Receiver Performance for Downlink OFDM with Training

Koushik SilECE 463: Adaptive Filter

Project Presentation

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.

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

System Model

• 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

For fixed subchannel:

System Model (contd..)

In matrix form, for one subchannel,

r1 h11h12 b1

= + n

r2 h21h22 b2

For all subchannels, we model H as block diagonal matrix:

r11 h111 h12

1 b11

r21 h211 h22

1 b21

r12 h112 h12

2 b12

r22 = h212 h22

2 b22 + n

. . .

. . .

r1N b1N

r2N b2N

Received covariance matrix: R = E{rrt} = HHt + 2I

Single User Matched Filter

r11 h111 b11

r21 h211

r12 h112 b12

r22 = h212 + n

. .

. .

r1N

r2N b1N

r = hb + n

where h is MNN channel matrix, and M is the number of antennas (2 in our case)

best = sign(htr)

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

Linear MMSE Receiver

• MSE = E[|b – best(r)|2], best = Flintr

• where

Flin = R-1H

• Decoding rule:

best = (R-1H)tr

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: MK feedforward matrixbest: K1 estimated bitsB: KK feedback filter

• Error at DFD output: edfd = b – x

• Error covariance matrix: ξdfd = E[edfd edfd

t]

• 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

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.

Optimal Soft Decision Device

• Minimimze MSE =

• Solution:

| tanhb E b y yi 2

E b bi

2

Performance with Perfect Channel Knowledge

Training Performance: Direct Filter Estimation

• Assumption: both users demodulate both pilots• Cost function =

where • Solution:

( ) ( )HT

r i b i t

i

T

11

( ) ( )RT

r i r i t

i

T

11

where T is the training length

F R H 1

b i b ii

T

( ) ( ) 2

1

( ) ( )b i F r it

Training Performance: Least Square Channel Estimation

• Minimize the objective function

• Minimizing objective function w.r.t. , we get

f r i H b ii

T0 2

1

( ) ( )

( ) ( ) ( ) ( )H b i b i b i r it t

i

Tt

i

T

1

1

1

H

Training Performance: Linear MMSE Receiver

Training Performance: Linear MMSE and DFD

Partial Knowledge of Pilots

• The pilot from the interfering BST may not be available.

Performance Comparison: Partial Knowledge of Pilots

Single pilot leads to performancewith full channel knowledge.

Here we need both pilots to achieveperformance with full channel knowledge.

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)