MIMO Wireless Communications over Generalized Fading Channels Dr Brijesh Kumbhani Prof Rakhesh Singh Kshetrimayum Pointtopoint MIMO Discussed in previous chapters Single transmitter single receiver ID: 809905
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Slide1
MIMO for 5G Mobile Communications
MIMO Wireless Communications over Generalized Fading Channels
Dr.
Brijesh
Kumbhani
Prof.
Rakhesh
Singh
Kshetrimayum
Slide2Point-to-point MIMO: Discussed in previous chapters
Single transmitter single receiverMultiple antennas at single location (with sufficient spacing)Also known as single user MIMOMultiuser MIMO Single/Multiple transmitters and single/multiple receivers with single/multiple antennas at one/both the transmitter and receiver
May be regarded as virtual MIMO
Multiple antennas distributed across locations
Introduction
Slide3No multiplexing gain for rank deficit channels
Line-of-sight propagationKeyhole channelFull potential of MIMO can not be utilizedMultiple RF chains Bulky hardware
TAS simplifies the hardware
But at the cost of feedback from receiver to transmitter
Some issues with point-to-point MIMO
Slide4Size and inter antenna spacing
Base station: no constraintMobile station: limited size – large number of antennas not possiblemmWave frequencies may be a solutionChannel estimation overhead
Large MIMO systems: 100s of antennas at each terminal
Large size of pilot signals Multi-user MIMO : A Solution?
Some issues with point-to-point MIMO
Slide5Overcomes shortcomings of point-to-point MIMO
Single base station with several antennasMultiple users with single antennasLet Base station has M antennasUsually M is greater than or equal to total number of users/user antennas
K number of users with single antennas
Users may have multiple antennas tooSingle antenna user is a simplified model
Multiuser MIMO (MU-MIMO)
Slide6MU-MIMO
MU-MIMO system with transmitter employing M=4 antennas serving
K=4 users
with single antenna (highly simplified model)
Slide7Two types of Communication in this scenario
Downlink (DL): communication from base station to mobile userUplink (UL): Communication from mobile user to base stationMultiuser MIMO (MU-MIMO)
Slide8Multiple access for K mobile users
K users transmit signal to base stationEach user may have single or multiple antennaSingle antenna: one symbol per transmission
Multiple antenna: Symbol vector per transmission
Multiuser MIMO uplink
Slide9Let signal transmitted by
ith user is
For general representation transmitted signal is shown as vector of symbols for multiple antenna
Channel matrix for each user can be given as
Multiuser
MIMO uplink
Slide10MU-MIMO
system with transmitter employing M antennas serving K users with single antenna (uplink)
Multiuser
MIMO uplink
Slide11The signal received at the BS can be given as
Where the channel matrix is combined channel matrix for all the users, given as Symbol vector is given as
Multiuser
MIMO uplink
Slide12is the AWGN with zero mean and diagonal covariance matrix.
Note: uplink transmission is like spatial multiplexing But from different locations
Multiple users regarded as single transmitter with multiple antennas
Challenge: synchronization of transmission from multiple users
Multiuser
MIMO uplink
Slide13Communication from BS to mobile users
Channel is considered as broadcast channelBS broadcast user data at using same time frequency resourcesUsually, uplink and downlink transmissions are done using time division duplexing (TDD)
Multiuser
MIMO downlink
Slide14Multiuser MIMO downlink
MU-MIMO system with transmitter employing M antennas serving K
users with
single antenna (downlink)
Slide15It is assumed that the channel state information is available only with the BS
Users do not have CSIBS uses the reciprocity property of the channelPrecoding is done while transmission
Detection without requiring CSI at the mobile user
Multiuser MIMO downlink
Slide16The signal received at the mobile terminal can be given as
Where the channel matrix, used for precoding, is combined channel matrix for all the users, given as Received signal vector containing K users’ data is given as
Multiuser
MIMO downlink
Slide17Several antennas at the BS
Few antennas at the mobile user (usually one or two)A special case of MU-MIMOAssume, number of antennas at BS tends to infinityTotal of user antennas is much less than the No. of antennas available at the base station
Massive MIMO
Slide18Mobile station small number of antennas (one or two)
Most signal processing at base stationSmall mobile deviceNo/less receive diversityInterference management by base stationBeamforming in downlink – reduction in interference and energy requirements
Uplink – separation of user signals at the base station through signal processing
TDD massive MIMOScalable system in terms of number of antennas
Channel estimation time is independent of the number of BS antennas
Massive MIMO
Slide19MU-MIMO system for a single base station employing M=14 antennas
serving K=3
users with single antenna (downlink transmission)
Massive MIMO
Slide20High spectral efficiency and diversity order*:
Simultaneous transmission/reception from many antennasBetter energy efficiency*: uplink transmission power inversely varying with the number of base station antennas
* As compared to the base station with single antenna
Massive MIMO
Slide21Consider M antenna BS serving K single antenna users
Channel coefficient between ith user to jth BS antenna
is small scale
fading coefficient and
is large scale fading coefficient
Massive MIMO: uplink capacity
Slide22The uplink channel matrix can be given as
with the matrices represented as
Massive MIMO: uplink capacity
Slide23When the channels are independent/orthogonal
Also, known as channel favorable conditionFor
,
favorable condition is satisfiedIn different channel conditionsFor different antenna array configurations
Massive MIMO: uplink capacity
Slide24Channel
favorable conditions: Irrespective of fading distributionClassical/generalized fading channels
Vast spatial diversity
small scale randomness dies
Massive MIMO: uplink capacity
Slide25Let, equal transmission power for uplink
to each userUplink capacity can be evaluated as
Further, it can be simplified as
Massive MIMO: uplink capacity
Slide26Capacity: Sum of individual user capacity
Decoupled signals are obtained through matched filteringMatched filter is simple linear processing as follows
Massive MIMO: uplink capacity
Slide27Further, use the substitutions
Decoupled signals are obtained as
being the diagonal matrix, signals are decoupled
Massive MIMO: uplink capacity
Slide28After matched filtering
Signal decoupling is obtained, i. e.K parallel independent Gaussian channelsEach user SNR is obtained as
Total Capacity is sum of channel capacity of each user
Massive MIMO: uplink capacity
Slide29BS has CSI.
So, Adaptive power allocation is possibleLet, power allocation matrix is with sum of all user power as constant for each transmission, i.e.
Massive MIMO: downlink capacity
Slide30The channel capacity can be given as
Base station knowing CSI, uses precoding as
Massive MIMO: downlink capacity
Slide31The downlink received signal can be given as
For favorable channel conditions
Again, signal decoupling is obtained in the downlink too.
Massive MIMO: downlink capacity
Slide32Linear
precoding is used at BS to obtain enhanced capacity through adaptive power allocationSome assumptions for capacity analysis are:Orthogonal channlesPerfect CSI at the BS
Reciprocal channel
Massive MIMO: downlink capacity
Slide33CSI is estimated only at the BS
Assume reciprocal channelsNo CSI is required at the mobile userCapacity analysis: presented for single cellPractical: many cells near by (Figure in next slide)
Interference to/from near-by cells
Massive MIMO: downlink precoding
Slide34Multi-cell MIMO based cellular network (BS equipped with M=14
antennas and
single antenna MS or user, each cell has K=2 users for illustration purpose)
Massive MIMO:
Multicell
network
Slide35Pilot transmission from users
Orthogonal pilots from every userLimited number of orthogonal pilotsPilots may be reused in other cells for multicell networks This causes interference of pilot signals
Received signal: linear combination of pilots from home cell and neighbour cell
Massive MIMO: downlink
precoding
Slide36Pilot signal power: proportional to distance of user from the BS
Cell edge user transmits more powerThis results in interference to the neighbouring cell while CSI estimation known as pilot contamination
Massive MIMO
: downlink precoding
Slide37Due to pilot contamination, matched filter
precoding fails for downlink transmissionOther precoding techniques are useful, likeZero forcing (ZF)Regularized zero forcing (RZF)
Minimum mean square error (MMSE)
Massive MIMO
: downlink
precoding
Slide38Multiplier for downlink
precoding can be given by where
with
as the estimated CSI at
l
th
base station,
and
Massive MIMO
: downlink
precoding
Slide39The above
precoding multiplier is a general case for RZF.Some of the special cases of RZF are: for MF
for
ZF
for MMSE
Massive MIMO
: downlink
precoding
Slide40Base station cooperation : to combat pilot contamination, also known as coordinated multipoint transmission (
CoMP)Two types : Full or Partial cooperationFull cooperation: Network MIMO Partial
cooperation: coordinated
beamforming/scheduling
Massive MIMO
: downlink
precoding
Slide41Loss of reciprocity in uplink and downlink channels
Limited number of orthogonal pilots: pilot reuse leading to pilot contaminationHigh interference at the cell edgeNo CSI at base station prior to link establishmentTransmit beamforming not possible
STBC may be used
Favourable channel condition may not satisfy all the time leading to performance degradation
Massive MIMO
:
Challenges
Slide42Outage probability: a metric of system performance
Consider downlink transmission for user outage probability Suppose BS use MF precoding and each user has single antennaTransmitted signal at BS can be represented as
Massive MIMO
:
outage probability
Slide43Received signal at the
ith user is Received signal comprises of three components
intended signal (first term),
interference (second term), i.e. signal for other usersNoise (
) – let it be zero mean unit variance
Massive MIMO
:
outage probability
Slide44The signal to interference plus noise ratio in this can be given by
where
is the power per user (equal power allocation),
Massive MIMO
:
outage probability
Slide45In general,
and
may be assumed to be coming from any distribution depending on the scenario
Consider they are Gamma distributed for this analysisThe PDF of
can be given as
So,
Massive MIMO
:
outage probability
Slide46The PDF of
can be given as
where
,
Massive MIMO
:
outage probability
Slide47The
PDF of can be simplified as
where
,
Massive MIMO
:
outage probability
Slide48On simplification the above expression reduces to
It can be evaluated as
Massive MIMO
: outage probability
Slide49The outage probability can be given as
So, the approximate outage probability can be given as
where
and
Massive MIMO
:
outage probability
Slide50To be implemented at
mmWave frequency regionShorter wavelength – smaller antenna size – allows large number of antennas at single terminalOne of the technology candidate for 5G communication
mmWave
Massive MIMO
Slide515G mobile technology requirements and comparison with 4G
mmWave
Massive MIMO
Parameter
Unit
5G
4G
Area traffic capacity
Mbps/m
2
10
0.1
Peak data rate
Gbps
20
1
User experienced data rate
Mbps
100
10
Spectrum
efficiency
3X
1X
Energy efficiency
100X
1X
Connection density
devices/km
2
10
6
10
5
Latency
ms
1
10
Mobility
km/h
500
350
Slide52Ten pillars for 5G mobile wireless communications
Small cellsmmWaveMassive MIMOMulti-radio access technology (RAT)
Self organizing networks (SON)
mmWave
Massive MIMO
Slide53Ten pillars for 5G mobile wireless communications
Device-to-device (D2D) communicationsBackhaulEnergy efficiency (EE) New spectrum and its sharing
Radio access network (RAN) virtualization
mmWave
Massive MIMO
Slide54Three big pillars for 5G mobile wireless communications
Small cell networks: femto cells, pico cells Enhanced spatial frequency reuseBetter system capacity
Reduced propagation loss
Improved energy efficiency and data rateQualcomm demonstrated almost double network capacity with doubling the number of small cells
mmWave
Massive MIMO
Slide55Three big pillars for 5G mobile wireless communications
mmWave frequencyCrowded microwave frequencies Huge available bandwidth at mmWave
Relatively un/less crowded spectrum
High capacity is expected with larger bandwidth
mmWave
Massive MIMO
Slide56Three big pillars for 5G mobile wireless communications
Large antenna arraysCapacity enhancementDiversity improvementEfficient beamforming
Reduced power transmission – energy efficiency
Improved spectrum efficiency
mmWave
Massive MIMO
Slide57Major Hurdles to
mmWave technologyHigher pathlossHigh attenuation at high frequenciesAttenuation due to rainfall, snowfall, fog, foliage, atmospheric absorption
Large penetration loss: coverage problems in buildings and non-LOS areas
mmWave
Massive MIMO
Slide58Typical
mmWave losses at 200m from transmitterAtmospheric absorption due to H2O and O2 : 0.02 dBHeavy rainfall @ 110mm/h : 4dB
Heavy snowfall @ 10mm/h and fog with 50m visibility: 0.1dB
Path loss coefficient larger than 2.
mmWave
Massive MIMO
Slide59mmWave
signal propagationTends to be LOS, minimal effect of small scale fadingPossible to estimate direction of arrival (DOA)May overcome pilot contamination
Low rank channel matrix:
No multiplexing gain for point to point communicationMultiplexing gain for multiuser communicaiton
mmWave
Massive MIMO
Slide60mmWave
signal propagationDifferent cells indoor and outdoor: no penetration through wallsWireless adaptive backhaul by electronic beamsteeringBeamstearing: Also useful to track mobile users
mmWave
Massive MIMO
Slide61Channel model for 60GHz
mmWave WPANIEEE 802.15.3c indoor channel impulse response
where
is the time of arrival (TOA)
is the DOA
is the gain coefficient for the LOS component
mmWave
Massive MIMO
Slide62Channel model for 60GHz
mmWave WPAN is the channel gain for
ray in
cluster
is the TOA of the
cluster
is the TOA
for
ray in
cluster
is the DOA for
cluster
is the DOA
for
ray in
cluster
mmWave
Massive MIMO
Slide635G would be known for applications that connect machines/devices
Expected to have 50 billion connected devices by 2020 (projected by Ericsson)Some application areas of device-to-device (D2D)/ machine-to-machine (M2M) communicationWireless meteringMobile payments
Smart grid
Cont…
Device-to-device communication for
IoT
Slide64Some application areas of device-to-device (D2D)/ machine-to-machine (M2M) communication
Critical infrastructure monitoringConnected homeSmart transportationTelemedicine
Vehicle-to-vehicle (V2V)/ vehicle-to-infrastructure (V2I) networks
Device-to-device communication for
IoT
Slide65IoT
is backed by D2D communication systemsUsually for communication to nearby devicesDoes not use long radio hops via base stations
Device-to-device communication for
IoT
Slide66V2V and V2I channel models
Usually modelled by Weibull distributionMultipath components reaching early are stronger than Rayleigh fadingPDF can be given as
Device-to-device communication for
IoT
Slide67V2V and V2I channel models
where is the shape factor and
is the scale parameter
RMS delay spread fits lognormal distribution
V2V spectrum is smoother than classical Jake spectrum
Device-to-device communication for
IoT
Slide68V2V channel characteristics for different environments
Device-to-device communication for IoT
Parameter
Highway
Rural
Urban
Path
loss exponent, n
1.8-1.9
1.8-1.9, 4
1.6-1.7
Mean RMS delay spread (ns)
40-400
20-60
40-300
Mean Doppler spread (Hz)
100
782
30-350
Slide69V2I channel characteristics for different environments
Device-to-device communication for IoT
Parameter
Rural
Urban
Microcells
Path
loss exponent, n
2-2.2
3.5
2.3-2.6 (LOS)
3.8 (Non LOS)
Delay spread (ns)
100
100-1000
5-100 (LOS)
30-500 (Non LOS)
Angular Spread
1
o
-5
o
5
o
-10
o
20
o
Shadowing
6
dB
6-8 dB
Varies widely
Slide70Consider hundreds of antennas at both the transmitter and the receiver
Point to point MIMO like D2D Large antenna arrays channel hardening effect
Channel no longer random
Marcenko-Pastur law of random matrix theoryUsed to obtain empirical distribution of the eigenvalues of
Large scale MIMO systems
Slide71Empirical
distribution of the eigenvalues of converges to
for the channel matrix
of dimensions
,
Large scale MIMO systems
Slide72Low complexity detection for Large MIMO systems
Machine learning based algorithms are found to give performance comparable to maximum likelihood (ML) detectionFor 5X5 MIMO system with 16-QAM modulation, detection needs 165 number of metric calculationsFor hundreds of antennas and higher order of modulation this complexity increases exponentially
Large scale MIMO systems
Slide73Low complexity detection for Large MIMO systems
Some low complexity algorithms Likelihood ascent search Reactive Tabu search K-neighbourhood search for ZF and MMSE
L
attice reduction for ZF and MMSEReduced neighbourhood search algorithms
Large scale MIMO systems
Slide74Perfect space time codes
Implemented at the transmitterSuch STC achieves full diversityNon-vanishing determinant for increased spectral efficiencyUniform average transmitted energy per antenna
Minimum code rate of 1
Large scale MIMO systems
Slide75Perfect space time codes
For N transmit antennas, perfect STC can be constructed as where
is designed to meet energy constraint
is unit magnitude complex number
with
as
i
th
column of NXN identity matrix
Large scale MIMO systems
Slide76Bounds on capacity
Instantaneous capacity for point to point MIMO system with equal power allocation where
is the rank of channel matrix and
Q is the complex Wishart channel matrix
Large scale MIMO systems
Slide77Bounds on capacity
For full rank channel, i.e.
The instantaneous channel capacity can be given as
Using the relation between trace of
Q
and its eigenvalues, the capacity bounds can be
obtained as discussed in the next slide.
Large scale MIMO systems
Slide78Bounds on capacity
The worst case: channel has only one singular valueThe best case: all singular values are equal
Large scale MIMO systems
Slide79Bounds on capacity
For normalized channel gain coefficients:
W
ith
, the bounds on capacity can be represented as
Large scale MIMO systems