University of Central Florida STARS Retrospective Theses and Dissertations 1987 Design and Analysis of a Voice Band QPSK Modem John F. Doud University of Central Florida Part of the 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 Doud, John F., "Design and Analysis of a Voice Band QPSK Modem" (1987). Retrospective Theses and Dissertations. 5090. https://stars.library.ucf.edu/rtd/5090 UNIVERSITY OF CENTRAL FLORIDA OFFICE OF GRADUATE STUDIES RESEARCH REPORT APPROVAL DATE: July 17, 1987 I HEREBY RECOMMEND THAT THE RESEARCH REPORT PREPARED UNDER MY SUPERVISION BY John F . Doud ENTITLED "The Design and Analysis of a Voice-Band QPSK Modem" BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE DEGREE OF -----------------------------Master of Science FROM THE COLLEGE OF ___E_n_g_in_e_e_r_i_n~g _______________ Report RECOMMENDATION CONCURRED IN: Coordinator of Degree Program COMMITTEE ON FINAL EXAMINATION THE DESIGN AND ANALYSIS OF A VOICE BAND QPSK MODEM BY JOHN F. DOUD B.S.E., The Johns Hopkins University, 1981 RESEARCH REPORT Submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering in the Graduate Studies Program of the College of Engineering University of Central Florida Orlando, Florida Summer Term 1987 ABSTRACT The objective of this paper is to design and construct a modem using the Quadrature Phase Shift Key digital modulation technique. The modem is designed to transmit information over a telephone line at the rate of 1200 bits per second subject to noise and imperfect channel response in the form of magnitude and delay distortion. The device is constructed using CMOS logic to minimize power consumption. To analyze the design with respect to the above constraints, it was necessary to build a pseudorandom bit sequence generator and correlator, a variable magnitude white noise generator and a digital error detector/indicator. ACKNOWLEDGEMENTS Listing all of those who provided me assistance during the writing of this paper would not be feasible, yet my gratitude for their input is nonetheless significant. Here, I would like to acknowledge those whose contribution went beyond that normally rendered. Without the assistance of Greg Milne throughout the entire curriculum, completing it would have been much more difficult. I am truly grateful for the patience he exhibited in some of my slower moments. The guidance provided by Dr. Robert Martin helped me overcome any difficulties that arose. His advice steered me through technical difficulties, while his constant encouragement maintained my motivational level. Finally, I would like to thank my wife Mary Jo. During the emotional transients typical of such a project, she displayed nothing but love and support. This is as much her accomplishment as mine. Since it would be impossible to adequately express my appreciation in the short space here, I'll just offer my thanks and love. iii TABLE OF CONTENTS LIST OF FIGURES . ................................ V SECTION 1. INTRODUCTION ............................. 1 2. MODULATOR DESIGN ......................... 9 3. DEMODULATOR DESIGN ...................... 17 4. AUXILIARY CIRCUITS ...................... 31 5. PERFORMANCE ANALYSIS .................... 36 6. CONCLUSION .............................. 41 APPENDIX A MODULATOR AND DEMODULATOR SCHEMATICS ........................ 43 APPENDIX B WAVEFORM PLOTS .................... 48 LIST OF REFERENCES ............................. 51 iv LIST OF FIGURES 1. Pe as a Function of S/N •••••..•.•..••....•..•.. 3 2. S/N as a Function of Bandwidth for a Given Channel Capacity ....•.........•......•... 6 3. Modulator Block Diagram ...................•.•.. 9 4. Power Spectral Density for a Random QPSK Signal ................................... 12 5. Phase Constellation for QPSK .....•..••...•.... 14 6. Demodulator Block Diagram ..•.••••••......•..•• 18 Q ••••••••••••••• 7. Delay as a Function of w and 0 20 8. Bandwidth Limiting Degradation of QPSK Signals ....................................... 21 9. Pseudorandom Sequence Correlation .....•...••.. 32 10. Probability of Error System .....•......••••... 37 V SECTION 1 INTRODUCTION In a communication system, the fundamental purpose is ·to transfer information between two points which are usually separated by a significant distance. The considerations in the design of such a system include the form of the information to be conveyed, the channel through which it must travel, speed and accuracy requirements of the end user and the cost. For this purpose, information is defined differently than its common interpretation. In the context of communication, information represents just that which is transmitted to the user. The amount of information transferred is completely determined by the user's uncertainty prior to receiving it, and does not depend at all on the actual content of the message or its interpretation. Therefore, assuming the form of the information is preset, as is usually the case, the initial concern of the designer is focused on the transmission channel and the performance limitations imposed by it. These restrictions arise from the signal attenuation and bandwidth limiting of the imperfect channel as well as the presence of noise in the channel. The peak channel 2 performance is referred to as the channel capacity. Channel capacity may be thought of as the maximum rate at which information can be reliably transmitted through the medium, that is with an arbitrarily small probability of error. In his pioneering work of 1948, Shannon used the basis of information theory to define and quantify this capacity. Sparing a discourse on that discipline, his result is stated here: C = (1/T) * log2 (u) ( 1) where C = channel capacity in bits per second (bps) T = transmission time of each message u = number of equiprobable messages in the available alphabet. Finally, having assessed all of these factors, the designer chooses a system that comes closest to this capacity, or at least as a minimum, meets the performance requirements of the application within given cost constraints. The communication system design and construction to which this paper is dedicated is a quadrature phase-shift key (QPSK) modem transmitting digital data at a rate of 1200 bits per second over a standard telephone line. Briefly, the phase-shift key modulation technique transmits data via the changing phase of a sinusoid. Quadrature phase-shift key is a specific case in which four discrete 3 phases are employed to represent two bits of data at a time. This sinusoid is then transmitted over the communication channel where a receiver, or demodulator, using synchronous detection recovers the message. At the present time, this application of the QPSK scheme is somewhat of an anomaly since most telephone line modems transmitting data at relatively low speeds (less than or equal to 2400 bits per second) use frequency-shift key modulation. One advantage of using a coherent phase shift key design is its probability of error performance with respect to power, as can be seen in Figure 1. 10-' ,o-i to-a Pe ID-4 te,-1·~ 10-' 0 • to di t& 20 S/N Figure 1. Pe as a function of S/N. 4 It is this characteristic that makes coherent phase-shift keying, especially QPSK, the predominant choice for satellite communications. Another advantage gained by using this multi-level, or M-ary, signaling scheme is the increased data throughput accomplished by representing multiple bits with each transmitted symbol. In general, the baud rate (fs), or symbols per second, is related to the bit rate (fb) by the following equation: (2) Obviously, in this case (M = 4), the baud rate is one-half the bit rate. Extending this order, it is easy to see how this bandwidth efficiency can be exploited to transmit higher bit rates through band-limited channels. This concept may also be shown using equation ( 1). There, we see that the capacity of the channel can be improved by increasing the transmission rate (i.e. decreasing message transmission time) or by enlarging the message alphabet. For the case of the band-limited telephone line, the former may not be feasible. As an alternative, the number of possible symbols to transmit . can be increased, surpassing the one bps/hz limit of binary signaling schemes. The main disadvantage of quadrature phase shift keying is that it must be coherently demodulated. The requirement of establishing a coherent reference in the 5 receiver increases its complexity, driving up the cost. It also poses a stiff problem when dealing with channels that exhibit fading, like the satellite example cited above. For the present design, fading does not apply and cost was a secondary concern. The purpose of the modulation process is to match the characteristics of the information signal to those of the medium through which it must pass. This design matches non-return-to-zero (NRZ), unipolar digital data to the standard telephone line. A basic voice band telephone channel has three kilohertz of bandwidth (300 - 3300 Hz), a phase delay that is non-linear with frequency and a variable signal attenuation with a maximum degradation of fifteen decibels. The noise in the channel is assumed to be additive