Survey on MIMO-related Technologywrawn.ru.is/Janson.pdf · Survey on MIMO-related Technology In The Fourth Workshop on Realistic models for Algorithms in Wireless Networks (WRAWN),

Survey on MIMO-related TechnologyIn The Fourth Workshop on Realistic models for Algorithms in Wireless Networks(WRAWN), Montreal, Canada, 21 July 2013

Thomas Janson, Christian SchindelhauerChair of Computer Networks and Telematics, Albert-Ludwigs-Universität FreiburgWRAWN, Montreal, July 21, 2013

Problem Setting

MIMO Technology in IEEEstandards 802.11n, ac

device

antenna antenna

device

MultipleInput Output

Multiple

3 parallel

channels

MIMO channel

Goal: higher bandwidth, largertransmission range

in research extended to ad hocnetworks

source target


Multiple

Parallel Channels

Ad hoc network

Network layer

Physical layerData link layer

Host layer

Media layer

OSI

model

WRAWN T. Janson, C. Schindelhauer – Survey on MIMO-related Technology 2 / 24

Outline

1 Physical model for MIMO communication

2 Influence of Obstacles on MIMO performance

3 Routing algorithms using MIMO-technology


Communication Channel

power decay of dipole antenna indistance d

free space 1/d2

for obstacles, walls 1/dα withpath-loss exponent α ∈ [2,6)

reception of signal in presence ofnoise

Additive White Gaussian Noise(AWGN)

N ∼ C N(0,σ2

)

reception quality depends onsignal-to-noise ratio

SNR=SignalNoise

Received Power [dB]

distance d

AWGN

Signal / 1

d2

receiver antenna

distance d

0 20 40 60 80 100

5¥10-40.001

0.0050.010

0.0500.100

sender antenna


Data Modulation

fixed carrier frequency f ,e.g. 2.4 GHz, 5 GHz

amplitude a & phase φ modulation (QAM)a ·ejφ = a · (cosφ + j sinφ)

2 · ej2⇡ft 1 · ej2⇡(ft+⇡/2) 3 · ej(2⇡ft+⇡)

period T = 1/f

time t

amplitude phasetimefrequency

Codeword 3Codeword 2Codeword 1

signal strength


Capacity of Communication Channel

codeword is point in complexspace with error range

number of detectable codewordsproportional to SNR

Shannon theorem shows channelcapacity

high SNR:C = W · log2 (1+SNR)low SNR:C ≈W ·SNR

<

=phase

16 Quadrature Amplitude Modulation

code word

noise

(16-QAM)

amplitude


Directional Radio with MIMO Beamforming

signal propagates with speed of light c⇒ causes phase shift between signalsSuperposition of electrical fields ofantennas pi at point p

E (p) =X

i

ai · ej2⇡

f

c|pi � p| + �i

|pi � p|path loss

phase shift

amplitude

set up beam direction with phases φi

t t

Amplification Attenuation

signal 1 signal 2

-4

-2

0

2

4

-4

-2

0

2

4

same phase

strong signal

weak signal

Two antennas

in the plane


Beamforming Characterizationby Janson, Schindelhauer (2012)

What we analyze:m antennas randomly positionedon a disk

h(α) signal strength for angle α

Characterization:main beam towards targetside beams with strong signalAverage white Gaussian noisewith strongly attenuated signal

x

y

target direction

for beamforming

antenna

d



What we analyze:m antennas randomly positionedon a diskh(α) signal strength for angle α


x

y

array h (α)α = π

α = π/2

α = 3π/2

α = 0




Characterization:main beam towards target

side beams with strong signalAverage white Gaussian noisewith strongly attenuated signal

x

y

array h (α)

κ

−κ

main beam




Characterization:main beam towards targetside beams with strong signal

Average white Gaussian noisewith strongly attenuated signal

x

y

array h (α)

κ

−γ

−κ

main beam

side beams

side beams

γ





�Var[h] = 1/

√m

x

y

array h (α)

κ

−γ

−κ

main beam

side beams

E[h] = 1/√

m

side beams

γ

noiseGaussianwhite

Average


Cases of Multiple Antennas

signal-to-noise ratio(SNR) limits rangeMISO: senderbeamformingSIMO: receiverbeamformingMIMO:

sender+receiverbeamformingmultiplexingm parallel channelsfor m sender and mreceiver antennas

Multiple Input Single OutputMISO

Single Input Single OutputSISO

sender receiver

transmissionrange

1 channel

sender

receiver

1 channel

array

Single Input Multiple OutputSIMO

sender

receiver

1 channel

array

Multiple Input Multiple OutputMIMO

sender receiverarray

m channel

array


Beamforming achieves Power Gain

Communication with n sender and m receiver

transmit power P = ∑i Pi = const.

Signal power gain

SISO: SINR1,1 =P

N+I

MISO: SINRn,1 = n ·SINR1,1

SIMO: SINR1,m = m ·SINR1,1

MIMO: SINRn,m ≤ n ·m ·SINR1,1(equality for rank(H) = 1)

Channel Capacity: O (log(1+SINR))

low SINR: C ≈W ·SINR⇒ large gain

n m1 channel

n1 channel

1

m1 channel

1

1 channel1 1


Spatial Multiplexing

n parallel channels for n sender and n receiver antennas

device

antenna antenna

device


Multiple

3 parallel

channels

MIMO channel

for high SINR channel capacity grows with O (n)


Transmission Model for MIMOCommunication

Transmission:0@

y1

. . .ym

1A =

0@

h11 h1m

. . .hm1 hmm

1A ·

0@

x1

. . .xm

1A +

0@

w1

. . .wm

1A

Multiple

Output Input

Multiple Noise

at receiverchannel matrix H

hik = transmission from input xi tooutput yk with path-loss, phase shift,echoes, reverb

for line-of-sight:

aik · ej2⇡f |ui�vk|/c

|ui � vk|path-loss

for distance

phase shiftattenuation

hik =receiver

sender

noise w1

w2

w3

h21 · x1

h22 · x2

h23 · x3

Signal superposition of receiver 2

y2 = h21 · x1 + h22 · x2 + h23 · x3 + w2


Receiving Multiple Channels

Transmission:y = H · x + w

Multiple

Output Input

Multiple Noise

Inverse H−1 for receiving

x = H�1 · y � H�1 w

Received

OutputInputReceived Noise Error

receiversender

noise w1

w2

w3

h21 · x1

h22 · x2

h23 · x3

Signal superposition of receiver 2

y2 = h21 · x1 + h22 · x2 + h23 · x3 + w2


Multiplexing Architecture

independent channels cancancel out and not be received

operation at sender andreceiver that transmission onlyaffects signal attenuation

with the known channel H

Singular Value Decomposition0B@

�1 0 0

0. . . 0

0 0 �n

1CAH = U · · V⇤

channel

matrix

unitary

rotationmatrix

unitary

rotationmatrix

diagonal

matrixwith singualar values �i

0B@

�1 0 0

0. . . 0

0 0 �n

1CAU · · V⇤U⇤ · · V

= I= Ichannel H

· xy =preprocessingpostprocessing


Multiplexing and Line-of-Sight

alle receivers get same signal yibut with different delay aiy1

a1

=y2

a2

= · · · =ym

am

channel matrix H has rank 1only one eigenvalue > 0and column vectors linear dependent0@

y1

. . .ym

1A ⇡

0@

a1h1 a1h2 . . . a1hm

. . .amh1 amh2 . . . amhm

1A ·

0@

x1

. . .xm

1A +

0@

w1

. . .xm

1A

Multiple

Output Input

Multiple Noise

at receiver

channel matrix H

with rank 1

no multiplexing possibleonly one channel,improve with beamforming

receiver

sender

line-of-sight

signal

far apart


Multipath Channel

individual multipaths enablespatial multiplexing

additional paths produced byreflections at obstacles

each obstacle has individualangle to sender and receiver

phases of multiple antennasare shifted for each angle

discrete number of bins fortransmitter/receiver angle isresolvable (table)

non-empty bins improvespatial multiplexing

310 MIMO I: spatial multiplexing and channel modeling

of as a (time-)resolvable path, consisting of an aggregation of individualphysical paths. The bandwidth of the system dictates how finely or coarselythe physical paths are grouped into resolvable paths. From the point of viewof communication, it is the behavior of the resolvable paths that matters,not that of the individual paths. Modeling the taps directly rather than theindividual paths has the additional advantage that the aggregation makesstatistical modeling more reliable.Using the analogy between the finite time-resolution of a band-limited

system and the finite angular-resolution of an array-size-limited system, wecan follow the approach of Section 2.2.3 in modeling MIMO channels. Thetransmit and receive antenna array lengths Lt and Lr dictate the degree ofresolvability in the angular domain: paths whose transmit directional cosinesdiffer by less than 1/Lt and receive directional cosines by less than 1/Lr

are not resolvable by the arrays. This suggests that we should “sample” theangular domain at fixed angular spacings of 1/Lt at the transmitter and atfixed angular spacings of 1/Lr at the receiver, and represent the channel interms of these new input and output coordinates. The !k" l#th channel gain inthese angular coordinates is then roughly the aggregation of all paths whosetransmit directional cosine is within an angular window of width 1/Lt aroundl/Lt and whose receive directional cosine is within an angular window ofwidth 1/Lr around k/Lr . See Figure 7.11 for an illustration of the lineartransmit and receive antenna array with the corresponding angular windows.In the following subsections, we will develop this approach explicitly foruniform linear arrays.

Figure 7.11 A representationof the MIMO channel in theangular domain. Due to thelimited resolvability of theantenna arrays, the physicalpaths are partitioned intoresolvable bins of angularwidths 1/Lr by 1/Lt . Herethere are four receiveantennas (Lr = 2) and sixtransmit antennas (Lr = 3).

4

45

5

0

0

0

0

2

2

22

3

1

1

1

1

3

3

3

+1

+1 –1

–1

path B

1 / Lr

1 / Lt

path A

path B

path A

Resolvable bins!t

!r

[Tse, Viswanath, ”Fundamentals

of Wireless Commuication”]

Sender

Receiver

Obstacles

path Bpath A

path A

Resolvable bins


Model for Obstacles Rayleigh Fading

Assumption:large number ofscatterers uniformlydistributed in spaceproduce statisticallyindependent paths

Properties:phases are uniformlydistributedamplitudes are random

MIMO channel capacity:grows linearly for n sender,n receiver and large n

receiver

scattering

sender

objects

far apart


Scaleability in Ad Hoc Networks

Gupta and Kumar (2000)

network capacity=∑

connection ibitsi ·distancei

capacity is O(√

n)for single antennas

⇒ bandwidth of node is O(1/√

n)

MIMO

if nodes have k multiple antennas,capacity increases by factor O(k)

when coupling n antennas of n nodes,capacity is upper bounded with O (n)⇒ bandwidth of node is O (1)

source target


Multiple

Parallel Channels

Ad hoc network


Hierarchical Cooperationby Özgür, Lévêque, and Tse (2007)

reaches upper bound of network capacity O (n)

each hierarchical step consists of 3 phases:

Phase 1 Phase 2 Phase 3

Transmit

Setting Up MIMO

Cooperation Transmissions

Cooperate

to decode

sender

receiverreceiver

sender

phase 1 & 3 in parallel in non neighboring clusters,phase 2 sequentially



3 phases are performed in a hierarchy

area grows exponentially

parallel MIMO

ÖZGÜR et al.: HIERARCHICAL COOPERATION ACHIEVES OPTIMAL CAPACITY SCALING IN Ad Hoc NETWORKS 3555

Fig. 3. The upper graph illustrates the salient features of the three-phase hierarchical scheme. The time division in this hierarchical scheme is explicitly given thegraph below.

Fig. 4. Buffers of the nodes in a cluster are illustrated before and after the data exchanges in Phase 1. The data stream of the source nodes are distributed to thenodes in the network as depicted. denotes the th subblock of the source node . Note the 9-TDMA scheme that is employed over the network in this phase.

squares. The following lemma upper-bounds the probability ofhaving large deviations from the average. Its proof is relegatedto the end of the section.

Lemma 4.1: Let us partition a unit area network of size intocells of area , where can be a function of . The numberof nodes inside each cell is betweenwith probability larger than where isindependent of and satisfies when .

Applying Lemma 4.1 to the squares of area , we see thatall squares contain order nodes with probability larger than

. We assume , where , inwhich case this probability tends to as increases. This condi-tion is sufficient for the followinganalysisonscaling laws tohold.However, in order to simplify the presentation, we assume that

there are exactly nodes in each square. The clustering is usedto realize a distributed MIMO system in three successive steps.

Phase 1. Setting Up Transmit Cooperation: In this phase,source nodes distribute their data streams over their clusters andset up the stage for the long-range MIMO transmissions thatwe want to perform in the next phase. Clusters work in parallelaccording to the 9-TDMA scheme depicted in Fig. 4, which di-vides the total time for this phase into nine time slots and as-signs simultaneous operation to clusters that are sufficiently sep-arated. The nine different patterns used to color the clusters inFig. 4 correspond to these nine-time slots. The clusters with thesame pattern are operating simultaneously in the same time slotwhile the other clusters stay inactive. Note that with this sched-uling, in every time slot there are at least two inactive clustersbetween any two clusters that are active.

parallelism withspatial reuse

spatial multiplexinghierarchy

short

rangelong

range

1 ⇥ MIMO channel O (n)

O (n) parallel TDMA

channel with

Phase 1 Phase 2 Phase 3

Phase 1 Phase 2 Phase 3 Phase 1 Phase 2 Phase 3



network capacity depends onpath-loss 1/dα for distance d

α = 2 (free space)linear scaling O (n) withhierarchical cooperation2< α ≤ 3order-optimal scaling withhierarchical cooperationα > 3transmissions near the cutdominate and nearest neighbormultihop optimal

cut

pn nodes

powertransmit

pn

nodes


Capacity Scaling in Arbitrary Networksby Niesen, Gupta, and Shah (2009)

Özgür et al. showed hierarchicalcooperation for uniform node density

extension of Niesen et al. to arbitrarynetworks

hierarchical relaying scheme:multiple antenna relay inregions with high node densitySIMO from sender to relayMISO from relay to receiverrecursion in relay region todecode data

scheme achieves same throughput

NIESEN et al.: ON CAPACITY SCALING IN ARBITRARY WIRELESS NETWORKS 3963

Fig. 1. Sketch of one level of the hierarchical relaying scheme. Hereare three source–destination pairs. Groups of source–destina-

tion pairs relay their traffic over dense squarelets, which contain a number ofnodes proportional to their area (shaded). We time share between the differentdense squarelets used as relays. Within all these relay squarelets, the scheme isused recursively to enable joint decoding and encoding at each relay.

Moreover, by Theorem 5, there exist node placements with thesame regularity such that for random permutation traffic withhigh probability is (essentially) of the same order, in thesense that

In particular, for (i.e., regular node placement), and for(i.e., random node placement), we ob-

tain the order scaling as expected. For (i.e., com-pletely irregular node placement), we obtain the orderscaling as in Theorems 1 and 3.

IV. HIERARCHICAL RELAYING SCHEME

This section describes the architecture of our hierarchical re-laying scheme. On a high level, the construction of this schemeis as follows. Consider nodes placed arbitrarily on thesquare region with a minimum separation . Divide

into squarelets of equal size. Call a squarelet dense, if itcontains a number of nodes proportional to its area. For eachsource–destination pair, choose such a dense squarelet as arelay, over which it will transmit information (see Fig. 1).

Consider now one such relay squarelet and the nodes that aretransmitting information over it. If we assume for the momentthat all the nodes within the same relay squarelet could coop-erate, then we would have a multiple-access channel (MAC)between the source nodes and the relay squarelet, where eachof the source nodes has one transmit antenna, and the relaysquarelet (acting as one node) has many receive antennas. Be-tween the relay squarelet and the destination nodes, we wouldhave a broadcast channel (BC), where each destination node hasone receive antenna, and the relay squarelet (acting again as onenode) has many transmit antennas. The cooperation gain fromusing this kind of scheme arises from the use of multiple an-tennas for these multiple access and broadcast channels.

To actually enable this kind of cooperation at the relaysquarelet, local communication within the relay squarelets

is necessary. It can be shown that this local communicationproblem is actually the same as the original problem, but at asmaller scale. Hence, we can use the same scheme recursivelyto solve this subproblem. We terminate the recursion afterseveral iterations, at which point we use simple time-divisionmultiple access (TDMA) to bootstrap the scheme.

The construction of the hierarchical relaying scheme ispresented in detail in Section IV-A. A back-of-the-envelopecalculation of the per-node rate it achieves is presented inSection IV-B. A detailed analysis of the hierarchical relayingscheme is presented in Sections VI and VII.

A. Construction

Recall that

is the square region of area . The scheme described here as-sumes that nodes are placed arbitrarily in with minimumseparation . We want to find some rate, say , thatcan be supported for all source–destination pairs of a givenpermutation traffic matrix . The scheme that is describedbelow is “recursive” (and hence hierarchical) in the followingsense. In order to achieve rate for nodes in , it willuse as a building block a scheme for supporting rate for anetwork of

nodes over (square of area ) with

for any permutation traffic matrix of nodes. Here thebranching factor is a function such that as

. We will optimize over the choice of later. Thesame construction is used for the scheme over , and soon. In general, our scheme does the following at level ofthe hierarchy (or recursion). In order to achieve rate for anypermutation traffic matrix over

nodes in , with

use a scheme achieving rate over nodes infor any permutation traffic matrix . The recursion is ter-minated at some level to be chosen later.

We now describe how the hierarchy is constructed betweenlevels and for . Each source–destina-tion pair chooses some squarelet as a relay over which it trans-mits its message. This relaying of messages takes place in twophases—a multiple-access phase and a broadcast phase. We firstdescribe the selection of relay squarelets, then the operation ofthe network during the multiple-access and broadcast phases,and finally, the termination of the hierarchical construction.

Authorized licensed use limited to: Alcatel Lucent. Downloaded on August 18, 2009 at 13:21 from IEEE Xplore. Restrictions apply.

SIMO

MISO

Relay ofmultiple

antennasNIESEN et al.: ON CAPACITY SCALING IN ARBITRARY WIRELESS NETWORKS 3963

Fig. 1. Sketch of one level of the hierarchical relaying scheme. Hereare three source–destination pairs. Groups of source–destina-

tion pairs relay their traffic over dense squarelets, which contain a number ofnodes proportional to their area (shaded). We time share between the differentdense squarelets used as relays. Within all these relay squarelets, the scheme isused recursively to enable joint decoding and encoding at each relay.

Moreover, by Theorem 5, there exist node placements with thesame regularity such that for random permutation traffic withhigh probability is (essentially) of the same order, in thesense that

In particular, for (i.e., regular node placement), and for(i.e., random node placement), we ob-

tain the order scaling as expected. For (i.e., com-pletely irregular node placement), we obtain the orderscaling as in Theorems 1 and 3.

IV. HIERARCHICAL RELAYING SCHEME

This section describes the architecture of our hierarchical re-laying scheme. On a high level, the construction of this schemeis as follows. Consider nodes placed arbitrarily on thesquare region with a minimum separation . Divide

into squarelets of equal size. Call a squarelet dense, if itcontains a number of nodes proportional to its area. For eachsource–destination pair, choose such a dense squarelet as arelay, over which it will transmit information (see Fig. 1).

Consider now one such relay squarelet and the nodes that aretransmitting information over it. If we assume for the momentthat all the nodes within the same relay squarelet could coop-erate, then we would have a multiple-access channel (MAC)between the source nodes and the relay squarelet, where eachof the source nodes has one transmit antenna, and the relaysquarelet (acting as one node) has many receive antennas. Be-tween the relay squarelet and the destination nodes, we wouldhave a broadcast channel (BC), where each destination node hasone receive antenna, and the relay squarelet (acting again as onenode) has many transmit antennas. The cooperation gain fromusing this kind of scheme arises from the use of multiple an-tennas for these multiple access and broadcast channels.

To actually enable this kind of cooperation at the relaysquarelet, local communication within the relay squarelets

is necessary. It can be shown that this local communicationproblem is actually the same as the original problem, but at asmaller scale. Hence, we can use the same scheme recursivelyto solve this subproblem. We terminate the recursion afterseveral iterations, at which point we use simple time-divisionmultiple access (TDMA) to bootstrap the scheme.

The construction of the hierarchical relaying scheme ispresented in detail in Section IV-A. A back-of-the-envelopecalculation of the per-node rate it achieves is presented inSection IV-B. A detailed analysis of the hierarchical relayingscheme is presented in Sections VI and VII.

A. Construction

Recall that

is the square region of area . The scheme described here as-sumes that nodes are placed arbitrarily in with minimumseparation . We want to find some rate, say , thatcan be supported for all source–destination pairs of a givenpermutation traffic matrix . The scheme that is describedbelow is “recursive” (and hence hierarchical) in the followingsense. In order to achieve rate for nodes in , it willuse as a building block a scheme for supporting rate for anetwork of

nodes over (square of area ) with

for any permutation traffic matrix of nodes. Here thebranching factor is a function such that as

. We will optimize over the choice of later. Thesame construction is used for the scheme over , and soon. In general, our scheme does the following at level ofthe hierarchy (or recursion). In order to achieve rate for anypermutation traffic matrix over

nodes in , with

use a scheme achieving rate over nodes infor any permutation traffic matrix . The recursion is ter-minated at some level to be chosen later.

We now describe how the hierarchy is constructed betweenlevels and for . Each source–destina-tion pair chooses some squarelet as a relay over which it trans-mits its message. This relaying of messages takes place in twophases—a multiple-access phase and a broadcast phase. We firstdescribe the selection of relay squarelets, then the operation ofthe network during the multiple-access and broadcast phases,and finally, the termination of the hierarchical construction.

Authorized licensed use limited to: Alcatel Lucent. Downloaded on August 18, 2009 at 13:21 from IEEE Xplore. Restrictions apply.

SIMO


Summary

MIMOtechnology

Multiplexing

Beamforminglow SNR

high SNR

low angularspread

capacity ⇠ #antenna

capacity ⇠ log (1+SNR)

#antenna ⇠ SNR

prosregime

Rayleigh

fading

Spatial

power gain

Communication:hierarchical cooperationachieves with MIMO up tolinear capacity for path-lossexponent 2≤ α ≤ 3for α > 3 multihop best choice


Multiple

parallel

channels

ÖZGÜR et al.: HIERARCHICAL COOPERATION ACHIEVES OPTIMAL CAPACITY SCALING IN Ad Hoc NETWORKS 3555

Fig. 3. The upper graph illustrates the salient features of the three-phase hierarchical scheme. The time division in this hierarchical scheme is explicitly given thegraph below.

Fig. 4. Buffers of the nodes in a cluster are illustrated before and after the data exchanges in Phase 1. The data stream of the source nodes are distributed to thenodes in the network as depicted. denotes the th subblock of the source node . Note the 9-TDMA scheme that is employed over the network in this phase.

squares. The following lemma upper-bounds the probability ofhaving large deviations from the average. Its proof is relegatedto the end of the section.

Lemma 4.1: Let us partition a unit area network of size intocells of area , where can be a function of . The numberof nodes inside each cell is betweenwith probability larger than where isindependent of and satisfies when .

Applying Lemma 4.1 to the squares of area , we see thatall squares contain order nodes with probability larger than

. We assume , where , inwhich case this probability tends to as increases. This condi-tion is sufficient for the followinganalysisonscaling laws tohold.However, in order to simplify the presentation, we assume that

there are exactly nodes in each square. The clustering is usedto realize a distributed MIMO system in three successive steps.

Phase 1. Setting Up Transmit Cooperation: In this phase,source nodes distribute their data streams over their clusters andset up the stage for the long-range MIMO transmissions thatwe want to perform in the next phase. Clusters work in parallelaccording to the 9-TDMA scheme depicted in Fig. 4, which di-vides the total time for this phase into nine time slots and as-signs simultaneous operation to clusters that are sufficiently sep-arated. The nine different patterns used to color the clusters inFig. 4 correspond to these nine-time slots. The clusters with thesame pattern are operating simultaneously in the same time slotwhile the other clusters stay inactive. Note that with this sched-uling, in every time slot there are at least two inactive clustersbetween any two clusters that are active.

Hierarchical CooperationBeamforming Multiplexing

main beam


Thank youfor your attention.

Email:[email protected]

Web:http://cone.informatik.uni-freiburg.de/staff/janson


Documents

Survey on MIMO-related Technologywrawn.ru.is/Janson.pdf · Survey on MIMO-related Technology In The Fourth Workshop on Realistic models for Algorithms in Wireless Networks (WRAWN),