receiver performance for downlink ofdm with training koushik sil ece 463: adaptive filter project...
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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)