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hw8_2010 - EE 5505 Wireless Communication Prof N Jindal...

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EE 5505 Prof. N. Jindal Wireless Communication April 13, 2010 Homework 8 Due: Tuesday, April 20, 11:15 AM 1. You are provided Matlab code that computes the ergodic capacity of a MIMO channel without CSIT and with CSIT (and SVD-based waterfilling), and produces plots of capacity versus SNR. (a) Modify the code so that it also plots the rate achieved if the TX has CSIT and allocates all of its available power to the eigenmode (i.e., spatial channel) with the largest eigenvalue. (b) Using the approximation log(1 + x ) x , argue that the optimal waterfilling strategy at low SNR is to allocate all power to the strongest eigenmode. (c) For n T = n R = 4, plot the ergodic capacity with and without CSIT along with the rate for beamforming in the strongest eigenmode. Explain the differences between the curves. (d) Again using the approximation log(1 + x ) x , argue that the ergodic capacity with no CSIT for an N × N system is about the same as that of a 1 × N system at low SNR.
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