MIMO for 5G Mobile Communications

1. MIMO Wireless Communications over Generalized Fading Channels MIMO for 5G Mobile Communications Dr. BrijeshKumbhani 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 • For general representation transmitted signal is shown as vector of symbols for multiple antenna • Channel matrix for each user can be given as

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 • 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 • is small scale fading coefficient and • 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 , 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 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 • 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 • 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 with as the estimated CSI at lth base station, and

39. Massive MIMO: downlink precoding • The above precoding multiplier is a general case for RZF. • Some of the special cases of RZF are: • for MF • for ZF • 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 () – 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 is the power per user (equal power allocation),

45. Massive MIMO: outage probability • In general, and may be assumed to be coming from any distribution depending on the scenario • Consider they are Gamma distributed for this analysis • The PDF of can be given as • So,

46. Massive MIMO: outage probability • The PDF of can be given as • where ,

47. Massive MIMO: outage probability • The PDF of can be simplified as • where,

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 and

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