Reduced Feedback Schemes for Waveform Adaptation

1. Reduced Feedback Schemes for Waveform Adaptation Rekha Menon June 28, 2005

2. Revisiting Interference Avoidance Different types of users reside in a network Waveforms of users reside in common signal dimensions Centralized and common control of users might not be possible Shape the waveform in a distributed way such that interference in the network is minimized

3. Co-located Receiver System Model

4. Potential Game Model The utility function is given by,

5. Best Response � Maximum Feedback Best Response for each user is the minimum eigenvector of Rkk Rkk and hence sk can be calculated only at the receiver Real valued signature needs to be fed-back to the transmitter from the receiver

6. Better Response/ Reduced Feedback Schemes Random better response Gradient based better response

7. Random Better Response Random better response User iteratively chooses a random signature Receiver Indicates if the signature improves utility User reverts to old sequence if it does not Process iteratively repeated for each user Convergence Converges by Zangwill�s convergence theorem Only NE constitute fixed points Hence algorithm converges to NE of the game

8. Random Better Response Limitation Large number of iterations required for convergence

9. Gradient based Better Response Receiver finds k (1, �N) dimensions in which the gradient of the utility function has the largest magnitude Receiver finds the optimum step size along this K-dimensioned direction Receiver indicates direction and optimum step size to the transmitter

10. Gradient based Better Response (2)

11. Convergence By Zanwill�s theorem, the better response algorithm converges Since the utility function for each user is bounded, in each iteration, ,in the ascent dimension is zero Hence at the convergence point, is zero However, is zero for any eigenvector of Rii and FP might not be NE.

12. Convergence � (2) To aid convergence to NE a random better response spacer step is added If the receiver notices that the convergent sequence is not the minimum eigenvector, the transmitter randomly chooses a signature sequence that improves utility NE are the fixed points of a random better response. Hence this algorithm with the spacer steps also theoretically converges to NE.

13. Simulation Results

14. Simulation Results � (2)

15. Simulation Results � (3)

16. Simulation Results � (4)