Multi-User Gain Maximum Eigenmode Beamforming, and IDMA. Peng Wang and Li Ping City University of Hong Kong

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1 Multi-User Gain Maximum Eigenmode Beamforming, and IDMA Peng Wang and Li Ping City University of Hong Kong 1

2 Contents Introduction Multi-user gain (MUG) Maximum eigenmode beamforming (MEB) MEB performance analysis SIMO, MEB and optimal MIMO Implementation of MEB using IDMA Conclusions 2

3 For detail see Peng Wang and Li Ping, On multi-user gain in MIMO systems with rate constraints, IEEE GlobeCom, Washington, DC, USA, Nov ,

4 Contents Introduction Multi-user gain (MUG) Maximum eigenmode beamforming (MEB) MEB performance analysis SIMO, MEB and optimal MIMO Implementation of MEB using IDMA Conclusions 4

5 A 8 8 MIMO System Great performance, but do we want to buy such a bulky handset? Also, performance may be seriously affected by imperfect feedback and correlation among antennas. 5

6 Advantage of MIMO Average Power MSP (db) R (bits/symbol) Rate 6

7 Can we do better? 7

8 Multi-user MIMO MSP (db) single user 4 4 single user Average Power multi-user Rate R (bits/symbol) 8

9 The Problems with Multi-user MIMO Optimized multi-user MIMO are very complicated, involving - decoding order optimization, - correlation matrix optimization, - singular value decomposition (SVD), - eigenmode water filling. 9

10 The Focus of This Talk - What are the advantages of multi-user MIMO? - Are there simple approaches to multi-user MIMO? 10

11 Contents Introduction Multi-user gain (MUG) Maximum eigenmode beamforming (MEB) SIMO, MEB and MIMO Implementation of MEB using IDMA Conclusions 11

12 Multi User Gain MUG We know that power saving can be achieved by multi-user concurrent transmission. But how much is the multi-user gain (without scheduling)? 12

13 Multi-user Gain for SIMO 1 4 single user Average Power 1 4 multi-user Rate 13

14 Multi-user Gain for MIMO 4 4 single user Average Power 4 4 multi-user Rate 14

15 Multi-user Gain MSP (db) single user 4 4 single user 1 4 multi-user Average Power multi-user Rate R (bits/symbol) 15

16 Notes (1) There is subtle difference between multi-user gain and multi-user diversity gain (used by David Tse). - The former is for up-link multi-user concurrent transmission. - The latter is for down-link opportunistic transmission. (2) For the down-link, multi-user detection is more difficult. Thus single-user opportunistic transmission becomes attractive. (3) For the up-link, multi-user detection is relatively easier. (4) Quasi-static fading model. (5) No scheduling is assumed. (Fixed rates.) 16

17 What is the reason of multi-user gain? For detail, see Peng Wang, Jun Xiao, and Li Ping, "Comparison of orthogonal and nonorthogonal approaches to future wireless cellular systems," IEEE Vehicular Technology Magazine, vol. 1, no. 3, pp. 4-11, Sept

18 Stripping Decoding Decode x by treating x as noise Decoding x arrival power q arrival power q q'' R / 2 = log2(1 + ) N + q' q' R / 2 = log2(1 + ) N t t Assume that q > q. 18

19 Power Matching Strategy q t > q t user-2 signal user-1 signal channel gain g 1 channel gain g 2 arrival power q 2 arrival power q 1 The question is to assign (q, q ) to (q 1, q 2 ). If we do it randomly, the resultant sum-power is the same as TDMA. However, we can do better. 19

20 Power Matching Strategy q t > q t user-2 signal user-1 signal channel gain g 1 channel gain g 2 arrival power q 2 arrival power q 1 (1) Assign q 2 =q and q 1 =q. Then sum transmitted power = q /g 2 + q /g 1 (2) Assign q 2 =q and q 1 =q. Then sum transmitted power = q /g 1 + q /g 2 Assume q > q. Which method leads to smaller transmitted power? 20

21 Multi User Gain in SISO Channels Transmitted power can be minimized by matching smaller receiving power with smaller channel gain. This principle can be generalized to any number of users. This is the reason of multi-user gain in multi-user SISO fading channels. There is no such gain in AWGN (or when g 1 =g 2 ). user-2 signal channel gain g 1 arrival power q 2 user-1 signal channel gain g 2 arrival power q 1 21

22 Multi-User Gain in MIMO Channels In a MIMO channel, there is one more reason for multi-user gain. A MIMO system provides more dimensions for signaling. This is explained in the following example. Three receiver antennas can provide a maximum three degrees of freedom. We need the help of the transmitters to achieve this degree of freedom. (We may view each degree of freedom as an eigenvector.) If there is one user, we need more antennas to achieve these degrees of freedoms. However, if there are multiple users, we can achieve these degrees of freedoms more easily by allowing con-current transmission. 22

23 An Example: 2 2 MAC aggregate power (db) K = 1 (TDMA) K = 2 K = 4 K R (bits/symbol) More concurrent transmitting user, more gain. 23

24 Assumptions Delay sensitive services without scheduling. Perfect channel state information (CSI). Channel includes path loss, lognormal and Rayleigh fading Lognormal fading Path loss Rayleigh fading r 24

25 Contents Introduction Multi-user gain (MUG) Maximum eigenmode beamforming (MEB) MEB performance analysis SIMO v.s. MIMO Implementation of MEB using IDMA Conclusions 25

26 The MEB Strategy Each mobile transmits only on its maximum eigenmode. Power allocation is applied according to the maximum eigenmode gains {g k }. Stripping decoding is applied at the receiver. The user with the largest channel gain is decoded first. 26

27 The Advantages of MEB simple and nearly optimal. 27

28 Optimal MIMO MAC and MEB Optimal MIMO MAC MEB 28

29 Contents Introduction Multi-user gain (MUG) Maximum eigenmode beamforming (MEB) MEB performance analysis SIMO, MEB and MIMO Implementation of MEB using IDMA Conclusions 29

30 Theorem 1 When K, the MSP for a multi-user N M MIMO system is given by MSP N M RFN M ( x)/ M 2 ( K, R) = R ln 2 f N M ( x) dx 0 x K: the number of users number; R: sum rate; F M N (x) the CDF of λ max 2 ; f M N (x) the PDF of λ max 2 ; 30

31 Theorem 2 When K, the MSP for a multi-user MEB N M MIMO system is given by MSP N M RFN M ( x)/ M 2 ( K, R) = R ln 2 f N M ( x) dx 0 x Therefore MEB is asymptotically optimal. 31

32 Proof Outline The derivation is based on upper and lower bounds. When K, the upper and lower bounds converge so we obtain the true MSP. The upper bound is derived from a realizable system using maximum eigenmode beamforming (MEB). The lower bound is derived from an idealized parallel channel. 32

33 Upper Bound (Achievability) The MEB provides an upper bounds on the MIMO MSP. MSP N M K R( k 1)/ (1 + δ )2 ( K, R) Rln2 1 F ( k / K) k = εk N M MK 1 K where δ is an arbitrarily small constant, ε the outage probability and F N M ( ) the CDF of the maximum singular value. When K, MSP Rt / M 1 2 ( R ln 2 dt F ( t) N M K, R) 0 1 N M 33

34 Proof SNR p d u u 2 H 2 k k,max k,max k,max k = k 1 2 H pd 1 i i,max uk,max ui,max i = = pd 1 + φ k,i 2 k k,max k 1 2 pd i= 1 i i,max lim SNR = k 1 R / K R / K ( 2 1)( 1 + (2 1)/ M ) ( 1+ δ ) 1 i 1 / / ( )( M ) ( δ ) k K k R K R K (2 1)/ 1+ i = 1 k 1 R / K R / K ( 2 1)( 1 + (2 1)/ M ) R / K 2 1 k 1 i R / K ( M ) i = (2 1)/ M = R / K M lim K p Rk ( 1)/ ( + δ ) K MK 1 2 Rln2 1 = lim ( k/ K) K k K K 1 k= εk k= εk FN M = (1 + δ ) R ln 2 1 ε F 2 Rt / M 1 N M () t dt 34

35 Lower Bound MIMO: MSP Rt / M 1 2 ( K, R) R ln 2 dt F ( t) N M K = k k + k = 1 y H x n Its minimum sum-power (MSP) is lower bounded by that of the following idealized system: Parallel Channel: y = k k = 1 max d k where max d is the maximum singular value of H k k. Each user in this channel sees M parallel sub-channels. Thus 0 1 N M I M x k + n same as the upper bound when K 35

36 End of the Proof When K, the upper and lower bounds converge to MSP N M RFN M ( x)/ M 2 ( K, R) = R ln 2 f N M ( x) dx 0 x 36

37 Observations MEB is asymptotically optimal when K. MEB is nearly optimal even for a quite small K. MEB is insensitive to antenna correlation. MEB is insensitive to CSI error. For detail, see Li Ping and Peng Wang, "Multi-user gain and maximum eigenmode beamforming for MIMO systems with rate constraints," IEEE Inform. Theory Workshop (ITW), Bergen, Norway, July 1-6,

38 Optimal MIMO MAC and MEB Optimal MIMO MAC MEB 38

39 MEB Is Nearly Optimal Average Power 2 2 MIMO MAC rate (bits/channel use) 39

40 Summary MIMO asymptotic MSP MSP N M RFN M ( x)/ M 2 ( K, R) = R ln 2 f N M ( x) dx 0 x The degrees of freedom is increased by M times. Why M? Effectively, we have a KN M system. The limiting factor is M. What is the impact of N? F N M ( ) 40

41 Conditions Delay sensitive services without scheduling. Perfect channel state information (CSI). Channel includes path loss, lognormal and Rayleigh fading Lognormal fading Path loss Rayleigh fading r 41

42 Contents Introduction Multi-user gain (MUG) Maximum eigenmode beamforming (MEB) MEB performance analysis SIMO, MEB and optimal MIMO Implementation of MEB using IDMA Conclusions 42

43 Comparison of Different Gains 25 K =1 single-user SIMO MSP (db) K = single-user MIMO multi-user SIMO multi-user MEB K=16 multi-user MIMO MIMO gain multi-user gain BF gain optimization gain R (bits/symbol) single-user SIMO Single-user MIMO multi-user SIMO Multi-user MEB multi-user MIMO 43

44 Some details For detail, see Peng Wang and Li Ping, On multi-user gain in MIMO systems with rate constraints, IEEE GlobeCom, Washington, DC, USA, Nov ,

45 (1) Single-User SIMO This is used as the reference. single-user SIMO 45

46 (2) Single-User MIMO SVD is sensitive to channel information error (water-filling). Bulky. Closely located antennas may be rank-deficient. This is a serious problem for a handset unit. 46

47 (3) Multi-User SIMO SIMO MAC is a special case of MIMO MAC. SIMO MAC can also achieve good MUG. SIMO MAC requires only one antenna per handset. 47

48 (4) Multi-User MEB Easy to design (no water filling). Robust against imperfect CSI Near optimal performance with multi-user detection. But, multiple transmit antennas. Rank deficiency is not a problem. 48

49 (5) Multi-User MIMO Very sensitive to channel information error. Bulky. Very complicated to optimize. 49

50 Comparison of Different Gains 25 K =1 single-user SIMO MSP (db) K = single-user MIMO multi-user SIMO multi-user MEB K=16 multi-user MIMO MIMO gain multi-user gain BF gain optimization gain R (bits/symbol) single-user SIMO Single-user MIMO multi-user SIMO Multi-user MEB multi-user MIMO 50

51 Types of Gains in Multi-User MIMO - MIMO gain achievable by single-user MIMO - Multi-user gain achievable by multi-user SIMO - Beamforming gain achievable by multi-user MEB - Optimization gain achievable by multi-user MIMO single-user SIMO Single-user MIMO multi-user SIMO Multi-user MEB multi-user MIMO 51

52 Optimization Gain Optimization involves decoding order optimization, correlation matrix optimization, singular value decomposition (SVD), eigenmode water filling. Therefore to achieve optimization gain is a very complicated task. As we can see, the difference between MEB and optimal MIMO Is marginal. Thus optimization gain is not significant. 52

53 Contents Introduction Multi-user gain (MUG) Maximum eigenmode beamforming (MEB) MEB performance analysis SIMO v.s. MIMO Multi-user gain (MUG) Implementation of MEB using IDMA Conclusions 53

54 MEB-Based IDMA x c1 1 π 1 p 1 ck π K xk p K π 1 π 1 π K π K 54

55 Performance of MEB-Based IDMA R = 4 bits/symbol 55

56 MIMO Broadcasting and Duality Based on the MAC-BC duality principle (Yu, Cioffi, Vishwanath, Jindal, Goldsmith), the conclusions in this talk can be also applied to BC channels. For simplicity, we will concentrate on MIMO MAC below. 56

57 Contents Introduction Multi-user gain (MUG) Maximum eigenmode beamforming (MEB) MEB performance analysis SIMO v.s. MIMO Implementation of MEB using IDMA Conclusions 57

58 Conclusions Optimal MIMO systems are bulky and sensitive. They are also complicated to design and to decode. Multi-user SIMO can achieve very impressive gain. If multiple antennas are affordable, MEB is a low-cost, almost optimal strategy. IDMA provides an efficient framework to realize MUG. 58

59 Thank You! 59