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Title
Interference Management: A New Paradigm for Wireless Cellular Networks
Permalink
https://escholarship.org/uc/item/13x468jt
Author
Garcia-Luna-Aceves, J.J.
Publication Date
2009-10-18
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California
Interference Management: A New Paradigm for
Wireless Cellular Networks
Zheng Wang
†
, Mingyue Ji
†
, Hamid R. Sadjadpour
†
, J.J. Garcia-Luna-Aceves
‡
Department of Electrical Engineering
†
and Computer Engineering
‡
University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA
‡
Palo Alto Research Center (PARC), 3333 Coyote Hill Road, Palo Alto, CA 94304, USA
Email:{wzgold, davidjmy, hamid, jj}@soe.ucsc.edu
Abstract— We introduce a new interference management tech-
nique for wireless cellular networks when the base station (BS)
has K antennas and there are M mobile stations (MS), each
with a single antenna. Our interference management scheme
takes advantage of multiuser diversity to transmit K independent
data streams to K out of M mobile stations. The new approach
achieves the dirty paper coding (DPC) capacity of K log log(M )
as M tends to infinity. Surprisingly, the new scheme does not
require full channel state information (CSI) and needs only close
to K integers related to CSI are fed back to the transmitter.
Moreover, the encoding and decoding of the new scheme is
significantly simpler than existing MIMO schemes and is similar
to point-to-point communications.
I. INTRODUCTION
Information theorists have pursued computing the capacity
of wireless networks in the presence of interference for several
decades. The main observation in such networks is the fact that
the capacity of such networks is limited by interference. Based
on the strength of the interference, there are three remedies to
solve this problem. If the interference is very strong, then the
receiver can decode the interfering signal and then subtract it
using successive interference cancelation [1]. In some cases,
the interference signal is weak compared to the desired signal
and it is treated as noise. The third and most common case is
when the interference is comparable with the desired signal.
The solution for this case is to avoid the interference by
orthogonalizing it with the signal using such techniques as
time division multiple access (TDMA) or frequency division
multiple access (FDMA).
In wireless cellular networks, base stations (BS) can have
large numbers of antennas, while most mobile stations (MS)
have only a single antenna. In order to achieve the maximum
multiplexing gain in these systems, a BS requires to transmit
independent packets from its antennas, but all of these packets
do arrive at the MSs. One remedy to solve this problem is to
use a distributed MIMO at the receiver side, which requires the
MSs to exchange significant information in order to be able to
decode the packets. Although there are many papers related to
distributed MIMO decoding, they are not very practical due
to the significant feedback requirement between MSs.
The multiuser diversity scheme [2] was introduced as an
alternative to increase the capacity of wireless networks. The
main idea behind this approach is that the BS selects an MS
that has the best channel condition by taking advantage of
time varying nature of fading channels, thus maximizing the
signal-to-noise ratio (SNR). This idea was later extended to
mobile wireless ad hoc [3] and MIMO cellular [4] networks.
Sharif and Hassibi [5] proposed to construct K random beams
and transmit information to the users with the highest signal-
to-noise plus interference ratio (SINR).
This paper introduces a new multiuser diversity scheme that
utilizes fading in channels to mitigate interference. Unlike all
existing techniques that are trying to fight fading and inter-
ference in wireless channels individually, our scheme actually
takes advantage of one of them (fading channel) to reduce
the negative effects of the other one (interference). By taking
advantage of multiuser diversity, we attempt to maximize the
SNR beyond a threshold while minimizing the interference-
to-noise ratio (INR) below another threshold such that the
interference signal strength is no longer significant. The result
is very effective, and constitutes a powerful technique that
achieves the dirty paper coding (DPC) capacity asymptotically
and yet requires minimum feedback and simple point-to-point
encoding and decoding techniques.
The remaining of this paper is organized as follows. Section
II presents an overview of related work. Section III introduces
the model used in our analysis. Section IV presents the
new interference management approach. Simulation results are
presented in Section V and we conclude the paper in Section
VI.
II. RELATED WORK
Our work is mainly motivated by the multiuser diversity
concept. Knopp and Humblet [2] derived the optimum capacity
for the uplink of a wireless cellular network taking advantage
of multi-user diversity. They proved that if the “best” channel
(i.e., the channel with the highest SNR in the network) is
selected, then all of the power should be allocated to this
specific user with good “channel,” instead of water-filling
power control technique. Furthermore, Viswanath et al in
[4] used similar idea for the downlink channel using the so
called “dumb antennas” by taking advantage of opportunistic
beamforming. Grossglauser et al [3] extended this multi-
user diversity concept to mobile ad hoc networks and took
advantage of node mobility to scale the capacity.
Interference alignment [6], [7] is another technique to
manage interference. The main idea in this approach is to use
part of the degrees of freedom to transmit the signal and the
remaining part to transmit the interference. For example, the
approach in [7] considers K × M interference channel and
demonstrate that achievable degrees of freedom is
KM
K+M −1
.
The drawback of interference alignment is that it requires
global knowledge of the channel state information (CSI),
which is very difficult to attain in practice, and the feedback
of the CSI is M K complex numbers in K × M interference
channels.
In this paper, we present an interference management tech-
nique for the downlink of wireless cellular networks such that
the BS can transmit D independent data streams when the
BS has K antennas and there are M MSs in the network.
Furthermore, we demonstrate that D can be any number with
probability one up to the maximum value of K, as long as M
satisfies certain conditions. Therefore, interference manage-
ment is capable of achieving the maximum multiplexing gain
as long as there is a minimum number of MSs in the network.
Surprisingly, by fully taking advantage of fading channels in
multiuser environments, the feedback requirement to achieve
maximum multiplexing gain is close to K, while the encoding
and decoding schemes needed are very simple and similar
to the point-to-point communications. The original multiuser
diversity concept was based on looking for the best channels,
while our approach shows that searching simultaneously for
the best and worst channels is important and can lead to
significant capacity gains. This technique can asymptotically
achieve the DPC capacity when M → ∞.
Sharif and Hassibi introduced a new approach [5], [8] to
search for the best SINR in the network. Their approach
requires M complex numbers for feedback instead of full CSI
knowledge while achieves the same capacity of K log log M
similar to DPC. There are major differences between our
approach and the design by Sharif and Hassibi [5]. First, our
approach does not require beamforming, while the proposed
techniques in [5], [8] take advantage of beamforming. Second,
the cooperation requirement in our technique is significantly
lower than that of [5], [8]. Third, the feedback requirement in
our scheme is proportional to K integers, while this value is
proportional to M complex numbers in [5], [8]. When M
grows, the feedback requirement for [5], [8] approaches a
linear growth, while in our scheme, this complexity is close
to the number of antennas at the BS. Finally, we can achieve
the same capacity of K log log M.
III. NETWORK MODEL
The BS has K antennas and there are M MSs, each having
a single antenna. In this paper, we assume that M À K. The
channel between the BS and MS users H is a M × K matrix
with elements h
ij
where i ∈ [1, 2, . . . , K] is the antenna index
of the BS and j ∈ [1, 2, . . . , M ] is the mobile station index. We
consider block fading model, where the channel coefficients
are constant during coherence interval of T . Then the received
signal Y
M×1
can be expressed as
Y = Hx + n, (1)
where x is the transmit K ×1 signal vector and n is the M ×1
noise vector. The noise at each of the receive antennas is i.i.d.
with CN (0, σ
2
n
) distribution.
IV. INTERFERENCE MANAGEMENT
A. The scheduling protocol
During the first phase of communication, the antennas of
the BS sequentially transmit a pilot signal, which requires K
time slots. In this period, all the MSs listen to these known
messages. After the last pilot signal is transmitted, MS users
evaluate the SNR for each antenna. If the SNR for only one
transmit antenna is greater than a pre-determined threshold
SNR
tr
and below another pre-determined threshold of INR
tr
for the remaining K − 1 antennas, that particular MS user
selects that particular antenna at the BS. In practice, some MS
users have this property for the same or different antennas of
the BS. The number of MS users with this property can be
smaller, greater or equal to K. For this reason, in the second
phase of communications, these MS users notify the BS about
their corresponding BS antenna. Clearly, many MS users will
be silent during this time, because they do not have the above
conditions. We will prove later that the number of MS users
with interference management capability can be close to K by
selecting the appropriate network parameters with probability
arbitrarily close to 1. We will not discuss the MAC protocol
required for these MS users to contact the BS. Once the BS
receives all information related to qualifying MS users, it
selects and notifies those MS users in one time slot, because
the BS can transmit their individual messages from their
corresponding antennas without any significant interference
between the messages. Note that, if we choose appropriate
values for SNR
tr
and INR
tr
such that SNR
tr
À INR
tr
, then
the BS can simultaneously transmit different packets from its
antennas to different MS users. The MS users only receive
their corresponding packets with strong signal and can treat
the rest of packets as noise. The value of SNR
tr
(or INR
tr
)
can be selected as high (or low) as required for a given system
as long as M is large enough. We will show their relationship
in detail later. Figure 1 illustrates the system that is used here.
Without loss of generality, we assume that the MS user i
for i ∈ [1, 2, . . . , K] is assigned to antenna i in the BS. In
this figure, solid and dotted lines represent strong and weak
channels respectively.
B. Capacity Computation
Define SNR
ij
as the signal-to-noise ratio when antenna i at
the BS is transmitting packet to MS user j in the downlink.
The objective of interference management is to find K MS
users out of M choices to satisfy the following criterion.
SNR
ij
≥ SNR
tr
, ∀i, j ∈ 1, 2, · · · , K, i = j
INR
ij
≤ INR
tr
, ∀i, j ∈ 1, 2, · · · , K, i 6= j (2)
Base Station
…...
…...
K
K
User 1 User 2 User K
…...
User M
[ ]K M´
H
Fig. 1. Wireless cellular network model
This condition basically states that for each MS user j, 1 ≤
j ≤ K, each one of them has a very good channel with only
a single antenna in the BS and strong fading channel with
all other BS antennas. It also implies that different MS users
have good channel condition with different BS antennas. It
is important to note that the number of MS users that have
the interference management condition is a random variable
X. This value can change at each epoch when the channel
state information in the network changes. The parameter D
is actually the average value of X, i.e., D = E(X). We will
later compute the probability distribution function of X.
Further, we define SINR
ii
as
SINR
ii
=
SNR
ii
P
D−1
j=1,j6=i
INR
ij
+ 1
(3)
and SINR
tr
as
SINR
tr
=
SNR
tr
(D − 1)INR
tr
+ 1
. (4)
Hence, the average sum rate capacity can be written as
C
proposed
= E
Ã
X
X
i=1
log (1 + SINR
ii
)
!
,
= E
Ã
X
X
i=1
log
Ã
1 +
SNR
ii
P
D−1
j=1,j6=i
INR
ij
+ 1
!!
,
≥ D log
µ
1 +
SNR
tr
(D − 1)INR
tr
+ 1
¶
,
= D log(1 + SINR
tr
). (5)
The third line is derived based on the fact that SINR
ii
≥
SNR
tr
, INR
ij
≤ INR
tr
, and D = E(X).
In the following, we first prove that for any value of SINR
tr
,
there exists a minimum value of M that will satisfy Eq. (5). We
will then demonstrate that this scheme achieves the optimum
capacity of DPC. To prove the validity of this algorithm, we
need to prove that there are K MS users that satisfy (2) with
probability one.
To prove the condition in Eq. (5), we assume that the
channel distribution is Rayleigh fading channel. However, any
time-varying channel model can be utilized for the following
derivations. Note that for a Rayleigh fading channel H distri-
bution, the probability distribution of SNR is given by
p(x) =
1
σ
exp
³
−
x
σ
´
, x > 0
0, x ≤ 0
(6)
where x is the SNR value and σ = E
H
(x).
Assume that event A is for any mobile station that satisfies
condition in (2). This probability can be derived as
P (A) =
Z
∞
SNR
tr
p(x)dx
µ
Z
INR
tr
0
p(x)dx
¶
K−1
.
= e
−
SNR
tr
σ
³
1 − e
−
INR
tr
σ
´
K−1
. (7)
Note that P (A) is the probability of a MS user satisfying
the condition in Eq. (2) for any of the K antennas at the BS.
Therefore, the probability that any MS user satisfy at least
one of the BS antennas is K × P (A). Also, we assume that
the channels between different MS users and BS antennas are
i.i.d. which means all of them have the same probability of
satisfying condition in (2). If there are only a total of D MS
users that satisfy condition in (2), then we have
1
M × (K × P (A))
∼
=
D. (8)
From Eq. (8), the relationship between M and P (A) can
be derived. Note that M is a function of network parameters
such as K, D, SNR
tr
, INR
tr
, and σ. The parameters K, D and
σ are really related to the physical properties of the network
and are not design parameters. Furthermore, the parameters
SNR
tr
and INR
tr
can be replaced with a single parameter
SINR
tr
using (4).
M(K , D, SNR
tr
, INR
tr
, σ)
∼
=
D
K
(P (A))
−1
(9)
In order to compute a lower bound for M, the minimum
value for (P (A))
−1
must be derived such that the SINR
tr
condition in (4) is satisfied.
minimize
D
K
(P (A))
−1
(10)
subject to SINR
tr
=
SNR
tr
(D − 1)INR
tr
+ 1
(11)
This optimization problem can be rewritten as
min
Eq.(11)
µ
D
K
(P (A))
−1
¶
=
D
K
min
Eq.(11)
e
SNR
tr
σ
³
1 − e
−
INR
tr
σ
´
K−1
(a)
=
De
SINR
tr
σ
K
min
INR
tr
e
(D−1)
SINR
tr
INR
tr
σ
³
1 − e
−
INR
tr
σ
´
K−1
(b)
∼
=
De
SINR
tr
σ
σ
K−1
K
min
INR
tr
Ã
e
(D−1)
SINR
tr
INR
tr
σ
(INR
tr
)
K−1
!
(12)
1
The probability that two MS users satisfy (2) for the same antenna in BS
is ignored in this analysis. Hence the above analysis is approximation.
We derive the second equality (a) above by replacing SNR
tr
with INR
tr
and SINR
tr
using Eq. (4). The approximation in
(b) is derived by assuming
INR
tr
σ
is a value much smaller than
1 and the fact that lim
x→0
(1 − exp(−x)) = x. Note that the
unique characteristic of this new scheme is to take advantage
of fading and clearly, under this circumstance the value of
INR
tr
σ
is small.
The minimum value of
µ
e
(D−1)SINR
tr
σ
INR
tr
INR
K−1
tr
¶
is derived by
taking its first derivative with respect to INR
tr
and making it
equal to zero.
e
(D−1)SINR
tr
σ
INR
tr
× (13)
µ
(D − 1)SINR
tr
σ
INR
K−1
tr
− (K − 1)INR
K−2
tr
¶
= 0
The solution for INR
∗
tr
is
INR
∗
tr
=
K − 1
D − 1
σ
SINR
tr
. (14)
Then the optimum value for M is given by
2
M
∗
= d
D
K
e
SINR
tr
σ
µ
D − 1
K − 1
SINR
tr
e
¶
K−1
e. (15)
This value is derived by replacing the optimum value of
INR
∗
tr
into (12) and using the approximation of (b) in this
equation. σ represents the strength of fading channel and as
this parameter increases or equivalently the channel experi-
ences more severe fade, then this technique can work at lower
values of SNR
tr
when SINR
tr
is constant. The main reason is
the fact that fading environment helps to combat interference.
Furthermore, the optimum value for M demonstrates that by
increasing the SINR
tr
, the minimum number of MS users
increases exponentially.
For constant values of SINR
tr
and when σ → ∞, then the
minimum M
∗
is
lim
σ →∞
M
∗
= d
D
K
µ
D − 1
K − 1
SINR
tr
e
¶
K−1
e. (16)
This results implies that there exists a minimum value of
MS users to implement this technique, even for very strong
fading channels.
Now we investigate the asymptotic behavior of the network
( i.e., M → ∞) and try to compute the maximum achievable
capacity and scaling laws for this scheme. Clearly, when M
tends to infinity, the SINR
tr
increases because we can select a
higher value for SNR
tr
and a smaller value for INR
tr
. Under
such conditions, the minimum value of M is given by
M
∗
∼
=
d
D
K
µ
e
D − 1
K − 1
¶
K−1
e
SINR
tr
σ
e. (17)
Then SINR
tr
is
SINR
max
tr
∼
=
σ log
Ã
K
D
µ
1
e
K − 1
D − 1
¶
K−1
M
!
. (18)
2
Note that M has to be an integer and consequently, we need to use the
ceil function in this equation.
When D = K, then the SINR
max
tr
scales as log M , so that
by utilizing (5), the scaling laws of this network is
C = Θ(K log log M). (19)
This is exactly the same scaling laws as in [5], [8], which
is equivalent to the DPC capacity. However, our scheme
requires a finite number close to K feedback information,
which is much smaller than M or 2KM for [5], [8] or DPC,
respectively. Furthermore when K = D > log(M), we can
see from Eq. (18) that the SINR
max
tr
tends to zero. This result
implies that the number of antennas at the BS should not grow
faster than log(M) in order to assure that we can achieve the
maximum capacity. This result was also reported in [5], [8].
It is worth pointing out that this technique cannot achieve
the optimum value of K multiplexing gain in the downlink if
σ is small or, equivalently, if the channel fading is not strong.
In a multiuser environment, fading actually is very helpful.
Our proposed multi-user diversity scheme is different from
the original scheme that requires the transmitter to search for
the node with the best channel condition. As we showed in
this paper, searching for both strong and weak channels is
important in combating the multiuser interference.
When K = 1, then our approach is similar to that of [2].
Moreover, if M → ∞ and D = K, then our scheme has
the same asymptotic scaling laws capacity result as that of
[5], [8]. The cost of the proposed scheme is the need for a
minimum number of MS users, M . In most practical cellular
systems, in any given frequency and time inside a cell, there
is only one assigned MS, while this technique suggests that
we can have up to the number of BS antennas utilizing the
same spectrum at the same time with no bandwidth expansion.
Clearly, this approach can increase the capacity of wireless
cellular networks significantly. This gain is achieved with
a modest feedback requirement that is proportional to the
number of transmitter antennas at the BS. We conclude our
results in the following theorem.
Theorem 4.1: In wireless cellular networks with M mobile
stations, each one having a single antenna and the base station
with K antennas, we can achieve D multiplexing gain in
the downlink when M satisfies Eq. (15). This scheme only
requires D integers as feedback CSI where D = Θ(K).
C. Feedback requirements
A natural question regarding our interference management
scheme is what the number of MS users is that satisfies the
interference management criterion. Clearly, this number is a
random variable, which we denote by X. We will prove that
this value is at most K with probability arbitrarily close to
one if the network parameters are appropriately selected. More
specifically, the probability that X ≤ K MS users satisfy
the interference management criteria denoted as η can be
arbitrarily close to 1 if we select proper SINR
tr
based on
network parameters such as fading the parameter σ and M .
For any MS, the probability that it satisfies the interference
management condition is K × P (A), i.e., the MS has a very
strong channel with a single BS antenna and a very weak
