Multi-user diversity in
slow fading channels
“Opportunistic Beamforming Using Dumb Antennas”
P. Vishwanath, D. Tse, R. Laroia, IT 2002
Fading : Rapid fluctuations of signal strength due to
constructive and destructive interference between multi-
Diversity : Technique to compensate for fading channel
impairments. It can be obtained over:
Time - Interleaving of coded bits
Frequency – Spread spectrum & frequency hopping
Space – Multiple antennas
Fast fading channels : Diversity inherent
Slow fading channels: Diversity induced
Focus on downlink of wireless
Multiple antennas at the base station to transmit the same
Fundamental difference :
“Multi-user diversity takes advantage of rather than
Opportunistic Beam forming
The information bearing signal at each of the transmit antenna
is multiplied by a random complex gain.
Formation of random beam.
Slow Fading Environment : Before
Slow Fading Environment : After
Fading channel is Better Than AWGN
Total average SNR = 0 dB.
Long term total throughput can be maximized by always
serving the user with the strongest channel.
Maximizing information theoretic capacity
--In a large system with users channels fading
independently, there is likely to be a user with a very
good channel at any time.
--Schedule to the user with best channel to transmit to
--Channel tracked by receiver and SNR fed back to BS.
--Peak transmit power constraint.
Issues in scheduling
Fading statistics identical:
-- Strategy not only maximizes the total capacity but
also throughput of individual users.
Fading statistics different : Two major issues
Proportional Fair Scheduling
At time slot t, given
User’s average throughputs T1(t), T2(t)…in past window of
Feedback of channel quality in terms of requested data rate
Schedule the user ‘k’ with the highest ratio
Rk = current requested rate of user k
Tk = average throughput of user k in the past tc time slots.
Average throughputs Tk (t) updated by an exponential filter.
Inspection of algorithm
When tc is small- Serves all users
When tc is large
-- Case-1 : Identical channels
Tk remains same .Pick user with greater Rk.
-- Case-2 : Different channels
If Tk is large then Rk is also large. Pick user with
Comparison with space time code
Space time code : Intelligent use of transmit diversity to
improve reliability of point-to-point link but reduce multi-
user diversity gain.
In contrast, opportunistic beam forming requires no
special multi-antenna encoder or decoder nor MIMO
Use of separate pilot signals for each antenna in space
Antennas are truly dumb, but yet can surpass
performance of space time code (with proportional
Overall performance Improvement
Cellular Environment : Opportunistic Nulling
In a cellular systems, users are scheduled when their
channel is strong and interference from adjacent base
station is weak.
Multi-user diversity allows interference avoidance as there
is beamforming to some users and null to other users.
Opportunistic beamforming combined with opportunistic
Modern design principle :
“Large and Rapid channel fluctuations are
Proactive Stance :
“Induce Larger and Faster Channel fluctuations”
-- Sufficient number of users in the system
-- Scheduling algorithm