University of Central Florida STARS Retrospective Theses and Dissertations 1984 AWQPSK : an optimum modulation technique for spread spectrum communication Madjid A. Belkerdid University of Central Florida Part of the Electrical and Computer Engineering Commons Find similar works at: https://stars.library.ucf.edu/rtd University of Central Florida Libraries http://library.ucf.edu This Doctoral Dissertation (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of STARS. For more information, please contact [email protected]. STARS Citation Belkerdid, Madjid A., "AWQPSK : an optimum modulation technique for spread spectrum communication" (1984). Retrospective Theses and Dissertations. 4728. https://stars.library.ucf.edu/rtd/4728 AWQPSK: AN OPTIMUM MODULATION TECHNIQUE FOR SPREAD SPECTRUM COMMUNICATION by Madjid A. Belkerdid A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Electrical Engineering and Communication Science at the University of Central Florida Orlando, Florida July 1984 Advisor: Dr. Brian Petrasko ABSTRACT Quadrature phase shift keying (QPSK) and minimum shift keying (MSK) are the two most used M-ary modula­ tion techniques in Direct-Sequence (DS) Spread Spectrum Communication systems. This thesis introduces a new modulation technique that can compete well with QPSK and MSK in many applications. This new modulation technique, made up of a superposition of one QPSK signal and two amplitude weighted QPSK signals, is called Amplitude­ Weighted Quadrature Phase Shift Keying (AWQPSK). It is found to have the same probability of error as QPSK and MSK techniques. It has a higher bandwidth efficiency in bits/sec/Hz than QPSK and MSK. It has 99.99 percent of its energy within the null bandwidth ·and its sidelobes are 63 db down from the main lobe. Intersymbol inter­ ference (ISI) was simulated on an HP 9845 computer and was shown to be smaller than the ISI in a QPSK or an MSK signal. Two different implementation schemes are pre­ sented. ACKNOWLEDGMENTS I wish to express my deep gratitude to my advisors Dr. Brian Petrasko and Dr. Donald Malocha. I also wish to thank Laura Wiechel for her typing. Finally many special thanks to my wife and son for their patience and collaboration. iii TABLE OF CONTENTS LIST OF FIGURES • • vi INTRODUCTION 1 I. DIGITAL COMMUNICATION SYSTEMS. 6 A. System Model 6 Transmitter and Receiver Model• • • . 6 Optimum Receiver • • • • • • . ••• 7 Matched Filter Receiver. • • . • • 9 Correlator Receiver. • • • . • • • . 9 B. MODULATION SCHEMES USED IN SPREAD SPEC- TRUM COMMUNICATIONS. • ••••••• 9 PS K • . • • · • • • • • • . 10 CPFSK • • • • • • • • • • • • • • • • 10 QPS K . • • . • • • • . • . • . 11 OQPSK. • • • . • • • . 12 MS K • • • • • • • • • • • • • • • 13 A comparison of MSK and QPSK waveforms • 15 C. PERFORMANCE EVALUATION OF QPSK AND MSK • 19 Overview .•.... • . 19 Spectral Efficiency •• • 19 Probability of Error •••• • • • • 21 Intersymbol Interference ..•. • • . 21 II. DESCRIPTION OF THE PROPOSED MODULATION TECH­ NIQUE: AWQPSK ••••••••••.•••• 30 A. Window Functions Overview. 30 Raised Cosine Function •••••.••• 31 Blackman Function. • • • • . 32 B. Eigen Function • • 3 2 Time Domain ••• 32 Frequency Domain • • 3 3 iv C. AWQPSK . • 37 Quadrature Modulation •.•••• . •••• 37 Analysis of AWQPSK ••..• 39 III. EVALUATION OF AWQPSK • • • 4 1 A. Spectral Efficiency. • • • 41 B. Probability of Error • • • • 4 1 C. Intersymbol Interference • • • • 51 D. Percent Amplitude Modulation • • • • 52 IV. IMPLEMENTATIONS ••.• • • • 5 7 A. Parallel Scheme. .•.•.•.. 57 B. SAW Device Implementation . ••.• 57 v. CONCLUSION • 61 Appendixes • 62 A. PROBABILITY OF ERROR FOR BINARY MODULA- TION TECHNIQUES •••••••••••.• 63 B. POWER SPECTRAL DENSITY FUNCTION OF RANDOM BINARY WAVEFORM • • . • • • . .. 68 c. INTERSYMBOL INTERFERENCE MODEL • • 71 REFERENCES 74 V LIST OF FIGURES 1. Direct Sequence Spread Spectrum Transmitter System . • . • . • . 4 2. Frequency Hopped Spread Spectrum Transmitter Sys tern • . • . • • . • . 5 3. Digital Communication System Model 8 4. QPSK Modulator Model • . 12 5. MSK Modulator Model .. • 16 6. MSK Time Domain Waveform • • 1 7 7. QPSK Time Domain Waveforms • • 18 8. QPSK Spectrum. • • • • • 21 9. MSK Spectrum • 22 10. MSK Spectrum Decomposition . 23 11. Filtered (ISI) QPSK Time Pulse (Linear Scale) . 26 12. Filtered (ISI) QPSK Time Pulse ( Log Scale) . 27 13. Filtered (ISI) MSK Time Pulse (Linear Scale) . 28 14. Filtered (ISI) MSK Time Pulse ( Log Scale) . 29 15. Blackman Function Spectrum . 34 16. RF Eigen Function Time Domain Pulse . 35 17. Eigen Function Spectrum Decomposition 36 18. Eigen Function Spectrum. • 37 19. Phasor Diagram • • 4 3 20. Quadrature Correlator Receiver • • • 4 4 21. Filtered (ISI) AWQPSK Time Pulse (Linear Scale) • • • • • • . • • • • • • • • . • • . • 53 vi 22. Filtered (ISI) AWQPSK Time Pulse (Log Scale) • 54 23. Inphase AWQPSK Component • • 5 5 24. Quadrature AWQPSK Component • 55 25. AWQPSK Time Domain Waveform with UI = +l and u = +l 56 q . 26. AWQPSK Time Domain Waveform with UI = +l and u = -1 56 q . 27. Parallel implementation of a AWQPSK Modula- tion • • . • • . • . • • • • • . • • . • • 59 28. SAW Device Implementation of a AWQPSK Modula- tion • . • . • • . • • • . • • 60 29. Receiver Structure • • 6 3 30. Binary Correlator Receiver • 66 31. Integrate and Dump Receiver • • • • 66 32. Binary Random Waveform • 68 33. Example of a Received Pulse Train. • • 7 3 vii INTRODUCTION Spread spectrum is a spreading of information energy in time and frequency beyond the required information bandwidth. This spreading operation brings the signal level below the noise level which makes a spread spec­ trum system capable of low probability of unwanted in­ tercept and high rejection of intentional or uninten­ tional jamming. Even though the signal to noise ratio is very low, the probability of error is low in a spread spectrum communication system. There are two fundamental elements characterizing a spread spectrum communication system: a spectrally ef­ ficient modulation technique, and a pseudo-random pulse generator [1]. A spectrally efficient modulation technique is char­ acterized by its modulated waveform having most of its energy contained in a frequency band centered around the carrier frequency, and very little energy outside this band [ 2] .. A pseudo-random pulse generator is used as a carrier in spread spectrum communication system. This generator introduces an element of unpredictability or randomness (Pseudo-Randomness) in each of the transmitted waveforms 2 which is known to the intended receiver only [3]. ,., When this pseudo-random pulse generator is used in conjunction with a phase modulator, the resulting modu­ lated signal is called a direct sequence (DS) or a pseu­ do-noise (PN) spread spectrum signal [4]. When the modulator is a binary or an M-ary FSK, the resulting transmitted signal is called a frequency hopped (FH) spread spectrum signal [3]. ADS and an FH spread spec­ trum transmitter systems are depicted in Figure 1 and Figure 2 respectively. A new modulation technique is introduced. Its per­ formance parameters will be evaluated and compared to the same parameters of QPSK and MSK modulation tech­ niques. The parameters used for evaluation are spectral efficiency, probability of error, and intersymbol inter­ ference. Spectral efficiency is very important in a crowded spectrum. The new modulation technique has 99.99 percent of energy within the null bandwidth, the sidelobes are 63 db down which makes spectrum spillage to other cochannels very minimum. The probability of error using a coherent correlator receiver is derived for this modulation technique and was found to be the same as for QPSK and MSK. Intersym­ bol interference arises from the spectrum truncation associated with finite bandwidths which generate time domain sidelobes (tails). ISI is generated by the over- 3 lapping tails of other pulses adding to the particular pulse which is examined at any one sampling time [1]. Intersymbol interference is simulated on an HP 9845 computer and was found to be less than the ISI produced by QPSK and MSK. - Finally a parallel implementation and a surface acoustic wave (SAW) implementation of a modulator are presented. 4 DS Spread Spectrum Signal BINARY _____,_,. MODULATOR DATA Pseudo-Rand. Pulse Generator Figure 1. Direct Sequence Spread Spectrum Trans­ mitter System. 5 FH Signal BINARY DATA MODULATOR FREQUENCY SYNTHESIZER PSEUDO-RANDOM PULSE GENERATOR Figure 2. Frequency Hopped Spread Spectrum Trans­ mitter System. I. DIGITAL COMMUNICATION SYSTEMS A Spread Spectrum Communication system consists of a transmitter and a receiver. The transmitter consists of a modulator followed by a spectrum spreading circuit. The receiver consists of a circuit which unspreads the spectrum followed by a demodulator. The modulation technique used is evaluated by some key parameters, such as the bandwidth efficiency of the transmitted signal, intersymbol interference, and prob­ ability of error. A. System Model Transmitter and Receiver Model The basic elements of a Digital communication system can be described by the block diagram depicted in Figure 3. The modulator is the most important part of the transmitter. Examples of modulation techniques used in spread spectrum communication systems are given in Sec­ tion II.B. 6 7 ·The transmitted signal is given by s (t-(k-l)T) if =