How many users are needed for non-trivial performance of random beamforming in highly- directional mm-wave MIMO downlink? Gilwon Lee School of Electrical

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


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




3. and further divides the chosen regioninto two sub-regions.

2nd stage




Training period can be significantly reduced.



3. and further divides the chosen regioninto two sub-regions.

3rd stage

However, power consumption for training is very large at early stages.


This approach is useful for single-user case.


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



Corollary 1


For


Need more training beams!


Effect of Training

Multiple Training Beams:

where is an offset angle.

Remark:


For , and any

such that , we have

where .

Proof of Theorem 2: omitted

Theorem 2 Corollary 2


For




Corollary 2


For




• 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

For , with and , we have

where for .

Sum Rate

As , (the optimal rate)


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.


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)

Documents

How many users are needed for non-trivial performance of random beamforming in highly- directional mm-wave MIMO downlink? Gilwon Lee School of Electrical