Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Electrical Engineering


Electrical Engineering

First Advisor

Vasant Prabhu


The proliferation of digital wireless communication services has increased the congestion of the available radio spectrum. In addition to that, wireless communications are encountered by multipath channel fading. To alleviate the scarcity of the radio spectrum and multipath channel fading, attention in this dissertation is placed on differentially coherent phase shift keying (DPSK) systems with equal gain combining (EGC) diversity reception. DPSK systems are capable of achieving high spectral efficiency with adequate performance over wireless fading channels. Several wireless communication systems have adopted DPSK such as the time division multiple access (TDMA) version of the North American Digital Cellular (NADC) system. DPSK systems together with multiple-input multiple-output (MIMO) antenna systems have the potential to further improve the diversity gain and increase the spectral efficiency in wireless communication systems. This dissertation analyzes the error rates of a variety of wireless digital techniques over fading channels with particular emphasis on the DPSK systems. This work leads to a useful framework to analyze the error rates of digital techniques over fading channels, and the proposal of a reduced-complexity and low-cost MIMO system for wireless communications. This dissertation also simplifies and generalizes the previous results of the error rates of wireless communication techniques over independent and correlated fading without resorting to approximations. In addition to that, this study investigates the impact of fading correlation and imperfect phase recovery on the performance of noncoherent and coherent digital wireless communication systems respectively. From practical point of view, this research study is expected to be helpful in the design of the practical radio communication receivers. First, this research starts with a study of the DPSK systems over independent and correlated fading channels. We present two approaches to analyze the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) systems with equal gain combining (EGC) diversity reception over fading channels. The first approach relies on the integral definition of the associated Legendre functions, which can lead to finite-series closed-form expressions for the average BEP of DQPSK over L independent Rayleigh and Nakagami-m, when the product Lm is integer, fading channels. In the second approach, we propose a finite sum of a finite-range integral for the average BEP of DQPSK with EGC over arbitrarily Nakagami-m and Rician fading channels. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. It is observed that the performance degradation due to the correlation among the diversity branches in Rician fading channels is severer than that in Nakagami-m fading channels as a result of the presence of the specular component. Second, we propose and analyze a reduced-complexity and low-cost DPSK system with MIMO employing EGC (MIMO EGC) diversity reception. The proposed structure provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC). The average BEP for DBPSK and DQPSK with MIMO EGC over independent Rayleigh fading channels has been derived. The associated Legendre functions approach has been used to analyze the average BEP of DQPSK with MIMO EGC. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Third, we present another useful utilization of the associated Legendre functions approach. The associated Legendre functions approach is devoted to analyze the performance of coherent PSK systems over fading channels in the presence of imperfect phase recovery. We address an evaluation (without any kind of approximation) for the average BEP of the PSK systems with imperfect phase recovery over fading channels. Moreover, using the Fourier series expansion and the associated Legendre functions, the exact average BEP of the binary and quaternary phase shift keying (BPSK and QPSK respectively) on a single channel (no diversity) in the presence of different kinds of slow fading channels (Rayleigh, Nakagami-m, and Rician), phase recovery error, and additive white Gaussian noise (AWGN) has been evaluated. The detection loss and phase precision for both of BPSK and QPSK have been calculated. The series expressions of the average BEP proposed in our study are found to be converged with reasonable number of terms. Fourth, we turn our attention onto the performance of the square M-ary quadrature amplitude modulation (MQAM) with maximal ratio combining (MRC) receive diversity. We present closed-form expressions for the average SEP of MQAM with arbitrarily fading index m. Two models of MQAM receivers are analyzed. Closed-form expressions are provided for the average SEP in terms of the Appell and Gauss hypergeometric functions. Simplified error expressions are proposed when the product Lm is either integer or half integer. Finally this dissertation is concluded with summarized remarks and future extensions.


Electrical and Computer Engineering | Engineering


Degree granted by The University of Texas at Arlington