Digital Techniques for Wideband Receivers

Front Matter......Page 2
Preface......Page 5
About the Author......Page 7
Table of Contents......Page 0
Table of Contents......Page 8
Glossary......Page 22
1.2 Digital Approach......Page 24
1.4 Organization of the Book......Page 27
1.5 Specific Remarks......Page 28
References......Page 29
2.2 Introduction to Electronic Warfare......Page 30
2.3 Difference between Intercept and Communication Receivers......Page 32
2.4 Signal Environment for EW Receivers......Page 33
2.5 Requirements of EW Receivers......Page 35
2.7 Frequency Information......Page 36
2.8 AOA Information......Page 40
2.9 Outputs of an EW Receiver......Page 41
2.10 Overview of Analog EW Receivers......Page 42
2.11 Instantaneous Frequency Measurement (IFM) Receivers......Page 43
2.12 Channelized Receivers......Page 44
2.13 Bragg Cell Receivers......Page 45
2.14 Compressive (Microscan) Receivers......Page 46
2.15 Digital Receivers......Page 48
2.16 Characteristics and Performance of EW Receivers......Page 49
2.16.1 Single Signal......Page 50
2.16.2 Two Simultaneous Signals......Page 51
2.17.3 Compressive Receiver Used for AOA Measurement......Page 52
2.17.5 Digital EW Receiver......Page 53
2.18.1 Deinterleaving......Page 54
2.18.5 Revisiting......Page 57
2.19 EW Receiver Design Goals......Page 58
References......Page 59
3.2 Fourier Transform......Page 62
3.3 Impulse Function......Page 65
3.4 Properties of Fourier Transform......Page 66
3.4.2 Even and Odd Functions......Page 67
3.4.3 Duality......Page 68
3.4.4 Scaling......Page 70
3.4.5 Time Shift......Page 71
3.4.8 Integral......Page 72
3.5 Fourier Series......Page 73
3.6 Comb Function......Page 74
3.7 Convolution......Page 78
3.8 Parseval's Theorem......Page 81
3.9 Examples......Page 82
3.10 Summary......Page 94
References......Page 99
4.2 Signal Digitization......Page 100
4.3 Graphical Description of Discrete Fourier Transform (DFT)......Page 101
4.4 Analytic Approach to Discrete Fourier Transform......Page 104
4.5.1 Limited Frequency Bandwidth......Page 106
4.5.3 Overlapping Aliasing Effect on Real Data......Page 107
4.6 Window Functions......Page 110
4.6.1 Rectangular Window......Page 112
4.6.2 Gaussian Window......Page 113
4.6.3 Cosine Window Raised to the alpha th Order......Page 114
4.6.4 Generalized Hamming Window......Page 115
4.7 Fast Fourier Transform (FFT)......Page 116
4.8 Possible Advantages of DFT Over FFT in Receiver Applications......Page 124
4.8.2 Sliding DFT......Page 125
4.9 Periodogram......Page 127
4.10 Averaged Periodogram......Page 128
References......Page 131
5.2 Zero Padding......Page 133
5.3 Periodic and Linear Convolutions......Page 135
5.4 Peak Position Estimation for Rectangular Window......Page 141
5.5 Peak Position Estimation for Manning Window......Page 145
5.6 Peak Position Estimation through Iteration......Page 146
5.7 Actual Frequency Determination by Fast Fourier Transform......Page 148
5.8 Real Input Computed by a Complex FFT Operator......Page 150
5.9 Autocorrelation......Page 152
5.10 Autocorrelation (Blackman-Tukey) Spectrum Estimation......Page 154
5.11 Application of FFT to Spectrum Estimation from Autocorrelation Function......Page 156
5.12 Basic Idea of Sub-Nyquist Sampling Scheme......Page 159
5.13 Phase Relation in a Sub-Nyquist Sampling System......Page 162
5.14 Problems and Potential Solutions of Sub-Nyquist Sampling Scheme......Page 165
5.15 Discrete Fourier Transform through Decimation......Page 168
5.16 Applications of Decimation Method to EW Receivers......Page 170
5.17 Simplified Decimation Method......Page 172
References......Page 174
6.2 ADC through Folding Technique......Page 176
6.3 ADC through Sigma-Delta Modulation......Page 178
6.4 Basic Sample and Hold Circuit......Page 181
6.5 Basic ADC Performance and Input Bandwidth......Page 183
6.6 Apparent Maximum and Minimum Signals to an ADC......Page 184
6.7 Quantization Noise of an Ideal ADC......Page 187
6.8 Noise Level Determined by Processing Bandwidth and Dithering Effect......Page 189
6.9 Spurious Responses......Page 190
6.10 Analysis on Spur Amplitudes......Page 193
6.11 Further Discussion on Spur Amplitudes......Page 197
6.12 Noise Effects in ADC......Page 200
6.13 Sampling Window Jittering Effect......Page 203
6.14 ADC Test through Histogram......Page 207
6.15 ADC Test through Sine Curve Fitting......Page 209
6.16 ADC Test through FFT Operation......Page 210
6.17 Requirements on ADC......Page 230
References......Page 233
Appendix 6.A......Page 235
Appendix 6.C......Page 237
7.1 Introduction......Page 239
7.3 Notations......Page 240
7.4 Comparison Sensitivity of Analog and Digital Receivers......Page 242
7.5 Noise Figure and Third-Order Intercept Point......Page 243
7.6 Characteristics of the Amplifiers in Cascade......Page 245
7.7 Analog-to-Digital Converter......Page 250
7.8 Noise Figure of Amplifier and ADC Combination......Page 251
7.9 Amplifier and ADC Interface......Page 252
7.10 The Meaning of M and M'......Page 254
7.11 Computer Program and Results......Page 255
7.12 Design Example......Page 257
7.13 Experimental Results......Page 258
7.13.1 Noise Figure Measurement......Page 259
7.13.2 Dynamic Range Test......Page 260
References......Page 264
Appendix 7.A......Page 265
Appendix 7.B......Page 266
8.1 Introduction......Page 268
8.3 Frequency Conversion......Page 269
8.4 In-Phase (I) and Quad-Phase (Q) Channel Conversion......Page 272
8.5 Imbalance in I and Q Channels......Page 274
8.6 Analog I and Q Downconverters......Page 278
8.8 Hilbert Transform......Page 281
8.9 Discrete Hilbert Transform......Page 284
8.10 Examples on Discrete Hilbert Transform......Page 287
8.12 Wideband I and Q Channels through a Special Sampling Scheme......Page 290
8.13 Hardware Considerations on Filter Design for Wideband Digital I-Q Channels......Page 293
8.14 Digital Correction of I and Q Channel Imbalance......Page 295
References......Page 298
Appendix 8.A......Page 299
9.1 Introduction......Page 301
9.2 Electronic Warfare Receiver Detection Approach......Page 302
9.3.1 Frequency Domain Detection......Page 303
9.3.2 Time Domain Detection......Page 304
9.4 False Alarm Time and Probability of False Alarm for One Data Sample......Page 305
9.5 Threshold Setting for One Data Sample......Page 306
9.6 Probability of Detection for Single-Sample Detection......Page 307
9.7 Detection Based on Multiple Data Samples......Page 309
9.8 Detection Scheme for Multiple Samples (L-Out-of-N)......Page 310
9.9 Probability Density Function and Characteristic Function......Page 311
9.10 Probability Density Function of Sum Samples with a Square Law Detector......Page 312
9.11 Detection of Multiple Samples Based on Summation......Page 314
9.12 An Example of Single-Sample Detection......Page 315
9.13 An Example of Multiple-Sample (L Out-of-N) Detection......Page 317
9.14 Selection of Threshold Level......Page 320
9.15 Optimizing the Selection of Threshold......Page 322
9.16 An Example of N Sample Detection (Summation Method)......Page 324
9.17 Introduction to Frequency Domain Detection......Page 326
9.18 A Suggested Approach to Frequency Domain Detection......Page 327
9.19 Probability of False Alarm in Frequency Domain......Page 329
9.20 Input Signal Conditions in Frequency Domain Detection......Page 330
9.21 Probability of Detection in Frequency Domain......Page 332
9.22 Examples on Frequency Domain Detection......Page 335
9.23 Comments on Frequency Domain Detection......Page 336
References......Page 337
Appendix 9.A......Page 338
Appendix 9.B......Page 339
Appendix 9.D......Page 340
Appendix 9.E......Page 341
Appendix 9.H......Page 342
Appendix 9.J......Page 343
Appendix 9.K......Page 344
Appendix 9.M......Page 345
10.1 Introduction......Page 346
10.2 Digital Phase Measurement......Page 347
10.3 Angle Resolution and Quantization Levels......Page 349
10.4 Comparison of Phase Measurement and FFT Results......Page 350
10.5 Application of the Phase Measurement Scheme......Page 351
10.6 Analysis of Two Simultaneous Signals......Page 352
10.7 Frequency Measurement on Two Signals......Page 355
10.8 Single-Frequency Measurement from Zero Crossing......Page 357
10.9 ILL Condition in Zero Crossing for Single-Signal and Remedy......Page 360
10.10 Simplified Zero Crossing Calculation for Single-Signal......Page 361
10.11 Experimental Results from Single-Frequency Zero Crossing Methods......Page 364
10.12 Application to Coherent Doppler Radar Frequency Measurement......Page 366
10.13 Zero Crossing Used for General Frequency Determination......Page 369
10.14 Basic Definition of the Zero Crossing Spectrum Analysis......Page 370
10.15 Generating Real Zero Crossings......Page 371
10.16 Calculating Coefficients for Zero Crossing Spectrum Analysis......Page 373
10.17 Possible Configuration of Zero Crossing Spectrum Analyzer......Page 376
References......Page 377
11.1 Introduction......Page 379
11.2 Filter Banks......Page 380
11.3 FFT and Convolution Operations......Page 381
11.4 Overlapping Input Data in the FFT Operations......Page 382
11.5 Output Data Rate from FFT Operation......Page 388
11.6 Decimation and Interpolation......Page 390
11.7 Decimation and Interpolation Effects on the Discrete Fourier Transform......Page 393
11.8 Filter Bank Design Methodology......Page 394
11.9 Decimation in the Frequency Domain......Page 396
11.11 Using Weighting Function to Widen the Output Filter......Page 400
11.12 Changing Output Sampling Rate......Page 403
11.13 Channelization through Polyphase Filter......Page 404
11.15 Filter Design......Page 406
References......Page 411
12.1 Introduction......Page 413
12.3 Monobit Receiver Idea......Page 414
12.4 Design Criteria......Page 415
12.6 RF Chain, ADC, and Demultiplexer......Page 419
12.7 Basic FFT Chip Design......Page 424
12.9 Selection of Thresholds......Page 426
12.10 Preliminary Performance of a Monobit Receiver......Page 429
12.11 Possible Improvements......Page 433
12.12 Chip Layout......Page 434
References......Page 435
13.1 Introduction......Page 437
13.2 Basic Considerations of Channelized Approach......Page 438
13.3 Filter Shape Selection......Page 439
13.4 Analog Filters Followed by Phase Comparators......Page 444
13.5 Monobit Receiver Followed by Phase Comparators......Page 445
13.6 Digital Filters Followed by Phase Comparators......Page 447
13.7 Analog Filters Followed by Monobit Receivers......Page 450
13.9 Increase the Output Sampling Rate by Two......Page 456
13.10 Digital Filters Followed by Monobit Receivers......Page 459
13.12 Digital Filter Bank Followed by another FFT......Page 462
References......Page 463
14.1 Introduction......Page 464
14.2 Autoregressive (AR) Method......Page 465
14.3 Yule-Walker Equation......Page 467
14.4 Levinson-Durbin Recursive Algorithm......Page 470
14.5 Input Data Manipulations......Page 472
14.5.1 Covariance Method......Page 474
14.5.2 Autocorrelation Method......Page 476
14.6 Backward Prediction and Modified Covariance Method......Page 477
14.7 Burg Method......Page 480
14.8 Order Selection......Page 482
14.9 Prony's Method......Page 485
14.10 Prony's Method Using the Least Squares Approach......Page 490
14.11 Eigenvectors and Eigenvalues......Page 492
14.12 MUSIC Method......Page 494
14.13 ESPRIT Method......Page 497
14.14 Minimum Norm Method......Page 502
14.15 Minimum Norm Method with Discrete Fourier Transform......Page 504
14.16 Adaptive Spectrum Estimation......Page 506
References......Page 512
Appendix 14.A......Page 514
Appendix 14.B......Page 515
Appendix 14.D......Page 516
Appendix 14.E......Page 517
Appendix 14.F......Page 519
Appendix 14.G......Page 520
Appendix 14.H......Page 521
Appendix 14.I......Page 523
15.1 Introduction......Page 524
15.2 Queuing Concept......Page 525
15.3 Digital Data from a Linear Antenna Array......Page 527
15.4 Outputs from a Circular Antenna Array......Page 529
15.5 Two-Element Phase Array Antenna......Page 532
15.6 AOA Measurement through Zero Crossing......Page 534
15.7 Phase Measurement in AOA Systems with Multiple Antennas......Page 535
15.8 Fourier Transform Over Space Domain......Page 536
15.9 Two-Dimensional Fourier Transform......Page 539
15.10 Frequency Sorting Followed by AOA Measurements......Page 542
15.11 Minimum Antenna Spacing......Page 544
15.12 Chinese Remainder Theorem......Page 546
15.13 Application of Chinese Remainder Theorem to AOA Measurements......Page 547
15.14 Practical Considerations in Remainder Theorem......Page 550
15.15 Hardware Considerations for Digital AOA Measurements......Page 551
References......Page 553
16.1 Introduction......Page 554
16.2 Types of Receiver Tests......Page 555
16.3 Preliminary Considerations in Laboratory Receiver Tests......Page 557
16.4 Receiver Tests through Software Simulation......Page 559
16.5 Laboratory Test Setup......Page 560
16.6 Anechoic Chamber Test Setup......Page 561
16.7 Preliminary Tests......Page 562
16.8.1 Frequency Accuracy Test......Page 564
16.9 False Alarm Test......Page 566
16.10 Sensitivity and Single-Signal Dynamic Range......Page 567
16.11 Pulse Amplitude and Pulse Width Measurements......Page 568
16.12 AOA Accuracy Test......Page 569
16.13 TOA Test......Page 570
16.14 Shadow Time, Throughput Rate, and Latency Tests......Page 572
16.16 Two-Signal Spurious Free Dynamic Range Test......Page 573
16.17 Instantaneous Dynamic Range Test......Page 574
16.19 AOA Resolution Test......Page 575
16.20 Simulator Test......Page 577
16.21 Field Test......Page 578
Appendix 16.A......Page 579
Appendix 16.B......Page 580
A......Page 581
B......Page 589
C......Page 590
D......Page 593
E......Page 598
F......Page 602
G......Page 610
H......Page 611
I......Page 613
J......Page 615
L......Page 616
M......Page 618
N......Page 621
O......Page 622
P......Page 623
Q......Page 627
R......Page 628
S......Page 630
T......Page 636
Z......Page 639