In this exercise we study the outage capacity of the parallel channel in further detail.
1. Find an approximation for the E-outage capacity of the parallel channel with L branches of time diversity in the low SNR regime.
2. Simplify your approximation for the case of i.i.d. Rayleigh faded branches and small outage probability E.
3. IS-95 operates over a bandwidth of 1.25 MHz. The delay spread is 1 µs, the coherence time is 50 ms, the delay constraint (on voice) is 100 ms. The SINR each user sees is -17 dB per chip. Estimate the 1%-outage capacity for each user. How far is that from the capacity of an unfaded AWGN channel with the same SNR?
Hint: You can model the channel as a parallel channel with i.i.d. Rayleigh faded sub-channels.