674
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 17, NO. 6, JUNE 2007
Total Power Minimization for Multiuser Video
Communications Over CDMA Networks
Xiaoan Lu, Member, IEEE, Yao Wang, Fellow, IEEE, Elza Erkip, Senior Member, IEEE, and
David J. Goodman, Fellow, IEEE
Abstract—In this work, we consider a CDMA cell with multiple
terminals transmitting video signals. We adapt the system parameters to minimize the sum of compression powers and transmitter
powers of all users while guaranteeing the received video quality
at each terminal. The adjustable parameters at user include the
transmitter power
, the video coding bit rate
, and video
encoder parameters that control the complexity and hence power
consumption of the video coder (referred simply as complexity
). Instead of determining
directly, we first determine the
desired signal to interference-noise ratio (SINR) . Based on the
optimal
and
, we then determine
. Our analysis shows
that the product of
and
is an important quantity. Given
the complexity
(i.e., given the compression power) and quality
constraint, in order to reduce the transmission power, one should
choose
and to minimize their product. When only the total
transmission power is concerned, the optimal operating points can
be determined at individual users separately: each user should
run the encoder to minimize the product of
and . When the
objective is to minimize the sum of compression and transmission
powers of all users, the optimal solution can be found in two steps.
The first step searches the optimal
and
that minimize
for each video category and each possible
while
satisfying the quality constraint at user . The second step searches
the optimal
for all users jointly, that minimizes the
=1 ...
sum of transmission and compression powers of all users. The
first step can be completed offline in advance, only the second step
needs to be computed in real time based on channel conditions
of the users. Our results indicate that for the same class of video
users, the one who is closer to the base station compresses at a
lower complexity. Simulation results show that significant power
savings are obtained by our adaptive algorithms over nonadaptive
approaches, where
are fixed regardless the channel
conditions.
Index Terms—CDMA network, power control, video coding,
wireless communication.
Manuscript received December 12, 2005; revised August 18, 2006. This work
was supported in part by NYSTAR through the Wireless Internet Center for Advanced Technology (WICAT) at Polytechnic University and by the National Science Foundation under Grant 0219822. A preliminary version of this work was
presented at Proceedings of 2004 IEEE Global Communications Conference.
X. Lu was with the Department of Electrical and Computer Engineering,
Polytechnic University, Brooklyn, NY 11201 USA. She is now with Thomson
Corporate Research, Princeton, NJ 08540 USA (e-mail: xiaoan.lu@thomson.
net).
Y. Wang, E. Erkip, and D. Goodman are with the Department of Electrical
and Computer Engineering, Polytechnic University, Brooklyn, NY 11201 USA
(e-mail: [email protected]; [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TCSVT.2007.896627
I. INTRODUCTION
E
FFECTIVE radio resource management is essential to efficient operation of a cellular network. Most studies concentrate on optimization of voice transmission, especially in systems that employ code division multiple access (CDMA) [1],
[2]. In [1], the quality of service (QoS) objective is to maximize
the number of simultaneous transmitters that meet a minimum
received SINR requirement. It is shown that an algorithm that
produces this optimum also possesses a minimum transmission
power property. Recent power control studies have examined
data transmission, where the QoS objective is a “utility” function, defined as the number of bits successfully transmitted per
unit energy. Goodman and Mandayam [3], [4] propose a network assisted power control scheme for data, in which the base
station broadcasts to all terminals the value of a common received SINR that optimizes network performance.
For video transmission, a widely adopted objective quality
measure is the peak signal-to-noise ratio (PSNR) of the received
video, defined as
(1)
where
is the distortion measured in mean squared error
(MSE) between the original signal and the reconstructed
signal at the receiver. Video quality suffers from both lossy
source compression and transmission errors. For the source
compressor of the th user in a cell, the operational distoris controlled by the bit
tion-rate (DR) function
(kbps), and parameters that control the compression
rate
complexity (referred simply as complexity and denoted as ).
The physical meaning of the complexity parameters depend on
the actual video encoder. For example, in a H.263 compliant
video coder [5] that employs a periodic INTRA update scheme,
each macroblock is encoded in the INTRA mode at an interval
of frames, and other macroblocks are encoded in the INTER
is a pamodes. The INTER rate defined as
rameter controlling the complexity. Throughout our work, the
complexity is defined such that the source compression power
consumption is controlled only by , which in general can
be a vector including multiple encoder parameters. In general,
not only affects the video encoder power consumption, but
also the coding efficiency and the resilience of the compressed
stream to transmission errors. In our previous work [6], we
derive power consumption models for a H.263 encoder. When
a full search motion estimation algorithm is used, the source
and is approxicompression power increases linearly with
. Generally,
decreases
mately independent of
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LU et al.: TOTAL POWER MINIMIZATION FOR MULTIUSER VIDEO COMMUNICATIONS OVER CDMA NETWORKS
Fig. 1. For a given complexity, (a) when the source bit rate increases from R
to R , the distortion due to lossy compression decreases from D to D ,
(b) to keep the total distortion constant, in other words, D
D
D
D , the decoder can tolerate more transmission errors at R > R , hence
a lower received SINR < is sufficient to maintain the end-to-end video
quality. (c) Overall for a given complexity, the required SINR is a decreasing
function of the bit rate.
+
=
+
when
or
increases as shown in Fig. 1(a). In a H.263
increases, more macroblocks are encoded in the
coder, as
INTER modes and the encoder has a higher coding efficiency.
Residual transmission errors that cannot be corrected by the
channel decoder also contribute to the distortion at the decoder.
is defined as the difThe channel error induced distortion
and the distortion
ference between the overall distortion
, i.e.,
. This discaused by compression
tortion can be described as a function of and the video packet
, with a notation
. Noticing that
is
loss rate
generally a function of , we can further write
or simply
. It is obvious that when increases, the
and causes
video bit stream arrives at the decoder at a lower
increases, the bit
less distortion. On the other hand, when
stream is less resilient to transmission errors and the decoder
sees more distortion. For example, for the H.263 video coder
with an INTRA update scheme, the use of motion estimation
removes temporal redundancy between adjacent video frames
and provides high coding efficiency. However, it also makes
the compressed bit stream very sensitive to transmission errors
because of interframe error propagation [7]. Since error propagation stops at INTRA macroblocks, for higher , there are
infewer macroblocks encoded in the INTRA modes and
and , is illustrated
creases. The relationship between
in Fig. 1(b).
If parameters for both source compression and transmission
are configurable, the total distortion can be allocated between
them to minimize the transmission power [8]–[16]. For exis given, to meet total
ample, as described in Fig. 1, when
, the minimum required
distortion requirement
are adjusted jointly. When more bits are used
SINR and
by the source encoder, the distortion caused by lossy compression is lower, hence more distortion caused by transmission
errors is tolerable. In other words, a lower is sufficient for a
to reach the same video quality. This opposite trend
higher
and
has conflicting effects on transmission power
in
consumption
. To be more specific, a higher
requires
since there are more bits to send, and a lower
a higher
requires a lower
. The choice of the optimum pair of
and
depends on
and channel conditions. In this paper
we show that when only
is considered for each user, the
and
for a given
has the minimum
optimum pair of
that meet disproduct among all possible vectors of
tortion constraints. This result was first reported in our previous
675
work [11] and summarized in Section II. A dual problem is to
minimize the distortion given the available transmission power.
In [17], the authors established the resource requirements of
. A joint
an individual user as being equal to
and
source coding and power control approach allocates
to obtain the optimal PSNR given the transmission power
constraint (the compression power is not considered). A significant quality improvement is obtained for a system with one or
more users.
It is known that in today’s wireless devices, the power
consumed by base-band signal processing is in the same
order of magnitude as that by radio transmission [6], [18].
Therefore, it is important to include the source compression
power into the power minimization problem. This optimization
problem is complex because of the large number of interrelated variables and multiple QoS measures. The adjustable
, and
parameters for the video transmission system are
and
of
the video compression parameters, including
all terminals. The QoS measures are the received video qualand total consumed power
ities at individual terminals
. There has been
some recent work that includes video compression power in
optimization for video transmission. One set of studies, confined to a single transmitter and receiver, minimizes the sum
of compression power and transmission power in digital image
and video transmission [12]–[14]. In particular, our previous
work [14] concentrates on the uplink for a single user, and minimizes the total power dissipation while keeping the end-to-end
distortion constant. We study a transform coded Gauss–Markov
source and a H.263 coded video source over an additive white
Gaussian noise (AWGN) channel. We consider path loss, so the
channel quality varies inversely with the distance between the
terminal and the base station. Our study shows that when the
distance is large, one should reduce the source rate by using
a higher complexity. On the other hand, when the distance is
small, the required SINR is low, so the source coder can operate
at a high bit rate by using a low complexity. Both systems show
that matching the source coding and transmission settings to
the channel produces substantial power savings.
In a practical multiuser cellular network, the operating parameters derived for one single user may not be appropriate,
considering that one user’s transmitted signal is interference
to other users. Hence, in a multiuser environment the operating parameters cannot be determined by merely adjusting
parameters at that terminal. All the users must cooperate in
some way to reach their optimum points. Numerical full search
can be used to select the overall optimum from all possible
choices of parameters for all users. Since the complexity of full
search depends on the search space, it is acceptable for a small
number of users, but is formidable if there are a large number
of users in one cell. To solve this problem, Zhang et al. [15]
propose an iterative algorithm. However, it is not clear if this
algorithm converges to the global optimum. In our prior work
[16], we propose an analytical framework based on simplified
and
models. We consider the interference between multiple users and analytically derive the
for all
users simultaneously. The
optimum
optimum operating points of the terminals are contained in
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 17, NO. 6, JUNE 2007
nonlinear equations. We illustrate our solutions by the example
of transform coders processing signals from Gauss–Markov
sources. This provides some insights into practical systems.
However, it does not provide solutions for a practical video
encoder with more complicated distortion models.
This paper proposes a practical fast two-step algorithm that is
applicable to general video coders with arbitrary
and
functions. Our analysis shows that the product
and is an important quantity. Given for each user,
of
and to minimize their product, while
one should choose
. When only
satisfying the distortion constraint
the transmission power is considered, each terminal should minto minimize its own transmission power, as
imize
well as the sum of the transmission powers of all users. When
the goal is to minimize the sum of transmission and compression powers of all users, our two-step algorithm first searches in
advance, for each possible video category and possible , the
and
that minimize
, while satisfying
optimal
for
the quality constraint. It then finds the optimal
all users jointly, that minimizes the total power. Together with
for this optimal
the corresponding optimum pair of
, we determine the best
for all users.
By separating the complicated optimization problem into two
steps and performing the first step offline, we significantly reduce the computation load at the base station while obtaining
the global minimum.
The rest of this paper is organized as follows. In Section II,
to minimize
we first derive the optimum pairs of
the transmission powers of all users for a given complexity
together with the correvector. We observe that the largest
provides the global optimum in this case.
sponding
In Section III, we propose our two-step fast algorithm to minimize the sum of transmission powers and compression powers
of all users. Simulation results using H.263 video coders are
presented in Section IV. We conclude this paper in Section V.
TABLE I
NOTATION FOR A MULTIUSER CDMA SYSTEM
tenuations dictated by the fade level or the channel state. The
transmission channels are therefore modelled by a distance-de, an additive noise power
pendent path loss
and interference. In our numerical study, we assume binary
differential phase shift keying (DPSK) with a bit error rate of
[19]. A packet error occurs when one single
bit in this packet is erroneous. Therefore, the packet error rate is
(2)
When transmission errors occurs, a CRC indicates this and error
concealment is implemented at the video decoder. The distortion caused by transmission errors
also depends on
the error concealment technique and the input video sequences
[20]–[22]. Notations used in this paper are described in Table I.
The received SINR is an important property of user , and
it can be written as
(3)
II. MINIMIZING THE TRANSMISSION POWER
In this section, we consider only the transmission powers and
leave the consideration of compression powers to the next section. Our study is confined to the uplink of a single cell in a
CDMA cellular system. We consider the scenario where each of
the users in the cell transmits a live video to the base station.
The raw video sources are compressed and then transmitted by
(chips/s). PSNR at the
a CDMA system with a chip rate of
receiver is used as the quality measure. We consider the source
and
(kbps), with
coder of user that has an adjustable
. Note that the varithe operational DR function
able bit rate results in a variable processing gain for a given chip
rate. We assume all terminals use the same packet length of
bits. Each packet consists of information bits and additional
bits for a cyclic redundancy check (CRC). In other words, for
, the transmission bit
source bit rate of
. We use an AWGN model and consider
rate is
the effects of path loss. This is justified for wireless environments where the terminals are stationary or moving slowly, so
the received signal strength can be tracked. Our analysis can
easily be extended to faster moving users with realistic speeds
by considering the average of packet loss rates over possible at-
In the following, we would like to formulate our problem in
terms of
instead of
.
After we get the optimum and , we derive the optimum
from (3).
To maintain an adequate quality for user , there are mulfor a certain , as illustrated in
tiple choices of
Fig. 1. If
is also adjustable, there will be multiple triplets
that satisfy the quality constraint. Among
of
that meet the quality constraint, we
all possible
choose the one that minimizes the total transmission power of
all users. This problem is formulated as choosing an optimal
to:
set of
Minimize
subject to
(4)
(5)
where
is the distortion constraint corresponding to the
target PSNR, and
is the maximum possible transmission
LU et al.: TOTAL POWER MINIMIZATION FOR MULTIUSER VIDEO COMMUNICATIONS OVER CDMA NETWORKS
power for the th user. In [20]–[23], the authors study how to
model the distortion models. In this paper, given that
describes the relationship between the channel conditions and
the packet loss rate, we assume the functions
and
are known for a given encoder algorithm and
decoder error concealment algorithm.
A. Minimizing the Transmission Power for a
Given Complexity Vector
We first minimize the transmission powers of all
users, provided the compression complexities of all
users
are fixed. Given the vector
, for a source rate vector
we can determine the corresponding SINR requirement
that satisfies
the quality constraint at each terminal from (4). The correis [24], [25]
sponding power
677
required for one possible
at user . Equation (6) indicates
combination of
, and . In this section, we would like to
that leads to the minimal transmission power by
find
all users, given and distortion constraints.
Assume
is one feasible set and
is the corresponding transmission power. Now consider anwith corresponding
. When
other set
,
, from (6) we observe the
following.
is also feasible.
1)
corresponding to
is lower than
2) The power
that of
, i.e.,
.
We see that
is an important parameter for our
work and define
(9)
as the quality factor. Based on the above observation, the
is, the lower
is consumed for the
larger
is preferred in this
same quality. Hence, a larger
minimization problem. We also observe that
(6)
(10)
The constraint (5) implies the following condition:
(7)
.
This inequality determines the feasibility of a set of
If this condition is satisfied for a set of
,
can be
obtained using (6). When there is no constraint on the maximum
transmission power, the following inequality has to be satisfied:
is the reciprocal of the carrier-to-interference-noise ratio
(CINR). Therefore, by operating with maximum a terminal
minimizes the required CINR. The maximum for user at
is expressed as
(11)
Using the definition of
, (6) is written as
(8)
(12)
This illustrates that even if there is no maximum transmission
power constraint, not all sets of
meet the positivity
constraint of .
When the video encoder and the transmission parameters are
adjusted separately, the power minimization problem has been
well studied. When only the video encoder is adjusted to reduce the transmission power, the video encoder will compress
as much as possible to transmit information at a very low bit
rate; when only the transmission parameters are investigated,
the power control theorem indicates that all users should target
the minimum required SINR if there is no benefit to working beyond it. However when the video encoder and the transmitter are
both configurable, joint consideration is needed. As illustrated
increases. If there is only one user
in Fig. 1, decreases as
in the cell, the transmission power is proportional to the product
. Therefore, we need to minimize
to minimize
the transmission power of a single terminal, subject to the distortion constraint. We prove in the following subsection that in
general minimizing
will minimize the sum
of all users’ transmission powers when there are multiple users
in the cell.
1) Quality Factor : From (4) we know that for each
and
, there is one that satisfies the distortion constraint
and the total transmission power is
(13)
It is clear from (12) and (13) that maximizing , not only minimizes
, but also minimizes
. Therefore, the minimized
total transmission power of all users is
(14)
This indicates that for each user, when
choose
and
so that (1)
is fixed, we should
; and (2)
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 17, NO. 6, JUNE 2007
is maximized. When the expressions of both
and
are complicated, it is not easy
in a closed form. A numerical search can be
to get
in this case. One way to carry out such a
used to find
for
numerical search is for a given , we select
all possible
to meet the distortion constraint. From (4),
depends on the video coding scheme
the choice of
),
and the contents of the video (reflected by
modulation and packetization (reflected by
that affects
), and error resilience of the decoder (reflected by
). Then we choose the pair of
,
denoted as
, that maximizes
.
Hence,
can be computed offline for different content
characteristics when we have the knowledge of the video codec
and the relation between the channel error rate and the received
should satisfy the feasibility
SINR. Note that
are not feasible, one or
constraint in (7). If
more users should be blocked to guarantee the quality of the
users remaining in the network.
B. Minimizing the Transmission Power Over
Multiple Complexities
In the previous section, we see that for each complexity vector
, there exists a bit rate vector
and a corresponding SINR
vector
giving us the maximum quality factors and consequently minimum transmission powers at all terminals. When
are configurable, among all possible , we will choose the
one that minimizes the total transmission power of all users.
From (12) and (13), we observe that this can be obtained by set, that produces their largest
ting all users work at
, that is,
. The solution
for
is independent of channel conditions, therefore it
can be predetermined for each video category for a given communication system. To reach the desired in presence of multiple users, one can use the distributed power control algorithm
[1].
We have observed from our simulation with the H.263 encoder that
increases as increases [11]. This shows that
if
is also configurable, the encoder may increase
to reduce the transmission power
for the H.263 coders we consider. Each video encoder should work at its highest possible
to reduce its
. In other words, less transmission power is
obtained at the expense of more computation for compression.
Since the minimization of the transmission power is controlled
by the highest possible complexity, which are affected by the resources available to the encoder, such as memory, time, etc, we
referred to such an algorithm as a complexity-bounded power
control method [11].
When the video compression power is also considered,
working at the highest complexity may lead to an excessive
power consumption at the video encoder and hence results in a
larger overall power consumption (source compression powers
transmission powers). For this case, should be chosen to
minimize the total power consumption. We will discuss this in
detail in Section III.
III. MINIMIZING TOTAL POWER CONSUMPTION FOR
MULTIPLE USERS
The preceding section considered how to minimize the transmission powers of all users while satisfying quality constraints.
Our previous work on the power consumption of a H.263 encoder [6] demonstrates that video compression consumes a significant amount of power. Therefore, it is important to consider the video compression power consumption besides the
transmission power. In this section, we consider the problem of
minimizing the the sum of compression powers and transmitter
powers of all users while keeping the received video quality of
each user above a target level. This optimization problem is forto:
mulated as choosing an optimal set of
Minimize
subject to
where
[14].
is the compression power that only depends on
A. Two-Step Fast Algorithm
Using the quality factor of Section II-A-1, the total power
consumption is
(15)
Given a complexity vector
, we know
from Section II-A that the minimum transmitter powers
for all users occurs at the maximum quality factors. Since
is fixed as
source compression power for
, the total power (the sum of compression powers and transmitter powers) of all terminals is
minimized by choosing the maximum quality factors
(16)
When there are multiple choices of , (16) indicates that we can
, and
optimize over only space if we know
get the minimum power
(17)
Note that in this case, choosing
to maximize
is not
necessarily optimal, as that may corresponds to a very high
. Based on the observation, we propose a centralized power
control scheme with a two-step fast algorithm as follows.
LU et al.: TOTAL POWER MINIMIZATION FOR MULTIUSER VIDEO COMMUNICATIONS OVER CDMA NETWORKS
At the first step, for each possible video category, corresponding distortion constraint, and each possible , we
, the correpre-determine the largest quality factor
sponding optimal
and
and store them in a look-up table
and
do not depend on the
in the base station. Note that
channel conditions. During the operation of a CDMA cell, the
base station periodically updates the information regarding the
,
number of users , their respective path losses
the type of video that each is sending and their quality constraints.1 Based on such information in the setup, the base
that minimizes
station determines the optimal
the total power in (16) by searching in the space of
only.
and , corresponding to
Then the base station finds
using the look-up table. Finally, the base station determines the
using (6) and forwards
optimal transmit power for user ,
,
and
to each user. Each user adjusts its encoder and
transmitter to work at these parameters until it receives a new
set of parameters from the base station. The update frequency
should be commensurate with how fast the users are moving.
Due to the interference and maximum power constraint, when
the number of users is large, the feasibility constraint may
fail and the system cannot accommodate all users. Under such
circumstances, either some users should be rejected or they
agree to accept degraded qualities.
B. Computation Requirement
We assume all users have the same number of choices for
each parameter. Let the dimensions of ,
and be
,
and
, respectively. When the expression of the distortion
are independent
functions is simple, only two of
variables because of the constraint in (4). Hence, for each user
we can derive one of three parameters from the other two. But
for a more complicated system, this is not easy and we need
, and to find the triplet for each user
search all possible ,
that satisfies the distortion constraint. Here we assume that we
cannot derive one parameter from the other two, and the dimension of the full search for a system with users is
(18)
For our two-step algorithm, the first step is implemented for
each user for each video category. In the extreme case, assuming
each user is transmitting a video in a different category, then
the computation for computing the look-up table is
. Note that this computation can be done
in advance. For the second step, the search is over only and
. The overall computation is
has a dimension of
proportional to
(19)
To compare the computation at the base station, we compare
with
(20)
1Here we consider only the scenarios where all users in a CDMA cell are
sending video.
679
TABLE II
SIMULATION PARAMETERS
When there are a large number of users, the saving in computation will be huge. This will be discussed in detail using simulation results in Section IV-D-3.
IV. SIMULATION RESULTS
In this section, we present simulation results for our optimization problems. We simulate over multiple sequences and
present results for two representative sequences: a slow-moving
“mother-daughter.qcif” and a fast-moving “foreman.qcif.” We
consider a H.263 video encoder using a periodic INTRA update
scheme [5], [26]. The INTER rate is taken as the complexity.
We use the models in [20] for distortion caused by both lossy
. We derive the models for
source compression
in
distortion caused by transmission errors using
in (2). The model parameters are given in [14].
[20] and
, we use
For the compression power consumption model
the model and parameters given in [6]. The quality constraint is
(this corresponds to
dB). Paramset to
eters used for our simulation are described in Table II.
and
We first study in Fig. 2 how the SINR requirement
the quality factor change with respect to the bit rate
. We
observe from Fig. 2 that when is given:
decreases as
increases;
1)
first increases, then decreases as
increases, so that
2)
some intermediate values of
and yield the largest
;
3) the dynamic range of varies by a factor of about four over
. This provides a large space to reduce the
the range of
transmission power.
We also observe from Fig. 2 that when there are multiple choices
increases as increases.
of ,
A. Effect of Source Statistics
Different video sequences have different end-to-end distortion even when compression algorithms and channel conditions
are exactly the same. Fast-moving pictures require more
bits for the same quality and have lower error resilience
than slow-moving pictures because of lower correlation between adjacent video frames. Therefore, for the same source
compression algorithm, channel condition and video quality
requirement, minimum SINR requirements are different for
different sequences, hence the transmission powers are also
different [14], [27]. For example, in Fig. 2(c) and (d) we see that
than a
a slow-moving “mother-daughter.qcif” has a higher
fast-moving sequence “foreman.qcif.” Since a higher has the
advantage of lowering transmission power, a user transmitting
a slow-moving video sequence consumes less transmission
power than a user transmitting a fast-moving video sequence
given the same desired end-to-end quality.
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 17, NO. 6, JUNE 2007
Fig. 2. SINR requirement and the quality factor vary with the bit rate at different INTER rates for (a) and (c) “foreman.qcif” and (b) and (d) “mother-daughter.qcif,”
respectively.
Fig. 3. Transmission power used by each user at the maximum quality factors and the lowest bit rates at different complexities, when both user at the systems
are equidistant from the base station and they transmit the same video. The compression power is not considered. (a) “mother-daughter.qcif.” (b) “foreman.qcif.”
The power is normalized by =h .
B. Minimizing the Transmission Power
To illustrate how our adaptive solution can reduce the total
transmission power (the power consumption by video compression is not considered now), we assume that all users are equidis. We also
tant from the base station, i.e.,
assume that all users transmit video sequences with similar characteristics. Note that since all users are faced with the same
channel conditions and transmit the same video, the minimum
total power in (13) can be reduced to
(21)
We first demonstrate how the transmission power can be reduced for a given as discussed in Section II-A. When com-
pression and transmission are considered separately, the video
encoder often compresses as much as possible to get the lowest
bit rate. Therefore, in Fig. 3, the powers consumed by the opare compared with the powers consumption by
timal
another set of
where
is set to the lowest bit rate
that satisfies the distortion constraint. The power in Fig. 3 is nor. It is clear that by choosing the largest quality
malized by
factor, we can obtain power savings up to 44.5%. The power
.
saving may be more substantial for other
from {60%, 70%,
Now we assume the users can choose
is, the smaller
80%, 90%}. We observe that the larger the
is. This is consistent with the analysis prethe minimum
sented in Section II-B: A lower transmission power is obtained
at the expense of more computations at the video encoder. To
investigate the effect of input sequences on the power consumption, we consider two video sequences in Fig. 3(a) and (b). As
LU et al.: TOTAL POWER MINIMIZATION FOR MULTIUSER VIDEO COMMUNICATIONS OVER CDMA NETWORKS
681
Fig. 4. Capacity regions for (a) an unconstrained power case and (b) a constrained power case when there are two classes of video users in the cell. These two
classes are represented by a fast-moving “foreman.qcif” and a slow-moving “mother-daughter.qcif,” respectively. The compression power is not considered.
described in Section IV-A, the fast-moving “foreman.qcif” consumes more power than the slow-moving “mother-daughter”
given the same complexity and distortion constraint.
C. Capacity Evaluation
Suppose that the users in the cell transmit two classes of video
sequences, “foreman.qcif” and “mother-daughter.qcif”. We denote the number of users transmitting “mother-daughter.qcif” as
, and the number of users transmitting “foreman.qcif” as
. We know both classes of users will work at their largest
and
that lead to the largest
.
for both classes of users be
and
, respecLet
tively. The feasibility constraints in (7) and (8) become
(22)
and
(23)
and
corresponding to a given quality conFor given
straint, we can compute the possible
that satisfy
the feasibility constraint. We plot the capacity (number of users)
31, 32, and
regions for different quality constraints (
34 dB respectively) in Fig. 4. In Fig. 4(a), the number
is plotted versus
when there is no maximum transmission
power constraint. In Fig. 4(b), the maximum transmission power
(watts) is imposed. We observe there is a capacity
reduction when there is power constraint. Both plots illustrate
that fewer users can be accommodated when there is a higher
quality (higher PSNR) requirement.
D. Minimizing the Total Power
In this section, we consider the problem of minimizing the
sum of transmission powers and the video compression powers
of all users. We will use our two-step fast algorithm to derive
the solution.
We investigate the effect of channel conditions by varying the
distances between the terminals and the base station. Considering only path loss, we adopt the familiar exponential propaga, where is the distance between the th
tion model:
terminal and the base station measured in km,
and
. We note from (16) that the optimal
depends on
, which in turn depends on . Consequently, the optimal op,
, and
all depend on the distances.
erating parameters
We know from [6] that
watts
(24)
where
indicates the power required for performing motion
estimation, and indicates the power required for computing
DCT, quantization, and some other operations. The values of
and
depend on the video compression algorithms and
in the power consumpvideo contents. The scaling factor
tion model can affect the optimization results significantly.
so that
and
are in the same order of
We choose
magnitude [6], [18]. In our simulation,
,
and
. We allow to vary at a range of 0–1. In
the following, we simulate our algorithm at different scenarios.
Users at the Same Distance: Let us consider a simple
1)
scenario where all users are equidistant (distance ) from the
base station and transmit video contents with similar characteristics as “mother-daughter.qcif.” We investigate how the optimal parameters vary with and . We also illustrate that we
can obtain a substantial power saving by working at the optimal
operating parameters.
When only transmission power is considered as in Section II,
to reduce the
the encoder tends to work at the highest
transmission power. However, when the compression power is
also taken into account, a higher requires more compression
power. Therefore, the highest is not necessarily the optimum.
km and
, the
As illustrated in Fig. 5(a), when
minimum total power occurs at an intermediate
.
When the distance increases, we observe from Fig. 5(a) that
the optimal increases. This is natural because when the users
move away from the base station, the transmission becomes
more and more expensive, and we need to reduce the transmission power as much as possible. As we know from Section II-A,
we need to increase to increase the quality factor and reduce
dethe transmission power. Correspondingly, the optimal
creases and the optimal increases.
We also observe from Fig. 5 that when the number of users
increases, due to higher interference, the system tends to operate
as if the distance has increased. Therefore, it operates at a higher
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 17, NO. 6, JUNE 2007
Fig. 5. (a) Optimum complexity. (b) Optimum bit rate. (c) Optimum received SINR. (d) Optimum total power consumption when all
the base station and are sending the same video “mother-daughter.qcif.” The compression power is considered.
, a lower
and a higher , and the total power consumption by all users increases as illustrated in Fig. 5(d).
In Fig. 5(d), we also plot the compression powers. When
and both users are close to the base station, the video
compression consumes a significant portion of power. As the
number of users or the distance increases, the transmission becomes more expensive and the transmission power get more
significant.
In Fig. 6, we compare the total power consumption using our
algorithm versus those using some other parameter settings that
aim to satisfy a common SINR target as in traditional power
control. For a given (which is fixed irrespective of user locations), we choose
and to meet the distortion constraint.
kbps,
, and
; and
We choose (1)
kbps,
, and
. Though the tra(2)
ditional power control algorithm with fixed adapts to some
range of distances very well, it consumes significantly more
power than our algorithm at other distances. For instance, at a
km, the one using fixed parameters
small distance
kbps,
, and
consumes 54.8% more
power than our algorithm; at a large distance
km, the
kbps,
, and
one using fixed parameters
consumes about five times as much power as our optimal solution. This suggests that to minimize the total power
should be adjusted as the channel condition
consumption,
changes.
2) Two Classes of Video Users at the Same Distance: In this
section, we consider two users transmitting “mother-daughter.
qcif” and “foreman.qcif,” respectively. To examine the effect of
video contents on the choice of the optimum operation parameters, we assume both users are equidistant from the base station
and the only difference between two users is the content.
N users are equidistant from
Fig. 6. Total power consumed by a traditional power control algorithm and our
algorithm for
= 5 users, all equidistant and sending the same video. The
compression power is considered.
N
and
for both users are shown in
The optimal ,
Fig. 7(a)–(d), respectively. We observe that as increases,
the transmission becomes more expensive, and both users
and decreased
. At the
have the same trend: increased
are required. However, the fast-moving
same time, higher
and higher
than the
“foreman.qcif” demands higher
slow-moving “mother_daughter.qcif”, resulting in a much
higher power consumption.
3) Two Users at Different Distances: Now we investigate the
scenario where two users have different distances to the base
km and carry out the optimization
station. We fix
for various from 0–1 km. We assume both users transmit the
same video sequence “mother-daughter.qcif”.
and for both users are illustrated in
The optimal ,
is small,
Fig. 8(a)–(c), respectively. We observe that when
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683
Fig. 7. (a) Optimum complexities, (b) optimum bit rates, (c) optimum received SINRs, and (d) optimum power consumption for two users sending “motherdaughter.qcif” and “foreman.qcif,” respectively. Both users are equidistant from the base station. The compression power is considered.
Fig. 8. (a) Optimum complexities, (b) the optimum bit rates, (c) the optimum received SINRs, and (d) the minimum power when a H.263 video encoder is used
for “mother-daughter.qcif.” The distance between the first user and the base station is represented in the horizontal axis. The second user’s distance is kept at
d
= 0:33 km. The compression power is considered.
the channel seen by the system is good, and both users work at
the first user has higher or the
the lowest . When
similar as the second user. This is because when one user is
further away from the base station, the transmission is costly and
compression is relatively inexpensive. Therefore, it compresses
at a higher to reduce the transmission power. This can be used
, only
to further restrict the search range: If
needs to be considered when user and have similar video
characteristics. In Fig. 8(d), it shows that when
the
first user spends less power than the second user, and vice versa
.
when
4) Computation Time: We simulate both the full search algorithm and our two-step fast algorithm for the scenario described
vary from 10
in Section IV-D-3 using C programs. We let
to 300 kbps, at a step size of 10 kbps, and from 0 to 1, at a step
size of 1%. is chosen to satisfy the distortion constraint. Both
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 17, NO. 6, JUNE 2007
algorithms obtain the same global optimum. The full search
algorithm completes in 59.3 seconds, while our two-step fast
algorithm completes in 0.01 seconds. This illustrates that our
algorithm is much faster than the full search.
V. CONCLUSION
In this work, we propose algorithms to determine the optimal
operating parameters for the video encoders and radio transmitters in a multiuser CDMA cellular network transmitting live
videos. Our analysis show that, given a set of complexity values
for all users, the total transmission power is minimized when the
encoding rate and the SINR at each terminal are chosen to maximize a quality factor (inversely proportional to the product of
the bit rate and the SINR) while meeting the target video quality.
Using this result we first derive how to reduce the transmission power consumption of all users. We prove that we need to
choose the complexities that maximize the quality factors to reduce the total transmission power. We also observe that this usually forces the encoders to work at their highest complexities.
Furthermore, we propose a two-step fast algorithm that
considers both the radio transmission powers and the video
compression powers and obtains the global minimum total
power consumption. First, for each possible complexity set
, we choose
and
that minimize the transmission power at each user. We then consider all possible
complexity sets to obtain the minimum total power. This
essentially reduces the search space in the second step from
to
only, and reduces the
computation load of the base station significantly. Simulation
results show this is much faster than a full search algorithm
and a sizable portion of power can be saved compared to a
traditional power control algorithm where the compression
parameters are fixed.
This work considers a centralized algorithm to obtain the
global power minimization. A fast algorithm is proposed to reduce the computation load at the base station. However, when
the number of users is large, our algorithm requires significant communication overhead for the information update. A distributed algorithm that can obtain the global optimum or suboptimum is desired to reduce the communication overhead at the
system [28].
We have considered minimizing the sum of the power consumptions by all users. Usually this results in much more power
dissipation from the user that is further away from the base station. To ensure fairness among users, other criteria may be more
appropriate, such as minimizing the maximum power of individual users.
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LU et al.: TOTAL POWER MINIMIZATION FOR MULTIUSER VIDEO COMMUNICATIONS OVER CDMA NETWORKS
Xiaoan Lu (S’01–M’06) received the B.S. and M.S.
degrees in electronic engineering from Tsinghua
University, Beijing, China, in 1997 and 2000, respectively, and the Ph.D. degree in electrical and
computer engineering from Polytechnic University,
Brooklyn, NY, in 2005.
She is currently a Member of Technical Staff at
Thomson Inc. Corporate Research, Princeton, NJ.
Her research interests are in multimedia communications, video compression and signal processing.
Yao Wang (M’90–SM’98–F’04) received the B.S.
and M.S. degrees in electronic engineering from
Tsinghua University, Beijing, China, in 1983 and
1985, respectively, and the Ph.D. degree in electrical
and computer engineering from University of California at Santa Barbara in 1990.
Since 1990, she has been with the faculty of Polytechnic University, Brooklyn, NY, and is presently
Professor of electrical and computer engineering.
She was on sabbatical leave at Princeton University,
Princeton, NJ, in 1998 and at Thomson Corporate
Research, Princeton, NJ, in 2004–2005. She was a consultant with AT&T Laboratories—Research, formerly ATT Bell Laboratories, from 1992 to 2000. Her
research areas include video communications, multimedia signal processing,
and medical imaging. She is the leading author of a textbook titled Video
Processing and Communications (Prentice Hall, 2002), and has published over
150 papers in journals and conference proceedings.
Dr. Wang has served as an Associate Editor for IEEE TRANSACTIONS ON
MULTIMEDIA and IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO
TECHNOLOGY. She received New York City Mayor’s Award for Excellence in
Science and Technology in the Young Investigator Category in year 2000. She
was elected Fellow of the IEEE in 2004 for contributions to video processing
and communications. She is a co-winner of the IEEE Communications Society
Leonard G. Abraham Prize Paper Award in the Field of Communications Systems in 2004.
685
Elza Erkip (S’93–M’96–SM’05) received the B.S.
degree in electrical and electronic engineering from
Middle East Technical University, Turkey, in 1990,
and the M.S. and Ph.D. degrees in electrical engineering from Stanford University, Stanford, CA, in
1993 and 1996, respectively.
She joined Polytechnic University, Brooklyn, NY,
in Spring 2000, where she is currently an Associate
Professor of electrical and computer engineering.
During 1996–1999, she was with the Department
of Electrical and Computer Engineering of Rice
University, Houston, TX.
Dr. Erkip received the 2004 Communications Society Stephen O. Rice Paper
Prize in the field of communications theory, the NSF CAREER award in 2001,
and the IBM Faculty Partnership Award in 2000. She is an Associate Editor
of IEEE TRANSACTIONS ON COMMUNICATIONS, a Publications Editor of IEEE
TRANSACTIONS ON INFORMATION THEORY, and a Guest Editor of IEEE SIGNAL
PROCESSING MAGAZINE, Special Issue on Signal Processing for Multiterminal
Communication Systems. She was the Technical Program Co-Chair of the 2006
Communication Theory Workshop. Her research interests are in wireless communications, information theory, and communication theory.
David J. Goodman (M’67–SM’86–F’88) is a Professor of electrical and computer engineering at Polytechnic University, Brooklyn, NY.
In 2006, he was a Program Director at the National
Science Foundation. Prior to joining Polytechnic
University, Brooklyn, NY, in 1999, he was at Rutgers
University, New Brunswick, where he was Founding
Director of WINLAB, the Wireless Information
Network Laboratory. Until 1988, he was a Department Head in Communications Systems Research at
AT&T Bell Laboratories.
Dr. Goodman was recently elected to the National Academy of Engineering
in recognition of his contributions to digital signal processing and wireless communications.