1. MIMO for 5G Mobile Communications
MIMO Wireless Communications over Generalized Fading Channels
MIMO for 5G Mobile Communications
Dr. Brijesh Kumbhani
Prof. Rakhesh Singh Kshetrimayum

2. Introduction Point-to-point MIMO: Discussed in previous chapters
Single transmitter single receiver
Multiple antennas at single location (with sufficient spacing)
Also known as single user MIMO
Multiuser 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

3. Some issues with point-to-point MIMO
No multiplexing gain for rank deficit channels
Line-of-sight propagation
Keyhole channel
Full potential of MIMO can not be utilized
Multiple RF chains
Bulky hardware
TAS simplifies the hardware
But at the cost of feedback from receiver to transmitter

4. Some issues with point-to-point MIMO
Size and inter antenna spacing
Base station: no constraint
Mobile station: limited size – large number of antennas not possible
mmWave frequencies may be a solution
Channel estimation overhead
Large MIMO systems: 100s of antennas at each terminal
Large size of pilot signals
Multi-user MIMO : A Solution?

5. Multiuser MIMO (MU-MIMO)
Overcomes shortcomings of point-to-point MIMO
Single base station with several antennas
Multiple users with single antennas
Let Base station has M antennas
Usually 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 too
Single antenna user is a simplified model

6. MU-MIMO
MU-MIMO system with transmitter employing M=4 antennas serving K=4 users with single antenna (highly simplified model)

7. Multiuser MIMO (MU-MIMO)
Two types of Communication in this scenario
Downlink (DL): communication from base station to mobile user
Uplink (UL): Communication from mobile user to base station

8. Multiuser MIMO uplink Multiple access for K mobile users
K users transmit signal to base station
Each user may have single or multiple antenna
Single antenna: one symbol per transmission
Multiple antenna: Symbol vector per transmission

9. Multiuser MIMO uplink
Let signal transmitted by ith user is 𝐱 𝑖 𝑈𝐿 ,𝑖=1,2,3.,𝐾
For general representation transmitted signal is shown as vector of symbols for multiple antenna
Channel matrix for each user can be given as
𝐇 𝑖 𝑈𝐿 ,𝑖=1,2,3.,𝐾

10. Multiuser MIMO uplink
MU-MIMO system with transmitter employing M antennas serving K users with single antenna (uplink)

11. Multiuser MIMO uplink The 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

12. Multiuser MIMO uplink
𝐧 𝑈𝐿 is 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

13. Multiuser MIMO downlink
Communication from BS to mobile users
Channel is considered as broadcast channel
BS broadcast user data at using same time frequency resources
Usually, uplink and downlink transmissions are done using time division duplexing (TDD)

14. Multiuser MIMO downlink
MU-MIMO system with transmitter employing M antennas serving K users with single antenna (downlink)

15. Multiuser MIMO downlink
It is assumed that the channel state information is available only with the BS
Users do not have CSI
BS uses the reciprocity property of the channel
Precoding is done while transmission
Detection without requiring CSI at the mobile user

16. Multiuser MIMO downlink
The 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

17. Massive MIMO Several antennas at the BS
Few antennas at the mobile user (usually one or two)
A special case of MU-MIMO
Assume, number of antennas at BS tends to infinity
Total of user antennas is much less than the No. of antennas available at the base station

18. Massive MIMO Mobile station small number of antennas (one or two)
Most signal processing at base station
Small mobile device
No/less receive diversity
Interference management by base station
Beamforming in downlink – reduction in interference and energy requirements
Uplink – separation of user signals at the base station through signal processing
TDD massive MIMO
Scalable system in terms of number of antennas
Channel estimation time is independent of the number of BS antennas

19. Massive MIMO
MU-MIMO system for a single base station employing M=14 antennas serving K=3 users with single antenna (downlink transmission)

20. Massive MIMO High spectral efficiency and diversity order*:
Simultaneous transmission/reception from many antennas
Better energy efficiency*: uplink transmission power inversely varying with the number of base station antennas
* As compared to the base station with single antenna

21. Massive MIMO: uplink capacity
Consider M antenna BS serving K single antenna users
Channel coefficient between ith user to jth BS antenna
𝑔 𝑗𝑖 is small scale fading coefficient and
𝑑 𝑖 is large scale fading coefficient

22. Massive MIMO: uplink capacity
The uplink channel matrix can be given as
with the matrices represented as

23. Massive MIMO: uplink capacity
When the channels are independent/orthogonal
Also, known as channel favorable condition
For 𝑀→∞>>𝐾, favorable condition is satisfied
In different channel conditions
For different antenna array configurations

24. Massive MIMO: uplink capacity
Channel favorable conditions:
Irrespective of fading distribution
Classical/generalized fading channels
Vast spatial diversity → small scale randomness dies

25. Massive MIMO: uplink capacity
Let, equal transmission power for uplink 𝑃 𝐾 to each user
Uplink capacity can be evaluated as
Further, it can be simplified as

26. Massive MIMO: uplink capacity
Capacity: Sum of individual user capacity
Decoupled signals are obtained through matched filtering
Matched filter is simple linear processing as follows

27. Massive MIMO: uplink capacity
Further, use the substitutions
Decoupled signals are obtained as
𝐃 being the diagonal matrix, signals are decoupled

28. Massive MIMO: uplink capacity
After matched filtering
Signal decoupling is obtained, i. e.
K parallel independent Gaussian channels
Each user SNR is obtained as 𝑀𝑃 𝑑 𝑖 𝐾 𝜎 𝑛 2
Total Capacity is sum of channel capacity of each user

29. Massive MIMO: downlink capacity
BS has CSI. So, Adaptive power allocation is possible
Let, power allocation matrix is
with sum of all user power as constant for each transmission, i.e.

30. Massive MIMO: downlink capacity
The channel capacity can be given as
Base station knowing CSI, uses precoding as

31. Massive MIMO: downlink capacity
The downlink received signal can be given as
For favorable channel conditions
Again, signal decoupling is obtained in the downlink too.

32. Massive MIMO: downlink capacity
Linear precoding is used at BS to obtain enhanced capacity through adaptive power allocation
Some assumptions for capacity analysis are:
Orthogonal channles
Perfect CSI at the BS
Reciprocal channel

33. Massive MIMO: downlink precoding
CSI is estimated only at the BS
Assume reciprocal channels
No CSI is required at the mobile user
Capacity analysis: presented for single cell
Practical: many cells near by (Figure in next slide)
Interference to/from near-by cells

34. Massive MIMO: Multicell network
Multi-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)

35. Massive MIMO: downlink precoding
Pilot transmission from users
Orthogonal pilots from every user
Limited number of orthogonal pilots
Pilots 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

36. Massive MIMO: downlink precoding
Pilot signal power: proportional to distance of user from the BS
Cell edge user transmits more power
This results in interference to the neighbouring cell while CSI estimation known as pilot contamination

37. Massive MIMO: downlink precoding
Due to pilot contamination, matched filter precoding fails for downlink transmission
Other precoding techniques are useful, like
Zero forcing (ZF)
Regularized zero forcing (RZF)
Minimum mean square error (MMSE)

38. Massive MIMO: downlink precoding
Multiplier for downlink precoding can be given by
where 𝐇 𝑙 = 𝐝 𝑙𝑙 −1 𝐆 𝑙 with 𝐆 𝑙 as the estimated CSI at lth base station, 𝛾 𝑙 = 𝑡𝑟𝑎𝑐𝑒( 𝐇 𝑙 𝐻 ) 𝐇 𝑙 𝐾 and

39. Massive MIMO: downlink precoding
The above precoding multiplier is a general case for RZF.
Some of the special cases of RZF are:
𝛿=0 for MF
𝛿=∞ for ZF
𝛿= 𝐾 𝜎 𝑛 2 2𝑆𝑁 𝑅 𝑑𝑜𝑤𝑛𝑙𝑖𝑛𝑘 𝑙𝑜 𝑔 2 𝑀 for MMSE

40. Massive MIMO: downlink precoding
Base station cooperation : to combat pilot contamination, also known as coordinated multipoint transmission (CoMP)
Two types : Full or Partial cooperation
Full cooperation: Network MIMO
Partial cooperation: coordinated beamforming/scheduling

41. Massive MIMO: Challenges
Loss of reciprocity in uplink and downlink channels
Limited number of orthogonal pilots: pilot reuse leading to pilot contamination
High interference at the cell edge
No CSI at base station prior to link establishment
Transmit beamforming not possible
STBC may be used
Favourable channel condition may not satisfy all the time leading to performance degradation

42. Massive MIMO: outage probability
Outage probability: a metric of system performance
Consider downlink transmission for user outage probability
Suppose BS use MF precoding and each user has single antenna
Transmitted signal at BS can be represented as

43. Massive MIMO: outage probability
Received signal at the ith user is
Received signal comprises of three components
intended signal (first term),
interference (second term), i.e. signal for other users
Noise ( 𝑛 𝑖 ) – let it be zero mean unit variance

44. Massive MIMO: outage probability
The signal to interference plus noise ratio in this can be given by
where 𝑃 𝑢 = 𝑃 𝐾 is the power per user (equal power allocation),
𝑋 𝑖 = 𝛥 1 𝑀 | 𝐡 𝑖 𝑢𝑝𝑙𝑖𝑛𝑘 𝐡 𝑖 𝑢𝑝𝑙𝑖𝑛𝑘 𝐻 |
𝑌 𝑖 = 𝛥 1 𝑀 𝑗=1,𝑗≠𝑖 𝐾 | 𝐡 𝑖 𝑢𝑝𝑙𝑖𝑛𝑘 𝐡 𝑗 𝑢𝑝𝑙𝑖𝑛𝑘 𝐻 | 2

45. Massive MIMO: outage probability
In general, 𝑋 𝑖 and 𝑌 𝑖 may be assumed to be coming from any distribution depending on the scenario
Consider they are Gamma distributed for this analysis
The PDF of 𝑋 𝑖 can be given as
So, 𝐸( 𝑋 𝑘 2 )=1+ 1 𝑀

46. Massive MIMO: outage probability
The PDF of 𝑌 𝑖 can be given as
where 𝑐 1 = 𝛥 𝐾−1 𝑀 +𝐾−2 ,
𝑐 𝑚 = 𝛥 𝐾+𝑚−1
𝑐 3 = 𝛥 𝑀 −1 𝑀

47. Massive MIMO: outage probability
The PDF of 𝑌 𝑖 can be simplified as
where 𝑐 4 = 𝑀 𝑀 +𝐾−2 ,

48. Massive MIMO: outage probability
On simplification the above expression reduces to
It can be evaluated as

49. Massive MIMO: outage probability
The outage probability can be given as
So, the approximate outage probability can be given as
where 𝑐 5 = 𝑀+1 𝛾 𝑡ℎ − 1 𝑃 𝑢 and 𝛤(𝑠,𝑥)= 𝑥 ∞ 𝑡 𝑠−1 𝑒 −𝑡 𝑑𝑡

50. mmWave Massive MIMO To be implemented at mmWave frequency region
Shorter wavelength – smaller antenna size – allows large number of antennas at single terminal
One of the technology candidate for 5G communication

51. mmWave Massive MIMO
5G mobile technology requirements and comparison with 4G
Parameter
Unit 5G 4G
Area traffic capacity
Mbps/m2 10
0.1
Peak data rate
Gbps 20 1
User experienced data rate
Mbps
100
Spectrum efficiency 3X 1X
Energy efficiency
100X
Connection density
devices/km2
106
105
Latency ms
Mobility
km/h
500
350

52. mmWave Massive MIMO Ten pillars for 5G mobile wireless communications
Small cells
mmWave
Massive MIMO
Multi-radio access technology (RAT)
Self organizing networks (SON)

53. mmWave Massive MIMO Ten pillars for 5G mobile wireless communications
Device-to-device (D2D) communications
Backhaul
Energy efficiency (EE)
New spectrum and its sharing
Radio access network (RAN) virtualization

54. mmWave Massive MIMO
Three big pillars for 5G mobile wireless communications
Small cell networks: femto cells, pico cells
Enhanced spatial frequency reuse
Better system capacity
Reduced propagation loss
Improved energy efficiency and data rate
Qualcomm demonstrated almost double network capacity with doubling the number of small cells

55. mmWave Massive MIMO
Three big pillars for 5G mobile wireless communications
mmWave frequency
Crowded microwave frequencies
Huge available bandwidth at mmWave
Relatively un/less crowded spectrum
High capacity is expected with larger bandwidth

56. mmWave Massive MIMO
Three big pillars for 5G mobile wireless communications
Large antenna arrays
Capacity enhancement
Diversity improvement
Efficient beamforming
Reduced power transmission – energy efficiency
Improved spectrum efficiency

57. mmWave Massive MIMO Major Hurdles to mmWave technology Higher pathloss
High attenuation at high frequencies
Attenuation due to rainfall, snowfall, fog, foliage, atmospheric absorption
Large penetration loss: coverage problems in buildings and non-LOS areas

58. mmWave Massive MIMO Typical mmWave losses at 200m from transmitter
Atmospheric absorption due to H2O and O2 : 0.02 dB
Heavy 110mm/h : 4dB
Heavy 10mm/h and fog with 50m visibility: 0.1dB
Path loss coefficient larger than 2.

59. mmWave Massive MIMO mmWave signal propagation
Tends to be LOS, minimal effect of small scale fading
Possible to estimate direction of arrival (DOA)
May overcome pilot contamination
Low rank channel matrix:
No multiplexing gain for point to point communication
Multiplexing gain for multiuser communicaiton

60. mmWave Massive MIMO mmWave signal propagation
Different cells indoor and outdoor: no penetration through walls
Wireless adaptive backhaul by electronic beamsteering
Beamstearing: Also useful to track mobile users

61. mmWave Massive MIMO Channel model for 60GHz mmWave WPAN
IEEE c indoor channel impulse response
where
𝑡 is the time of arrival (TOA)
𝜃 is the DOA
𝛽 is the gain coefficient for the LOS component

62. mmWave Massive MIMO Channel model for 60GHz mmWave WPAN
𝛼 𝑟,𝑐 is the channel gain for 𝑟 𝑡ℎ ray in 𝑐 𝑡ℎ cluster
𝑇 𝑐 is the TOA of the 𝑐 𝑡ℎ cluster
𝜏 𝑟,𝑐 is the TOA for 𝑟 𝑡ℎ ray in 𝑐 𝑡ℎ cluster
𝜃 𝑐 is the DOA for 𝑐 𝑡ℎ cluster
𝜙 𝑟,𝑐 is the DOA for 𝑟 𝑡ℎ ray in 𝑐 𝑡ℎ cluster

63. Device-to-device communication for IoT
5G 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) communication
Wireless metering
Mobile payments
Smart grid
Cont…

64. Device-to-device communication for IoT
Some application areas of device-to-device (D2D)/ machine-to-machine (M2M) communication
Critical infrastructure monitoring
Connected home
Smart transportation
Telemedicine
Vehicle-to-vehicle (V2V)/ vehicle-to-infrastructure (V2I) networks

65. Device-to-device communication for IoT
IoT is backed by D2D communication systems
Usually for communication to nearby devices
Does not use long radio hops via base stations

66. Device-to-device communication for IoT
V2V and V2I channel models
Usually modelled by Weibull distribution
Multipath components reaching early are stronger than Rayleigh fading
PDF can be given as

67. Device-to-device communication for IoT
V2V and V2I channel models
where 𝛽 is the shape factor and 𝛼= 𝐸( 𝑟 2 𝛤 1+ 2 𝛽 is the scale parameter
RMS delay spread fits lognormal distribution
V2V spectrum is smoother than classical Jake spectrum

68. Device-to-device communication for IoT
V2V channel characteristics for different environments
Parameter
Highway
Rural
Urban
Path loss exponent, n
, 4
Mean RMS delay spread (ns)
40-400
20-60
40-300
Mean Doppler spread (Hz)
100
782
30-350

69. Device-to-device communication for IoT
V2I channel characteristics for different environments
Parameter
Rural
Urban
Microcells
Path loss exponent, n
2-2.2
3.5
(LOS)
3.8 (Non LOS)
Delay spread (ns)
100
5-100 (LOS)
(Non LOS)
Angular Spread
1o-5o
5o-10o
20o
Shadowing
6 dB
6-8 dB
Varies widely

70. Large scale MIMO systems
Consider 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 theory
Used to obtain empirical distribution of the eigenvalues of 𝐇 𝐻 𝐇

71. Large scale MIMO systems
Empirical distribution of the eigenvalues of 𝐇 𝐻 𝐇 converges to
for the channel matrix 𝐇 of dimensions 𝑀×𝑁
𝑐= 𝑟−1 𝑟 ,
𝑟= 𝑁 𝑀
𝑎= 1− 𝑟 2
𝑏= 1+ 𝑟 2
𝑧 + =𝑚𝑎𝑥(𝑧,0

72. Large scale MIMO systems
Low complexity detection for Large MIMO systems
Machine learning based algorithms are found to give performance comparable to maximum likelihood (ML) detection
For 5X5 MIMO system with 16-QAM modulation, detection needs 165 number of metric calculations
For hundreds of antennas and higher order of modulation this complexity increases exponentially

73. Large scale MIMO systems
Low complexity detection for Large MIMO systems
Some low complexity algorithms
Likelihood ascent search
Reactive Tabu search
K-neighbourhood search for ZF and MMSE
Lattice reduction for ZF and MMSE
Reduced neighbourhood search algorithms

74. Large scale MIMO systems
Perfect space time codes
Implemented at the transmitter
Such STC achieves full diversity
Non-vanishing determinant for increased spectral efficiency
Uniform average transmitted energy per antenna
Minimum code rate of 1

75. Large scale MIMO systems
Perfect space time codes
For N transmit antennas, perfect STC can be constructed as
where 𝐃 𝑘 =𝑑𝑖𝑎𝑔( 𝑧 𝑘 ,𝜎( 𝑧 𝑘 ), 𝜎 2 ( 𝑧 𝑘 ),⋯, 𝜎 𝑁−1 ( 𝑧 𝑘 )
𝜆 is designed to meet energy constraint
𝛾 is unit magnitude complex number
𝛤=(𝛾 𝐞 𝑁 , 𝐞 1 , 𝐞 2 ,⋯, 𝐞 𝑁−2 , 𝐞 𝑁−1 with 𝐞 i as ith column of NXN identity matrix

76. Large scale MIMO systems
Bounds on capacity
Instantaneous capacity for point to point MIMO system with equal power allocation
where 𝑅 𝐻 is the rank of channel matrix and Q is the complex Wishart channel matrix

77. Large scale MIMO systems
Bounds on capacity
For full rank channel, i.e. 𝑅 𝐻 =min(𝑀,𝑁)=𝑚
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.

78. Large scale MIMO systems
Bounds on capacity
The worst case: channel has only one singular value
The best case: all singular values are equal

79. Large scale MIMO systems
Bounds on capacity
For normalized channel gain coefficients:
𝑡𝑟𝑎𝑐𝑒(𝐐)=𝑀𝑁
With 𝑛=max(𝑁,𝑀 , the bounds on capacity can be represented as