Consider the frequency-selective channel with CSI only at the receiver with L i.i.d. Rayleigh faded paths.
1. Compute the capacity of the fast fading channel. Give approximate expressions at the high and low SNR regimes.
2. Provide an expression for the outage probability of the slow fading channel. Give approximate expressions at the high and low SNR regimes.
3. We introduced a suboptimal scheme which transmits one symbol every L symbol times and uses maximal ratio combining at the receiver to detect each symbol. Find the outage and fast fading performance achievable by this scheme if the transmitted symbols are ideally coded and the outputs from the maximal-ratio are soft combined. Calculate the loss in performance (with respect to the optimal outage and fast fading performance) in using this scheme for a GSM system with two paths operating at average SNR of 15 dB. In what regime do we not lose much performance by using this scheme?