(Interaction between space-time codes and multiuser diversity schedul- ing) A design is proposed for the downlink IS-856 using dual transmit antennas at the base-station. It employs the Alamouti scheme when transmitting to a single user and among the users schedules the user with the best effective instantaneous SNR under the Alamouti scheme. We would like to compare the performance gain, if any, of using this scheme as opposed to using just a single transmit antenna and scheduling to the user with the best instantaneous SNR. Assume independent Rayleigh fading across the transmit antennas.
1. Plot the distribution of the instantaneous effective SNR under the Alamouti scheme, and compare that to the distribution of the SNR for a single antenna.
2. Suppose there is only a single user (i.e., K = 1). From your plot in part (1), do you think the dual transmit antennas provide any gain? Justify your answer. Hint: Use Jensen's inequality.
3. How about when K> 1? Plot the achievable throughput under both schemes at average SNR = 0 dB and for different values of K.
4. Is the proposed way of using dual transmit antennas smart?