Optimized Cross Correlation Waveforms for First Order Correlation Loops

In this work, the steady state mean square tracking error of first order correlation loops is minimized by varying the locally generated cross correlation function produced by the voltage controlled oscillator. This analysis should assist in the design of modified first order delay locked loops used for pseudonoise code synchronization in direct sequence spread spectrum receivers. The optimum cross correlation waveform is generated by filtering a replica of the originally transmitted signal. The optimal filter imposes a 90 degree phase shift at all frequencies and has an amplitude response that is a function of the channel signal to noise ratio. In the general case, this filter is not a differentiator, as is commonly assumed. The analytical difficulty of solving multi-dimensional, nonlinear, integral equations prevents us from finding a closed form solution. However, a number of asymptotic cases are analyzed and sample results from numerical evaluations are presente

A Gray-Code Type Bit Assignment Algorithm for Unitary Space-Time Constellations

Many techniques for constructing unitary space- time constellations have been proposed. To minimize bit-error rate (BER) in a wireless communication system, constellations constructed using these techniques should be given a Gray- code type bit assignment, where symbols which are close in signal space have bit assignments which have small Hamming distance. To the authors\u27 knowledge, no efficient general strategy for making this bit assignment has been suggested. This work proposes a prioritized distance (PD) algorithm for making this assignment in an optimal manner by minimizing the probability of bit error union bound. The algorithm can be used on constellations constructed using any technique. Simulation results show this algorithm significantly outperforms random searches and achieves near globally optimum results with moderate complexity

A GRASP for Unitary Space-Time Codes

Unitary space-time codes perform well at high signal-to-noise ratios on MIMO channels even when the propagation coefficients between transmitter and receiver are unknown. One method of constructing unitary space-time constellations uses a random search to find signal constellations that minimize the maximum pairwise correlation between transmitted signals. The work presented here uses a greedy randomized adaptive search procedure (GRASP) for finding good unitary space-time code constellations. Simulation results show that, on average, this technique finds codes with better correlation properties than the random search method. This new search procedure was also used to find signal constellations with better correlation properties than those previously obtained with the random search technique

Conservative Confidence Intervals of Importance Sampling Estimates

Confidence intervals (CI) are used to gauge the accuracy of bit error rate (BER) estimates produced by Monte Carlo (MC) simulations. This work attempts to objectively evaluate the performance of Important Sampling (IS) simulations by applying the same statistical analysis tool. While it is not possible to evaluate the minimum size CI for arbitrary IS estimates, it is possible to over-bound the interval using a technique called conservative confidence interval (CCI) estimation. This bounding procedure is applied to a simple IS biasing technique. While the IS estimate may be superior to the MC estimate, the CCI fails to support this claim. Since there has been little previous work published in the area of CI of IS estimates, this document is offered as a starting point. Hopefully others will be able to develop tighter bounds for the CI of IS estimate

Interval Estimation and Monte Carlo Simulation of Digital Communication Systems

This work quantifies the accuracy of bit error rate (BER) estimates produced by Monte Carlo simulations by carefully applying confidence interval estimation techniques. Due to numerical difficulties, some previous work in this area has assumed that the BER statistic possessed a Gaussian distribution. This work demonstrates that in some important regions the estimate is decidedly non-Gaussian, and application of central limit theorem arguments can result in errors in excess of an order of magnitude. This work investigates the accuracy of common approximations and the feasibility of exact calculation of confidence intervals, and presents a novel polynomial class approximation. By combining the new approximation with more conventional approaches, an algorithm is developed for estimating confidence intervals of BER estimates. The algorithm is nonrecursive and numerically stable, requires a trivial amount of compute time to evaluate, has a small margin of error, and can be used for all error rates less than 0.5

Object-Oriented Modeling of Communication Systems

Conventional communication system simulation programs and packages are written using procedural programming languages. Newly developed, object-oriented languages offer the simulation designer significantly different options and structures. By exploiting these new techniques it is possible to significantly increase the flexibility and extensibility of the simulation package. This allows the system analyst to efficiently re-use complex simulation code and quickly and reliably reconfigure the simulation. In addition, a single object-oriented simulation can be used in all stages of the design process, from conceptual design through fabrication and testing. A final benefit of the object-oriented techniques is that the simulation code closely matches the graphical user interface used in most modern simulation packages. This work discusses the basic attributes of an object-oriented model and examines why this may be an attractive simulation architecture

Simulation of Communication Systems

When both a complex system and a complex channel model are encountered, the result is typically a design or analysis problem that cannot be solved using traditional (pencil and paper) mathematical analysis. Computer-aided techniques, which usually involve some level of numerical simulation, can be a very valuable tool in these situations. The purpose of this article is to provide a tutorial review of some of the basic techniques of communication system simulation. The authors consider the basic techniques used to represent signals, generate signals, and model linear systems, nonlinear systems, and time-varying systems within a simulation. They consider the important problem of using a simulation to estimate the performance of a communication syste

Correlative Tracking of Pseudo-Noise Codes using a Phase Shifted Reference

This work investigates a first-order correlation loop for tracking pseudo-noise (PN) codes. The local reference is produced by a PN sequence generator in series with a Hilbert transform filter. The tracking performance of this non-linear loop is compared with conventional early-late delay-lock loops (ELDLL). Using a conservative definition of bandwidth, the new loop was found to be superior at moderate to low signal-to-noise ratios (SNR). Another advantage of the new structure is that it has a very large (arguably infinite) lock range

A Lower-Bound for the Error-Variance of Maximum-Likelihood Delay Estimates of Discontinuous Pulse Waveforms

A new lower bound is developed for the error variance of maximum-likelihood time-delay estimation when the received signal is a square pulse, corrupted by additive white Gaussian noise. The bound is generated by combining concepts previously developed for a special class of stochastic processes, induced by the signal model. For moderate signal to noise ratios, the new bound is significantly tighter than previously known ones

Performance of Bandlimited Gaussian Noise as a Spreading Code in AWGN and Single Tone Interference Channels

This paper examines the bit error rate (BER) of a direct sequence spread spectrum (SS) system that uses bandlimited white Gaussian noise (BLWGN) as a spreading code. The performance of this bandlimited-SS system is examined in both additive white Gaussian noise (AWGN) and single tone jamming environments. The BLWGN spreading code is inferior to conventional codes in AWGN channels, but is more robust when a narrow band interference signal is present