Beamforming Utilizing Channel Norm Feedback in Multiuser …ebjornson/poster_spawc2007.pdf ·...
Transcript of Beamforming Utilizing Channel Norm Feedback in Multiuser …ebjornson/poster_spawc2007.pdf ·...
– There is spatial information in the channel norm, especially when it is strong.
– This motivates beamforming communication with channel norm feedback.
BEAMFORMING UTILIZING CHANNEL NORMFEEDBACK IN MULTIUSER MIMO SYSTEMSEmil Björnson, David Hammarwall and Björn OtterstenSchool of Electrical EngineeringRoyal Institute of Technology (KTH)Stockholm, Sweden
– The channel norm provides substantial spatial information.
– Two simple channel norm feedback strategies are proposed that outperform
opportunistic beamforming with the same amount of feedback.
Spatial Correlation, example
What information is gained of vi if the norm
(v1,v2)2 = v21 + v2
2 is observed?
Figure 1:The shaded area shows how the probability mass is distributed over the circle, representing a given norm. The inner arrows indicate the standard deviation. Observe that the probability mass is more focused for larger norms.
Consider two real-valued Gaussian distributed variables
vi ∈ N (0,σ2i ), i = 1,2.
System Model
Limited Feedback Strategy
Opportunistic beamforming:
• The beamformer is chosen at random.
• Each user feeds back its SNR.
• Advantage: Knowledge of the SNR,Disadvantage: Neglects spatial information.
Channel norm supported eigenbeamforming:
• Each user feeds back its channel norm ρk.
• The beamformer is determined using conditionalchannel statistics.
• Advantage: Exploits spatial information,Disadvantage: Requires SNR estimation.
• This strategy is analyzed in the paper.
ρkPilot/Feedback
New channel realization
Scheduling Datak)/BFSNRk(ρ
Antenna Selection Simulation Results
Figure 2: The CDF (over scenarios) of the cell throughput in a system with a transmitting eight-antenna UCA and four receive antennas per user. Opportunistic beamforming is compared to the proposed Feed-back supported eigenbeamforming for different receive strategies: antenna selection and receive beamforming (increasing perfor-mance). The angular spread is 15 degrees.
Figure 3: The mean cell throughput for different angular spreads. The proposed channel norm supported eigenbeamforming with antenna selection (circles) and receive beamforming (diamonds) is compared to the corresponding opportunistic beamforming.
0 10 20 305
6
7
8
9
10
11
Angular spread [degrees]
Mea
n ce
ll th
roug
hput
[bits
/sym
bol]
Eigen−BFOpp. BF
6 7 8 9 10 110
0.2
0.4
0.6
0.8
1
Cell throughput [bits/symbol]
6 8 10 120
0.2
0.4
0.6
0.8
1
Cell throughput [bits/symbol]
Eigen−BFOpp. BF
• Elevated base station, nT antennas.
• Multiple users, nR antennas.
• Partial channel information at base station.
Some directions are more favorable to a user:
System Operation
Channel information:Only Rk and ρk = maxi hk,i2, for each user k, isknown to the base station.
• Only the strongest receive antenna is used.
• The channel norm is ρk.
MMSE estimation of SNR:
ESNRk
ρk
=E
hHk,strongestwTk
2
σ2k
ρk
=
wHTk
R(ρk)wTk
σ2k
VSNRk
ρk
=
EhHwT
4ρk
− (wH
TR(ρk)wT )2
σ4k
Closed-form expressions for R(ρk) and
EhHwT
4ρk
are previously known.
• The antennas are combined to maximize the SNR.
• The norm of the strongest receive channel is ρk.
• The other channel norms are known to be smaller.
MMSE estimation of SNR:
Receive Beamforming
A strategy is needed to determine:
• The beamforming vector for user k.
• The corresponding SNR (and supported rate).
• Proportional fair scheduling.
• Rich scattering around the users.
Capacity estimation based on:
with α chosen to achieve outage probability 5%.
Channel model:Rayleigh fading MIMO channel to user k:
Hk = [hk,1,...,hk,nR]H
with independent hk,i ∈ CN (0,Rk).
The received vector (user k):
yk(t) = HkwTksk(t) + nk(t),
with beamforming vector wTk, symbol sk(t) and
AWGN nk(t) ∈ CN (0,σ2kI).
ESNRk
ρk
=
wHTk
R(ρk)wTk
σ2k
+(nR−1)wH
Tk
R(0≤ρ≤ρk)wTk
σ2k
VSNRk
ρk
=V
SNRk
ρk
+(nR−1)V
SNRk
0≤ρ≤ρk
Closed-form expressions for R(0 ≤ ρ ≤ ρk)
and VSNRk
0 ≤ ρ ≤ ρk
are derived.
ESNRk
ρk
− α
V
SNRk
ρk
,