64
From Single-‐User to Multi-‐User• In Lecture 3 we studied various techniques for multiple
access and interference management in cellular systems• In Lecture 4 we learned about information theory and
investigate the capacity of point-to-point channels• In this lecture we extend the information theoretic
framework to multi-user channels• Present new techniques that emerge from the
information theoretic study:- Success interference cancellation (SIC)- Superposition coding- Multi-user diversity- Opportunistic communication paradigm
2
Plot• Two scenarios:- Uplink channel (many-to-one)- Downlink channel (one-to-many)
• Start with AWGN (no fading)- Uplink channel: successive interference cancellation (SIC)- Downlink channel: superposition coding
• Fast Fading- CSIR only - Full CSI
• Multi-user Diversity
3
Outline• Uplink/Downlink AWGN channel
• Uplink/Downlink fading channel
• Multi-user diversity
• Opportunistic beamforming
4
5
Uplink/Downlink AWGN Channel
Uplink and Downlink Channel
6
y[m] = h1x1[m] + h2x2[m] + w[m] y1[m] = h1x[m] + w1[m]
y2[m] = h2x[m] + w2[m]
• Channel gains are fixed over time and known to Tx & Rx• Uplink noise: • Downlink noise at User k, k = 1,2:
CN (0,�2)
Uplink
y
x1 x2h1 h2
User 1 User 2
Rx: decodes both users’ data
Downlink
x
y1 y2h1 h2
Tx: encodes both users’ data
User 1 User 2
CN (0,�2k)
• Point-to-point channel:- Capacity C
• Multi-user channel- Each user has its own data- Two data rates R1 & R2
- Capacity region- (R1,R2) is achievable ⟺- both error probability → 0
Capacity Region
7
Achievableif R < C
Not Achievableif R > C
0 C
R
R1
R2
C
Achievableif (R1,R2) ∈ C
Not Achievableif (R1,R2) ∉ C
C
Achievable ⟺ Pe(N) → 0 as N → ∞
Capacity Region of the UL Channel
8
R1
R2
log (1 + SNR1)
log (1 + SNR2)
log
⇣1 +
SNR11+SNR2
⌘
log
⇣1 +
SNR21+SNR1
⌘
CUplinkR1 +R2 log (1 + SNR1 + SNR2)
SNRk :=|hk|2Pk
�2, k = 1, 2
CUplink =
[8><
>:(R1, R2) � 0 :
8><
>:
R1 log (1 + SNR1)
R2 log (1 + SNR2)
R1 +R2 log (1 + SNR1 + SNR2)
9>=
>;
Non-‐Achievability Outside Cuplink• Rk ≤ log(1+SNRk): obvious, since log(1+SNRk) is the
point-to-point capacity as if there is only one Tx
• R1+R2 ≤ log(1+SNR1+SNR2): obvious, since the maximum received SNR from the two independent Tx is SNR1+SNR2, and therefore the total rate cannot exceed the capacity of the point-to-point channel with this SNR
9
CUplink
Successive Interference Cancellation
10
R1
R2
log (1 + SNR1)
log (1 + SNR2)
log
⇣1 +
SNR11+SNR2
⌘
log
⇣1 +
SNR21+SNR1
⌘
CUplink
A
BAchieving point AUser k encodes its data using a capacity achieving AWGN channel code at rate Rk, k=1,2
Rx first decodes User 2’s data, treating User 1’s signal x1 as Gaussian noise=) R2 = log
⇣1 +
|h2|2P2
|h1|2P1+�2
⌘
= log
⇣1 +
SNR21+SNR1
⌘
can be achieved
Rx then subtracts x2 from y and get a point-to-point channel for User 1
y
x1 x2h1 h2
User 1 User 2
Rx: decodes both users’ data
=) R1 = log (1 + SNR1)
can be achieved
Note: smaller R2 can also be achieved
Equivalent Point-‐to-‐Point Channels• Equivalent channels- For User 2, the equivalent noise is h1x1+w, with variance
- For User 1, after removing x2, Rx sees a clean point-to-point channel without interference
11
h2
x2[m]
h1x1[m] + w[m]
y[m]
|h1|2P1 + �2
x1[m]
h1 w[m]
y[m]� h2x2[m]
Time Sharing
12
R1
R2
log (1 + SNR1)
log (1 + SNR2)
log
⇣1 +
SNR11+SNR2
⌘
log
⇣1 +
SNR21+SNR1
⌘
CUplink
A
BSimilarly point B can be achieved
y
x1 x2h1 h2
User 1 User 2
Rx: decodes both users’ data
To achieve a rate point on AB, say, qA + (1-q)B, the system can take the following two strategies with a prescribed portion of time:
Strategy achieving A Decode User 2 first and then decode User 1; q of time
Strategy achieving B Decode User 1 first and then decode User 2; (1-q) of time
Comparison with Conventional CDMA• For each user, treat the other user’s signal as noise - No successive interference cancellation (SIC)- Hence a single-user receiver, not a multi-user receiver
• It is strictly suboptimal (achieving point C)
13
R1
R2
log (1 + SNR1)
log (1 + SNR2)
log
⇣1 +
SNR11+SNR2
⌘
log
⇣1 +
SNR21+SNR1
⌘
CUplink
A
B
C
UL Orthogonal Multiple Access• Consider time-division access- User 1 uses the first α of the time- User 2 uses the rest (1–α) of the time
• Power constraint: - User 1 can now use power P1/α during its transmission- User 2 can now use power P2/(1–α) during its transmission
• Achievable rates:
- When α = SNR1/(SNR1+SNR2), the sum capacity is achieved (i.e., R1+R2 = log(1+SNR1+SNR2) is achieved)
14
(R1 = ↵ log
�1 +
SNR1↵
�
R2 = (1� ↵) log⇣1 +
SNR21�↵
⌘ ↵ 2 [0, 1]
Orthogonal MA is Sum Rate Optimal
15
D
Orthogonal multiple access can only achieve the optimal sum rate at a single point, when !! α = SNR1/(SNR1+SNR2)
[
↵2[0,1]
((R1, R2) :
(R1 = ↵ log
�1 +
SNR1↵
�
R2 = (1� ↵) log⇣1 +
SNR21�↵
⌘)
(R1 = SNR1
SNR1+SNR2Csum
R2 = SNR2SNR1+SNR2
CsumD:
Csum = log (1 + SNR1 + SNR2)
Fairness is an issue
R1
R2
log (1 + SNR1)
log (1 + SNR2)
log
⇣1 +
SNR11+SNR2
⌘
log
⇣1 +
SNR21+SNR1
⌘
CUplink
• For a general K-user uplink channel- Capacity region:
- Sum capacity:
• For example, 3-user uplink channel capacity region:
K-‐user Uplink Channel Capacity
16
CUplink =
[((R1, . . . , RK) � 0 :
X
k2SRk log
1 +
X
k2SSNRk
!, 8S ✓ [1 : K]
)
CsumUplink = log
1 +
KX
k=1
SNRk
!
Rk log (1 + SNRk) , k = 1, 2, 3
R1 +R2 log (1 + SNR1 + SNR2)
R2 +R3 log (1 + SNR2 + SNR3)
R3 +R1 log (1 + SNR3 + SNR1)
R1 +R2 +R3 log (1 + SNR1 + SNR2 + SNR3)
Capacity Region of the DL Channel
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SNRk :=|hk|2P�2k
, k = 1, 2
CDownlink
R1
R2
log (1 + SNR1)
log (1 + SNR2)
Note: proof of non-achievability outside this region is beyond the scope of this course
WLOG assume SNR1≥SNR2
Maximum sum rate is achieved when β = 1
=) Csum
Downlink
= log (1 + SNR1
)
CDownlink
=
[
�2[0,1]
((R
1
, R2
) � 0 :
(R
1
log (1 + �SNR1
)
R2
log
⇣1 +
(1��)SNR2
1+�SNR2
⌘)
Superposition Coding• Tx sends x = x1+x2, where for k=1,2- User k’s data is encoded onto xk
- Power of x1 = βP; power of x2 = (1–β)P
• User 1 has a better received SNR- User 1’s channel is better than User 2- User 1 can decode whatever User 2 can decode
• Single-user decoding at User 2: - Decode x2 by treating x1 as noise- ⟹ can achieve
• SIC Decoding at User 1: - First decode x2 by treating x1 as noise, and remove it from y1
- Then decode x1 ⟹ can achieve
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x
y1 y2h1 h2
Tx: encodes both users’ data
User 1 User 2
R2 = log
⇣1 +
(1��)SNR2
1+�SNR2
⌘
R1 = log (1 + �SNR1)
Comparison with Conventional CDMA• Conventional CDMA: the same as before except that
User 1 does not do SIC
• Strictly suboptimal
• Exercise: how to choose β such that all DL users have the same received SINR?
19
DL Orthogonal Multiple Access• Consider time-division access- User 1 uses the first α of the time with power P- User 2 uses the rest (1–α) of the time with power P
• Achievable rates:
- Strictly suboptimal (except the two corner points when one of the users is shut down)
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(R1 = ↵ log (1 + SNR1)
R2 = (1� ↵) log (1 + SNR2)↵ 2 [0, 1]
K-‐user Downlink Channel Capacity• WLOG assume SNR1 ≥ SNR2 ≥ … ≥ SNRK
• Capacity region:
- βk denotes the portion of power allocated to User k’s codeword
• Sum capacity: achieved by sending only to the best user
21
CDownlink
=
[
�1,...,�K�0
�1+···+�K=1
8<
:(R1
, . . . , RK) � 0 :
Rk log
✓1 +
�kSNRk
1+
Pk�1j=1 �jSNRk
◆,
8 k 2 [1 : K]
9=
;
Csum
Downlink
= log (1 + SNR1
)
22
Uplink/Downlink Fading Channel
Setting
• Fast fading: ∀k, {hk[m]} is stationary and ergodic
• Symmetry: ∀k, {hk[m]} is identically distributed
• We shall focus on ergodic sum capacity
23
Uplink
y
x1 x2h1 h2
User 1 User 2
Rx: decodes both users’ data
Downlink
x
y1 y2h1 h2
Tx: encodes both users’ data
User 1 User 2
y[m] = h1[m]x1[m] + h2[m]x2[m] + w[m] y1[m] = h1[m]x[m] + w1[m]
y2[m] = h2[m]x[m] + w2[m]
Uplink Channel Capacity: CSIR Only• Without CSIT, the ergodic sum capacity is
- where SNRk := Pk/σ2, k = 1,2,…,K
• Comparison with AWGN capacity:
- due to Jensen’s inequality
• Similar to the point-to-point case: if there is no CSIT, fading makes things worse
24
CsumUL, CSIR = E
"log
1 +
KX
k=1
|hk|2SNRk
!#
CsumUL, CSIR = E
"log
1 +
KX
k=1
|hk|2SNRk
!#
log
1 +
KX
k=1
E⇥|hk|2
⇤SNRk
!= log
1 +
KX
k=1
SNRk
!= Csum
UL, AWGN
Downlink Channel Capacity: CSIR Only• Recall channel symmetry: - ∀k, {hk[m]} is identically distributed
• Due to the symmetry assumption:- There is a natural ordering of the users- based on the noise level σk2
• WLOG assume SNR1 ≥ … ≥ SNRK where SNRk := P/σk2
• Sum capacity is achieved by serving the best user only
• By Jensen’s inequality this is strictly worse than the AWGN downlink sum capacity
25
x
y1 y2h1 h2
Tx: encodes both users’ data
User 1 User 2
=) CsumDL, CSIR = E
⇥log
�1 + |h1|2SNR1
�⇤
Impact of Multiple Users• Under fast fading without CSIT:- The ergodic sum capacity of multiuser UL/DL channels is smaller
than that without fading- Similar to the point-to-point case
• As K (# of users) increases, this capacity loss behaves differently in the uplink and the downlink- In uplink, the loss vanishes as K → ∞- In downlink, the loss remains as K → ∞
• Explored in Homework 3
26
Downlink Channel Capacity: Full CSI• User symmetry assumption: σk = σ, ∀k = 1,…,K
• Downlink channel sum capacity is achieved by sending only to the instantaneously best user.
• Optimization problem:
• Solution:
27
max
P (h)�0Elog
✓1 +
maxk2[1:K] |hk|2P (h)
�2
◆�
s.t. E [P (h)] = P
P ⇤(h) =
✓⌫ � �2
maxk2[1:K] |hk|2
◆+
,
⌫ satisfies E"✓
⌫ � �2
maxk2[1:K] |hk|2
◆+#= P
Uplink Channel Capacity: Full CSI• Full CSI assumption: - At each time m, all users know the instantaneous realization of all
channel gains {hk[m] | k = 1,2,…,K}- In other words, a user can know not only its own channel but also
others’ channels
• User symmetry assumption: Pk = P, σk = σ, ∀k = 1,…,K
• Program in finding uplink sum capacity under full CSI:- Consider an L-parallel uplink AWGN channel- Relax individual power constraints to a total power constraint- Solve the new problem under finite L, and take L → ∞- By channel and user symmetry, argue that the found solution is
also feasible under individual power constraints
28
Power Allocation Problem• Original problem:
• Relaxed problem:
• We will solve the relaxed problem first, and verify that the solution found there is also feasible for the original one
29
Individual power constraint
max
Pk(h)�0k2[1:K]
E"log
1 +
PKk=1 |hk|2Pk(h)
�2
!#
s.t.
XK
k=1E [Pk(h)] = KP
max
Pk(h)�0k2[1:K]
E"log
1 +
PKk=1 |hk|2Pk(h)
�2
!#
s.t. E [Pk(h)] = P, k = 1, 2, . . . ,K
Total power constraint
Parallel Uplink Channel• L parallel K-user uplink channel:- Channel gains for the l-th sub-channel: {hk,l | k = 1,2,…,K}- Power allocated to the l-th sub-channel: {Pk,l | k = 1,2,…,K}
• Optimization problem (total power constraint):
30
total power constraint
max
Pk,l�0k2[1:K], l2[1:L]
1
L
LX
l=1
log
1 +
PKk=1 |hk,l|2Pk,l
�2
!
s.t.
KX
k=1
1
L
LX
l=1
Pk,l = KP
Optimal Allocation in Parallel UL (1)• Rewrite the total power constraint as
• For a fixed partition {Pl | l ∈ [1:L]} of the total power LKP, the sum rate of the l-th sub-channel is maximized if all of Pl is allocated to the best user: (! ! ! ! ! ! )
31
KX
k=1
1
L
LX
l=1
Pk,l = KP ()LX
l=1
KX
k=1
Pk,l
!
| {z }Pl
= LKP
max
Pk,l�0k2[1:K]
log
1 +
PKk=1 |hk,l|2Pk,l
�2
!
= log
1 +
�maxk2[1:K] |hk,l|2
�Pl
�2
!
Pl :=PK
k=1 Pk,l
Optimal Allocation in Parallel UL (2)• How to determine the best partition {Pl | l ∈ [1:L]} of the
total power LKP?
• Problem becomes:
• Water-filling solution:
32
P⇤l =
✓⌫ � �2
maxk2[1:K] |hk,l|2
◆+
, ⌫ satisfies
LX
l=1
P⇤l = LKP
max
Pl�0l2[1:L]
1
L
LX
l=1
log
1 +
�maxk2[1:K] |hk,l|2
�Pl
�2
!
s.t.
LX
l=1
Pl = LKP
Optimal Allocation in Parallel UL (3)• Optimal power allocation in L parallel K-user uplink
channel under the total power constraint:
- where
• Take L → ∞, we obtain the solution of the power allocation problem of the uplink fading channel under total power constraint
- where
33
P ⇤k,l =
(P⇤l , if k = argmaxj2[1:K] |hj,l|2
0, otherwise
P ⇤k (h) =
(P⇤
(h), if k = argmaxj2[1:K] |hj |2
0, otherwise
P⇤l =
✓⌫ � �2
maxk2[1:K] |hk,l|2
◆+
, ⌫ satisfies
LX
l=1
P⇤l = LKP
P⇤(h) =
✓⌫ � �2
maxk2[1:K] |hk|2
◆+
, ⌫ satisfies E [P⇤(h)] = KP
Solution to the Original Problem• Recall the original vs. the relaxed problem
• Note: solution to the relaxed problem is
• Due to channel symmetry, !! ! ! are equal ∀k ⟹ ! ! ! ! ∀k ⟹ feasible in the original problem!
34
P ⇤k (h) =
(P⇤
(h), if k = argmaxj2[1:K] |hj |2
0, otherwise
where P⇤(h) =
✓⌫ � �2
maxk2[1:K] |hk|2
◆+
, ⌫ satisfies E [P⇤(h)] = KP
maxPk(h)�0k2[1:K]
E"log
1 +
PKk=1 |hk|2Pk(h)
�2
!#
s.t. E [Pk(h)] = P, k = 1, . . . ,K Original Problem
s.t.XK
k=1E [Pk(h)] = KP Relaxed Problem
E [P ⇤k (h)]
E [P ⇤k (h)] = P
UL Capacity with Full CSI: Summary
• Solution:
35
max
Pk(h)�0k2[1:K]
E"log
1 +
PKk=1 |hk|2Pk(h)
�2
!#
s.t. E [Pk(h)] = P, k = 1, 2, . . . ,K
P ⇤k (h) =
(P⇤
(h), if k = argmaxj2[1:K] |hj |2
0, otherwise
where P⇤(h) =
✓⌫ � �2
maxk2[1:K] |hk|2
◆+
,
⌫ satisfies E"✓
⌫ � �2
maxk2[1:K] |hk|2
◆+#= KP
Remarks• Sum capacities and optimal power allocation solutions of
the DL and the UL channels are essentially the same- UL total power constraint: KP- DL total power constraint: P
• Full CSIT requirement in UL:- We begin with the assumption that all users know all the channels- However, to attain the optimal power allocation, each user only
needs to know its own channel and whether it is the best channel- Amount of feedback to each user is not increasing with K !
36
37
Multi-‐User Diversity
A Key Feature of Wireless Channel• Time variation!
• Multi-path fading• Large-scale channel variations (path loss, shadowing)• Time-varying interference
38
262 Multiuser capacity and opportunistic communication
path that is not varying, while Especular refers to the energy in the specularor time-varying component that is assumed to be Rayleigh distributed.The Doppler spectrum of this component follows Clarke’s model with aDoppler spread of 2Hz.
• Low mobility Users move at walking speeds (3 km/hr, Rayleigh).• High mobility Users move at 30 km/hr, Rayleigh.
The average channel gain !!!h!2" is kept the same in all the three scenariosfor fairness of comparison. The total throughput increases with the numberof users in both the fixed and low mobility environments, but the increaseis more dramatic in the low mobility case. While the channel varies in bothcases, the dynamic range and the rate of the variations is larger in the mobileenvironment than in the fixed one (Figure 6.18). This means that over thelatency time-scale (tc = 1#67 s in these examples) the peaks of the channelfluctuations are likely to be higher in the mobile environment, and the peaksare what determines the performance of the scheduling algorithm. Thus, theinherent multiuser diversity is more limited in the fixed environment.Should one then expect an even higher throughput gain in the high mobility
environment? In fact quite the opposite is true. The total throughput hardlyincreases with the number of users! It turns out that at this speed the receiverhas trouble tracking and predicting the channel variations, so that the predictedchannel is a low-pass smoothed version of the actual fading process. Thus,even though the actual channel fluctuates, opportunistic communication isimpossible without knowing when the channel is actually good.In the next section, we will discuss how the tracking of the channel can be
improved in high mobility environments. In Section 6.7.3, we will discuss ascheme that boosts the inherent multiuser diversity in fixed environments.
6.7.2 Channel prediction and feedback
The prediction error is due to two effects: the error in measuring the channelfrom the pilot and the delay in feeding back the information to the base-station.
Figure 6.18 The channelvaries much faster and haslarger dynamic range in themobile environment.
Mobile environment
Channelstrength
Dynamicrange
Dynamicrange
Time Time
Fixed environment
Channelstrength
Traditional Design Approach
39
262 Multiuser capacity and opportunistic communication
path that is not varying, while Especular refers to the energy in the specularor time-varying component that is assumed to be Rayleigh distributed.The Doppler spectrum of this component follows Clarke’s model with aDoppler spread of 2Hz.
• Low mobility Users move at walking speeds (3 km/hr, Rayleigh).• High mobility Users move at 30 km/hr, Rayleigh.
The average channel gain !!!h!2" is kept the same in all the three scenariosfor fairness of comparison. The total throughput increases with the numberof users in both the fixed and low mobility environments, but the increaseis more dramatic in the low mobility case. While the channel varies in bothcases, the dynamic range and the rate of the variations is larger in the mobileenvironment than in the fixed one (Figure 6.18). This means that over thelatency time-scale (tc = 1#67 s in these examples) the peaks of the channelfluctuations are likely to be higher in the mobile environment, and the peaksare what determines the performance of the scheduling algorithm. Thus, theinherent multiuser diversity is more limited in the fixed environment.Should one then expect an even higher throughput gain in the high mobility
environment? In fact quite the opposite is true. The total throughput hardlyincreases with the number of users! It turns out that at this speed the receiverhas trouble tracking and predicting the channel variations, so that the predictedchannel is a low-pass smoothed version of the actual fading process. Thus,even though the actual channel fluctuates, opportunistic communication isimpossible without knowing when the channel is actually good.In the next section, we will discuss how the tracking of the channel can be
improved in high mobility environments. In Section 6.7.3, we will discuss ascheme that boosts the inherent multiuser diversity in fixed environments.
6.7.2 Channel prediction and feedback
The prediction error is due to two effects: the error in measuring the channelfrom the pilot and the delay in feeding back the information to the base-station.
Figure 6.18 The channelvaries much faster and haslarger dynamic range in themobile environment.
Mobile environment
Channelstrength
Dynamicrange
Dynamicrange
Time Time
Fixed environment
Channelstrength
262 Multiuser capacity and opportunistic communication
path that is not varying, while Especular refers to the energy in the specularor time-varying component that is assumed to be Rayleigh distributed.The Doppler spectrum of this component follows Clarke’s model with aDoppler spread of 2Hz.
• Low mobility Users move at walking speeds (3 km/hr, Rayleigh).• High mobility Users move at 30 km/hr, Rayleigh.
The average channel gain !!!h!2" is kept the same in all the three scenariosfor fairness of comparison. The total throughput increases with the numberof users in both the fixed and low mobility environments, but the increaseis more dramatic in the low mobility case. While the channel varies in bothcases, the dynamic range and the rate of the variations is larger in the mobileenvironment than in the fixed one (Figure 6.18). This means that over thelatency time-scale (tc = 1#67 s in these examples) the peaks of the channelfluctuations are likely to be higher in the mobile environment, and the peaksare what determines the performance of the scheduling algorithm. Thus, theinherent multiuser diversity is more limited in the fixed environment.Should one then expect an even higher throughput gain in the high mobility
environment? In fact quite the opposite is true. The total throughput hardlyincreases with the number of users! It turns out that at this speed the receiverhas trouble tracking and predicting the channel variations, so that the predictedchannel is a low-pass smoothed version of the actual fading process. Thus,even though the actual channel fluctuates, opportunistic communication isimpossible without knowing when the channel is actually good.In the next section, we will discuss how the tracking of the channel can be
improved in high mobility environments. In Section 6.7.3, we will discuss ascheme that boosts the inherent multiuser diversity in fixed environments.
6.7.2 Channel prediction and feedback
The prediction error is due to two effects: the error in measuring the channelfrom the pilot and the delay in feeding back the information to the base-station.
Figure 6.18 The channelvaries much faster and haslarger dynamic range in themobile environment.
Mobile environment
Channelstrength
Dynamicrange
Dynamicrange
Time Time
Fixed environment
Channelstrength
• Compensates for channel fluctuations
Example: CDMA Systems• Two main compensating mechanisms:- Channel diversity- Interference management
• Channel diversity- Frequency diversity via Rake receiver- Macro-diversity via soft handoff- Tx/Rx antenna diversity
• Interference management- Intra-cell: power control- Inter-cell: interference averaging
40
What Drives this Approach?
41
262 Multiuser capacity and opportunistic communication
path that is not varying, while Especular refers to the energy in the specularor time-varying component that is assumed to be Rayleigh distributed.The Doppler spectrum of this component follows Clarke’s model with aDoppler spread of 2Hz.
• Low mobility Users move at walking speeds (3 km/hr, Rayleigh).• High mobility Users move at 30 km/hr, Rayleigh.
The average channel gain !!!h!2" is kept the same in all the three scenariosfor fairness of comparison. The total throughput increases with the numberof users in both the fixed and low mobility environments, but the increaseis more dramatic in the low mobility case. While the channel varies in bothcases, the dynamic range and the rate of the variations is larger in the mobileenvironment than in the fixed one (Figure 6.18). This means that over thelatency time-scale (tc = 1#67 s in these examples) the peaks of the channelfluctuations are likely to be higher in the mobile environment, and the peaksare what determines the performance of the scheduling algorithm. Thus, theinherent multiuser diversity is more limited in the fixed environment.Should one then expect an even higher throughput gain in the high mobility
environment? In fact quite the opposite is true. The total throughput hardlyincreases with the number of users! It turns out that at this speed the receiverhas trouble tracking and predicting the channel variations, so that the predictedchannel is a low-pass smoothed version of the actual fading process. Thus,even though the actual channel fluctuates, opportunistic communication isimpossible without knowing when the channel is actually good.In the next section, we will discuss how the tracking of the channel can be
improved in high mobility environments. In Section 6.7.3, we will discuss ascheme that boosts the inherent multiuser diversity in fixed environments.
6.7.2 Channel prediction and feedback
The prediction error is due to two effects: the error in measuring the channelfrom the pilot and the delay in feeding back the information to the base-station.
Figure 6.18 The channelvaries much faster and haslarger dynamic range in themobile environment.
Mobile environment
Channelstrength
Dynamicrange
Dynamicrange
Time Time
Fixed environment
Channelstrength
262 Multiuser capacity and opportunistic communication
path that is not varying, while Especular refers to the energy in the specularor time-varying component that is assumed to be Rayleigh distributed.The Doppler spectrum of this component follows Clarke’s model with aDoppler spread of 2Hz.
• Low mobility Users move at walking speeds (3 km/hr, Rayleigh).• High mobility Users move at 30 km/hr, Rayleigh.
The average channel gain !!!h!2" is kept the same in all the three scenariosfor fairness of comparison. The total throughput increases with the numberof users in both the fixed and low mobility environments, but the increaseis more dramatic in the low mobility case. While the channel varies in bothcases, the dynamic range and the rate of the variations is larger in the mobileenvironment than in the fixed one (Figure 6.18). This means that over thelatency time-scale (tc = 1#67 s in these examples) the peaks of the channelfluctuations are likely to be higher in the mobile environment, and the peaksare what determines the performance of the scheduling algorithm. Thus, theinherent multiuser diversity is more limited in the fixed environment.Should one then expect an even higher throughput gain in the high mobility
environment? In fact quite the opposite is true. The total throughput hardlyincreases with the number of users! It turns out that at this speed the receiverhas trouble tracking and predicting the channel variations, so that the predictedchannel is a low-pass smoothed version of the actual fading process. Thus,even though the actual channel fluctuates, opportunistic communication isimpossible without knowing when the channel is actually good.In the next section, we will discuss how the tracking of the channel can be
improved in high mobility environments. In Section 6.7.3, we will discuss ascheme that boosts the inherent multiuser diversity in fixed environments.
6.7.2 Channel prediction and feedback
The prediction error is due to two effects: the error in measuring the channelfrom the pilot and the delay in feeding back the information to the base-station.
Figure 6.18 The channelvaries much faster and haslarger dynamic range in themobile environment.
Mobile environment
Channelstrength
Dynamicrange
Dynamicrange
Time Time
Fixed environment
Channelstrength
• Main application is voice, with tight latency constraints• Need a consistent channel
Opportunistic Communication• A completely different view!
• Transmit more when and where the channel is good
• Exploits fading to achieve higher long-term throughput, but no guarantee that “the channel is always there”
• Appropriate for data with non-real-time latency requirements (file downloads, video streaming)
42
Single-‐User Fading Channel
43
203 5.4 Capacity of fading channels
the times when the channel strength is above the average cannot compensatefor the loss from the times when the channel strength is below the average.This again follows from the law of diminishing marginal return on capacityfrom increasing the received power.At low SNR, the capacity of the fading channel is
C = !!log"1+ !h!2SNR#$≈ !!!h!2SNR$ log2 e= SNR log2 e≈ Cawgn% (5.92)
where Cawgn is the capacity of the AWGN channel and is measured in bitsper symbol. Hence at low SNR the “Jensen’s loss” becomes negligible; thisis because the capacity is approximately linear in the received SNR in thisregime. At high SNR,
C ≈ !!log"!h!2SNR#$= log SNR+!!log !h!2$≈ Cawgn+!!log !h!2$% (5.93)
i.e., a constant difference with the AWGN capacity at high SNR. This differ-ence is −0&83 bits/s/Hz for the Rayleigh fading channel. Equivalently, 2.5 dBmore power is needed in the fading case to achieve the same capacity as inthe AWGN case. Figure 5.20 compares the capacity of the Rayleigh fadingchannel with the AWGN capacity as a function of the SNR. The differenceis not that large for the entire plotted range of SNR.
5.4.6 Transmitter side information
So far we have assumed that only the receiver can track the channel. But letus now consider the case when the transmitter can track the channel as well.There are several ways in which such channel information can be obtainedat the transmitter. In a TDD (time-division duplex) system, the transmitter
Figure 5.20 Plot of AWGNcapacity, fading channelcapacity with receiver trackingthe channel only (CSIR) andcapacity with both transmitterand the receiver tracking thechannel (full CSI). (Adiscussion of the latter is inSection 5.4.6.)
–5 0 5 10 15SNR (dB)
20
AWGN
CSIRFull CSI
C (b
its /s
/ Hz)
0–10–15–20
7
6
5
4
3
2
1
CFull CSI > CAWGN ≅ CCSIR
CAWGN > CFull CSI ≅ CCSIR
Single-‐User Channel: Low SNR Regime
44
207 5.4 Capacity of fading channels
the channel gain is h. The rate of that code is therefore log!1+P∗!h""h"2/N0"bits/s/Hz. No coding across channel states is necessary. This is in contrastto the case without transmitter channel knowledge, where a single fixed-rate code with the coded symbols spanning across different coherence timeperiods is needed (Figure 5.22). Thus, knowledge of the channel state at thetransmitter not only allows dynamic power allocation but simplifies the codedesign problem as one can now use codes designed for the AWGN channel.
Waterfilling performanceFigure 5.20 compares the waterfilling capacity and the capacity with channelknowledge only at the receiver, under Rayleigh fading. Figure 5.23 focuseson the low SNR regime. In the literature the former is also called the capacitywith full channel side information (CSI) and the latter is called the capacitywith channel side information at the receiver (CSIR). Several observationscan be made:
• At low SNR, the capacity with full CSI is significantly larger than theCSIR capacity.
• At high SNR, the difference between the two goes to zero.• Over a wide range of SNR, the gain of waterfilling over the CSIR capacityis very small.
The first two observations are in fact generic to a wide class of fadingmodels, and can be explained by the fact that the benefit of dynamic powerallocation is a received power gain: by spending more power when thechannel is good, the received power gets boosted up. At high SNR, however,the capacity is insensitive to the received power per degree of freedom andvarying the amount of transmit power as a function of the channel state yieldsa minimal gain (Figure 5.24(a)). At low SNR, the capacity is quite sensitiveto the received power (linear, in fact) and so the boost in received power fromoptimal transmit power allocation provides significant gain. Thus, dynamic
Figure 5.23 Plot of capacitieswith and without CSI at thetransmitter, as a fraction of theAWGN capacity.
–10 –5 0 5 100.5
–15–20
3
2.5
2
1.5
1
CCawgn
SNR (dB)
CSIRFull CSI
C
CAWGN
Power gain due to dynamic power allocation
Hitting Peaks over Time
45
Optimal Best Only:Near-Optimal
�2
|h[m]|2
m
⌫
�2
|h[m]|2
m
Interpretation: at low SNR, one only transmits when the channel is at its peak!⟹ primarily a power gain at low SNR!
Multi-‐User Fading Channel
46
254 Multiuser capacity and opportunistic communication
Figure 6.11 Sum capacity ofthe uplink Rayleigh fadingchannel plotted as a functionof SNR= KP/N0.
2
4
6
5–5–10–15–20 10 15 20
8
AWGNCSIRFull CSI
Csum(bits /s / Hz)
SNR (dB)
K = 16
K = 2
K = 4
K = 1
AWGN
Figure 6.12 Sum capacity ofthe uplink Rayleigh fadingchannel plotted as a functionof SNR= KP/N0 in the lowSNR regime. Everything isplotted as a fraction of theAWGN channel capacity.
1
5–5–15–20–25–30 10
2
3
4
5
6
7
CSIRFull CSI
SNR (dB)
CsumCAWGN
K = 16
K = 4
K = 2
K = 1
–10
Several observations can be made from the plots:
• The sum capacity without transmitter CSI increases with the number of theusers, but not significantly. This is due to the multiuser averaging effectexplained in the last section. This sum capacity is always bounded by thecapacity of the AWGN channel.
• The sum capacity with full CSI increases significantly with the number ofusers. In fact, with even two users, this sum capacity already exceeds that
For UL, SNR := KP/σ2 For DL, SNR := P/σ2
Increase in spectral efficiency with number of users K(∀K>1) at all SNR’s, not just low SNR
Multi-‐User Channel: Low SNR Regime
47
254 Multiuser capacity and opportunistic communication
Figure 6.11 Sum capacity ofthe uplink Rayleigh fadingchannel plotted as a functionof SNR= KP/N0.
2
4
6
5–5–10–15–20 10 15 20
8
AWGNCSIRFull CSI
Csum(bits /s / Hz)
SNR (dB)
K = 16
K = 2
K = 4
K = 1
AWGN
Figure 6.12 Sum capacity ofthe uplink Rayleigh fadingchannel plotted as a functionof SNR= KP/N0 in the lowSNR regime. Everything isplotted as a fraction of theAWGN channel capacity.
1
5–5–15–20–25–30 10
2
3
4
5
6
7
CSIRFull CSI
SNR (dB)
CsumCAWGN
K = 16
K = 4
K = 2
K = 1
–10
Several observations can be made from the plots:
• The sum capacity without transmitter CSI increases with the number of theusers, but not significantly. This is due to the multiuser averaging effectexplained in the last section. This sum capacity is always bounded by thecapacity of the AWGN channel.
• The sum capacity with full CSI increases significantly with the number ofusers. In fact, with even two users, this sum capacity already exceeds that
Multi-‐User Gain• Let us compare the single-user and the multi-user cases:- Point-to-point capacity
- Multi-user downlink capacity
48
P ⇤(h) =
✓⌫ � �2
|h|2
◆+
, ⌫ satisfies E"✓
⌫ � �2
|h|2
◆+#= P
Cpoint-to-point
= Elog
✓1 + |h|2P
⇤(h)
�2
◆�
CDownlink
= Elog
✓1 + max
k2[1:K]
|hk|2P ⇤
(h)
�2
◆�
P ⇤(h) =
✓⌫ � �2
maxk2[1:K]|hk|2
◆+
, ⌫ satisfies E"✓
⌫ � �2
maxk2[1:K]|hk|2
◆+#= P
Multi-‐User Opportunistic Communication
49
…
• Dedicate full power to serve only the best user + the peak value is higher than the mean ⟹ multi-user gain!
• Hitting peaks not only over time (at low SNR), but also over users (at all SNR)
User 1
User 2
User K
Multi-‐User Diversity• In a large system with users fading independently:- Likely to have a user with very good channel at any time- Different users peak at different times
• The more random the channel is, the higher the rate is
50
255 6.6 Multiuser diversity
of the AWGN channel. At 0 dB, the capacity with K = 16 users is about afactor of 2.5 of the capacity with K = 1. The corresponding power gain isabout 7 dB. Compared to the AWGN channel, the capacity gain for K = 16is about a factor of 2.2 and an SNR gain of 5.5 dB.
• For K= 1, the capacity benefit of transmitter CSI only becomes apparent atquite low SNR levels; at high SNR there is no gain. For K> 1 the benefitis apparent throughout the entire SNR range, although the relative gain isstill more significant at low SNR. This is because the gain is still primarilya power gain.
The increase in the full CSI sum capacity comes from a multiuser diversityeffect: when there are many users that fade independently, at any one timethere is a high probability that one of the users will have a strong channel.By allowing only that user to transmit, the shared channel resource is used inthe most efficient manner and the total system throughput is maximized. Thelarger the number of users, the stronger tends to be the strongest channel, andthe more the multiuser diversity gain.
The amount of multiuser diversity gain depends crucially on the tail ofthe fading distribution !hk!2: the heavier the tail, the more likely there is auser with a very strong channel, and the larger the multiuser diversity gain.This is shown in Figure 6.13, where the sum capacity is plotted as a functionof the number of users for both Rayleigh and Rician fading with !-factorequal to 5, with the total SNR, equal to KP/N0, fixed at 0 dB. Recall from
Figure 6.13 Multiuser diversitygain for Rayleigh and Ricianfading channels !"= 5#;KP/N0 = 0 dB.
0 5 10 15 20 25 30 350.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
Number of users
Sum
cap
acity
at S
NR
= 0
dB
(bits
/s / H
z)
AWGNRayleigh fadingRician fading
Multi-‐User vs. Classical Diversity• Both due to the existence of independently faded paths- Classical diversity: over time, frequency, antennas in a link- Multi-user diversity: over multiple users in the network
• Classical diversity is to compensate channel fluctuation• Multi-user diversity aims to exploit channel fluctuation
• Classical diversity increases reliability- Suitable for application with stringent latency constraints (voice)
• Multi-user diversity increases total throughput (long-term)- Suitable for application with long latency constraints (data)
51
Issues in System Implementation• Fairness: - Multi-user diversity offers a system-wide benefit (sum capacity ↑)- How to share this benefit among all users in a fair way (in an
asymmetric environment)?
• Slow and limited fluctuations:- Channels are less random ⟹ multi-user diversity gain ↓ - How to retain the benefit even in a rather static environment?
• Channel measurement and feedback:- Tracking channel is crucial in getting multi-user diversity- Overhead has to be considered
52
Proportional Fair Scheduler• At each time slot,- Each user will request a data rate from the base station- A scheduler decides which user to transmit and at what rate
• To obtain multi-user diversity:- Transmit to the best user + stronger user requests higher rates- ⟹ Most likely will select the statistically strongest all the time- Highly unfair!
• Solution: schedule the user with the highest ratio Rk/Tk, where- Rk := current requested rate of user k- Tk := average throughput of user k in the past tc time slots
53
Proportional Scheduler: Two-‐User
54
259 6.7 Multiuser diversity: system aspects
Figure 6.14 For symmetricchannel statistics of users, thescheduling algorithm reducesto serving each user with thelargest requested rate.
0 50 100 150 200 250 3000.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time slots
Req
uest
ed ra
tes
in b
its /s
/ H
z
Figure 6.15 In general, withasymmetric user channelstatistics, the schedulingalgorithm serves each userwhen it is near its peak withinthe latency time-scale tc .
0 50 100 150 200 250 3000.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Time slots
Req
uest
ed ra
tes
in b
its / s
/ Hz
requested rate. Thus, each user is scheduled when its channel is good and atthe same time the scheduling algorithm is perfectly fair in the long-term.
In Figure 6.15, due perhaps to different distances from the base-station, oneuser’s channel is much stronger than that of the other user on average, eventhough both channels fluctuate due to multipath fading. Always picking theuser with the highest requested rate means giving all the system resources tothe statistically stronger user, and would be highly unfair. In contrast, underthe scheduling algorithm described above, users compete for resources notdirectly based on their requested rates but based on the rates normalized bytheir respective average throughputs. The user with the statistically strongerchannel will have a higher average throughput.
Thus, the algorithm schedules a user when its instantaneous channel qualityis high relative to its own average channel condition over the time-scale tc.
259 6.7 Multiuser diversity: system aspects
Figure 6.14 For symmetricchannel statistics of users, thescheduling algorithm reducesto serving each user with thelargest requested rate.
0 50 100 150 200 250 3000.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time slots
Req
uest
ed ra
tes
in b
its /s
/ H
z
Figure 6.15 In general, withasymmetric user channelstatistics, the schedulingalgorithm serves each userwhen it is near its peak withinthe latency time-scale tc .
0 50 100 150 200 250 3000.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Time slots
Req
uest
ed ra
tes
in b
its / s
/ Hz
requested rate. Thus, each user is scheduled when its channel is good and atthe same time the scheduling algorithm is perfectly fair in the long-term.
In Figure 6.15, due perhaps to different distances from the base-station, oneuser’s channel is much stronger than that of the other user on average, eventhough both channels fluctuate due to multipath fading. Always picking theuser with the highest requested rate means giving all the system resources tothe statistically stronger user, and would be highly unfair. In contrast, underthe scheduling algorithm described above, users compete for resources notdirectly based on their requested rates but based on the rates normalized bytheir respective average throughputs. The user with the statistically strongerchannel will have a higher average throughput.
Thus, the algorithm schedules a user when its instantaneous channel qualityis high relative to its own average channel condition over the time-scale tc.
Statistically Symmetric Asymmetric
• The statistically stronger user gets an higher avg. rate• But the statistically weaker user still gets served fairly!• The algorithm serves each user when it is near its peak
within the latency time-scale tc
Multi-‐User Diversity in Practice
• Fixed environment has limited fluctuation• High mobility environment has a lot of fluctuation, but it is
difficult to get this gain because the system cannot track the channel!
55
Fixed environment: 2Hz Rician fading with κ = 5
Low mobility environment: 3 km/hr, Rayleigh fading
High mobility environment: 120 km/hr, Rayleigh fading
19
6: Opportunistic Communication and Multiuser Diversity
Fundamentals of Wireless Communication, Tse&Viswanath
Performance
Fixed environment: 2Hz Rician fading with Efixed /Escattered =5.Low mobility environment: 3 km/hr, Rayleigh fadingHigh mobility environment: 120 km/hr, Rayleigh fading
2 4 6 8 10 12 14 160
100
200
300
400
500
600
700
800
900
1000
1100
Low mobility environment
Fixed environment
Number of users
Tota
l thr
ough
put (
kbps
)
High mobility environment
latency time scale tc = 1.6s
Average SNR = 0dB
Inducing Randomness• Scheduling algorithm exploits the nature-given channel
fluctuations by hitting the peaks
• Not enough fluctuations ⟹ multi-user diversity gain ↓
• Why not purposely induce fluctuations?
56
Dumb Antennas
• Multiply the information bearing signal at each Tx antenna by a random complex gain- α(t): portion of power allocated to the first antenna- θ(t): phase shift
57
264 Multiuser capacity and opportunistic communication
Figure 6.19 Same signal istransmitted over the twoantennas with time-varyingphase and powers.
User kx(t)
h1k(t)
h2k(t)
√α (t)
√1– α(t) e jθ(t)
multiplied by a complex number√!l"m# ej$l"m# at antenna l, for l= 1% & & & %nt ,
such that∑nt
l=1!l"m# = 1, preserving the total transmit power. The receivedsignal at user k (see the basic downlink fading channel model in (6.50) forcomparison) is given by
yk"m#=(
nt∑
l=1
√!l"m# ej$l"m#hlk"m#
)
x"m#+wk"m#' (6.58)
In vector form, the scheme transmits q"m#x"m# at time m, where
q"m# (=
⎡
⎢⎢⎣
√!1"m# ej$1"m#
'''√!nt
"m# ej$nt "m#
⎤
⎥⎥⎦ (6.59)
is a unit vector and
yk"m#= )hk"m#∗q"m#*x"m#+wk"m# (6.60)
where hk"m#∗ (= )h1k"m#% & & & %hnt%k"m#* is the channel vector from the trans-
mit antenna array to user k.The overall channel gain seen by user k is now
hk"m#∗q"m#=nt∑
l=1
√!l"m# ej$l"m#hlk"m#' (6.61)
The !l"m# denote the fractions of power allocated to each of the transmitantennas, and the $l"m# denote the phase shifts applied at each antenna to the
Slow Fading → Fast Fading
58
25
6: Opportunistic Communication and Multiuser Diversity
Fundamentals of Wireless Communication, Tse&Viswanath
Slow Fading Environment: Before
26
6: Opportunistic Communication and Multiuser Diversity
Fundamentals of Wireless Communication, Tse&Viswanath
AfterBefore After
Opportunistic Beamforming• Dumb antennas create a beam in
random time-varying directions
• In a large system, there is likely to be a user near the beam at any one time
• By transmitting to that user, close to true beamforming performance is achieved
59
27
6: Opportunistic Communication and Multiuser Diversity
Fundamentals of Wireless Communication, Tse&Viswanath
Slow Fading: Opportunistic Beamforming
• Dumb antennas create a beam in random time-varying direction.• In a large system, there is likely to be a user near the beam at any
one time.• By transmitting to that user, close to true beamforming performance
is achieved.
Performance Improvement
• Opportunistic beamforming with dumb antennas increases the performance of the fixed environment significantly
60
30
6: Opportunistic Communication and Multiuser Diversity
Fundamentals of Wireless Communication, Tse&Viswanath
Overall Performance Improvement
Mobile environment: 3 km/hr, Rayleigh fadingFixed environment: 2Hz Rician fading with Efixed /Escattered =5.
Fixed environment: 2Hz Rician fading with κ = 5
Mobile environment: 3 km/hr, Rayleigh fading
Dumb, Smart, and Smarter Antennas• Smart antennas (space-time code in Lecture 3)- Improve reliability of point-to-point links- Reduce multi-user diversity (less fluctuations)
• Dumb antennas- Add fluctuations to point-to-point links - Increase multiuser diversity gains
• Smarter antennas- With full CSI, antennas can actually form beams pointing to users- Coherent beamforming
61
Dumb vs. Smarter in Slow Fading
62
28
6: Opportunistic Communication and Multiuser Diversity
Fundamentals of Wireless Communication, Tse&Viswanath
Opportunistic Beamforming: Slow Fading
• As # of users grow, performance of opportunistic beamforming → that of coherent beamforming
Comparison
63
270 Multiuser capacity and opportunistic communication
Table 6.1 A comparison between three methods of using transmit antennas.
Dumb antennas(Opp. beamform)
Smart antennas(Space-time codes)
Smarter antennas(Transmitbeamform)
Channel knowledge Overall SNR Entire CSI at Rx Entire CSI at Rx, Tx
Slow fadingperformance gain
Diversity andpower gains Diversity gain only
Diversity and powergains
Fast fadingperformance gain No impact Multiuser diversity ↓
Multiuser diversity ↓power ↑
How about in a fast Rayleigh fading environment? In this case, we haveobserved that dumb antennas have no effect on the overall channel as the fullmultiuser diversity gain has already been realized. Space-time codes, on theother hand, increase the diversity of the point-to-point links and consequentlydecrease the channel fluctuations and hence the multiuser diversity gain.(Exercise 6.31 makes this more precise.) Thus, the use of space-time codesas a point-to-point technology in a multiuser downlink with rate control andscheduling can actually be harmful, in the sense that even the naturally presentmultiuser diversity is removed. The performance impact of using transmitbeamforming is not so clear: on the one hand it reduces the channel fluctuationand hence the multiuser diversity gain, but on the other hand it provides anarray power gain. However, in an FDD system the fast fading channel maymake it very difficult to feed back so much information to enable coherentbeamforming.
The comparison between the three schemes is summarized in Table 6.1.All three techniques use the multiple antennas to transmit to only one userat a time. With full channel knowledge at the transmitter, an even smarterscheme can transmit to multiple users simultaneously, exploiting the multipledegrees of freedom existing inherently in the multiple antenna channel. Wewill discuss this in Chapter 10.
6.7.4 Multiuser diversity in multicell systems
So far we have considered a single-cell scenario, where the noise is assumedto be white Gaussian. For wideband cellular systems with full frequency reuse(such as the CDMA and OFDM based systems in Chapter 4), it is importantto consider the effect of inter-cell interference on the performance of thesystem, particularly in interference-limited scenarios. In a cellular system, thiseffect is captured by measuring the channel quality of a user by the SINR,signal-to-interference-plus-noise ratio. In a fading environment, the energiesin both the received signal and the received interference fluctuate over time.Since the multiuser diversity scheduling algorithm allocates resources based
Summary
64
274 Multiuser capacity and opportunistic communication
Thus, for a system designer, the opportunistic beamforming techniqueprovides a compelling case for implementation, particularly in view of theconstraints of space and cost of installing multiple antennas on each mobiledevice. Further, this technique needs neither any extra processing on the partof any user, nor any updates to an existing air-link interface standard. In otherwords, the mobile receiver can be completely ignorant of the use or non-useof this technique. This means that it does not have to be “designed in” (byappropriate inclusions in the air interface standard and the receiver design)and can be added/removed at any time. This is one of the important benefitsof this technique from an overall system design point of view.In the cellular wireless systems studied in Chapter 4, the cell is sectorized
to allow better focusing of the power transmitted from the antennas and alsoto reduce the interference seen by mobile users from transmissions of thesame base-station but intended for users in different sectors. This techniqueis particularly gainful in scenarios when the base-station is located at a fairlylarge height and thus there is limited scattering around the base-station. Incontrast, in systems with far denser deployment of base-stations (a strategythat can be expected to be a good one for wireless systems aiming to pro-vide mobile, broadband data services), it is unreasonable to stipulate that thebase-stations be located high above the ground so that the local scattering(around the base-station) is minimal. In an urban environment, there is sub-stantial local scattering around a base-station and the gains of sectorizationare minimal; users in a sector also see interference from the same base-station(due to the local scattering) intended for another sector. The opportunisticbeamforming scheme can be thought of as sweeping a random beam andscheduling transmissions to users when they are beamformed. Thus, the gains
Table 6.2 Contrast between conventional multiple access and opportunisticcommunication.
Conventional multipleaccess
Opportunisticcommunication
Guiding principle Averaging out fastchannel fluctuations
Exploiting channelfluctuations
Knowledge at Tx Track slow fluctuationsNo need to track fast ones
Track as many fluctuationsas possible
Control Power control the slowfluctuations
Rate control to allfluctuations
Delay requirement Can support tight delay Needs some laxity
Role of Tx antennas Point-to-point diversity Increase fluctuations
Power gain in downlink Multiple Rx antennas Opportunistic beamform viamultiple Tx antennas
Interference management Averaged Opportunistically avoided
Conventional Multiple Access vs. Opportunistic Communication
