Transcript Robust Optimal Cross Layer Designs for TDD

Robust Optimal Cross Layer Designs for TDDOFDMA Systems with Imperfect CSIT and
Unknown Interference
— State-Space Approach based on 1-bit ACK/NAK Feedbacks
Wang Rui, Vincent K. N. Lau
Department of EEE, The Hong Kong University of Science &
Technology
-1-
HKUST
Outline
Slow Fading OFDMA System Model
Average System Goodput &Problem
Formulation
Cross-layer Scheduler Design with ARQ
Feedback
Simulation Results and Conclusions
-2-
HKUST
System Model
er
erf
Int
• We Consider the downlink transmission of
a TDD-OFDMA system with slow fading
channel and Gaussian interference.
• The channel is quasi-static within a
scheduling slot which consists of N packet
bursts.
• The channel model is given by the
following equation, where the k, m, n are
the indices of user, subcarrier and packet
bursts respectively.
ce
en
User 1
BS
User 2
In
te
rfe
r
en
c
...
e
User 3
Yk ,m,n  hk ,m X m,n  Zk ,m,n  I k ,m,n
Scheduling Slot n
1
Received Symbol
Transmitted Symbol
2
3
4
...
Scheduling Slot n+2
Scheduling Slot n+1
N
1
2
3
4
...
N
1
2
3
4
...
N
Interference
Noise
-3-
HKUST
CSIT Error Model
• The CSIT estimation is done (at the base station) at the very beginning
of each scheduling slot only based on dedicated uplink pilots from the
mobiles.
• The channel state information at the transmitter (CSIT) is imperfect.
– Due to CSIT estimation noise from uplink pilots.
– Due to Outdatedness of CSIT estimation (duplexing delay).
– Although the CSIT is imperfect, it still can be used to improve the system
performance.
• A general model of CSIT error is given below:
hkb,m  hk ,m  k ,m
Estimated CSIT
CSIT Error
Actual CSI
-4-
HKUST
Packet Error Model (1)
•
In slow fading channels, there are two reasons of packet error
–
–
Finite block length of channel coding [channel noise effect]
Transmitted data rate exceeding the instantaneous mutual information of the channel [channel outage]
•
By applying strong channel coding (e.g. LDPC) with reasonable block length (e.g. 2k byte), it can
be shown that Shannon’s limit can be achieved to within 0.05dB for a target FER of 10^{-2}.  the
effect of channel noise can be ignored with strong coding.
•
Yet, the second factor (channel outage) is systematic and will be the major contributor of packet
error (esp when strong coding is used). Hence, we assume Packet Error Rate = Pr [r > mutual
information].
•
In most existing cross layer design [Lau:06,Wong:99], perfect knowledge of CSIT is assumed.
System ergodic capacity is used as optimization objective and the potential penalty of packet errors
is completely ignored in cross layer design. This is reasonable because packet error can be ignored
through strong channel coding and rate adaptation.
•
However, it is shown [Lau:06b] that “naïve cross layer designs” (designed for perfect CSIT) all
have very poor performance when we have imperfect CSIT. The key contributions to the
performance penalty is packet errors.
•
Hence, when we have imperfect CSIT, the issue of potential packet errors cannot be ignored and
must be taken into the cross layer design.
-5-
HKUST
Packet Error Model (2)
•
The instantaneous mutual information of user k at the n-th subcarrier is given by:

| hk ,m ,n |2 

Ck ,m ,n  log2 1  pk ,m ,n 2
2 
 z  I 

–
–
•
With imperfect CSIT, the BS does not know the exact mutual information.
It’s possible that the scheduled data rate is larger than the mutual information, which leads to channel outage.
Hence, when strong coding (LDPC) is used, the packet error probability (PER) is given by:


| hk ,m,n |2  b 
|h 
PER(h )  Prrk ,m,n  log2 1  pk ,m,n 2
2 
 z   I  


b
•
To account for penalty of packet errors, we shall consider system goodput (b/s/Hz successfully
delivered to the mobiles) as our optimization objective.
•
In [Palomar:06, Lau:06c], the authors proposed a cross layer design that optimize the system
goodput (rather than ergodic capacity) and the cross layer design achieves very good performance
even at high CSIT errors.
–
–
–
Yet, the design requires knowledge of the CSIT error statistics (which is sometimes difficult to obtain and
time varying as well).
In this paper, we shall extend the work to consider a robust cross layer design which account for potential
packet errors in the cross layer but without requiring the knowledge of CSIT error variance
Utilizing the ACK/NAK feedbacks, the cross layer design is modeled as a Closed-Loop State Space
Control Problem
-6-
HKUST
Cross Layer System Model (1)
•
•
There are ACK/NAK feedbacks after each packet transmission.
MAC layer is responsible to select the appropriate user on each subcarrier in
each packet burst and schedule the corresponding data rate and transmit power
according to the channel estimation and the ACK/NAK feedback.
-7-
HKUST
Outline
Slow Fading OFDMA System Model
Average System Goodput &Problem
Formulation
Cross-layer Scheduler Design with ARQ
Feedback
Simulation Results and Conclusions
-8-
HKUST
Problem Formulation --- Goodput
• Due to the potential packet outage, we use the goodput, which measures
bit/sec/Hz successfully delivered to the receiver, to measure the system
performance.
• The instantaneous goodput of user k in the m-th subcarrier and n-th
packet burst is

r
 I [C
r ]
k ,m,n
k , m, n
k , m, n
k ,m,n
• The average system goodput (Optimization objective) is
I[] is 1 when the event
is true and 0 otherwise.
N M

N M

U  A, P, R      Am,n ,m,n    hb  h   Am,n ,m,n | h b     hb G  h b 
 n1 m1

 n1 m1

• Given the CSIT, the conditional average goodput is
G h
b




|
h
  h  Am,n ,m,n 
N
b
Am,n denotes the
selected user
M
n 1 m 1
-9-
HKUST
Problem Formulation --- Policies
• The average system goodput U is a function of the user selection
policy A, power allocation policy P and rate allocation policy R.
• User selection policy A: determine the active user for each
subcarrier and each packet burst according to the CSIT and
ACK/NAK feedbacks
Am,n  hb , feedbacksof thepreviouspackets
• Power allocation policy P: determine the transmit power for active
users according to the CSIT and ACK/NAK feedbacks.
p Am ,n ,m ,n    hb ,feedbacks of the previous packets 
• Rate allocation policy R: determine the transmit data rate for active
users according to the CSIT and ACK/NAK feedbacks.
rAm ,n ,m,n  R  hb ,feedbacks of the previous packets 
- 10 -
HKUST
Problem Formulation --- States
• Define the system states to be the combination of
CSIT and the feedbacks.
• The state of user k in the m-th subcarrier before the
n-th packet transmission is give by:
sk ,m,n  {hkb,m ,{ f k ,m,1,..., f k ,m,n1}}
The ACK/NAK feedback of
the (n-1)-th packet
• The states are updated after each packet burst.
• The selected users, transmit power and data rate are
completely determined by the system states Sn:
Sn  {sk ,m,n | k , m}
- 11 -
HKUST
Problem Formulation --- Objective
• The optimal user selection policy A*, the optimal
power allocation policy P* as well as the optimal rate
allocation policy R* are given by:
 A , P , R   arg max U  A, P, R 
*
*
*
A, P , R
– subject to the following constraint:
• Total transmit power constraint:
p
k , m, n
 P0
k , m, n
• The conditional packet error probability of all users is less than a
target ε
- 12 -
HKUST
Outline
Slow Fading OFDMA System Model
Average System Goodput &Problem
Formulation
Cross-layer Scheduler Design with ARQ
Feedback
Simulation Results and Conclusions
- 13 -
HKUST
Solutions --- Recursive Relationship
• Let Fn be the conditional average goodput from the n-th
packet burst to the N-th packet burst. It can be expressed
recursively. F (P, h , S )  g ( p , h , S )  Pr(S | S , h )F (P  p , h , S )

b
n
b
n
n
n
n1
n
b
n
n1
b
n
n
Sn1
Conditional average goodput of the n-th packet burst
Total Goodput (nN) = goodput (n) + f(Total Goodput (n+1 N)
• F1 equals to the conditional average goodput G.
• The optimization on F1 can be solved by Markov Decision
Process in two steps.
– Backward recursive: derive the close form of F and the user
selection, power and rate allocation in terms of the arbitrary system
state.
– Online strategy: according to the current system state and the result
of backward recursion, determine the current user selection, power
and rate allocation.
- 14 -
HKUST
Solutions
• The optimal user selection policy, rate allocation policy and
power allocation policy is given below:
N
Am , n  arg max k ,m ,i
k
i n
rk , m , n  log2 (1  pk , m , n k , m , n )
pk , m , n
 1
1



 n  k ,m,n





for k  Am , n
• θ is the scaling factor to guarantee the target outage
probability.
• λn is the Lagrange multiplier to guarantee the total power of
the n-th packet burst to be pn:
N M
M
P
1
1
pn 



 A ,m,i 
N  n  1 N  n  1 i n m1 m ,i
m 1  k , m, n
- 15 -
HKUST
Solutions
• For sufficiently large number of feedbacks N, we
can prove that
lim Am,n  max pk ,m,n
n
k
| hk ,m,n |2
 z2   I2
• Hence, the system will perform as if the CSIT were
perfect in steady state  Zero Steady State Error.
• The ACK/NAK feedbacks can compensate the
inaccuracy of the CSIT.
- 16 -
HKUST
Outline
Slow Fading OFDMA System Model
Average System Goodput &Problem
Formulation
Cross-layer Scheduler Design with ARQ
Feedback
Simulation Results and Conclusions
- 17 -
HKUST
Simulation Results
 2H  0.1 M  4 I  {0.1,1,2}
- 18 -
HKUST
Simulation Results
 2H  0.1 M  4 I  {1,2}
- 19 -
HKUST
Conclusions
• The performance of the proposed closedloop cross layer design is very robust with
respect to imperfect CSIT, unknown
interference as well as channel variation due
to Doppler.
- 20 -
HKUST
Reference
•
•
•
•
•
[Lau:06] V. K. N. Lau, “Coverage-optimized downlink scheduling design for
wireless systems with multiple antennas”, IEEE Trans. On Wireless
Communication , Oct. 2006.
[Wong:99] C. Y. Wong, R. S. Cheng, K. B. Lataief, R. D. Murch, “Multiuser
OFDM with adaptive subcarrier, bit, and power allocation”, IEEE J. Sel. Areas
Commun. , Oct. 1999.
[Lau:06b] V. K. N. Lau, M. L. Jiang, Y. J. Liu, “Cross layer design of uplink
multi-antenna wireless systems with outdated CSI”, IEEE Trans. On Wireless
Communication , June 2006.
[Lau:06C] V. K. N. Lau, M. L. Jiang, “Performance analysis of multiuser
downlink space-time scheduling for TDD systems with imperfect CSIT”,
IEEE Trans. On Vehicular Technology , Jan. 2006.
[Palomar:06] A. Pascual-Iserte, D. P. Palomar, A. I. Perez-Neira, M. A.
Lagunas, “A robust maximin approach for MIMO communications with
imperfect channel state information based on convex optimization”, IEEE
Trans. On Signal Processing, Jan. 2006.
- 21 -
HKUST
Thank You !
- 22 -
HKUST