Consider a spread-spectrum signal transmitted over a multipath channel with a LOS component and a single multipath component, where the delay of the multipath relative to the LOS is greater than the chip time Tc. Consider a two-branch RAKE receiver, with one branch corresponding to the LOS component and the other to the multipath component. Assume that, with perfect synchronization in both branches, the incoming signal component at each branch (after despreading) has power that is uniformly distributed between 6 mW and 12 mW. The total noise power in the despread signal bandwidth is 1 mW. Suppose, however, that only the first branch is perfectly synchronized, while the second branch has a timing offset of Tc/2.366. The code autocorrelation is that of a maximal linear code with N » 1. The two branches of the RAKE are combined using maximal-ratio combining with knowledge of the timing offset.
(a) What is the average SNR at the combiner output?
(b) What is the distribution of the combiner output SNR?
(c) What is the outage probability for DPSK modulation with a BER of 10-4?