IF band width optimization of envelope detection system in presence of phase noise

In many radar and EW applications, after some processing, the envelope of the received pulse is calculated and is used for target detection. Most of the time only the effect of thermal noise is considered in such detectors, but in most of the practical applications, before envelope detection, the signal should be down converted from radio frequency (RF) to an intermediate frequency (IF). In this case, the phase noise of the local oscillator will affect the signal, too. Surprisingly, in contrast to thermal noise, the effect of phase noise on the envelope of signal becomes more considerable whenever the IF bandwidth is decreased. So there exists an optimum IF bandwidth for the receiver. In signals with higher bandwidths, thermal noise degrades the signal and in signals with lower bandwidths, the phase noise affects it. In this paper the optimum bandwidth is calculated under some realistic approximations.