is Just a Bowl of Cherries! u(n) u(n-1) u(n-2) J(w,w ) 1 2 w 1 w 2 e(n) w 1 w 2 2 {[ ( ) 1 ( 1) 2 ( 2)] J = E d n - w u n - - w u n - 63 Gradient Descent J(w) i (min) w w i (n ) w i (n) i + 1 w i w ( n i w( n w( n 1) 1) 1) w ( n) i w( n) w( n) dj ( w) 2 dw J ( w) 2 [ r ud i R w uu ( n)] r ud - J (w) w(n +1 ) Z -1 w(n) R uu 64 31

32 Gradient Decent Morphs into LMS r Ud - - ^ (W) J W(n+1) Z -1 W(n) R UU d (n) U(n) r Ud - - ^ (W) J W(n+1) Z -1 W(n) U(n) H U (n) d (n) - e (n) U(n) - ^ (W) J W(n+1) Z -1 W(n) H U (n) 65 LMS and Leaky LMS Algorithms d (n) - e (n) - ^ (W) J U(n) H U (n) W(n+1) Z -1 W(n) H d ( n) U ( n) W ( n) hat e( n) d( n) d ( n) hat W n W n e n U n ( 1) ( ) ( ) ( ) d (n) - e (n) - ^ (W) J U(n) H U (n) W(n+1) Z -1 W(n) H d ( n) U ( n) W ( n) hat e( n) d( n) d ( n) hat W n W n e n U n ( 1) ( ) ( ) ( ) 66 32

33 Summary of Transversal LMS Algorithms µ : step size M : Number of Coefficients 0 µ a: Standard LMS b: Normalized LMS c: Error Sign Algorithm d: Data sign Algorithm e: Sign Algorithm Update Coefficients: H e( n) d( n) w ( n) u ( n) M 1 ( ) ( ) m( ) k 0 d n u n k w n w( n 1) w( n) u( n) e ( n) w( n 1) w( n) Compute error: u ( n) e ( n) M 1 2 u( n k) k 0 ( 1) ( ) ( ) [ ( )] w n w n u n sign e n w( n 1) w( n) sign[ u( n)] e ( n) w( n 1) w( n) sign[ u( n)] sign[ e ( n)] 67 Summary of the Transversal RLS Algorithm Initialize Algorithm (0) 1 w(0) 0 For each n: ( n), small positive Constant 1 ( n 1) u( n) 1 H 1 u ( n) ( n 1) u( n) H e( n) d( n) w u( n) w n w n n e n ( ) ( 1) ( ) ( ) P n P n n u n n 1 1 H ( ) ( 1) ( ) ( ) ( 1) d (n) - e(n) -1 H U (n) P(n-1) K(n) - H U (n) 1 ^ J (W) U(n) K(n) H U (n) W(n+1) Z -1-1 H U (n) P(n-1) U(n) - 1 Z -1 W(n) P(n) P(n-1) n -1 P(n)= n k H U( k) U ( k) n I -1 R UU (n) k

34 LMS Equalizer x(n) Input z -1 x(n-1) x(n-2) x(n-3) x(n-n+2) x(n-n+1) z -1 z -1 z -1 z -1 z -1 z -1 z -1 z -1 z -1 c -k(n) c -k+1(n) c -k+2 (n) c -k+3(n) c k-1 (n) c k(n) N ˆ( ) ( 1 ) k ( ) k 1 d n u n k w n e( n) d ( n) dˆ ( n) w n w n e n u n k I k y(n)= ^ I k - k( 1) k( ) ( ) ( 1 ) + e(n) Output 69 Zero Forcing Equalizer Input v(n) z -1 v(n-1) z -1 v(n-2) z -1 v(n-3) v(n-l+1) z -1 v(n-l) f 0(n) f 1(n) f 2(n) f 3(n) f L-1(n) f L(n) z -1 z -1 z -1 z -1 z -1 z -1 ~ I(n) z -1 z -1 z -1 z -1 ^ I(n) ^ I(n-1) ^ ^ I(n-2) I(n-3) ^I(n-L+1) ^I(n-L) Detector ^I(n) Output L ~ I(n)= v(n-k) f(n) e(n)= ^ ~ ^ I(n)- I(n) f (n+1)=f (n) + e(n) I(n-k) k k k k=0 Zero Forcing Algorithm 70 34

35 Decision Feedback Equalizer input z -1 z -1 z -1 z -1 z -1 z -1 z -1 z -1 z -1 z -1 c -3(n) c -2(n) c -1(n) c 0(n) c 1(n) c 2(n) c 3(n) z -1 z -1 z -1 2:1 en - + ^ ~ I(n) - DET I(n) output output Decision Feedback Equalizer 71 Least Mean Square (LMS) Algorithm d(n) ^ - d(n) U(n) U(n) e(n) Z -1 W(n+1) W(n) J (W) e(n) U(n) 72 35

36 Grand Alliance VSB Equalizer (Terrestrial High Definition TV) Input symbol Waveform fs=24 MHz Field Synch NTSC Rejection Comb Filter In/Out 12 MHz 78-Tap Filter Filter Coefficient Calculator Coefficients Coefficients 6 MHz 177-Tap Filter Output Equalized Symbol Samples fs=6 MHz Slicer Training Signal 73 Property Matching Adaptive Equalizer x(n) w(n) Adaptive Filter x(n) y(n) F[y(n)] Property Estimate P(y(n)) Filter Adaptation e(n) - + e( n) P ( y ) F ( y ( n)) 74 36

37 Decision and Sato Directed Equalization w ( n 1) w ( n) w ( n) e( n) sign( y ( n)) y ( n) e( n) R1sign ( y ( n)) y ( n) R 1 E E { x ( n) } 2 { x ( n) } Decision Directed Sato w ( n 1) w ( n) x ( n) e ( n) 75 Goddard, Modified Sato Directed Equalization w ( n 1) w ( n) w ( n) e n y n y n R y n p 2 p ( ) ( ) ( ) [ p ( ) ] R p e( n) Sign( y ( n)) [ R1 y ( n) ] R 1 E p E { x ( n) } 2p { x ( n) } E E { x ( n) } 2 { x ( n) } w ( n 1) w ( n) x ( n) e ( n) Goddard P=1, Modified Sato 76 37

38 Constant Modulus or Goddard Blind Equalization w ( n 1) w ( n) w ( n) e n y n y n R y n p 2 p ( ) ( ) ( ) [ p ( ) ] R e n y n R y n 2 ( ) ( ) [ 2 ( ) ] R p E p E { x ( n) } 2p { x ( n) } 4 E { x ( n) } 2 2 E { x ( n) } w ( n 1) w ( n) x ( n) e ( n) Goddard P=2, Constant Modulus 77 x(n) Shaping Filter Midamble Channel Probe L-Tap Channel Estimate L 2 Reference Waveforms Metric Table Bandwidth Limited N(t) Non-Distorting T Matched Viterbi Channel Channel Filter s(t) Equalizer r(t) ^ y(t) y(n) x(n) 78 38

39 Base Station Mobile Station Base Station Mobile Station Transmitter Spectrum Channel Response Transmitter Spectrum Channel Response f f Receiver Spectrum f Receiver Spectrum f Flat Fading Frequency Selective Fading 79 Energy Energy Energy time time time f r e q f r e q f r e q TDMA FDMA CDMA Energy Energy Energy time time time f r e q f r e q f r e q TDMA FDMA CDMA 80 39

40 User 1 seq 1 Composite CDMA Signal De-Spread User 1 seq 2 Energy Energy User 2 User 3 seq 3 seq 4 Composite Signal f r e q time f r e q time User 4 seq 1 User 5 seq 5 Composite Signal Integrator User 1 Spread & Sum Users Reflection Scattering Base Station Diffraction Mobile Station 82 40

41 4/16/2012 G (t) 1 (t) 1 Path 1 Delay 1 Correlator 1 Delay 1 G (t) 2 (t) 2 Path 2 Correlator 2 Delay 2 AWGN Delay 2 G (t) 3 (t) 3 Path 3 Corrlator 3 Delay 3 Delay 3 Multiple Access Interference > < Path M Delay M G (t) M Correlator M Delay M (t) M

42 Complements of Charan Langton Loral Space Systems, 85 QAM Trucking Company OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking OFDM Trucking Complements of Charan Langton Loral Space Systems,

43 43 IFFT IFFT.... Series to Parallel Parallel to Serial Constellation Mapping Symbol Detection Real Real Imaginary Imaginary DAC ADC DAC ADC LPF LPF LPF LPF Quad Osc Quad Osc PA LNA - 87 BW= Spacing= f f T T T N 64 Point FFT 128 Point IFFT 64- Point Input Time Array 64- Point Input Freq. Array 128- Point Input Freq. Array 128- Point Output Time Array 160- Point Output Time Array CP 88

44 Normalized Output Level Filter Spectrum 4/16/2012 CP 64 Point FFT 256 Point IFFT 64- Point Input Time Array 64- Point Input Freq. Array 256- Point Input Freq. Array Point Point Output Output Freq. Time Array Array 320- Point Output Time Array Perfect Linearity Transfer Function Efficiency P RMS PAPR (5dB) 0 BO (2dB) P SAT Normalized Input Level 90 44

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47 16-QAM Histogram at Amplifier Input 10 0 Probabilty of Level Crossing Normalized Amplitude (x/ x ) QAM Histogram at Amplifier Output std dev =1.03 clip level Normalized Amplitude (x/ x ) Normalized Amplitude (x/ x )

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49 Probability Probability 4/16/ Probabilty of Level Crossing Cum. Comp. Density Standard OFDM 64-QPSK Bins in 256 Pont FFT 10-3 Cum. Comp. Density Unshaped Dirichlet OFDM 64-QPSK Kernels in 256 Pont FFT Normalized Amplitude (x/ x ) Probabilty of Level Crossing Sample Comp. Cum. Prob. for Shaped Dirichlet OFDM with 32 QPSK Bins 0% 10% Sample Comp. Cum. Prob. for Standard OFDM with 32 QPSK Bins , 80, 90, 96% 60% 50% 20% 30% 40% Normalized Amplitude (x/ x )

50 /16/2012 x(n) S-P V(k) IFFT P-S s(t) Bandwidth Limited Distorting Channel N(t) r(t) P-S FFT ^ Y(k) Probed Channel Estimate Equalizer ^ V(k) S-P ^ v(n) Detector ^ x(n)

51 GSM: Groupe Spécial Mobile GPRS: General Packet Radio Service EDGE: Enhanced Data Rates for GSM Evolution HSDPA: High Speed Downlink Packet Access HSPA: High Speed Packet Access UMTS: Universal Mobile Telecommunications System LTE: Long Term Evolution 100Gb/s 10Gb/s 1Gb/s 100Mb/s 10Mb/s 1Mb/s 100Kb/s 10Kb/s USB GSM Gerhard Fettweis, TU Dresden USB b GPRS UWB ag 3G EDGE HSDPA n USB c HSPA UMTS Short Links (1m) WLAN (10m) ac/ad LTE Advanced Cellular (100m) QAM CDMA OFDM LTE Tb/s 100 Gb/s 10 Gb/s 1 Gb/s 100 Mb/s 10 Mb/s 1 Mb/s 100 kb/s 10 kb/s GSM GPRS Clk: 100x Data Rate Baseband: 1-Chip Clk: 500x Data Rate Baseband: 1-Chip Clk: 1000x Data Rate Baseband: 1-Chip Clk: 2000x Data Rate Baseband: 3-Chips HSDPA 3G EDGE Clk: 100x Data Rate Baseband: 1-Chip HSPA Computational Complexity of PHY Clk: 2x Data Rate Baseband: 1/N? - Chip Clk: 10x Data Rate Baseband: 1/4 - Chip LTE LTE Advanced Gerhard Fettweis, TU Dresden

52 Gerhard Fettweis, TU Dresden

53 4/16/ db 200 khz 80 db -6 db/octave 200 khz 20 MHz f 20 MHz Input Sample Rate 400 Tap FIR Filter 20 MHz Output Sample Rate khz 50-to Taps Polyphase Low Pass Filter 8 Taps khz 1 20 MHz khz

54 4/16/ Taps 400 Taps 20 MHz Polyphase 400 khz Polyphase 20 MHz Low Pass Filter Low Pass Filter 50-to-1 1-to-50 8-taps 8-taps MHz 20 MHz 400 khz MHz Input Sample Rate 400 Tap FIR Filter 20 MHz Output Sample Rate 20 MHz 20 MHz 400 khz 8-tap 8-tap Select Coefficient Bank Coefficient Bank Select

55 20MHz 360-Ops/Input 400-Tap Lowpass Filter White Box 20MHz 20MHz 16-Ops/Input 8-Tap Filter Coefficient Bank 400 khz 8-Tap Filter White Box Coefficient Bank 20MHz Select State Machine Select 111 H 0(Z ) H 0(Z ) H 1(Z ) H 1(Z ) x(n) H (Z ) y(nm) 2 H 2(Z ) y(n) H M-1(Z ) H M-1(Z ) f f f

56 j 0k 2 e M j 0k 2 e M x(n) H 0(Z ) H 0(Z ) j 1k 2 e M j 1k 2 e M H 1(Z ) H 1(Z ) j 2k 2 M j 2k 2 e M e H 2(Z ) y(nm,k) H 2(Z ) j (M-1)k 2 e M j (M-1)k 2 e M H M-1(Z ) H M-1(Z ) y(n,k) f f f 113 j rk 2 1 e M j rk 2 2 e M j rk 2 2 j rk 2 1 e M e M y(nm,k 2) H (Z ) H (Z ) 0 0 H (Z ) H (Z ) 1 1 x(n) H (Z ) H (Z ) 2 2 y(n,k )+y(n+k ) 1 2 y(nm,k ) 1 H (Z ) H (Z ) M-1 M-1 f f f f

57 ... 4/16/ Hmm. this is very good stuff Polyphase Partition h (n) 0 h (n) 1 FDM fs h (n) 2 h (n) 3 M-PNT IFFT. TDM h M-2(n) h M-1(n) h (n)=h(r+nm) r

58 input buffer output buffer 4/16/2012 F 0 F 1 f Sample F 2 fs M f BW F M-2 F M-1 Compact Support Orthogonal Filters f F 0 F 1 f Sample F 2 fs M f BW F M-2 F M-1 Compact Support Nyquist Filters f 117 FFT FFT spectral mask

59 4/16/2012 M Path Filter M/2 Point Shift M-Point Circular Buffer M Point IFFT x x x x M Point FFT M/2 Point Shift M-Point Circular Buffer M Path Filter

60 4/16/ Tap FIR Filter M Path Filter M/2 Point Shift M-Point Circular Buffer M Point IFFT x x x x M Point FFT M/2 Point Shift M-Point Circular Buffer M Path Filter (a) Complex Input Samples

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62 M Point FFT P Point FFT M Point IFFT M Point IFFT M Path Filter P Path Filter M Path Filter M Path Filter M-Point Circular Buffer M-Point Circular Buffer M-Point Circular Buffer P-Point Circular Buffer x x x x x x 126 P1 Point FFT P2 Point FFT M Point IFFT P1 Path Filter P2 Path Filter M Path Filter M-Point Circular Buffer P1-Point Circular Buffer P2-Point Circular Buffer

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64 Magnitude (db) Magnitude (db) Magnitude (db) 4/16/2012 Sig 3 Sig 6 Sig Sig 4 Sig 5 Sig Frequency (MHz) Frequency (MHz) Frequency (MHz) Sig 1 Sig Frequency (MHz) Frequency (MHz)

65 4/16/ P1 Path Filter P2 Path Filter P1-Point Circular Buffer P2-Point Circular Buffer P1 Point IFFT P2 Point IFFT M Point FFT M-Point Circular Buffer M Path Filter

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67 4/16/ M Path Filter M/2 Point Shift M-Point Circular Buffer M Point IFFT M Point FFT M/2 Point Shift M-Point Circular Buffer M Path Filter

68 4/16/ M Path Filter M/2 Point Shift M-Point Circular Buffer M Point IFFT M Point FFT M/2 Point Shift M-Point Circular Buffer M Path Filter

69 Two Filters: Matched Filter and Equalizer Filter Frequency Domain Equalizer Frequency Domain Matched Filter (M/2)-to-1 Reampling M-Path M-Channel Analysis Channelizer 1-to-(M/2) Reampling M-Path M-Channel Synthesis Channelizer Channel Equalizer Weights 139 Time and Frequency Response of Analysis Channellizer Nyquist Filter

70 Time and Frequency Response of Synthesis Channelizer Filter 141 Out-of Band Attenuation and In-Band Ripple

71 Impulse Response of Channelizer Matched Filter 143 Frequency Response and Details of Channelized Matched Filter

72 Composite Response of Shaping Filter and Channelizer Matched Filter 145 Frequency Response and Details of Cascade Shaping Filter and Channelizer Matched Filter

73 Artifact Response levels of Channelizer Matched Filter 147 Matched Filter Constellations: Channelizer & FIR Filter

74 Channelizer Matched Filter Response 149 Channel Distorted, Match Filtered Signal

75 Channel Distorted, Channelizer Matched Filter and Equalizer Response 151 Triangle Shaped Filter Spectrum for Analysis Channelizer

76 Triangle Shaped Analysis Filter and Rectangle Shaped Synthesis Filter 153 Sum of Rectangle Shaped Channels

77 Sum of Triangle Shaped Channels 155 The Shape of Things to come! Frequency Domain Equalization Filter Frequency Domain Matched Filter h (n) 0 h (n) 1 M/2:1 M/2:1 cos(n ) C 0 C 1 H (0) MF H (1) MF 1:M/2 1:M/2 g (n) 0 g (n) 1 r(n) y(n) h 2M-2(n) h 2M-2(n) M/2:1 M/2:1 cos(n ) C M-2 C M-1 H H MF MF (M-2) (M-1) 1:M/2 1:M/2 g M-2(n) g M-1(n) Analysis Filter Bank Intermediate Processing Synthesis Filter Bank

78 SOFTWARE DEFINED RADIO MAN Is Open For Questions

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