**Chin Fong Kou**

*Packet CDMA Performance with Imperfect Power Control*

M.Eng. Thesis, November 1994

Supervisor: H. Leib

This work considers both single-cell and multi-cell packet CDMA cellular systems in the presence of power level variations due to imperfect power control. The teletraffic is modeled as an M/G/infinity queuing system. Average error rates and outage probabilities are evaluated for single-cell and multi-cell CDMA systems. Traffic capacities in terms of a fixed average error rate or outage probability are presented. Often in the literature the analysis of multi-cell systems assumes a regular cell geometry with precisely defined boundaries. This condition is rarely met in practice. We have derived an analysis technique that does not assume a precise cell geometry, where the portable unit is connected to the base station from which it receives the highest power. In our opinion this represents a situation that is closer to reality than geographically specified cells. Both CDMA systems with two-dimensional and three-dimensional cell layouts have been considered. Numerical results for CDMA systems with different processing gains and coding gains are presented. It is shown that imperfect power control reduces significantly the CDMA traffic capacity.

**John B. McCluskey III**

*Multi-tone Signals in the Baseband Clipping Channel*

M.Eng. Project, October 1994

Supervisor: H. Leib

This thesis examines the problem of peak limiting or clipping in communication channels that use multiple independent sinusoidal signals for digital communication. It presents a simple comparison between the discrete sample peak limited memoryless channel and the average power constrained channel when transmitting large numbers of independent, equally spaced, and equal power QPSK signals. Using the gaussian assumption for a multi-tone signal, it is shown that (for piecewise linear clipping of a white spectrum gaussian signal followed by AWGN) there is a unique clipper input power that minimizes the average probability of bit error for a given value of channel noise. An Optimum non-linear receiver is derived for a clipping transmitter and further techniques are developed for analyzing and optimizing clipping of gaussian signals with a non-white spectrum. In the final chapter, a design example is given with complex transmitter modulation, forward error correction, and a non-linear receiver.

**Nagi N. Abboud**

*Receiver Structures and Performance Analysis for Fading
Multipath Channels*

M.Eng. Thesis, February 1994

Supervisor: H. Leib

In this research, we introduce a model for a fading multipath channel. The channel impulse response consists of an infinite series of delta-functions whose amplitude has a Rician probability density function and whose phases are randomly distributed. The arrival times of the various pulses follow an non-homogeneous Poisson process. This model is well structured and quite flexible for characterization of mobile and indoor radio environment. A Bayesian decision approach is employed for the derivation of the optimal receiver for this channel model with additive white Gaussian noise (AWGN). Simplified forms of the receiver are presented under assumption of high and low SNR. The performance of the system is investigated for the high SNR case when the intensity of the Poisson process is constant. In this case, the performance of this system is compared to what has been found for differential phase shift keying (DPSK) when using diversity reception. A performance analysis is also done for a more realistic situation when the rate of the Poisson process is a decaying oscillatory function. This non-homogeneous Poisson process generates the observed phenomenon of ray clustering.

**Raymond Knopp**

*Module-Phase-Codes with Non-Coherent Detection and
Reduced-Complexity Decoding*

M.Eng. Thesis, December 1993

Supervisor: H. Leib

This thesis considers M-ary phase coding for the non-coherent AWGN channel.
More precisely, we develop block-coded MPSK modulation schemes specifically for
non-coherent block detection which significantly surpass the performance of
ideal uncoded *coherent* MPSK. A class of block codes which are
well-matched to MPSK modulation, called *module-phase codes*, is presented.
The algebraic framework used for defining these codes relies on elements of
module theory which are discussed along with a method for constructing such
codes for non-coherent detection. It is shown that differential encoding, when
considered on a block basis, may be viewed as a specific code from a particular
class of module-phase codes. Two classes of more powerful codes which achieve
significant coding gain with respect to coherent detection of uncoded MPSK are
presented. In the first class of module-phase codes, the coding gain is achieved
at the expense of bandwidth expansion. In the second class, however, the coding
gain is achieved at the expense of signal constellation expansion without
expanding bandwidth. A reduced-complexity/sub-optimal decoding strategy based on
a modification of *information set decoding* is described. Its performance
is analyzed through the use of computer simulations for various different codes.
Finally we address the performance of these codes combined with the
reduced-complexity decoding method over correlated Rayleigh fading channels.

**Kiran Mehta**

*Fourier Domain Techniques for Lattice Codes*

M.Eng. Thesis, January 1993

Supervisor: H. Leib

Lattice codes find good use as higher dimensional signal constellations. When used with QAM, the constituent 2-D constellations of a lattice code determine important properties of the transmitted signal. Using multidimensional Fourier techniques, this work presents a robust method to efficiently generate the point distribution of all the constituent 2-D constellations of a lattice code. The multidimensional discrete Fourier transform (MDFT) is computed for a periodic extension of the lattice code. The MDFT is used in conjunction with a version of the Projection-Slice theorem, derived for the discrete case, to obtain the point distribution of all the constituent 2-D constellations. The implementation of the MDFT is via a multidimensional generalization of the FFT using the Cooley-Tukey decomposition, well matched to lattice properties. Numerical results show that for signal constellations which are not large, the continuous approximation technique is not accurate, and therefore the exact calculations should be used.