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

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LIST OF FIGURES1.1 Representation of a wireless channel with multipath. . . . . . . . . . . . . 21.2 A wireless channel in time and frequency. . . . . . . . . . . . . . . . . . . 21.3 Intersymbol interference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 OFDM with cyclic prefix (CP). . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Subcarrier and overall spectrum. (N = 16; |I 0,k | = 1, for all k) . . . . . . 71.6 OFDM converts wideband channel to N narrowband frequency bins. . . . 81.7 Frequency offset causes ICI. (ɛ fo = 0.25) . . . . . . . . . . . . . . . . . . . 91.8 A typical OFDM signal (N = 16). The PAPR is 9.5 dB. . . . . . . . . . . 101.9 Power amplifier transfer function. . . . . . . . . . . . . . . . . . . . . . . . 111.10 Comparison of OFDM and CE-OFDM signals. . . . . . . . . . . . . . . . 132.1 Sampling instances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Circular convolution with channel and the inverse channel. . . . . . . . . . 212.3 Block modulation with cyclic prefix and FDE. . . . . . . . . . . . . . . . . 212.4 OFDM is a special case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5 OFDM system diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.6 Complementary cumulative distribution functions. (N = 64) . . . . . . . 252.7 PAPR CCDF lower bound (2.31) for N = 2 k , k = 5, 6, . . . , 10. . . . . . . . 262.8 AM/AM (solid) and AM/PM (dash) conversions (SSPA=thick, TWTA=thin)for various backoff ratios K. . . . . . . . . . . . . . . . . . . . . . . . . . . 292.9 Fractional out-of-band power of OFDM with ideal PA and with TWTAmodel at various input power backoff. (N = 64, IBO in dB) . . . . . . . . 312.10 Spectral growth versus IBO. (N = 64) . . . . . . . . . . . . . . . . . . . . 312.11 Performance of QPSK/OFDM with nonlinear power amplifier with variousinput power backoff levels. (N = 64) . . . . . . . . . . . . . . . . . . . . . 332.12 Performance of M-PSK/OFDM with SSPA. (N = 64) . . . . . . . . . . . 342.13 The potential range of system is reduced with input backoff; the range isreduced further from nonlinear amplifier distortion. . . . . . . . . . . . . . 362.14 Power amplifier efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.15 Block diagram. The system is evaluated with and without PAPR reduction. 382.16 Unclipped OFDM signal (9.25 dB PAPR). The rings have radius A maxwhich correspond to various clipping ratios γ clip (dB). . . . . . . . . . . . 39viii
2.17 PAPR CCDF of clipped OFDM signal for various γ clip (dB). [N = 64] . . 402.18 PAPR of clipped signal as a function of the clipping ratio. (N = 64) . . . 402.19 A comparison of the total degradation curves of clipped and unclippedM-PSK/OFDM systems. (N = 64) . . . . . . . . . . . . . . . . . . . . . . 413.1 The CE-OFDM waveform mapping. . . . . . . . . . . . . . . . . . . . . . 433.2 Instantaneous signal power. . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3 Basic concept of CE-OFDM. . . . . . . . . . . . . . . . . . . . . . . . . . 453.4 Phase discontinuities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.5 Continuous phase CE-OFDM signal samples, over L blocks, on the complexplane. (2πh = 0.7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.6 Estimated fractional out-of-band power. (N = 64) . . . . . . . . . . . . . 523.7 Double-sided bandwidth as a function of modulation index. (N = 64) . . 533.8 Power density spectrum. (N = 64, 2πh = 0.6) . . . . . . . . . . . . . . . . 543.9 Fractional out-of-band power. (N = 64, 2πh = 0.6) . . . . . . . . . . . . . 553.10 CE-OFDM versus OFDM. (N = 64) . . . . . . . . . . . . . . . . . . . . . 563.11 CE-OFDM versus OFDM with nonlinear PA. (N = 64) . . . . . . . . . . 574.1 Phase demodulator receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2 Bandpass to baseband conversion. . . . . . . . . . . . . . . . . . . . . . . 604.3 Discrete-time phase demodulator. . . . . . . . . . . . . . . . . . . . . . . . 624.4 Performance with and without phase offsets. System 1 (S1) has phaseoffsets {(θ i + φ 0 ) ∈ [0, 2π)}, and System 2 (S2) doesn’t (θ i + φ 0 = 0).[M = 2, N = 64, J = 8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.5 Threshold effect at low CNR. (M = 8, N = 64, J = 8, 2πh = 0.5) . . . . . 684.6 Threshold effect at low CNR, various 2πh. (M = 8, N = 64, J = 8) . . . 684.7 Performance for various filter parameters L fir , f cut /W .(M = 2, N = 64, J = 8, 2πh = 0.5 and E b /N 0 = 10 dB) . . . . . . . . . . 694.8 Magnitude response of various Hamming FIR filters. . . . . . . . . . . . . 704.9 CE-OFDM performance with and without FIR filter.(M = 2, N = 64, J = 8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.10 The optimum receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.11 Correlation functions ρ m,n (K). . . . . . . . . . . . . . . . . . . . . . . . . 764.12 CE-OFDM optimum receiver performance. (M = 2, N = 8) . . . . . . . . 77ix
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: 7 Conclusions . . . . . . . . . . .
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 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)
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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
Page 115 and 116:
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
Page 133 and 134:
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
Page 143 and 144:
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
Page 157 and 158:
140set ticscale 0.5set border 31 li
Page 159 and 160:
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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