Receiver Performance for
Downlink OFDM with Training
Koushik Sil
ECE 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
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 antennas
N = # of channels
K = # of users
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
r21
h211
h221
r12
h112
h122
r22
=
h212
h222
.
.
r1N
r2N
Received covariance matrix: R = E{rrt} = HHt + 2I
.
.
b11
b21
b12
b22
.
.
b1N
b2N
+n
Single User Matched Filter
r11
r21
r12
r22
.
.
r1N
r2N
h111
h211
=
b11
h112
h212
b12
+n
.
.
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)
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: 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
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
2

MSE = E bi  b


• Solution:
bi  Eb| y  tanh 2 y
Performance with Perfect
Channel Knowledge
Training Performance:
Direct Filter Estimation
• Assumption: both users
demodulate both pilots
T
2

b
(
i
)

b
(
i
)
• Cost function = 
i 1
t

where b (i )  F r (i )
• Solution:
F  R 1 H
T
1
R   r (i )r (i ) t
T i 1
T
1
H   r (i )b(i ) t
T i 1
where T is the training length
Training Performance:
Least Square Channel Estimation
• Minimize the objective function
T
f
0


2

r (i )  Hb(i )
i 1
• Minimizing objective function
w.r.t. H , we get
1
 T
 T
t
t
t

H    b(i )b(i )    b(i )r (i ) 
 i 1
  i 1

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 performance
with full channel knowledge.
Here we need both pilots to achieve
performance 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)