Receiver Performance for Downlink OFDM with Training

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 For fixed subchannel: • ri = received signal at antenna i • bk = transmitted bit for user k r1 = h11b1 + h12b2 + n1 r2 = h21b1 + h22b2 + n2 • M = # of antennasN = # of channelsK = # of users

5. System Model (contd..) In matrix form, for one subchannel, r1 h11 h12 b1 = + n r2 h21 h22 b2 For all subchannels, we model H as block diagonal matrix: r11 h111 h121 b11 r21 h211 h221 b21 r12 h112 h122 b12 r22 = h212 h222 b22 + n . . . . . . r1N b1N r2N b2N Received covariance matrix: R = E{rrt} = HHt + 2I

6. Single User Matched Filter r11 h111 b11 r21 h211 r12 h112 b12 r22 = h212 + n . . . . r1N r2N b1N r = hb + n where h is MNN channel matrix, and M is the number of antennas (2 in our case) best = sign(htr)

7. Maximum-Likelihood Receiver • Choose b 2 SML = {(1,1),(1,-1),(-1,1), (-1,-1)} to minimize L(b) = || Hb – r ||2 • Decoding rule: best = arg minb 2 SML ||Hb – r ||2

8. Linear MMSE Receiver • MSE = E[|b – best(r)|2], best = Flintr • where Flin = R-1H • Decoding rule: best = (R-1H)tr

9. DFD: Optimal Filters with Perfect Feedback • Assume perfect feedback: best = b(to compute F and B) • Input to the decision device for each channel: x = Ftr – Btbest where, F: MK feedforward matrix best: K1 estimated bits B: KK feedback filter • Error at DFD output: edfd = b – x • Error covariance matrix: ξdfd = E[edfd edfdt] • Minimizing tr[ξdfd] gives F = R-1H (I + B) I + B = (HtH + 2I)(|A|2 + 2I)-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 best, 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 functionw.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)