how many users are needed for non-trivial performance of random beamforming in highly- directional...
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How many users are needed for non-trivial perfor-mance of random beamforming in highly-direc-
tional mm-wave MIMO downlink?
Gilwon Lee
School of Electrical EngineeringKAIST
Oct. 14, 2015
Information Theory Workshop 2015, Jeju island, Korea
Joint work with Prof. Youngchul Sung and Junyeong Seo
5G Key Technologies
Average rate (bits/s/active user) 10~100x
Average area rate (bits/s/km2) 1000x
Active devices (per km2) 10-100x
Energy efficiency (bits/Joule) 1000x
5G Requirements
3 GHz 30 GHz 300 GHz
Cellular band Mm-wave band
Key Technologies
Massive MIMO Mm-wave MIMO
(argos ant.)(Prof. Heath’s Fig)
Focus of this talk
Mm-wave Channel Characteristics
• Quasi-optical nature of propagation • Very few multi-path components
Channels are sparse
S. Sun, T. S. Rappaport, “Wideband mmWave Channels: Implications for De-sign and Implementation of Adaptive Beam Antennas ,” IEEE 2014 Intl. Mi-crowave Symp. (IMS), June 2014, Tampa, Fl
Many literatures use geometric channel model
Ex)
cf.
Channel sparsity
Mm-wave Channel Characteristics
• Large path-loss• High noise power due to large-bandwidth
Mm-wave noise BW
microwave noise BW
(Friis’ law)
Exploiting large-array antenna gain
Massive antennas
G. R. MacCartney, M. K. Samimi, and T. S. Rappaport, "Omnidirectional Path Loss Models in New York City at 28 GHz and 73 GHz,“ IEEE 2014 PIMRC.
A Challenging Issue: Channel Estimation
• Channel sounding also requires highly-directional training beams due to large path-loss and high noise power.
• Furthermore, there are few multi-path components in channels
Long training period is required!
Full-training method
A Challenging Issue: Channel Estimation
An efficient method: Multi-resolution Hierarchical approach
1. Divide full-range of the BS into two regions and transmit training beams to each of them
2. After feedback, the BS chooses the better region
1st stage
A. Alkhateeb, O. E. Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for millimeter wave cellular systems,” IEEE JSTSP, Oct. 2014.
feedback
A Challenging Issue: Channel Estimation
1. Divide full-range of the BS into two regions and transmit training beams to each of them
2. After feedback, the BS chooses the better region
3. and further divides the chosen regioninto two sub-regions.
2nd stage
A. Alkhateeb, O. E. Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for millimeter wave cellular systems,” IEEE JSTSP, Oct. 2014.
An efficient method: Multi-resolution Hierarchical approach
A Challenging Issue: Channel Estimation
Training period can be significantly reduced.
1. Divide full-range of the BS into two regions and transmit training beams to each of them
2. After feedback, the BS chooses the better region
3. and further divides the chosen regioninto two sub-regions.
3rd stage
However, power consumption for training is very large at early stages.
A. Alkhateeb, O. E. Ayach, G. Leus, and R. W. Heath, “Channel estimation and hybrid precoding for millimeter wave cellular systems,” IEEE JSTSP, Oct. 2014.
This approach is useful for single-user case.
An efficient method: Multi-resolution Hierarchical approach
Properties of the method
A Fundamental Question
• We have seen some results of singe-user systems.
• Then, what about multi-user systems?
• Is long training period still needed to obtain reasonable performance for multi-user systems?
Some Insights
• Let’s assume the BS transmits a highly directional training beam to a random angle direction.
• Now we ask what happens if there are many users in the cell.
• Intuitively, we can expect the single random beam performs well when the number of users is large.
• Then how many users are needed? Specify the # of users!
Multi-User Diversity
• In fact, many works on the multi-user diversity (opportunisticbeamforming) have been conducted in the Rayleigh fading channel model which is usually suitable for the cellular band.
• Ex. Random beamforming (RBF), Semi-orthogonal user selection (SUS)
i.i.d.
• However, there are no any analysis results on multi-user diversity in the mm-wave band.
M. Sharif and B. Hassibi, “On the capacity of MIMO broadcast channels with partial side information,” IEEE Trans. Inf. Theory, vol. 51, pp. 506–522, Feb. 2005.
T. Yoo and A. Goldsmith, “On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming,” IEEE J. Sel. AreasCommun., vol. 24, pp. 528–541, Mar. 2006
Exploring Multi-User Diversity in Mm-wave
• System Model
MU-MISO downlink
BS with ULA of antennas
single-antenna users
• Channel Model
Uniform-Random Single-Path (UR-SP)
Path gain
Steering vector
AoD
Channel vector of user k
UR-SP Channel Model
• UR-SP Channel Model
When LoS exists
Considering not only LoS environment but also one dominant path in NLoS environment
When LoS does not exist
One dominant NLOS path
The different path gain between LoS and NLoS components can be captured by the assumption
Singe Beam Case
• The BS transmits a randomly directional training beam to receivers
in the direction of a random angle .
Singe Beam Case
• The BS transmits a randomly directional training beam to receivers
in the direction of a random angle .
• Then, each user feeds back the signal power to the BS.
• After the feedback is over, the BS selects the user that has the maximum
signal power, and transmits a data stream with the beamforming vector .
(single beam rate)
Fejer Kernel of Order M
• Since mm-wave systems use many antennas, we adopt asymptote.
Beam pattern
Fejer kernel of order M
• The value of beam pattern w.r.t. the difference btw and .
Fejer Kernel of Order M: Observation
Order of 1/M
Singe Beam Rate
• If we can find a user k such that almost surely, we have
Observation
• When for all k, and for fixed , we have
• Based on the above facts, we have the following observation.
Q) How many users K as a function of M are needed to obtain non-trivial performance?
(trivial performance)
(non-trivial performance)
Lemma 1
• To explicitly derive it, we assume for simple explanation
and provide a lemma related to signal power as follows.
(The effect of is fully considered in the paper, but is trivial so we
omitted it in this presentation.)
For any constant and sufficiently large M, we have
where
signal power
Proof of Lemma 1: omitted
Lemma 1
Theorem 1 – Asymptotic Rate of
For and any given , we have
where .
Proof of Theorem 1: omitted
Theorem 1
is the performance transition point !
• Based on Lemma 1, we can show the following theorem.
Corollary 1
Rate when perfect CSI is available
For
Theorem 1 – Asymptotic Rate of
is the performance transition point !
Corollary 1
Rate when perfect CSI is available
For
Theorem 1 – Asymptotic Rate of
Need more training beams!
is the performance transition point !
Effect of Training
Multiple Training Beams:
where is an offset angle.
Remark:
Theorem 2 – Asymptotic Rate of
For , and any
such that , we have
where .
Proof of Theorem 2: omitted
Theorem 2 Corollary 2
Rate when perfect CSI is available
For
is the performance transition point !
Theorem 2 – Asymptotic Rate of
is the performance transition point !
Corollary 2
Rate when perfect CSI is available
For
Theorem 2 – Asymptotic Rate of
is the performance transition point !
Theorem 2 – Asymptotic Rate of
• When the number of users is too small to achieve non-trivial performance,
Theorem 2 specify how much training is required to achieve it!
Simulation Results
Single beam case Multi-beam case
M=1000
Extension to the Multi-User Selection
• Multi-user selection with multi-beam
1. Each user k feeds back the maximum SINRand the corresponding beam index.
2. For each beam, the BS chooses the user thathas the maximum SINR
3. and transmits data streams to the chosen users through the corresponding beams at the same time.
Random beamforming (RBF)
Rate of a selected user
where
G. Lee, Y. Sung, and J. Seo, “Randomly directional beamforming in millimeter wave multi-user MISO downlink,” to appear in IEEE Tran. Wireless Commun.
Theorem 3 – Asymptotic Rate of
Theorem 3
For , with and , we have
where for .
Sum Rate
As , (the optimal rate)
G. Lee, Y. Sung, and J. Seo, “Randomly directional beamforming in millimeter wave multi-user MISO downlink,” to appear in IEEE Tran. Wireless Commun.
Asymptotic Results of RBF in UR-SP
• Linear sum rate scaling w.r.t. M can be achieved, if K increases linearly w.r.t. M.
• This result is contrary to the existing result in the Rayleighfading channel model where linear sum rate scaling w.r.t. Mcan be achieved, if K increases exponentially w.r.t. M.
As ,
• Furthermore, the optimal sum rate can be achieved if K increases linearly w.r.t. M.
G. Lee, Y. Sung, and J. Seo, “Randomly directional beamforming in millimeter wave multi-user MISO downlink,” to appear in IEEE Tran. Wireless Commun.
Conclusion
• There exists a performance transition point in the numberof users (relative to the number of antennas) for non-trivialperformance.
• We specify how much training is required for obtaining non-trivial performance.
• Furthermore, the performance of random beamforming canachieve the optimal sum rate if K increases linearlyw.r.t. M.
(Single beam case)
(Single-user selection with multi-beam case)
(Multi-user selection with multi-beam case)