Constant Envelope OFDM Phase Modulation - Dr. James R. Zeidler

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21Channels[i]DFTH[k]IDFTr[i]Inverse channelr[i]DFT1H[k]IDFTs[i]Figure 2.2: Circular convolution with channel and the inverse channel.Frequency-domain equalizerData{I k }ModulatorChannelDFTMultiplierbankIDFTDemodulatorData{Î k }Figure 2.3: Block modulation with cyclic prefix and FDE.Frequency-domain equalizerData{I k }IDFTMultiplierChannel DFTbankIDFTDFTData{Îk}Data{I k }IDFTChannelDFTMultiplierbankData{Îk}Figure 2.4: OFDM is a special case.
22(FDE). Such an equalizer can be used only when the effect of the channel is a circularconvolution. This is the case for OFDM, but isn’t unique to OFDM since any modulationcan use a cyclic prefix. This observation was first identified by Sari et al. [462] andsuggests a more general modulation approach: block modulation with cyclic prefix andfrequency-domain equalization. Figure 2.3 shows a simplified block diagram of sucha system. (The insertion of the cyclic prefix at the transmitter and removal at thereceiver is implied but not included in the diagram for simplicity.) For the special caseof OFDM, the modulation is a IDFT and the demodulation is a DFT as shown in Figure2.4. Notice that the DFT and IDFT cancel each other and the resulting diagram depictsthe conventional OFDM system.The multiplier bank at the output of the DFT is often referred to as a one-tapequalizer, one complex multiplication per frequency bin. This operation is required fordata symbols that rely on coherent demodulation, such as M-ary phase-shift keying(M-PSK) and M-ary quadrature-amplitude modulation (M-QAM).As Sari et al. pointed out, OFDM doesn’t eliminate the equalization problem (associatedwith conventional single carrier modulation); rather, OFDM converts the problemto the frequency domain. Since Sari’s original paper, there has been a considerable numberof publications focused on the block modulation technique using conventional singlecarrier modulations [8, 30, 54, 107, 116, 132, 142, 153, 154, 196, 197, 245, 388, 460, 461, 463,481, 533, 565, 574].2.1.4 System DiagramThe block diagram in Figure 2.4 conceptually illustrates the OFDM system. Figure2.5 shows a more detailed description of OFDM’s functional blocks.The encoder adds redundancy to the bit stream for error control. The encoded bitsare then mapped to the data symbols I k . In general, the data symbols are complexnumbers which result from mapping the bits to points on the complex plane. Next, thesymbols are serial-to-parallel (S/P) converted and processed by the IDFT. The cyclicprefix is added and the signal samples, s[i], are passed through the digital-to-analog(D/A) converter to obtain the continuous-time OFDM signal s(t). Finally, the signal isamplified and transmitted.
Page 1 and 2: UNIVERSITY OF CALIFORNIA, SAN DIEGO
Page 3 and 4: The dissertation of Steve C. Thomps
Page 5 and 6: TABLE OF CONTENTSSignature Page . .
Page 7 and 8: 7 Conclusions . . . . . . . . . . .
Page 9 and 10: 2.17 PAPR CCDF of clipped OFDM sign
Page 11 and 12: B.3 Running average of papers read
Page 13 and 14: ACKNOWLEDGEMENTSI want to first tha
Page 15 and 16: S. C. Thompson, J. G. Proakis, and
Page 17 and 18: this thesis, the fundamental aspect
Page 19 and 20: 2point A¢£Propagation pathspoint
Page 21 and 22: 4All of these techniques require kn
Page 23 and 24: 6frequency of the kth subcarrier is
Page 25 and 26: 85Channel power (dB)0-5-10-15-20-25
Page 27 and 28: 10OFDM signal isandR {s(t)} =I {s(t
Page 29 and 30: 12Nonlinearities in the transmitter
Page 31 and 32: 141.5 Thesis OverviewIn Chapter 2 t
Page 33 and 34: 162.1 More OFDM Basics2.1.1 The Cyc
Page 35 and 36: 18where b(t) ≠ ∑ N−1k=0 I ke
Page 37: 20where {n[i]} are samples of the n
Page 41 and 42: 242.2 PAPR StatisticsThe peak-to-av
Page 43 and 44: 26level the bound is tight. Notice
Page 45 and 46: 28To reduce nonlinear distortion in
Page 47 and 48: 30than the K = −3 dB curves for a
Page 49 and 50: 322.4.2 Performance DegradationNext
Page 51 and 52: 341010 −1Ideal PASSPA: IBO = 3 dB
Page 53 and 54: 36Potential rangePotential range w/
Page 55 and 56: 38Signal ClippingThe remainder of t
Page 57 and 58: 4010 010 −1ClippedUnclippedP (PAP
Page 59 and 60: 42efficiency). The distortion cause
Page 61 and 62: 445OFDMCE-OFDM4Instantaneous signal
Page 63 and 64: 46The idea of transmitting OFDM by
Page 65 and 66: 48where σ 2 Iis the data symbol va
Page 67 and 68: 50Unit circleStarting point(a) L =
Page 69 and 70: 5210 0FOBP(f) ˆB rms10 −1Fractio
Page 71 and 72: 540Welch estimateterms from (3.30)
Page 73 and 74: 56figure shows that the CE-OFDM spe
Page 75 and 76: Chapter 4Performance of ConstantEnv
Page 77 and 78: 60Lowpassfilterr bp (t)Bandpassfilt
Page 79 and 80: 62Phase demodulatorr[i]FIRfilterarg
Page 81 and 82: 64for DCT and DFT modulations [(3.7
Page 83 and 84: 6610 0System 1System 2Approx (4.35)
Page 85 and 86: 68Bit error rateBit error rate10
Page 87 and 88: 700L fir , f cut/W−209, 0.7Magnit
Page 89 and 90:
72receiver, as shown in Figure 4.10
Page 91 and 92:
74constant K = 2πhC N , isρ m,n (
Page 93 and 94:
7610.5p1/πKρm,n(K)0−0.5012K345(
Page 95 and 96:
784.2.2 Asymptotic PropertiesIn Fig
Page 97 and 98:
8010 0p ξ (x)GaussianProbability d
Page 99 and 100:
82To plot the spectral efficiency v
Page 101 and 102:
84Figure 4.18 compares CE-OFDM with
Page 103 and 104:
Chapter 5Performance of CE-OFDM inF
Page 105 and 106:
88and for the Rayleigh channel, as
Page 107 and 108:
901Transition regionConditional bit
Page 109 and 110:
92Bit error rate(a) M = 2, 2πh = 0
Page 111 and 112:
Chapter 6Performance of CE-OFDM inF
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96the signal-to-noise ratio, making
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98µs, which results in N c = ⌊τ
Page 117 and 118:
100Using a DFT size N DFT = JN = N
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1020.90.84|h[i]| 20.70.60.50.40.30.
Page 121 and 122:
104|h[i]| 20.60.50.40.30.2Magnitude
Page 123 and 124:
106|h[i]| 20.350.30.250.20.150.1Mag
Page 125 and 126:
108Channels C, E and F—degrades p
Page 127 and 128:
110• Delay spread:B (2)ττ =√
Page 129 and 130:
112The last model, Channel D f , ha
Page 131 and 132:
114propagation paths [the WSSUS ass
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116by (2.9).So long as the duration
Page 135 and 136:
118Table 6.3: Data symbol contribut
Page 137 and 138:
12010 −1Bit error rate10 −210
Page 139 and 140:
122This problem can be suppressed w
Page 141 and 142:
Appendix AGenerating Real-Valued OF
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126i = 0, 1, . . . , N − 1. Thus,
Page 145 and 146:
Appendix BMore on the OFDM Literatu
Page 147 and 148:
130First, to get an idea of the siz
Page 149 and 150:
1328Papers read per day (log scale)
Page 151 and 152:
Appendix CSample CodeThe simulation
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136CN=sqrt(2/(N*varI));% normalizin
Page 155 and 156:
138end%% Demodulate and detecthatph
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140set ticscale 0.5set border 31 li
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142kHz kilohertz (1 thousand cycles
Page 161 and 162:
144x(t) x as a function of tx[i] di
Page 163 and 164:
146f ′f cf saFOBP(f)FOBP(f) ˆg(t
Page 165 and 166:
Bibliography[1] N. Abramson, “Ban
Page 167 and 168:
150[24] A. G. Armada, “Phase Nois
Page 169 and 170:
152[50] P. A. Bello, “Characteriz
Page 171 and 172:
154[78] R. Castle and A. Jones, “
Page 173 and 174:
156[104] L. J. Cimini, Jr. and N. R
Page 175 and 176:
158[131] Debian—The Universal Ope
Page 177 and 178:
160[157] O. Feely, “Nonlinear Dyn
Page 179 and 180:
162[185] S. Gifford, J. E. Kleider,
Page 181 and 182:
164[213] H.-H. Hsieh and C.-H. Wei,
Page 183 and 184:
166[241] S. M. Ju and S. H. Leung,
Page 185 and 186:
168[269] ——, “PAR Reduction i
Page 187 and 188:
170[297] Y. G. Li, L. J. Cimini, Jr
Page 189 and 190:
172[325] M. M. Martone, “A Multic
Page 191 and 192:
174[353] R. Morrison, L. J. Cimini,
Page 193 and 194:
176[379] H. Ochiai and H. Imai, “
Page 195 and 196:
178[408] A. Peled and A. Ruiz, “F
Page 197 and 198:
180[435] ——, “Pilot Spacing i
Page 199 and 200:
182[462] ——, “Channel equaliz
Page 201 and 202:
184[491] E. A. Sourour and M. Nakag
Page 203 and 204:
186[520] C. Tellambura and M. G. Pa
Page 205 and 206:
188[548] C. van den Bos, M. H. L. K
Page 207 and 208:
190[575] W. D. Warner and C. Leung,
Page 209 and 210:
192[604] H. Yang, “A Road to Futu
Page 211:
Production NotesThis thesis was typ
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Constant Envelope OFDM Phase Modulation - Dr. James R. Zeidler

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