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

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2911Normalized output value, G(A)/g0Asat0.50−0.5Normalized output value, G(A)/g0Asat0.50−0.5−1−1−0.5 0 0.5Normalized input value, A/A max1−1−1−0.5 0 0.5Normalized input value, A/A max1(a) K = 10 dB(b) K = 3 dB11Normalized output value, G(A)/g0Asat0.50−0.5Normalized output value, G(A)/g0Asat0.50−0.5−1−1−0.5 0 0.5Normalized input value, A/A max1−1−1−0.5 0 0.5Normalized input value, A/A max1(c) K = −3 dB(d) K = −10 dBFigure 2.8: AM/AM (solid) and AM/PM (dash) conversions (SSPA=thick,TWTA=thin) for various backoff ratios K.
30than the K = −3 dB curves for about 5% of the OFDM blocks (the 0.05 PAPR is 9 dB).Therefore, even with a large IBO of 6 dB, the PA can impose high nonlinear distortionon the transmitted signal. Also, the degree of distortion for a given OFDM block israndom (given a fixed IBO) since the PAPR for a given block is random.2.4 Effects of Nonlinear Power AmplificationPower amplifier nonlinearities cause spectral leakage and performance degradationto OFDM systems. These undesirable effects can be reduced with increase input backoff.This is an unsatisfactory solution, however, since PA efficiency reduces with IBO. Also,reducing the average transmit power reduces the operational range of the system. Inthis section these various issues are studied.2.4.1 Spectral LeakageThe first problem considered is spectral leakage. By using the Welch method [422, pp.911–913], the power density spectrum at the output of the power amplifier can be quicklyestimated. The result is used to calculate estimated fractional out-of-band power curves,defined as∫ fFOBP(f) ˆ0=ˆΦ s (x)dx0.5 ˆP, f > 0, (2.42)swhere ˆΦ s (f) is the estimated power density spectrum of the signal and ˆP s = ∫ ∞−∞ ˆΦ s (f)dfis the signal power. Figure 2.9 shows the curves for an N = 64 subcarrier OFDM signalamplified by the TWTA power amplifier according to (2.36) at various backoff levels.Also plotted is the FOBP curve for ideal linear amplification. These results show thatat least 6 dB backoff is required by the TWTA to avoid spectral broadening.Figure 2.10 shows the 99.5% bandwidth as a function of IBO. The bandwidth of theundistorted OFDM signal is f = 1.07W . For sufficient backoff, the bandwidth of thenonlinearly amplified signal is the same. However, for IBO < 6 dB, the bandwidth isshown to grow roughly linearly with IBO. For IBO = 1 dB, the 99.5% bandwidth is 73%larger than the undistorted signal. Notice that the spectral leakage is roughly the samefor the two amplifier models.
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 and 38: 20where {n[i]} are samples of the n
Page 39 and 40: 22(FDE). Such an equalizer can be u
Page 41 and 42: 242.2 PAPR StatisticsThe peak-to-av
Page 43 and 44: 26level the bound is tight. Notice
Page 45: 28To reduce nonlinear distortion in
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
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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
Page 119 and 120:
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
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12010 −1Bit error rate10 −210
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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
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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
Page 157 and 158:
140set ticscale 0.5set border 31 li
Page 159 and 160:
142kHz kilohertz (1 thousand cycles
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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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