Fsk and Bpsk Modulation and an Implementation
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ANALYSIS OF FREQUENCY HOPPING SYSTEM WITH 2-ARY FSK AND BPSK MODULATION AND AN IMPLEMENTATION OF A COHERENT 2-ARY FSK/FH MODEM : A Thesis Presented to The Faculty of the College of Engineering and Technology Ohio University In Partial Fulfillment of the Requirements for the Degree of Master of Science b Y Yaim B. Zaxawi March 1983 OHIO UNIVERSITY LIBRARY ATHENS, OHIO Acknowledgment I am indebted to my advisor, Dr. Joseph E. Essman, for his encouragement, valuable suggestions and guidance during the course of this work. Also the author wishes to express his thanks to Dr. M. Jameel for his help, particularly in the real time simulation. Special appreciation and affection is recorded to my parents for their support and understanding during the course of this work. TABLE OF CONTENTS Page ACKNOWLEDGMENT ......................... i LISTOFTABLES ........................ iv LISTOFFIGURES ........................ v Chapter INTRODUCTION ...................... 2 . SPECTRAL ANALYSIS ................... 4 Introduction 2.2 Analysis of Frequency Shift Keying/Frequency Hopping (FSK/FH) ................. 4 2.2.a Analysis of Frequency Hopping Signal Using a PN-Code Sequence .......... 4 2.2.b Analysis of Frequency Shift Keying (FSK) Signal ................... 8 2.2.c Spectrum Analysis ............. 11 2.3 Spectrum Analysis of Binary Phase Shift Keying/ Frequency Hopping (BPSK/FH) ............ 27 2.4 Summaryand Conclusions .............. 34 3 . PERFORMANCE OF THE FREQUENCY HOPPING SYSTEE.1 ...... 39 3.1 Introduction ................... 39 3.2.a Partial-Band Noise Jan?ming Model ...... 39 3.2.b Partial-Band kltitone Jaming Model .... 40 3.3 Probability of Error Calculations in the Presence of Partial-Band Noise Jamming ...... 40 3.3.a Detection of Yon-Coherent Binary Frequency Shift Keying in Frequency Hopping Environment (2-ary FSK/FH) ......... 40 i i 3.3.b Worst Case Jamming Strategy Against Non-Cherent FSK/FH . 43 3.3 .c Detection of Coherent Frequency Shift Keying in Frequency Hopping Environment (Coherent FSK/FH) . 46 3.3.d Binary Differential Phase Shift Keying in Frequency Hopping Environment (BDPSK/FH) . 49 3.4 Calculations of the Probability of Error in the Presence of Partial-Band Multitone Jamming . 52 3.4.a 2-ary Non-Coherent FSK/FH with Jam Tone Spacing Equal to the Bit Rate . 55 3.4.b 2-ary Non-Coherent FSK/FH with Jam Tone Spacing Equal to Twice Bit Rate . 57 3.4.c Probability of Error of the BDPSK/FH with Jam Tone Spacing Equal to the Bit Rate . 57 3.5 Conclusions. 60 4. REALTIMESIMULATION. 62 4.1 Introduction . 62 4.2 Design and Description of the Coherent FSK/FH Modem 62 4.3 Results andcomments . 72 4.3 Summary and Conclusions . 54 BIBLIOGRAPHY.... ..................... 91 APPENDIX A. COMPUTER LISTINGS LIST OF FIGURES Figure Page 2.1 Spread Spectrum Frequency Hopping Model ......... 5 2.2 Carrier Frequency Versus Time for the FH Signal Using a PN-Code Sequence ................... 7 2.3 The Periodic Rectangular Function Used in the Expression of the FH Signal ............... 7 2 -4 Frequency Synthesizer's Waveforms with B = 2 ...... 9 a) Code Sequence b) Carrier Frequency Versus Time c) The Periodic Rectangular Function d) Output Waveform 2.5 The FSK Modulator Waveforms ...............10 a) Baseband Signal (Input) b) Output Waveform c) Frequency Versus Time 2.6 Frequency Versus Time Relationship for the FSK/FH Signal Assuming T~ = 2~~ for B = 2 ...............13 2.7 The General Periodic Gate Function Used in the FSK/FH Analysis ........................13 2.3 Frequency Versus Time for the FSK/FH Signal with B = 3 and T~ = ~,/3 .....................14 a) Code Sequence b) Rectangular Functions for the FSK and FH Signal c) Carrier Frequency Versus Time 2.9 Magnitude Line Spectra for the Plain FSK Signal Considering the Second Zero Crossing (Positive Frequencies Only) ....................20 2.10 Magnitude Line Spectra for the Plain FH Signal with B = 2 Considering the Second Zero Crossing (Positive Frequencies Only) ...............21 2.11 Magnitude Line Spectra for the Plain FH Sigcal with B = 3 Considering the First Zero Crossing (Positive Frequencies Only! ...............22 Figure Page Magnitude Line Spectra for the Plain FH Signal with B = 4 Considering the First Zero Crossing ........23 Magnitude Line Spectra for the FSK/FH Signal with B = 2 and rh = 2rm (urn = 4%) After Th Seconds, Considering the First Zero Crossing ...........24 Magnitude Line Spectrum for the FSK/FH Signal with B = 2 and -rh = 2r for the Special Case Where Awl m Magnitude Line Spectra for the FSK/FH Signal with B = 2 and rh = r,/4 (b+, = 2um) After 2Th Seconds, Considering the First Zero Crossing (Positive Frequencies Only) ....................26 BPSKWaveforms .....................28 a) Baseband Signal b) Output Signal Carrier Frequency Versus Time for the BPSK/FH Signal with B = 2 and rh = 2rm .............30 Magnitude Line Spectra for the BPSK Signal .......32 Magnitude Line Spectra for the BPSK/FH Signal with B = 2 and r = 2rm 33 h .............. Partial-Band Noise Jamming Model ............41 Partial-Band Multitone Jamming Model ..........41 Bit Probability of Error Versus Bit Energy to Jam Noise for the Non-Coherent FSK/FH in the Presence of Partial-Band Noise with a = 1.0 ...........44 The Product XPB(x) Versus E/NJ for the Coherent and Non-Coherent FSK/FH in the Presence of Partial- BandNoiseJa~ming ...................35 Bit Probability of Error Versus the Bit Energy of Jam Noise Density in the Presence of Partial-Sand Noise with a = 1.0 for the Coherent and Non- Coherent FSK/FH .....................47 Figure Page 3.6 The Jammed Fraction of the RF Bandwidth vs the Bit Energy to Jam Noise Density Ratio in the Presence of Partial Band Noise (Worst Case) for the FSK/FH (Coherent), FSK-FH (Non-Coherent) , and BDPSK/FH Waveforms .......................50 3.7 Maximum Bit Probability of Error vs Bit Energy to Jam Noise Density in the Presence of Partial-Band Noise for the Coherent and Non-Coherent FSK/FH Waveforms (Worst Case) . 51 3.8 The Product XPB(x) Versus (E/NJ) for the BPSK/FH Waveform in the Presence of Partial-Band Noise Jamming. ........................53 3.9 Bit Probability of Error vs the Bit Energy to Jam Noise in the Presence of Partial-Band Noise Jamming for the BFSK/FH and BDPSK/FH (Worst Case) . 54 3.10 Bit Probability of Error Versus the Bit Energy to Jam Noise Density in the Presence of Partial- Band Multitone Jamming (Worst Case) for the Non-Coherent FSK/FH and for the BPSK-FH Waveforms ....58 3.11 Bit Probability of Error Versus the Bit Energy to Jam Noise Density (Worst Case) for All the Different Waveforms Considered .............59 4.1 Block Diagram of the Implemented Coherent FSK/FH Modem. .........................63 4.2 Circuit Diagram Connection for the Coherent FSK/FH Modem. .........................64 a) Transmitter's Side b) Receiver's Side 4.3 Input Waveforms to the FSK/FH Modem ...........74 a) Input Data (A Stream of Square Wave Pulses with r = 15 msec and duty cycle = 50%) m b) The Spreading Frequency Hopping Signal with a Center Frequency = 150 KHz, Number of Output Frequencies = 11, and Hopping Step Size = 5 KHz 4.4 Output Waveforms from the FSK Modulator .........75 a) The Mark Frequency f M = 2 KHz b) The Space Frequency fS = 1 KHz c) The FSK Signal Figure Page Amplitude Response of the Receiver's 4-Pole Butterworth Band Pass Filter with Center Frequency f = 1.5 KHz and Quality Factor = C QBp=2........................ 76 The Complete Transmitted FSK/FH Signal Waveform (Output of the Transmitter's Mixer) ...........77 Output Waveform of the Receiver's BPF ..........77 Output Data (Output of the FSK Demodulator) .......77 Frequency Spectrum for the FH Signal Coming from the Synthesizer with a Center Frequency = 150 KHz, Number of Output Frequencies = 11, Hopping Step Size = 5 KHz and Time/Hopping Step -rh = 30 msec ...................78 Frequency Spectrum for the FSK Signal with the Mark Frequency f = 2 KHz, Space Frequency fS = 1 KHz M and Pulse Width rm = 15 msec .............78 Frequency Spectrum for the Frequency Hopping Signal of Fig. 4.9 ...................79 a) When Mixed with the Mark Frequency Only b) When Mixed with the Space Frequency Only Frequency Spectrum for the FSK/FH Signal with a Center Frequency = 150 KHz, Number of Output Frequencies = 11, Hopping Step Size (Awi) = 5 KHz, ;h = 30 msec and -rm = 15 msec (Slow Frequency Hopping) ...................80 Frequency Spectrum for the De-spread Signal After Being Passed Through the BPF ...........80 Frequency Spectrum for the FH Signal with a Center Frequency = 500 KHz, Number of Output Frequencies = 101, Hopping Step Size = 5 KHz and Time/Step = 30 msec. ........................S1 Frequency Spectrum for the FH Signal (Whose Spectrum is Shown in Fig. 4.14) When Mixed with the FSK Signal with -rm= 15 msec ............81 Portion of the Spectrum of the Signal Whose Spectrum is Shown in Fig. 4.15. [Horizontal Scale is Set to 10 KHz/cm.] ...............82 Figure Page 4.17 Frequency Spectrum for the FSK/FH Signal with a Center Frequency = 150 KHz, Number of Output Frequencies = 11, Hopping Step Size = 0.5 KHz, T~ = 30 msec and T~ = 15 msec . 82 4.18 Frequency Spectrum for the FSK/FH Signal with a Center Frequency = 150 KHz, Number of Output Frequencies = 11, Hopping Step Size = 5 KHz and T~ = ~,/2 = 30 msec (Fast Frequency Hopping) . 83 a) After t < 3Th b) After t > 3Th Chapter 1 INTRODUCTION Shannon's original work in 1948 in the field of statistical communication theory showed that the capacity of a channel to transfer error-free information is enhanced by increasing the bandwidth of the transmitted signal, and this was the basis of spread spectrum develop- ment. At the beginning, this new concept of communication did not draw much attention because it was very difficult to implement any such system with the circuit technology that was available at that time.