1. Receiver Performance for Downlink OFDM with Training Koushik Sil ECE 463: Adaptive Filter Project Presentation

2. Goal of this Project Simulate and compare the error rate performance of single- and multiuser receivers for the OFDM downlink with training. Identify a receiver structure, which has excellent performance with limited training, complexity, and variable degrees of freedom.

3. Assumptions Downlink channel Modulation scheme: OFDM Binary symbols 2 users on cell boundary (worst case scenario) Dual-antenna handset Block (i.i.d.) Rayleigh fading Separate spatial filter for each channel Training interval followed by data transmission

4. System Model r i = received signal at antenna i b k = transmitted bit for user k r 1 = h 11 b 1 + h 12 b 2 + n 1 r 2 = h 21 b 1 + h 22 b 2 + n 2 M = # of antennas N = # of channels K = # of users For fixed subchannel :

5. System Model (contd..) In matrix form, for one subchannel, r 1 h 11 h 12 b 1 = + n r 2 h 21 h 22 b 2 For all subchannels, we model H as block diagonal matrix: r 11 h 11 1 h 12 1 b 11 r 21 h 21 1 h 22 1 b 21 r 12 h 11 2 h 12 2 b 12 r 22 = h 21 2 h 22 2 b 22 + n... r 1N b 1N r 2N b 2N Received covariance matrix: R = E{rr t } = HH t +  2 I

6. Single User Matched Filter r 11 h 11 1 b 11 r 21 h 21 1 r 12 h 11 2 b 12 r 22 = h 21 2 + n.. r 1N r 2N b 1N r = hb + n where h is MN  N channel matrix, and M is the number of antennas (2 in our case) b est = sign(h t r)

7. Maximum-Likelihood Receiver Choose b 2 S ML = {(1,1),(1,-1),(-1,1), (-1,-1)} to minimize L(b) = || Hb – r || 2 Decoding rule: b est = arg min b 2 S ML ||Hb – r || 2

8. Linear MMSE Receiver MSE = E[|b – b est (r)| 2 ], b est = F lin t r where F lin = R -1 H Decoding rule: b est = (R -1 H) t r

9. DFD: Optimal Filters with Perfect Feedback Assume perfect feedback: b est = b (to compute F and B) Input to the decision device for each channel: x = F t r – B t b est where, F: M  K feedforward matrix b est : K  1 estimated bits B: K  K feedback filter Error at DFD output: e dfd = b – x Error covariance matrix: ξ dfd = E[e dfd e dfd t ] Minimizing tr[ξ dfd ] gives F = R -1 H (I + B) I + B = (H t H +  2 I)(|A| 2 +  2 I) -1 where A is the matrix of received amplitudes

10. DFD: Single Iteration Initial bit estimates for feedback are obtained from linear MMSE filter Given refined estimate b est, can iterate. –Numerical results assume a single iteration.

11. Optimal Soft Decision Device Minimimze MSE = Solution:

12. Performance with Perfect Channel Knowledge

13. Training Performance: Direct Filter Estimation Assumption: both users demodulate both pilots Cost function = where Solution: where T is the training length

14. Training Performance: Least Square Channel Estimation Minimize the objective function Minimizing objective function w.r.t., we get

15. Training Performance: Linear MMSE Receiver

16. Training Performance: Linear MMSE and DFD

17. Partial Knowledge of Pilots The pilot from the interfering BST may not be available.

18. Performance Comparison: Partial Knowledge of Pilots Single pilot leads to performance with full channel knowledge. Here we need both pilots to achieve performance with full channel knowledge.

19. Conclusions DFD (both hard and soft) performs significantly better than conventional linear MMSE receiver with perfect channel knowledge. Two different types of training have been considered:  Direct filter coefficient estimation  Least square channel estimation Both have almost identical performance when pilot symbols for both users are available Knowledge of the interfering pilot can give substantial gains (plots show around 4 dB)