Minimum mitigation bandwidth for a time-limited pulse

Mitigation bandwidth is a measure of pulse bandwidth based on the effectiveness of the pulse shape in mitigating the effects of Rayleigh fading. The variance of the received signal power becomes inversely proportional to the mitigation bandwidth for asymptotically large values of this bandwidth measure. Thus, it is desirable to maximize the mitigation bandwidth. This paper finds the worst-case time-limited pulse; the pulse which minimizes the mitigation bandwidth. First a simple bound is developed to show that a real-valued pulse limited to duration T can have mitigation bandwidth no less than 2/T. Using Fourier series theory and solving the problem numerically yields a minimum mitigation bandwidth of 2.9113/T for real, symmetric pulse shapes. This worst case value is only 3% less than the mitigation bandwidth of a rectangular pulse