Regardless of the branch of science or engineering, theoreticians have always been enamored with the notion of expressing their results in the form of closed-form expressions. Quite often, the elegance of the closed-form solution is overshadowed by the complexity of its form and the difficulty in evaluating it numerically. In such instances, one becomes motivated to search instead for a solution that is simple in form and simple to evaluate. A further motivation is that the method used to derive these alternative simple forms should also be applicable in situations where closed-form solutions are ordinarily unobtainable. The search for and ability to find such a unified approach for problems dealing with evaluation of the performance of digital communication over generalized fading channels is what provided the impetus to write this book, the result of which represents the backbone for the material contained within its pages.
For at least four decades, researchers have studied problems of this type, and system engineers have used the theoretical and numerical results reported in the literature to guide the design of their systems. Whereas the results from the earlier years dealt mainly with simple channel models (e.g., Rayleigh or Rician multipath fading), applications in more recent years have become increasingly sophisticated, thereby requiring more complex models and improved diversity techniques. Along with the complexity of the channel model comes the complexity of the analytical solution that enables one to assess performance. With the mathematical tools that were available previously, the solutions to such problems, when possible, had to be expressed in complicated mathematical form which provided little insight into the dependence of the performance on the system parameters. Surprisingly enough, not until recently had anyone demonstrated a unified approach that not only allows previously obtained complicated results to be simplified both analytically and computationally but also permits new results to be obtained for special cases that heretofore had resisted solution in a simple form. This approach, which the authors first presented to the public in a tutorialstyle article that appeared in the September 1998 issue of the IEEE Proceedings, has spawned a new wave of publications on the subject that, we foresee based on the variety of applications to which it has already been applied, will continue well into the new millennium.