Master Thesis Presentation

1. Master Thesis Presentation ‘Capacity of Hybrid Open-loop and Closed-loop MIMO with Channel Uncertainty at Transmitter.’ Lu Wei, Communications Laborartory. Thesis advisor: Prof. Olav Tirkkonen. 18th, March 2008.

2. Outline • Transmit diversitytechniques. • Our research problem. • Formulations and Simplifications. • Numerical results. • Conclusion.

3. Transmit diversity techniques: Open-loop case • Open-loop case: space-time block code. 2 transmit and 1 receieve antennas: Alamouti code: • Optimal linear open-loop transmit diversity scheme: It provides full diversity, with linear matched filter detection and it reaches channel capacity.

4. Closed-loop case • Requring channel state information at transmitter • Optimal w is: • Being able to have complete channel state information gives us a 3dB gain in SNR over the Alamounti code

5. Hybrid Open-loop and Closed-loop Methods • Significant performance gap between open-loop and closed-loop schemes. • Assuming the transmitter has partial but not perfect knowledge about the channel. • Question: how to improve a predetermined code so that the channel imperfection is taken into account ? reqiures: 1. modeling the channel imperfection. 2. adopted an appropriate signal model.

6. Channel Imperfection • One model exists in the literature is: • Degree of correlation, normalized correlation coefficient: • pdf of the true channel, conditioned on the imperfect CSI, is complex Gaussian distributed: conditional mean: conditional covariance:

7. The Signal Model • Consider a predetermined Alamouti code, diagonal beam weighting matrix: the unitary beamforming matrix: • When • When

8. Our Research Problem • What is the value of P matrix that will maximize the mutual information between Tx and Rx, when certain channel feedback is available? • This same problem has been solved by George Jongren, et al. under the criterion of minimizing block error rate. • Our work considers the information theoretic performance criterion of maximizing the mutual information and which permits an analytical solution.

9. Formulations and Simplifications • The capacity can be expressed as: • Average out the true but unknown channel to obtain: • Our objective is:

10. Formulations and Simplifications • Under the i.i.d fading assumption: • With the change of variable: the capacity expression is now, • Making a change of variable again to obtain: and the capacity over the corresponding distribution is:

11. Formulations and Simplifications • Remind that our problem is to maximize the capacity with respect to P: • We could rely on numerical methods to find the optimal P value. • An efficient approximation method can be utilized for the capacity integration as well.

12. Capacity Approximation Two steps approaches for the appro. • First, weighted sum of non-central chi-square variables approximated by a single central one: • Mean fits: • Variance fits:

13. Capacity Approximation • Second, using a Lemma by Porteous: Lemma, • Combining the chi-square approximation in equation with the Porteous Lemma, the capacity can be calculated as:

14. Numerical Results

15. Numerical Results

16. Numerical Results

17. Numerical Results

18. Conclusion • The proposed beamformer could benefit the from open-loop and closed-loop methods according to the channel feedback quality. • We have achieved the optimal combing of open-loop and closed-loop in mutual information optimal sense. • The analytical framework could possibly be extented to more than 2 Tx case.

19. Thank you!