1. Orthogonal Frequency Division Multiplexing OFDM
fred harris
Cubic Signal Processing Chair
San Diego State University
Vehicular Technology Conference

2. Textbooks and References
“Wireless OFDM Systems: How to Make Them Work”
Marc Engels, Editor
“OFDM Wireless LANs: A Theoretical and Practical Guide”
Juha Heiskala and John Terry
“OFDM for Wireless Multimedia Communications”
Richard Van Nee and Ramjee Prasad
“Single and Multi-Carrier Quadrature Amplitude Modulation”
Lajos Hanzo, William Webb, and Thomas Keller
“ADSL, VDSL, and Multicarrier Modulation”
John Bingham
“Implementing ADSL”
David Ginsburg
“DSL Advances
Massimo Sorbara, John Cioffi, and Peter Silverman

3. OFDM OFDM also known as Multi-Carrier or Multi-Tone Modulation
DAB-OFDM
Digital Audio Broadcasting
DVD-OFDM
Digital Video Broadcasting
ADSL-OFDM
Asynchronous Digital Subscriber Line
Wireless Local Area Network
IEEE a, IEEE g
ETSI BRAN (Hyperlan/2)

4. OFDM Systems System Transform Size Number Carriers Channel Spacing kHz
Bandwidth
MHz
Sample
Rate
Symbol
Duration
sec
Data
Mbits/s
HyperLAN/2 64 52 4
312.5
16.25 20
3.2
0.8
6-54
802.11a
16.56
DVB-T
2048
1024
1712
842
4.464
7.643
9.174
224
DAB
8192
1536
1.00
1.536
2.048
24/48/96
msec
3.072
ADSL
256 (down)
64 (up)
36-127
7-28
4.3125
1.104
231.9

5. OFDM Advantages Efficiently Deals With Multi-path Fading
Efficiently Deals With Channel Delay Spread
Enhanced Channel Capacity
Adaptively Modifies Modulation Density
Robustness to Narrowband Interference

6. OFDM Disadvantages OFDM Sensitive to Small Carrier Frequency Offsets
OFDM Exhibits
High Peak to Average Power Ratio
High Frequency Phase Noise
Sampling Clock Offsets

7. Single Carrier System Sequential Transmission of Waveforms
Waveforms are
Short Duration T
Waveforms Occupy
Full System Bandwidth 1/T

8. Multi-Carrier System Parallel Transmission of Waveforms Waveforms are
Long Duration MT
Waveforms Occupy 1/M th
Of System Bandwidth 1/T

9. OFDM: Dense Multichannel System
Conventional Multichannel System
Non Overlapping Adjacent Channels.
Channels separated by More
Than Their Two Sided bandwidth
OFDM Multichannel System
50% Overlap of Adjacent Channels
Available bandwidth is Used Twice
Channels separated by Half
Their Two Sided bandwidth

10. Standard Digital Communication System

11. Bandlimited Channel Nyquist Spectrum With Cosine Taper
Infinite Duration Nyquist Pulse
Finite Duration Nyquist Pulse

12. Translation in Time Domain Phase Slope in Frequency Domain
Translated Signals Are Orthogonal When Peak is Translated to Zero Crossings of Original

13. Channel Distortion Modifies Received Wave Shape

14. Inter Symbol Interference (ISI) Due to Channel Distorted Signal

15. Steady State Response of a Filter to a Sine Wave is a Sine Wave

16. Rectangle Pulse: DC Centered Spectrum with Equally Spaced Zeros

17. Shift Spectrum with Linear Phase on DC Pulse: Move Spectrum to First Spectral Zero

18. Real Part of Complex Exponential Time Series: Integer Number of Cycles per Interval

19. Imaginary Part of Complex Exponential Time Series: Integer Number of Cycles per Interval

20. Spectra Of Complex Exponential Time Series: Integer Number of Cycles per Interval

21. Continuous Time: Orthogonal Time Signal Set

22. Discrete Time: Orthogonal Time Signal Set

23. OFDM Modulator

24. OFDM Demodulator

25. OFDM is a Block Process

26. Adjacent Symbol Interference (ASI) Symbol Smearing Due to Channel

27. Guard Interval Inserted Between Adjacent Symbols to Suppress ASI

28. Cyclic Prefix Inserted in Guard Interval to Suppress Adjacent Channel Interference (ACI)

29. Data Length Defines Sinc Width: Spectral Spacing Matches Width

30. Extended Data Length Reduces Sinc Width: Spectral Spacing Preserved

31. OFDM Symbol: Time and Spectra Channel Input and Output

32. OFDM Spectra Without and with Cyclic Prefix

33. Overlaid Constellations , All Frequencies, Without and With Cyclic Prefix

34. Constellations: Different OFDM Bins Without Cyclic Prefix

35. Constellations: Different OFDM Bins With Cyclic Prefix

36. Channel Estimate with Pilots

37. DFT (FFT) as Signal Generator for Complex Sinusoids

38. DFT (FFT) As Signal Analyzer for Complex Sinusoids

39. Radix-2 FFT Flow Diagrams

40. Input Vector FFT Mapped to Output Time Series, Up-Sampled, Converted Via DAC to Waveform, and I-Q Up-Converted

41. The FFT as Signal Generator and Interpolator

42. OFDM Modulation With IFFT and Interpolator

43. OFDM Demodulation With FFT

44. OFDM Transceiver

45. Time and Spectra of Sparse OFDM Symbol

46. Time and Spectra With Frequency Offset = 0.1 Bin

47. Time and Spectra With Sample Clock Offset = 1.02 fs

48. Time and Spectra With Sample Clock Offset = 0.98 fs

49. Ideal I-Q Up and Down Conversion

50. Spectral and Time Description of Real Sinusoids

51. Complex Sinusoids-I

52. Complex Sinusoids-II

53. Complex Baseband and Complex Band-Centered Spectra

54. Complex Baseband and Real Band-Centered Spectra

55. Complex Down Conversion

56. Gain and Phase Imbalance in I-Q Mixers

57. Spectral Image Due to Gain Imbalance

58. Spectral Image Due to Phase Imbalance

59. Line Spectral Images Due to I-Q Mismatch

60. Coupling Between Positive and Negative FFT Indices Due to I-Q Imbalance and First Order Correction Mechanism

61. Test Bench: Demonstration of Receiver I-Q Imbalances, Carrier Offset, and Timing Offset

62. Carrier Offset: 4% of FFT Bin Width

63. Timing Offset: 10% of Sampling Time Period

64. Timing Clock Offset: 5% of Sampling Time Period per Frame

65. Gain Imbalance: 10% Error

66. Phase Imbalance: 0.1 Radian Error

67. I-Q Mixer Imbalance; 20% Gain, 0.2 Radians

68. Differential Delay to I/Q Mixers, 10% of Sample Interval

69. Periodic Time Segments in OFDM Frame Obtained by Zero Packing Spectrum

70. Probe Mismatch During Short Repeated Preamble

71. Power Amplifier Non-Linearity

72. 16-QAM Input and Output Envelopes
16-QAM Input and Output Envelopes. Saturation and 1-dB Compression Circles

73. Limiting Amplifier Effect on Received QAM Constellation

74. Limiting Amplifier Effect on Signal Spectra

75. 16-QAM (a=0.2) Envelope Statistics

76. OFDM Input and Output Envelopes: Saturation and 1-dB Compression Circles

77. Limiting Amplifier Effect on OFDM Constellation

78. OFDM Envelope Statistics

79. OFDM Envelope Statistics with Selected Alternate Mapping

80. Clipping

81. Smart Clipping

82. Reserve Frequency Bins Form Clipping Pulses

83. Selecting Reserve Frequency Bins

84. Reserve Bin Canceller Clipping at 2.5 s (8 dB)

85. Statistics for Clip at 2.5 (8 dB)

86. Reserve Bin Canceller Clipping at 2.2 s (6.9 dB)

87. Statistics for Clip at 2.2 (6.9 dB)

88. Reserve Bin Canceller Clipping at 2.0 s (6 dB)

89. Statistics for Clip at 2.0 (6 dB)

90. OFDM a

91. Time-Frequency Profile of 802.11a Tones Pilot Tones Shown in Yellow

92. Preamble and Pilot Structure
Short Symbols
Start of Frame Detection
Signal Strength Indication
Frequency Offset Resolution
Long Symbols
Channel Estimate
Fine Time Resolution
Distributed Pilots
Carrier Tracking
Sample Clock Tracking

93. Preamble Time Structure

94. Detecting Frame Start with Repeated Short Symbols

95. Signals in Preamble Detector

96. Detail of Signal in Preamble Detector

97. Maximum Likelihood Estimator for Frequency Offset

98. Frequency and Signal Strength Estimates

99. Cross Correlation of Long Preamble

100. Clipped Cross Correlation of Long Preamble

101. Channel Probe With Long Preamble

102. Constellation with Residual Carrier Offset

103. Frequency Domain Residual Carrier Offset

104. Constellations with Sample Clock Offset

105. Frequency Domain With Sample Clock Offset

106. Other Variants of OFDM Amplitude and Phase Overlays
Shaped OFDM
OQAM OFDM
Coded OFDM
CI OFDM

107. Shape to Control Spectral Side Lobes

108. Overlapped OFDM Frames

109. Polyphase Filter For Shaped OFDM Shaping and Matched Filter

110. Impulse Response of Shaped OFDM Modulator and Demodulator

111. Orthogonal: Adjacent Time Slots Non Adjacent Frequency Bins

112. Impulse Response Time-Frequency Profile

113. Orthogonality Between Real and Imaginary Part of Shaped OFDM Frequency Bins

114. Even and Odd Symmetric Wave Shapes from Adjacent Bins are Orthogonal in Shaped OFDM

115. Symmetry Considerations in Real and Imaginary Components of Offset Shaped OFDM Frames

116. Offset OFDM

117. Compare Spectra

118. OFDM and Shaped OFDM PAR

119. Complementary Codes

120. Canceling Correlation Side Lobes

121. Inserting CC in OFDM

122. CC and Digital Filters

123. Equivalent Phase Coding

124. PAR in CCK OFDM and Standard OFDM

125. OFDM and CC-OFDM PAR

126. C-I OFDM Carrier Interferometry
OFDM with Phase Overlay
In Conventional OFDM
Rectangle Envelope in Time
Dirichlet Kernel in Frequency
In CI-OFDM
Rectangle Envelope in Frequency
Dirichlet Kernel in Time
Sin(x)/x in Time Domain Without Excess Bandwidth,
No Square-Root Nyquist Shaping Filter

127. Frequency Domain Phase Slope in Continuous and in Sampled Data Domains

128. Circularly Shifted Time Domain Dirichlet Kernels

129. Linear Versus Circular Convolution

130. Fast Circular Convolution with the FFT

131. Single Symbol in CI-OFDM

132. M-Symbols in CI-OFDM

133. 1-to-2 Interpolated Time Domain Data Points

134. CI-OFDM Data Frame

135. CI-OFDM Statistics

136. CI-OFDM Statistics

137. That’s all Folks