Appendix D: Allpass Filter as Group Delay Equalizer
D.2 Second-Order Allpass Filter
A transfer function of the second-order allpass filter is given by
Hað Þ ¼s s2ωQ0sþ ω20
s2þωQ0sþ ω20
ðD:8Þ
whereω0is the pole frequency andQ is the quality factor. Compared with the first-order allpass filter, the second-first-order allpass filter has two adjustable parameters so that it has more shapes of the group delay. In general, it is easy to design the allpass Fig. D.2 Active circuit
with positive unit gain of the first-order allpass filter [22]
filter starting from a normalized transfer function. Then, the actual transfer function can be obtained by de-normalizing the normalized transfer function through the actual cut-off frequencyωc.
By using the normalized frequency,sn¼ s=ωc, (D.8) can be written as
Hað Þ ¼sn s2n eωQ0snþ eω20
s2nþ eωQ0snþ eω20
ðD:9Þ
whereeω0¼ ω0=ωcis the normalized pole frequency. The phase and group delay of the second-order allpass filter are given by
θað Þ ¼ 2tanωn 1
ωneω0
Q
eω20 ω2n 0
@
1
A ðD:10Þ
GDað Þ ¼ ωn dθað Þωn
dωn ¼
2eω0
Q eω20þ ω2n
eω20 ω2n
2
þ ωneω0
Q
2 ðD:11Þ
The group delay response of the second-order allpass filter versus the factorQ at eω0¼ 1 is plotted in Fig. D.3. It is clear that the shape of the group delay is dependent on the factorQ. It was calculated that the group delay has a peak when Q> 1= ffiffiffi
p3
0:577. Otherwise, the group delay decreases monotonously from the zero frequency, and has its maximum delay at the zero frequency. The group delay
Delay
Normalized frequency 00
2 4 6 8 10 12 14
0.5
0.5 0.2
Q=3
1 1
2
1.5 2 2.5
Fig. D.3 Group delay of the second-order allpass filter with different Q values ateω0¼ 1
with such a peak in the range from 0 toeω0¼ 1 makes the second-order allpass filter more flexible to compensate for the distorted delay with a shallow null in such a range, which cannot be compensated by the first-order allpass filter.
It can be seen from (D.11) that the delay at zero frequency is GDað Þ ¼0 2
Qeω0
ðD:12Þ
When Q> 1= ffiffiffi p3
, the delay curve has the peak at about eω0, and this peak is equal to
GDa,MAXð Þ eω0 4Q
eω0 ðD:13Þ
The group delays versus different values of eω0atQ¼ 2 are plotted in Fig.D.4.
It is clear that the peak almost occurs at the pole frequency of eω0. Thus, we can determine the peak position througheω0.
Like the first-order allpass filter, the second-order allpass filter can be realized in either the active circuits or the passive circuits. FigureD.5shows the second-order allpass filter constructed in the active circuits ofThomas1. Its transfer function is given by
Hað Þ ¼ s s2þRR35RR5C62sþR2R5RR68C1C2
s2þR31C2sþR2R5RR86C1C2 ðD:14Þ For the realization of the allpass filter, the relationship betweenR5andR6is R6¼ 2R5. Thus, (D.14) is rewritten as
Fig. D.4 Group delay of the second-order allpass filter with differenteω0
values atQ¼ 2
Hað Þ ¼ s s2R31C2sþR2R5RR86C1C2
s2þR31C2sþR2R5RR86C1C2 ðD:15Þ The minus sign in (D.15) is due to inverting amplification operation. This can be corrected by adding one more stage of inverting amplification.
Comparing (D.15) with the standard form of (D.9), we have the following appropriate parameters as
eω20¼ R6
R2R5R8C1C2
, Q¼ R3
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R6C2
R2R5R8C1
r
ðD:16Þ
In the following, we give an example of using the first-order and the second-order allpass filters to compensate for the group delay of a fourth-second-order Butterworth lowpass filter.
Design Example D.1 In digital communications, a bandlimited channel with a constant group delay or small group delay variation is preferable for minimizing ISI. Using both first-order and second-order allpass filters design a group delay equalizer to reduce the group delay variation of a fourth-order Butterworth lowpass filter with a cut-off frequency of 17.2 kHz. As introduced in Design Example 2.1, this analog filter was used to approximate a pulse-shaping root raised-cosine filter with α ¼ 0.5 for QPSK data transmission at a bit rate of 64 kbps.
Solution With a First-Order Allpass Filter We begin the design with a fourth-order Butterworth lowpass filter with a normalized frequency ωn¼ ω=ωc, where ωc¼ 2πfcis the cut-off frequency. We use the subscript n here to distinguish the normalized frequency with the actual frequency. Thus, the normalized transfer function of the fourth-order Butterworth lowpass filter is
Fig. D.5 Active circuit of the second-order allpass filter
HLð Þ ¼sn 1 s2nþ 0:7654snþ 1
s2nþ 1:848snþ 1
ðD:17Þ
It is easy to calculate the group delay response of Butterworth lowpass filter by using a MATLAB calculation script. This group delay response is plotted in Fig.D.6. The group delay monotonically increases in the frequency range from 0 to 0.9 and variation is about 1.3 s within this frequency range.
The normalized transfer function of the first-order allpass filter is Hað Þ ¼sn sn σn
snþ σn
ðD:18Þ
Its group delay is given in (D.5) and is rewritten here GDað Þ ¼ 2ωn σn
σ2nþ ω2n
ðD:19Þ
FigureD.6shows the group delay of the first-order allpass filter with differentσ values. Unlike the group delay shape of the Butterworth filter, the group delay of the first-order allpass filter withσn ¼ 1 monotonically decreases in the same frequency range from 0 to 0.9 and variation is about 1 s.
Therefore, an appropriate compensation delay would be created withσn< 1. As a try, we first chooseσn¼ 0:6 and plot the delay of the allpass filter in Fig.D.6, which is labeled “allpass delay w/0.6”. The cascaded group delay is labeled
7
6
5
4
3
2
1
0
0 0.5
Normalized frequency
Delay
1 1.5 2
Cascaded delay w/ 0.6
Cascaded delay w/ 0.82 Allpass delay w/ 0.6
Butterworth delay
Allpass delay w/ 0.82
Fig. D.6 Group delay responses of the normalized fourth-order Butterworth lowpass filter and the first order allpass filter
“cascaded delayw/0.6”. It is obvious that the allpass filter withσn¼ 0:6 adds too much delay to the Butterworth filter. Fortunately, it is relatively easy to find the optimal sigma value σn ¼ 0:82 to achieve small delay variation with several trials due to only one parameter. Thus, the cascaded delay with σn¼ 0:82 gives the smallest delay variation of aboutΔGD ωð Þ ¼ 0:3 s, which is much smaller thann
the un-equalized delay variation of 1.3 s within the specified frequency range. After the delay equalization, the absolute delay increases about two times at the DC frequency, or from 2.6 to 5.0 s, but the absolute delay does not cause any problem in digital communications.
With σn¼ 0:82, the transfer function of the first-order allpass filter can be de-normalized by substituting σ ¼σn ωc¼ 0:82 2π 17, 200 ¼8:8618 104 into (D.18)
Hað Þ ¼s s 8:8618 104
sþ 8:8618 104 ðD:20Þ
Finally, the values of R and C are solved with σ ¼ 1/(RC), or RC¼ 1=σ ¼ 11:284μs. If C ¼ 10 nF is chosen, then the resistor is calculated to be equal toR¼ 1.13 kΩ.
Meanwhile, the transfer function of the Butterworth filter can be also de-normalized to the true transfer function by substituting the normalized frequency with two slightly different cut-off frequencies around the target cut-off frequency of 17.2 kHz, or sn¼ s= 2π 17, 096ð Þ and sn ¼ s= 2π 17, 193ð Þ, into two second-order sections in (D.17), respectively,
HLð Þ ¼s 1:15391010
1:1671010
s2þ 8:2386104sþ1:1539 1010
s2þ1:9724 105sþ1:1671010
ðD:21Þ If the lowpass filterHL(s) is implemented by cascading two Sallen-Key lowpass filters [22], its transfer function is expressed as
HLð Þ ¼s
1 r21c1c2
s2þr12c1sþr21 1c1c2
1 r22c3c4
s2þr22c1sþr21 2c3c4
ðD:22Þ
Parameters can be solved by comparing (D.21) and (D.22) as follows:
r1¼ 8.45 kΩ, c1¼ 1.2 nF, c2¼ 1.0 nF, r2¼ 3.57 kΩ, c3¼ 6.8 nF, and c4¼ 1.0 nF.
Figure D.7 shows the group delay curves of two transfer functions that are expressed in (D.20) and (D.21) and their cascaded group delay curve in an actual frequency range. The actual delay variation is de-normalized by dividing the normalized group delay variation ΔGD ωð Þ ¼ 0:3 by ωn c,or ΔGD ωð Þ ¼ 0:3=ωc
¼ 0:3= 2π 17, 200ð Þ ¼ 2:776μs within the bandwidth, which can also be seen in Fig.D.7.
Solution With a Second-Order Allpass Filter First of all, we observe from Fig.D.6that the group delay of the Butterworth filter increases monotonically up to the normalized frequency of 0.9. This means that the group delay of the second-order allpass filter should decrease monotonically in second-order to have the inverse characteristic of the group delay of the fourth-order Butterworth filter. From Fig.D.3, we can see that the group delay of the second-order allpass filter contin-uously decreases starting from zero frequency when Q< 1= ffiffiffi
p3
0:577. We initially try to set eω20¼ 1 and Q ¼ 0.5, and solve eω0=Q ¼ 2. Substituting these parameters into (D.11), we plot the group delay in Fig.D.8. From the initial cascade
5x 10−5 4.5
4 3.5 3 2.5 2 1.5 1 0.5
00 5 10 15
Frequency (kHz)
Group delay (s)
20 25 30 35 40
Cascaded delay
Butterworth delay
Allpass delay
Fig. D.7 Group delay responses of the fourth-order Butterworth and first-order allpass filters in an actual frequency range
Fig. D.8 Group delay responses of the Butterworth lowpass and the second-order allpass filters for ExampleD.1
response, we can see that it is low at a frequency of around 0.5. To get more delay within such a range, we need to make the “initial allpass” delay flat around the normalized frequency of 0.5 by reducingeω0and increasingQ as well. With several further trials, the smallest delay variation curve labeled‘Final cascade’ is obtained with eω20¼ 0:71 and Q 0.577, and its peak-to-peak variation is about ΔGD ωð Þ 0:15s, within the range from 0 to 0.8 rad/s, which is smaller by an
half than ΔGD ωð Þ 0:3s in the case of the first-order allpass filter. Hence, then
group delay variation with the second-order allpass filter is reduced to 0.15 from its original value of 1.3, or 8.5 times smaller than its original delay variation within the specified frequency range, respectively.
The normalized transfer function of the second-order allpass filter is given by substitutingeω0¼ ffiffiffiffiffiffiffiffiffi
0:71
p andQ 0.577 into (D.9)
Hað Þ ¼sn s2n 1:46snþ 0:71
s2nþ 1:46snþ 0:71 ðD:23Þ It is clearly shown that the second-order allpass filter with two adjustable parameters can achieve many different shapes, so that it is more flexible to compensate for different group delay responses than the first-order allpass filter.
Figure D.9 shows the group delay responses of the Butterworth lowpass filter cascaded with the first-order allpass filter and the second-order allpass filter in the actual frequency range.
Next, the actual delay variation isΔGD ωð Þ ¼ 0:15=ωc¼ 0:15= 2π 17, 200ð Þ
¼ 1:388μs within the specified frequency range, which is also a half of 2.776 μs in the case of the first-order allpass filter. The actual parameters of the second-order
Fig. D.9 Group delay response of the fourth-order Butterworth lowpass filter cascaded with the first-order and second-order allpass filters in the actual frequency range for ExampleD.1
allpass filter areω20¼0:71 2π 17, 200ð Þ¼8:292 109, andω0=Q¼1:578105, and its transfer function is given by substituting these two parameters into (D.9):
Hað Þ ¼s s2 1:578 105sþ 8:292 109
s2þ 1:578 105sþ 8:292 109 ðD:24Þ From (D.24), we can solve resistor and capacitor real values. Compared (D.24) with (D.15), we have the relationshipω0=Q ¼ 1= Rð 3C2Þ ¼ 1:578 105. By choos-ingC2¼ 1nF resistor is R3¼ 1= 1:578 10 5 109
¼ 6:34kΩ. Then, from the relationshipω20¼ R6= Rð 2R5R8C1C2Þ and with R6 ¼ R8 ¼ 20kΩ, R5¼ 10kΩ and C1¼ 1nF, the resistor R2is given byR2¼ 1= R5C1C2ω20
¼ 12:1kΩ. FigureD.10 shows the active implementation structure of the fourth-order Butterworth lowpass filter with a cut-off frequency of 17.2 kHz cascaded with the second-order allpass filter.
Fig. D.10 Active circuits of the fourth-order Butterworth lowpass filter cascaded with the second-order allpass filter
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Index
A
Accumulated phase, 156, 158, 217
Adaptive algorithm, 266, 269, 270, 277, 282 Adaptive compensation, 307
Adaptive equalization, 182–190
Adaptive equalization techniques, 118–120 Additive white Gaussian noise (AWGN), 115,
136, 205, 209, 211
Adjacent channel interference (ACI), 44, 55, 56, 92, 382
Adjacent channel leakage ratio (ACLR), 287 Adjacent channel power ratio (ACPR), 55,
101, 124, 131, 154, 266
Adjacent channel rejection (ACR), 133, 138 Advanced mobile phone system (AMPS),
379, 406
Aeronautical Telemetry Standard IRIG, 175 Allpass filter, 55–58
Alternative current (AC), 363 Amplitude, 49, 51
AM-AM, 153, 259, 260, 273 AM-PM, 153, 259, 260, 273 aperture compensator, 51, 53, 66 distortion, 56
equalizer, 8 modulation, 17
Amplitude modulation to amplitude modulation (AM-AM), 153, 254, 259, 260, 273
Amplitude-modulation pulse (AMP), 206 Amplitude modulation to phase modulation
(AM-PM), 153, 254, 259, 260, 273
Amplitude shift keying (ASK), 19
Analog baseband (ABB), 122, 180, 310, 384
Analog Costas loop baseband waveforms, 212 binary bit information, 210 BPSK plus noise, 208 data modulation, 207
hard-limiter in-phase branch, 210, 211 lowpass filters, 210
phase detector characteristics, 212, 213 phase error, 211
QPSK, 211, 212 Analog lowpass filter, 384
Analog pre-distortion (APD), 254, 273 baseband I and Q signals, 278 baseband signal, 278 coefficient adaption, 282–283 complex gain expressions, 280 IMD products, 278
in-phase and quadrature gains, 281 power amplifier, 280
quadrature model, 280 RF input signal, 277 vector modulator, 277
Analog-to-digital converter (ADC), 285, 307, 334, 410, 414, 417, 423 Angle modulation, 18
8-Angle phase shift keying (8PSK) modulation, 7
Antenna switch insertion loss (IL), 136 Anti-aliasing filter, 344
Atheros’ WLAN 802.11n Transceiver, 421–423
Auto-correlation, 24, 25, 103, 105, 109, 111
© Springer International Publishing Switzerland 2017
W. Gao,Energy and Bandwidth-Efficient Wireless Transmission, Signals and Communication Technology, DOI 10.1007/978-3-319-44222-8
475
Automatic gain control (AGC), 103, 105, 139 adjustment procedure, 399
analog channel selection filters, VGAs and RSSI circuits, 397 analog gain, 391
gain distribution, 399 gain-setting modes, 397
maximum voltage gain value, 399 NF and RX EVMvs. RX input power, 400 RSSI, 397
SNR, 397
SNR and P1dB/Svs. antenna input power, 401
transmitter and receiver, 391 verification, 399
B
Bandpass filter (BPF), 294, 296 Bandwidth-efficiency
actual filter, 10 connectivity, 2 limitations, 3
Nyquist frequency, 8, 9 OFDM
with amplitude fading distortion, 117 baseband signals, 80, 82, 89 closed-loop calibration, 149
continuous time domain, modulator, 83 fifth-order Chebyshev lowpass
filter, 146
modulation and coding scheme, 147 simulation parameters, 114 subcarrier frequency location, 85 timing-related main parameters, 84 transmitter and receiver, 96 waveforms, 87
windowed OFDM symbols in time domain, 93
WLAN based applications, 145 spectral efficiency, 8, 9
system channel, 10 theoretical minimum, 10
Bandwidth-efficient transmission, 7, 26 Baseband I–Q signals, 95, 148, 168–170, 191,
200, 246, 263, 285, 286, 300, 302, 353, 355, 356, 358, 408, 410, 422 Baseband modulation, 18–28
Baseband signal, 5, 16, 25, 33, 72 Baseband waveforms, 27, 31
Behavioral modeling, 259, 263, 273, 275 Binary phase shift keying (BPSK), 19,
78, 85, 91, 95, 120
Bit energy to noise density ratio (Eb/No), 134
Bit error rate (BER), 18, 40–44, 154, 254, 299
Blind equalizer, 189–190 Bluetooth system, 232, 336, 458 BPSK modulation, 332 Brick-wall filter, 9, 47, 49 Butterworth filters, 42, 55, 419
Butterworth lowpass filter, 41, 42, 58, 60
C
Calibration methods, 292, 298, 311 Calibration process, 287
Calibration techniques, 405 Carrier feed-through, 294 Carrier frequency, 15, 16, 19 Carrier frequency offset (CFO), 102,
106–111, 113
Carrier frequency synchronization, 103, 106 Carrier phase, 19, 22, 42, 263
Carrier signal, 5, 6, 16, 22, 42 Carrier suppression, 302, 303, 311 Carrier synchronization, 192, 193 Carrier-to-interference ratio (C/I), 375 CDMA2000 system, 293, 407 CdmaOne, 292
Cellular systems, 292, 406 of 3G, 2
of 4G, 2
Channel bandwidth, 10, 44
Channel estimation technique, 114, 115 Channel filter, 51
Channel impulse response (CIR), 116 Channel-select filter, 328, 387 Channel selection digital filter (CSDF)
analog, 381 domain, 387–391 filter, 382
baseband I–Q signals, 380 Butterworth/Chebyshev, 381 digital, 381
frequency responses, 382
group delay characteristics, 384, 385 lowpass filter/bandpass filter, 380 RFIC transceiver, 383
RX EVMvs. fine-tune parameter code, 385, 386
WCDMA QPSK signalvs. RF input signal, 385, 386
Chebyshev analog filters, 55 Class AB, 259, 287
mode, 13
Clipping and peak window (CPW), 101, 102 CMOS process, 418, 421, 423
CMOS technology, 344
Code division multiple access (CDMA), 6, 292, 406, 412
Coefficient extraction, 262, 263, 273 Coherent demodulation, 182–226 Coherent demodulator, 41, 42 Coherent detection, 156, 168, 182
carrier synchronization techniques, 192 information-bearing signal, 192 MSK receiver, 191
pilot signal, 192
squaring loop carrier recovery, 192 transmitter and receiver signal, 191 Compensation filter, 68
Compensation methods, 303, 304 Complex signal, 25
Conduction angle, 13
Conexant’s GSM transceiver, 410–412 Constant envelope, 7, 371
characteristics, 2 modulations, 3, 154
Constant modulus algorithm (CMA), 189 Constellation, 299, 314, 316
Continuous phase frequency shift keying (CPFSK), 154
Continuous phase modulation (CPM), 206 Continuous wave (CW), 159, 160, 245, 278 Correlation detection, 191
Crest factor (CF), 101
Crest factor reduction (CFR) technique, 101 Cross-correlation, 103, 105, 175, 176, 179,
180, 192, 264 Cross-talk, 356, 358 Cut-off frequency, 46, 58 Cyclic prefix (CP), 112
D
Damping factor, 58, 71, 214, 216, 235 Data-aided (DA) based frequency offset
estimation, 112 DBB pre-distortion
equivalent baseband, 268, 269
indirect and direct learning structures, 268 LS algorithm, 269
NMSE, 270
PA characteristics, 269 and power amplifier, 267 3-dB corner frequency, 56 DC current, 13
DC-offset correction (DCOC), 408, 414, 420, 422 DC offsets, 296, 298–310
DCOC, 408, 414, 420, 422
and I–Q imbalance calibration, 131 DC power, 11
Decision-directed carrier recovery, 182 adaptive algorithm, 266
baseband I-Q signals, 266 equalizer, 224
error signal, 224
frequency offset and phase jitter, 221, 223 local oscillator signal, 221
practical baseband equalizer, 225, 226 QPSK/OQPSK-type signals, 224 second-order carrier recovery loop, 222 transmission channel, 222
typical baseband equalizer, 224, 225 Decision-feedback equalizer (DFE), 183 90 Degree phase shifter, 317
Delay distortion, 56
Delta-sigma modulator, 233, 234 Demodulation, 291, 311 Desensitization, 414, 415
Device under test (DUT), 262, 263, 278 π/4 - Differential quadrature phase shift
keying (π/4-DQPSK), 10 Differential quadrature phase-shift keying
(DQPSK), 314, 316 Digital baseband (DBB), 138–141, 293 Digital communications, 292
Digital Costas loop BPSK signals, 218
communication systems, 212 digital filter, 213
digital loop filter, 220 NCO, 213, 216, 217 noise bandwidth, 216 PLL discriminators, 218, 219 phase detection gain, 218 transfer functions, 213–215 Digital design implementation, 64 Digital European Cordless Telephone
(DECT), 232
Digital filter approximation, 59–64 Digital modulation techniques, 26
Digital pre-distortion (DPD), 139, 254, 256, 267, 270, 273
Digital RSSI (DRSSI), 397
Digital signal-processor/processing (DSP), 55, 189, 254, 271, 292
Digital-to-analog converters (DAC), 67, 71, 72, 270, 294, 310, 312, 414, 416, 422, 423
Digital TV (DTV), 348
Digital video broadcasting (DVB), 348 Direct conversion transmitter, 294
Direct current (DC), 363
Direct-down conversion receiver, 392 Direct learning, 268
Direct search, 282
Direct sequence spread spectrum (DSSS), 314, 316, 418 Doherty amplifiers, 287 Dual-band, 421
Dual-band single input single output (SISO) WLAN transceiver, 142
E
Effective number of bits (ENOB), 382 Efficient modulation in mobile and
WLAN applications, 4 Elliptic, 387
Energy efficiency, 254 basic PA efficiency, 12 green energy characteristics, 2 hardware solutions, 2 harvesting and transfer, 2 longer battery usage time, 2 network planning and development, 2 PAs, 2
PAE, 12
performance factor, 2
reduced DC power consumption, 3 resource allocations, 2
Enhanced data rates, GSM evolution, 7 Envelope fluctuation, 7, 28, 30, 32, 35, 37 Envelope-tracking (ET) technique, 3 Equivalent lowpass signal, 25
Equivalent noise bandwidth, 334, 381, 393 Error vector magnitude (EVM), 13, 124, 126,
128, 154, 296, 298, 299, 317, 322 back-off requirements, 145
I–Q gain and phase imbalance, RF modulator, 97
and PAPRvs. PA output power back-off, 130
rate-dependent specification, 144 VCO phase noise, 97
vs. transmitter IQ gain and phase imbalance, 129
Even-order nonlinearity, 269 Excess bandwidth, 49
Eye diagram, 30, 35, 42, 51, 58, 165, 166, 179, 184, 189, 207
F
Fast Fourier transform (FFT) operation, 285 Federal Communications Commission (FCC), 1
Feedback filter, 183 Feedback linearization, 267 Feed-forward linearization, 267 Feher-patented quadrature phase shift
keying (FQPSK) FQPSK-B, 180–182 IJF-OQPSK, 175 PA, 171
satellite and cellular systems, 175 spectral efficiency and power
efficiency, 171 XPSK modulation, 175–179 FFT operation, 304
Fifth generation (5G), 293 Filter bandwidth, 10 Filter design, 60–62
Finite impulse response (FIR), 165, 182 Flicker noise, 328
FM systems, 292
Fourier transforms, 15, 16, 68, 344, 373 Fourth generation (4G), 293, 298 Fractional-N synthesizer digital calibration circuits, 240 equivalent baseband model, 233 Gaussian filtered data, 235 Gaussian filtered modulation, 233 linearized model, 235
loop filter, 236
modulation transfer function, 237, 238 parameters, 236
pre-distortion filter, 235
simplified compensation model, 237 transmitter, 242
Fractional subcarrier spacing FCO, 106 Frame error rate (FER), 379
Frequency deviation, 17, 155, 232 Frequency division duplex (FDD), 412, 414 Frequency-division multiple access
(FDMA), 332 baseband signal, 6
cellular communication systems, 6 communication systems, 5
Frequency division multiplex (FDM), 6, 406 Frequency modulation, 18
Frequency offset, 189, 212, 220, 223, 247 Frequency offset estimator, 110
Frequency translation loop, 408, 412 Front-end block, 134, 368, 374, 375, 399 Front-end module, 293
Front-end module designs, 142, 143
G
Gary code, 22
Gaussian-filtered MSK (GMSK), 296 design, 165
I-Q modulation, 167–170 modulation, 7, 407 pulse response, 164, 165 signal, 336, 401 square waveform, 164
VCO-based GMSK implementation, 163 Gaussian frequency shift keying (GFSK), 231,
232, 336
Gaussian lowpass filter (LPF), 162, 169, 233 Gaussian noise, 175, 193, 201
General Packet Radio Service (GPRS), 410, 416 GFSK signal, 336
Global system for mobile communications (GSM), 6, 292, 296, 406–408 mixer-based frequency up-conversion, 229,
230
open-loop–based, 231–232 phase-locked loop, 230–248 quad-band GSM transmitters, 228 Godard’s algorithm, 189
3GPP WCDMA system, 336 Group delay equalizer, 57 GSM system, 336, 344, 367, 368 Guard band, 10
Guard interval based frequency detection, 112
H
Harmonic frequencies, 294, 298, 314, 317 Harmonics, 352, 353, 355, 385
Heterodyne receiver, 328–334 bandpass filter, 328 IF signal, 328 image-reject filter, 328 image rejection, 330–334
microwave communication systems, 330 satellite communication, 330
wireless receiver RF and mixed BB circuit, 328
Highpass filter (HPF), 294, 336
High peak-to-average power ratio (PAPR) of OFDM signal, 97
High speed downlink packet access (HSDPA), 414, 416
Hilbert transformer, 348
I
IEEE 802.11WLAN standard, 311 IM2 (Second-Order Intermodulation), 416 Image frequency, 328, 330, 375
Image reject filter, 330, 350 Image rejection ratio (IRR), 304, 348 Image signal, 328, 330, 337, 340, 343, 352, 353 Impulse invariance, 62, 63
Impulse response, 15, 16, 29, 30, 32, 37, 47, 54, 60, 62, 64
Indirect learning method, 267, 268 Industrial Scientific and Medical (ISM), 418 Infinite duration, 60
Information rate, 8 Input IP2 (IIP2), 370
Input IP3 (IIP3), 375, 376, 380, 396, 397 Instantaneous frequency, 17
Instantaneous phase deviation, 17
Instantaneous phase deviation, 17