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July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 1
doc.: IEEE 802.11-05/0790r1
Submission
A Novel Soft MIMO Detector for MIMO-OFDM (802.11n) Receivers
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Date: 2005-07-21Author
Name Company Address Phone Email
Behrouz Farhang-Boroujeny Univ of Utah Sal Lake City, UT 84112 +801-587-7959 [email protected]
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 2
doc.: IEEE 802.11-05/0790r1
Submission
Outline Introduction Channel model Soft Information: Log-likelihood ratio, LLR values
■ what is the problem?
Zero-forcing / MMSE / VBLAST detectors■ computation of LLR values
Our solution to LLR computation Simulation results
Conclusions
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 3
doc.: IEEE 802.11-05/0790r1
Submission
IntroductionWe answer the following question:
■ In a MIMO set-up how one can efficiently obtain soft information, e.g., log-likelihood ratio (LLR) values, of the data bits?
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 4
doc.: IEEE 802.11-05/0790r1
Submission
Introduction
We answer the following question:■ In a MIMO set-up how one can efficiently
obtain soft information, e.g., log-likelihood ratio (LLR) values, of the data bits?
The material presented here are protected by a patent application owned by the university of Utah.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 5
doc.: IEEE 802.11-05/0790r1
Submission
Channel ModelWe consider: A frequency selective channel. OFDM is used to convert the frequency selective channel to a
number of parallel flat fading channels. Accordingly, each subcarrier channel has the following model:
y = Hd+n
where
d is a vector of transmit symbols
y is a vector of received signal
H is the channel gain matrix
n is an additive noise vector.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 6
doc.: IEEE 802.11-05/0790r1
Submission
Receiver Structure
Channel Decoder
MIMO Detector
y
ˆ d
(soft)
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 7
doc.: IEEE 802.11-05/0790r1
Submission
Receiver Structure
Channel Decoder
MIMO Detector
y
ˆ d
(soft)
We address an implementation of this block
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 8
doc.: IEEE 802.11-05/0790r1
Submission
Receiver Structure
Channel Decoder
MIMO Detector
y
ˆ d
(soft)
Feedback from the output of the channel decoder to MIMO detector, allows near capacity performance.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 9
doc.: IEEE 802.11-05/0790r1
Submission
Soft Information: Log-likelihood ratio (LLR) values
Symbol vector d is obtained from a vector b=[b1 b2 … bN] of information bits through some mapping.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 10
doc.: IEEE 802.11-05/0790r1
Submission
Soft Information: Log-likelihood ratio (LLR) values
Symbol vector d is obtained from a vector b=[b1 b2 … bN] of information bits through some mapping.
We wish to calculate
where
is calculated in the same way.
k lnP(bk 1 | y)
P(bk 1 | y)ln
P(bk 1 | y,b k )b k
P(bk | y)
P(bk 1 | y,b k )b k
P(bk | y)
b k [b1 b2 bk 1 bk1 bN ],bk [b1 b2 bk 1 1 bk1 bN ]
P(bk 1 | y)
and bk [b1 b2 bk 1 1 bk1 bN ]
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 11
doc.: IEEE 802.11-05/0790r1
Submission
Soft Information: Log-likelihood ratio (LLR) values
Symbol vector d is obtained from a vector b=[b1 b2 … bN] of information bits through some mapping.
We wish to calculate
where
is calculated in the same way. Problem: the number of combinations that b-k takes is 2N-1!
k lnP(bk 1 | y)
P(bk 1 | y)ln
P(bk 1 | y,b k )b k
P(bk | y)
P(bk 1 | y,b k )b k
P(bk | y)
b k [b1 b2 bk 1 bk1 bN ],bk [b1 b2 bk 1 1 bk1 bN ]
P(bk 1 | y)
and bk [b1 b2 bk 1 1 bk1 bN ]
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 12
doc.: IEEE 802.11-05/0790r1
Submission
Soft Information: Log-likelihood ratio (LLR) values
Symbol vector d is obtained from a vector b=[b1 b2 … bN] of information bits through some mapping.
We wish to calculate
where
is calculated in the same way. Problem: the number of combinations that b-k takes is 2N-1!
k lnP(bk 1 | y)
P(bk 1 | y)ln
P(bk 1 | y,b k )b k
P(bk | y)
P(bk 1 | y,b k )b k
P(bk | y)
b k [b1 b2 bk 1 bk1 bN ],bk [b1 b2 bk 1 1 bk1 bN ]
P(bk 1 | y)
and bk [b1 b2 bk 1 1 bk1 bN ]
The key point here is that most of the terms in the numerator and denominator are insignificant.
Thus, a handful of the significant terms may be sufficient for accurate estimation of k.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 13
doc.: IEEE 802.11-05/0790r1
Submission
Log-likelihood ratio values:max-log algorithm
k lnmax
b k
P(bk 1 | y,b k )P(bk | y)
maxb k
P(bk 1 | y,b k )P(bk | y)
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 14
doc.: IEEE 802.11-05/0790r1
Submission
Log-likelihood ratio values:max-log algorithm
k lnmax
b k
P(bk 1 | y,b k )P(bk | y)
maxb k
P(bk 1 | y,b k )P(bk | y)
This incurs an insignificant loss (in the order of a a fraction of 1 dB) in performance.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 15
doc.: IEEE 802.11-05/0790r1
Submission
Zero-forcing / MMSE / VBLAST detectors
Zero-forcing detector: ■ Estimate of d = Q[(H*H)-1H*y]
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 16
doc.: IEEE 802.11-05/0790r1
Submission
Zero-forcing / MMSE / VBLAST detectors
Zero-forcing detector: ■ Estimate of d = Q[(H*H)-1H*y]
MMSE detector:■ Estimate of d = Q[(H*H+2I)-1H*y]
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 17
doc.: IEEE 802.11-05/0790r1
Submission
Zero-forcing / MMSE / VBLAST detectors
Zero-forcing detector: ■ Estimate of d = Q[(H*H)-1H*y]
MMSE detector:■ Estimate of d = Q[(H*H+2I)-1H*y]
VBLAST/Successive Interference Canceller (SIC) detector:■ Detects the strongest symbol first, subtract the detected
symbol, and continue with the successive detection and cancellation of the rest of the symbols.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 18
doc.: IEEE 802.11-05/0790r1
Submission
Zero-forcing / MMSE / VBLAST detectors: computation of LLR values
Starting with the detected d, for a chosen bit bk, it is identified that bk belongs to which element of d, say di.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 19
doc.: IEEE 802.11-05/0790r1
Submission
Zero-forcing / MMSE / VBLAST detectors: computation of LLR values
Starting with the detected d, for a chosen bit bk, it is identified that bk belongs to which element of d, say di.
All the elements of d, except di, are kept fixed. The symbol di is then given all possible values from the symbol constellation, and from all these choices, the maximum values of P(bk=+1|y,d-i) and P(bk=-1|y,d-i) are found and substitute in the max-log LLR formula
k lnmax
b k
P(bk 1 | y,b k )P(bk | y)
maxb k
P(bk 1 | y,b k )P(bk | y)
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 20
doc.: IEEE 802.11-05/0790r1
Submission
Our solution to LLR computation:Markov chain Monte Carlo (MCMC) simulation technique
y=Ad+n,
d d1
d2
d3
State d3 d2 d1
S0 -1 -1 -1
S1` -1 -1 +1
S2 -1 +1 -1
S3 -1 +1 +1
S4 +1 -1 -1
S5 +1 -1 +1
S6 +1 +1 -1
S7 +1 +1 +1
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 21
doc.: IEEE 802.11-05/0790r1
Submission
Our solution to LLR computation:Markov chain Monte Carlo (MCMC) simulation technique
y=Ad+n,
d d1
d2
d3
State d3 d2 d1
S0 -1 -1 -1
S1` -1 -1 +1
S2 -1 +1 -1
S3 -1 +1 +1
S4 +1 -1 -1
S5 +1 -1 +1
S6 +1 +1 -1
S7 +1 +1 +1
•This procedure gives us a set of selections of d that result in small distances |y-Ad(n)|.
•These may be viewed as important samples of d that correspond to significant terms in the LLR equation
or its max-log version.
k ln
P(bk 1 | y,b k )b k
P(bk | y)
P(bk 1 | y,b k )b k
P(bk | y)
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 22
doc.: IEEE 802.11-05/0790r1
Submission
Our solution to LLR computation:Markov chain Monte Carlo (MCMC) simulation technique
y=Ad+n,
d d1
d2
d3
State d3 d2 d1
S0 -1 -1 -1
S1` -1 -1 +1
S2 -1 +1 -1
S3 -1 +1 +1
S4 +1 -1 -1
S5 +1 -1 +1
S6 +1 +1 -1
S7 +1 +1 +1
•This procedure gives us a set of selections of d that result in small distances |y-Ad(n)|.
•These may be viewed as important samples of d that correspond to significant terms in the LLR equation
or its max-log version.
k ln
P(bk 1 | y,b k )b k
P(bk | y)
P(bk 1 | y,b k )b k
P(bk | y)
If implemented in some clever way, the number of samples that is required for estimation of each k is in the order of 10 to 30, even though the size of the state space can be in the order of billions.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 23
doc.: IEEE 802.11-05/0790r1
Submission
How Complex is MCMC? It turns out that MCMC can be implemented VERY
efficiently.
MCMC simulator for a MIMO channel with 4 transmit antenna and 16 QAM symbols has a complexity that is comparable or lower than that of a 16 bit-by-16 bit multiplier.
An implementation of this MCMC simulator on FPGA requires 600 slices.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 24
doc.: IEEE 802.11-05/0790r1
Submission
Simulation Results MIMO-OFDM
■ FFT size: 64■ Cyclic prefix length: 16■ Channel is estimated through pilot symbols transmitted at
the beginning of each frame■ Channel: convolutional code with polynomials [133,
171], R = 3/4
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 25
doc.: IEEE 802.11-05/0790r1
Submission
Simulation Results
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 26
doc.: IEEE 802.11-05/0790r1
Submission
Simulation Results
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 27
doc.: IEEE 802.11-05/0790r1
Submission
Simulation Results
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 28
doc.: IEEE 802.11-05/0790r1
Submission
Simulation Results
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 29
doc.: IEEE 802.11-05/0790r1
Submission
Simulation Results
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 30
doc.: IEEE 802.11-05/0790r1
Submission
Simulation Results
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 31
doc.: IEEE 802.11-05/0790r1
Submission
Wireless Communications Lab at ECE Dept of Univ of Utah
We are actively involved in development of MIMO detection techniques
In collaboration with L-3 Communication West in Salt Lake City, we have developed a MIMO testbed with 4 transmit and 4 receive antennae
A new version of our testbed that facilitates our research on MIMO detectors is under development.
We are open and seeking collaboration with industry. In particular, we are looking forward to any collaboration with IEEE 802.11n consortia.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 32
doc.: IEEE 802.11-05/0790r1
Submission
Conclusions The problem of soft estimation of information bits in a MIMO setup was addressed.
Using Markov chain Monte Carlo simulation technique, in the Wireless Communications lab of UofU, we have developed a very efficient detector for this task.
The proposed method could be used along with any conventional detector (ZF/MMSE/VBLAST-SIC) to improve its performance.
Gains in the order of 6 dB or more have been observed.
The proposed method is an excellent choice in systems that employ advanced channel coding, i.e., turbo and LDPC codes.
The proposed technology is extremely hardware friendly. The complexity of the MCMC simulator is not greater than a 16 bit-by-16 bit multiplier. Therefore, in a MIMO-OFDM where many subcarrier channels have to be examined in parallel, a number of MCMC simulators can be
run in parallel at a minimum cost.
July 2005
Behrouz Farhang-Boroujeny, Univ of Utah
Slide 33
doc.: IEEE 802.11-05/0790r1
Submission
Publications[1] B. Farhang-Boroujeny, H. Zhu, and Z. Shi, “Markov chain Monte Carlo algorithms for CDMA and MIMO
communication systems,” IEEE Trans. Signal Processing, Accepted for publication.
[2] H. Zhu, B. Farhang-Boroujeny, and R-R. Chen, “On performance of sphere decoding and Markov chain Monte Carlo detection methods,” IEEE Signal Processing Letters, Accepted for publication.
[3] R-R. Chen, B. Farhang-Boroujeny and A. Ashikhmin, “Capacity-approaching LDPC codes based on Markov chain Monte Carlo MIMO detection,” Submitted to IEEE Communications Letters, March 2005.
[4] H. Zhu, Z. Shi, and B. Farhang-Boroujeny, “MIMO detection using Markov chain Monte Carlo techniques for near-capacity performance,” Int. Conf. Acoustics, Speech and Signal Processing, ICASSP’05, Philadelphia, March 18 – 23, 2005.
[5] Z. Shi, Haidong Zhu, and B. Farhang-Boroujeny, Markov chain Monte Carlo techniques in iterative detectors: a novel approach based on Monte Carlo integration, IEEE Global Telecommunications Conference, GLOBECOM'04., vol. 2 , 29 Nov.-3 Dec., 2004, pp. 325 – 329.
[6] H. Zhu, B. Farhang-Boroujeny, and R-R. Chen, “On performance of sphere decoding and Markov chain Monte Carlo detection methods,” SPAWC 2005, the sixth IEEE International Workshop on Signal Processing Advances for Wireless Communications, June 5-8, 2005, Invited.
[7] R-R. Chen, B. Farhang-Boroujeny and A. Ashikhmin, “Capacity-approaching LDPC codes based on Markov chain Monte Carlo MIMO detection,” SPAWC 2005, the sixth IEEE International Workshop on Signal Processing Advances for Wireless Communications, June 5-8, 2005.