the case for optimum detection algorithms in mimo wireless ... · the case for optimum detection...
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The Case for Optimum Detection Algorithms inMIMO Wireless Systems
Helmut Bolcskei
joint work with A. Burg, C. Studer, and M. Borgmann
ETH Zurich
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Data rates in wireless double every 18 months
1990 1995 2000 2005 2010 20151 kbps
1 Mbps
1 Gbps
GSM
802.11802.11b 802.11g
802.11n
2-stream
UMTS HSDPA-1HSDPA-2
Edge
3GPP LTE
802.11n
4-stream
year
thro
ughp
ut
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Need for higher throughput cannot be met bysimply allocating more bandwidth
40 MHz
20 MHz
Interference
Achieving higher throughput requires higher spectral efficiency
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Spatial multiplexing: Transmit multiple data streamssimultaneously and in the same frequency band
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MIMO gains carry through to system level
Advantages of MIMO
� Larger range
� Better quality of service
� Higher peak throughput
� Higher system capacity
10 20 30 40 50 60 700
100
200
300
400
500
600
range
thro
ughp
ut[M
bps]
4stre
am
s2stream
s
1 stream
2x
2x
IEEE 802.11n PHY, 40 MHz bandwidth,TGn-C channel
MIMO is part of IEEE 802.11n, IEEE 802.16e, and 3GPP LTE
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The “Digital Home”: A challenging application forMIMO wireless systems
Ensure a wire-like experience throughout the entire home
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Meeting user expectations requires 4 spatial streams
� Requirement: 4 HDTV video streams @ 25 Mbps each
� Aggregate throughput requirement: 100 Mbps at a range of 30m
0 50 100 150 200 250 300 350 400
10203040506070
application layer throughput [Mbps] / 60% MAC efficiency
rang
e [m
]
aggregatethroughputrequirement
802.11g(SISO)
802.11n2-stream
802.11n4-stream
+
� Current IEEE 802.11n solutions support only 2 spatial streams
� Products with three spatial streams have just been announced
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Maximum likelihood (ML) MIMO detection
Dem
odula
tion a
nd s
epara
tion
Modula
tion a
nd m
appin
g
y = Hs + n
Maximum likelihood (ML) MIMO detection
s = arg mins∈OMT
||y −Hs||2
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ML detection through exhaustive search
Exhaustive search: Enumerate all possible candidate vectors
� Number of candidate vectors grows exponentially in the number ofantennas
� A 4×4 system with 64-QAM modulationrequires consideration of 16’777’216candidates
4x4 IEEE 802.11nbaseband ASIC
[ETH Zurich, 2008]
5mm
5mm
1.4 mm1.4 mm2x2 ML
detector64-QAM
3x3 MLdetector64-QAM
4x4 MLdetector64-QAM
91mm
91m
m
11.3mm
11.3m
m
20M GE
1'300M GE1.7M GE
0.3M GE
Exhaustive search is not economic for more than two spatial streams
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Soft-output (APP) MIMO detection
MIMO
channel
MIMO
detector
y = Hs + n
MIMO detector computes log-likelihood ratios (LLR) for each bit
L (xj,b) = log(P (xj,b = 1|y)P (xj,b = 0|y)
)Max-log approximation for LLRs
L (xj,b) = mins∈X (0)
j,b
||y −Hs||2 − mins∈X (1)
j,b
||y −Hs||2
X (0)j,b ,X
(1)j,b ... sets of vector symbols for which xj,b = 0, 1
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Linear equalization decomposes the MIMO channelinto parallel SISO channels
linear equalizersoft-metric
detector
soft-metric
LLRs are computedfor each stream
separately
� Compared to the remaining baseband processing, complexity ofequalization is very low even for a large number of streams
� Complexity of LLR computation is negligible
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MMSE is ill-suited for highly integrated devices
� Mini-PCI and half-mini PCI is becoming the de-facto standard
� Spacing of printed antennas can easily be below λ/4� Reduced antenna spacing leads to (severe) spatial correlation
Antenna 1
Antenna 2
18mm
54m
m
-75 -70 -65received power [dBm]
fram
e erro
r rat
e
Soft-outputMMSE
Close-to-optimum APP
10-1
100
10-2
IEEE 802.11n, MCS27, 40 MHz, TGn-D (MT = MR = 4, 16-QAM, rate 1/2)
MMSE detection suffers significantly from spatial correlation
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MMSE fails to provide robustness against varyingpropagation conditions
location
signa
l pow
er (d
B)
10 15 20 25 30 35
100
SNR [dB]
BE
R
10-1
10-2
10-3
10-4
10-5
10-6
4x4MMSE
4x4 Maximumlikelihood
4x5MMSE
MMSE diversity order
ML diversityorder
Diversity: Resilience against bad channels ⇒ more reliable operation
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The “business case” for high-end MIMO receivers
10 20 30 40 50 60050
100150200250300350400
range [m]
thro
ughp
ut[M
bps]
30.4m 35.7m 41.2m
4x4
MMSE
4x5
MMSE 4x4 APP
4x
4M
MS
E
4x
5M
MS
E4
x4
AP
P
Additional receive antennas canpartially compensate forsub-optimal receiver algorithms
� Each additional antenna costs 0.7 USD–1.0 USD� Overall manufacturing chipset cost is ≈ 9 USD� Space limitations can become critical (antenna spacing)
Boosting MMSE performance by using additional antennas isexpensive and not always possible
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Impact of RF non-idealities
RF limitations: SNR is limited to approximately 35 dB–40 dB
-90 -80 -70 -60 -50 -40 -30 -20 -1005
101520253035404550
received power [dBm]
mea
n SN
R [dB
]
0
SNR limited by poorRF noise figure
-65 -60 -55 -50average received power [dBm]
Close-to-optimum APP
10-1
100
10-2fra
me e
rror r
ate
Soft-outputMMSE
IEEE 802.11n, MCS 31 (600 Mbps), MT = MR = 4, Greenfield, 20MHz bandwidth, 1000B packets
In IEEE 802.11n, APP detection is needed for operation in the highestrate modes
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Performance of MMSE receiver is sensitive tointerference
Consider a 4× 5 MIMO system interfered by a single-stream system
� Information-theoretic arguments: Interference “knocks out” onereceive antenna
� Reduction to an effective 4× 4 system
MMSE detector� Diversity is lost and robustness is reduced
Optimum APP detector
� Receiver performs well even with an effectively symmetric antennaconfiguration
� Graceful performance degradation
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Sphere decoding: Exploiting the structure of thedetection problem
Tra
nsm
itte
r
Receiv
er
MIMO
Channel
s = arg mins∈OMT
||y −Hs||2
The MIMO ML-detection problem corresponds to finding the closestpoint in a skewed, finite lattice
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A brief history of the sphere decoding algorithm
� 1981: M. Pohst describes an algorithm to efficiently identify theclosest point in an infinite lattice
� 1993: E. Viterbo and E. Biglieri apply the Pohst algorithm to latticedecoding and introduce the sphere constraint
� 1999: E. Viterbo and J. Boutros employ sphere decoding for latticedecoding in fading channels
� 2000: M. O. Damen et al. describe the application of spheredecoding to space-time codes
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A brief history of the sphere decoding algorithmcont’d
� 2003: B. Hochwald and S. ten Brink propose the first soft-outputsphere decoder
� 2005: A. Burg et al. provide the first VLSI implementation ofhard-output sphere decoding
� 2008: C. Studer et al. develop single tree search soft-output spheredecoding and provide a corresponding VLSI implementation
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Sphere decoding reduces to a tree-search problem
1 Translate the problem into a tree search (triangularization)2 Nodes are associated with Partial Euclidean Distances (PEDs) d(s)3 Update rule: di(s(i)) = di+1(s(i)) + |ei|2, i = MT , . . . , 1 (tree level)4 ML detection corresponds to finding the leaf with the smallest PED
Partial Euclidean
distance
A branch-and-bound strategy realized through a sphere constraint leadsto efficient tree pruning
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Computing the LLRs by applying the spheredecoding algorithm
L (xj,b) = mins∈X (0)
j,b
||y −Hs||2︸ ︷︷ ︸λML
− mins∈X (1)
j,b
||y −Hs||2︸ ︷︷ ︸λML
j,b
Repeated Tree Search (RTS) [Wang and Giannakis, 2004]
1 Use the sphere decoding algorithm to find λML
2 Restart the search to identify the QMT remaining minima and
constrain the search to X (xMLj,b ) by operating on pre-pruned trees
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The single tree search (STS) philosophy [Studer etal., 2006]
Repeated tree search is highly inefficient
� For example, a 4-stream system employing 64-QAM modulationrequires 24+1 sphere decoder runs
� A given node may be visited more than once in consecutive runs
STS algorithm: Ensure that each node is visited at most once
� Search for the ML solution and all counterhypotheses concurrently
� Maintain a list containing
the ML hypothesis xML and its metric λML
the metrics of the counterhypotheses λMLj,b
� Search a subtree only if the result can lead to an update of eitherλML or of at least one of the metrics λML
j,b
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VLSI implementation of the STS algorithm [Studeret al., 2008]
Hard-output STS
Technology 0.25 µm, 1P/5M
System 4×4, 16-QAM
Decoding norm `∞ `2
Clock freq. 87 MHz 71 MHz
Area 36 kGE 57 kGE
MHz/kGE 2.41 1.25
Hardware complexity of STS is only 30% of that of RTS based onhard-output sphere decoding
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LLR clipping reduces complexity and providesscalability
In practice, wordwidth of LLRs must be constrained
LLR clipping
LLR clipping can be built into the STS algorithm ⇒ additional constraintfor pruning the tree
LLR clipping allows to realize aperformance/complexity tradeoff atrun-time
16 16.5 17 17.5 18 18.5 190
50100150
200250300350
400450
0.10.2
0.4
24
816
32
64
aver
age n
umbe
r of v
isite
d nod
es
required SNR [dB] for 1% FER
STS
List sphere decoder[Hochwald and ten Brink, 2005]
0.05 0.025
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Early termination and scheduling
Sphere decoding has variable detection effort
Achieving fixed throughput under latency constraints
� A scheduler with FIFO distributes runtime across symbols
� Latency constraints: Need to constrain the decoding effort throughearly termination
STS
STSScheduler Collector
terminate terminated early
FIFOterminated early
early termination
early termination+ scheduling
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Application of STS to IEEE 802.11n
� Data rates range from 6 Mbps to 600 Mbps
MMSE� MMSE is set to operate at a certain highest rate mode
� No performance improvement possible for lower-rate modes
STS: Adjust the decoding effort at runtime
� Use LLR clipping to reduce complexity in the highest rate modes ⇒graceful performance degradation, but still better than MMSE
� LLR clipping adjusts decoding effort to achieve close-to-optimumperformance for lower-rate modes
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Application of STS to IEEE 802.11n
Instantiation of 10 STS units� Meet throughput and latency requirements for 40 MHz bandwidth
� Enable 600 Mbps operation with real-world RF
4x4 IEEE 802.11nbaseband ASIC
[ETH Zurich, 2008]
5mm
5mm
1.7M GE
4x4 STSdetector0.6M GE
4x4 MMSEdetector0.05M GE
2.3M GE(estimated)
Commercially available 2-stream solutions require roughly 2M GEs
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Headaches
STS exploits (finite-alphabet) structure of transmitted vectors
� RF non-idealities limit transmit SNR to 32 dB. Transmit noiseappears spatially colored at the receiver
� Interference appears as spatially colored noise
� Phase-noise and residual frequency offset distort the discretelocations of the constellation points
MMSE� Linear detection suffers from fixed-point effects
� MMSE detection requires accurate noise estimation
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Iterative detection and decoding
Iterate between MIMO detector and FEC decoder
MIMOdetector deinterleaverLLRs
FECdeocoder
(BCJR,LDPC)
LLRsinterleaver
vectorsymbols
� Strong channel code: More iterations can compensate forsuboptimal MIMO detector
In practice, the code is given by the standard and code rates can beclose-to one for the highest (data) rate modes
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Tradeoff between detector complexity and numberof iterations
Guaranteed throughput requirement
� Need multiple instantiations of MIMO detectors and FEC decoders
� Area scales linearly with the number of iterations
Maximum latency constraints
� Increase throughput of the MIMO detector and the FEC decoder
� Additional area increase due to latency constraints
� Maximum throughput of the sequential FEC decoder is limited
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Tradeoff between detector complexity and numberof iterations cont’d
Additional hardware overhead� Iterations require additional storage for baseband samples
� For strong codes, hardware complexity for FEC decoding is high
� Complexity of soft-in soft-out MIMO and FEC decoders is higherthan for non-iterative schemes
� Iterative detection and decoding leads to significant increase inhardware complexity compared to one-shot operation
� If iterations are needed, the number of iterations must be kept low
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High-performance MIMO detector is key forefficient implementation of iterative receiver
STS I=1
MM
SEI=2
STS
I=2
MM
SEI=
410 11 12 13 14 15 16 17 18 2019
SNR [dB]
fram
e erro
r rat
e 10-1
100
10-2
10-3
MM
SE I=1
For the same performance, MMSE detection requires more iterationsthan soft-in soft-out STS sphere decoding
32