Consider the tri-dimensional vector channel shown below, where N is an i.i.d. normal random variable of...
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Consider the tri-dimensional vector channel shown below, where N is an i.i.d. normal random variable of mean 0 and variance o. N, N and N3 are independent of each other, and +02 +03-0, with 0 <02 < 03 The energy per symbol is defined as E, E(X)+E{X) +E{X}. Xi Ni + a) Calculate, for all possible values of Es, the optimum energy allocation. (El-E{X), E2-E{X2) and E3- E{X2}). Indicate also the optimal distribution of X1, X2 and X3. b) Calculate, for all possible cases in a), the capacity of the vector channel as a function of the parameters Es, 01, 02 and 03. Consider the tri-dimensional vector channel shown below, where N is an i.i.d. normal random variable of mean 0 and variance o. N, N and N3 are independent of each other, and +02 +03-0, with 0 <02 < 03 The energy per symbol is defined as E, E(X)+E{X) +E{X}. Xi Ni + a) Calculate, for all possible values of Es, the optimum energy allocation. (El-E{X), E2-E{X2) and E3- E{X2}). Indicate also the optimal distribution of X1, X2 and X3. b) Calculate, for all possible cases in a), the capacity of the vector channel as a function of the parameters Es, 01, 02 and 03.
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To solve this problem we first need to calculate the optimum energy allocation for all possible values of Es and then calculate the capacity of the ve... View the full answer
Related Book For
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman
Posted Date:
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