VARIABLE QUALITY OF SERVICE IN CDMA SYSTEMS

BY STATISTICAL POWER CONTROL

Louis C. Yun and David G. Messerschmitt
Department of Electrical Engineering and Computer Sciences
University of California at Berkeley, CA 94720-1770

ABSTRACT ask how variable QOS can be provisioned on wireless ac-

cess links so as to support flows, or similar concepts in other
The low bandwidth and high error rates of the wireless
protocols.
channel make joint source-channel coding desirable for op-
timizing resource usage. We argue that a mechanism for Specifying variable QOS for different traffic types
providing variable quality of service (QOS) is essential for gives the network an opportunity to fine-tune resource allo-
joint source-channel coding, and show that its implementa- cation through joint source-channel coding. This is particu-
tion by way of power control is a natural choice for CDMA. larly desirable on the wireless channel, with its low
Present-day power control techniques focus on controlling bandwidth and high error rates. To carry out joint source-
interference. In this work, we present a power control algo- channel coding, we break up an information source into
rithm which simultaneously minimizes interference and multiple substreams [8]. A substream is characterized by its
provides variable QOS contracts for different traffic types own QOS specification, like an Internet flow. It may consist
in a CDMA system. The algorithm accommodates different of one media type (e.g. an audio source) or one component
QOS requirements by assigning different power levels to of a media type (e.g. the coarse resolution portion of a mul-
each traffic type, and can add or drop connections dynami- tiresolution video signal [17]). The substream concept en-
cally while ensuring that QOS specifications are satisfied. hances network efficiency by only appropriating more
Both the uplink and downlink are analyzed, and the scheme resources - for example, lower latency and stronger error
is statistically formulated to handle variable-rate traffic. protection - to the parts of the user information that are more
important. Simultaneously, an application can perform
1 INTRODUCTION more aggressive source coding on substreams of less impor-
tance.
Power control can substantially impact the capacity and
perceived quality of service of a CDMA system. Regardless The concept of substreams is illustrated by the CDMA
of the mode of multiple access, power control is necessary system under study, shown in Fig. 1. The substreams are
in cellular systems to mitigate the intercell interference that
arises from frequency reuse. In direct sequence CDMA sys- substream 1

tems, power control is further employed to minimize the in-

mux coder x
tracell interference; it is especially crucial on the DS/
CDMA uplink for mitigating the near-far effect. This need substream n spread code
user 1
for power control to combat interference has been recog-
nized and is the subject of much research ([1]-[6]).
power
control ∑
to
substream 1 channel
We now motivate a less conventional use of power con-
trol. We start by considering how an application may spec- mux coder x
ify its QOS needs to the network. The three components of
substream n spread code
an application’s QOS are bandwidth, delay and reliability. user m
For packet networks, we may further distinguish between
corruption (errors in the packet payload) versus loss (errors substream 1
in the packet header, causing the entire packet to be lost).
The Internet Protocol defines flow headers [7] to support from channel
despread decode
demux
variable QOS across different applications. In this paper, we
substream n

This research was supported by the Advanced Research Projects Agency Figure 1. schematic of CDMA downlink with power control
Contract J-FBI-93-153, Tektronix, Bell Communications Research, and and joint source channel coding. Top figure -
transmitter; bottom figure - receiver for one user.
the Univeersity of California MICRO Program.

IEEE International Conference on Communications, ICC’95, June 18-21, Seattle, WA

variable-rate and statistically multiplexed into one aggre- tion that for a CDMA system it is beneficial to transmit the
gate stream for each user. How the statistical multiplexing minimum power necessary to support a given QOS for a
impacts the delay aspect of each substream’s QOS will not substream, as this creates the least interference to other us-
be discussed in this paper; instead, we concentrate our ef- ers. Apart from simplicity, fine granularity and the wide
forts on the loss and corruption aspects of QOS. We assume range of BERs achievable, a significant advantage to using
flow control is applied, so that the sum of the substream bit power control is that UEP is achieved in a manner complete-
rates for any user do not exceed the total bit rate of that us- ly transparent to the receiver. While UEP by power control
er’s stream. Each stream then undergoes channel coding, can be simultaneously applied at the bit level, the compres-
modulation and power control before being assigned a sion level and all higher levels, the receiver decoder can per-
spreading code and transmitted. form detection without any knowledge of the hierarchy of
UEP coding established by the transmitter. This eliminates
Key to joint-source channel coding and higher efficien-
the need for special packet framing structures for hierarchi-
cy on the wireless channel, then, is coding for unequal error
cal UEP coding.
protection (UEP) of different substreams. UEP may be re-
quired at many levels. At the highest level, some users may Present day power-control algorithms focus on control-
demand a more stringent reliability guarantee than others. ling interference by keeping the received power constant
At the application level, video, audio and data all have dif- [5][6] or performing carrier-to-interference ratio (CIR) bal-
ferent error sensitivities. At the compression level, motion ancing ([1]-[4]). Instead, we consider the problem of how to
vectors from an interframe video coder requires more pro- achieve different quality of service requirements for differ-
tection than do block differences. At a bit level, we may ent substreams or users, and show that it is possible to simul-
wish to afford greater protection to the most significant bits taneously achieve variable reliability requirements and
than to the least significant bits. minimize interference, by way of power control.
Embedded trellis coded modulation for UEP has been In [21], we describe a power control scheme that mini-
suggested [13][14], though its complexity grows quickly mizes the total transmit power while providing a hard
with the number of protection levels. Algebraic UEP codes bound on the QOS requirements - i.e. a deterministic guar-
have also been proposed [15]. Both these approaches are antee that the SNR experienced by every substream meets
better suited towards UEP at the bit level than at higher lev- or exceeds specifications at all times. A deterministic call
els. Recently, punctured convolutional codes have been ap- admission criterion works well when the system is lightly
plied to UEP [16], by which the reliability of a substream is loaded, but may lead to conservative utilization of system
increased through migration from a high rate to a low rate capacity. This stems from the very definition of a determin-
code. However, moving to greater redundancy without al- istic guarantee: it must always satisfy the worst case, name-
tering the source information rate requires bandwidth ex- ly when all the users simultaneously transmit substreams of
pansion. On a wireless channel with constrained bandwidth, the highest reliability. In this paper, we extend [21] to a sta-
changing the error protection of a substream dynamically tistical formulation which provides QOS guarantees for
over time becomes difficult. variable-rate traffic, improve the underlying wireless
CDMA model, and generalize the analysis to include uplink
As noted above, the capacity of CDMA is interference-
as well as downlink power control.
limited[10][11][12]: the greater the power of one’s own sig-
nal relative to the aggregate power of other users, the lower
the probability of error. This observation suggests that 2 PROBLEM FORMULATION
CDMA lends itself to a different approach for UEP. Rather The measure of reliability in CDMA systems is usually
than use a UEP channel coder, which has suboptimal coding specified by the energy to interference density ratio [10] or
gain in comparison with a fixed-rate coder, we utilize a by the signal to noise interference ratio (SNR) [1]. As these
more efficient fixed-rate coder, then vary the degree of error two quantities differ only by the time-bandwidth product
protection by modulating the power level instead. Trellis 2BT , a parameter common to the system, we will keep no-
coding is particularly attractive for the bandlimited radio tation simple and henceforth specify the QOS requirement
channel, as it provides redundancy without increasing band- of an individual substream by its desired SNR.
width. However, it is difficult to produce the trellis equiva-
lent of a variable-rate convolutional code by varying the To maintain independent control of loss and corruption,
constellation size, as virtually all of the coding gain is at- we treat the packet header and packet payload of a sub-
tained by doubling the alphabet size[9]. A solution is to per- stream as two logically separate substreams. Hence, the
form UEP by using a fixed rate trellis code and varying the packet header may specify a higher reliability requirement
power. By modulating the power level, we exploit the no- than the payload, which the network then provides by as-
signing a higher power level to the header than to the pay- only one of the user’s substreams is active at any time. f m, n
load in the power control algorithm.
is the partial correlation coefficient between codes of users
m and n: because signals from different mobiles travel
2.1 Uplink power control through different multipath channels to reach the receiver,
Denote the number of users by M, and let N m be the f m, n is usually non-zero. Uplink transmission is inherently
number of substreams of user m. The SNR experienced by asynchronous, so f m, n is well modelled by f, the correla-
the i-th substream of user m on the uplink is
tion between random signature sequences, with
G m x i, m E [ f ] = 2 ⁄ 3 [12][19].
SNR exp erienced = ------------------------- , (1)
2
σ + Im
intra The indicator function of a substream as it evolves over
time, β k, m ( t ) , t ∈ [ 0, ∞) , is a random process. Let
where G m is the path gain ([1]-[3]) from mobile m to the β k, m denote the time-average of β k, m ( t ) ; e.g.
base station; x i, m is the transmit power assigned to sub-
β k, m = 1 ⁄ 4 if the average bitrate of substream k is
intra
stream i; Im is the intracell interference experienced by 500 kbps and it belongs to a 2 Mbps user stream. We assume
the process is ergodic in the mean, so that
2
mobile m, and σ is the lump sum of background noise and E [ β k, m ( t ) ] = β k, m . This is based on the intuition that at
intercell interference experienced at the base station.
any given time slot, the probability that you receive a packet
The uplink and downlink path gains are assumed equal, from substream k equals the average rate of that substream,
with the latter derived from the pilot strength or the auto- divided by the aggregate rate of the user stream to which it
matic gain control circuit in the mobile. There are several belongs. The expected value of the total power is then
2
ways to measure σ . The simplest approach is to simulta- Nm
M
neously hold all mobiles silent for a short period. During
this interval, the received power at the base station is mea-
E[ P] = E ∑ ∑ βk, m ( t )xk, m (3)
n = 1k = 1
2
sured and equals σ . Synchronization between mobiles is
M Nn
achieved by the base station. Alternatively, the base station
knows the power received from each mobile and corre- = ∑ ∑ β k, n x k, n . (4)
spondingly the intracell interference experienced by each n = 1k = 1
user. The information can be relayed to each mobile user,
Our objective is to minimize the average overall power
who subtracts this quantity from the total power it measures
2
E [ P ] , while promising each substream that the expected
to obtain σ . Whereas the “silent period” scheme uses up- value of the SNR it experiences will meet or exceed the de-
link bandwidth, the second method uses the downlink. On sired SNR:
an asymmetric wireless channel in which downlink has
much greater bandwidth than the uplink [23], the second ap- M Nn
proach may be preferable. minimize E [ P ] = ∑ ∑ β k, n x k, n such that (5)
The intracell interference experienced by a substream of n = 1k = 1
mobile m is
G m x i, m
M Nn ∀i, m , -----------------------------------------------------------------------------
N
- ≥ SNR i, m , (6)
M n

∑ ∑
intra
β k, n x k, n .
∑ ∑ β k, n x k, n
2
Im = f m, n G n (2) σ + E[ f ] Gn
n = 1 k=1 n = 1 k=1
n≠m n≠m

β k, n is an indicator function, equalling one if substream k x i, l ≥ 0 , SNR i, l > 0 (7)

of user n is currently active, zero otherwise. A user may
have multiple substreams, but the substreams are statisti-
cally multiplexed together onto one user stream, so that
SNR i, m is the signal-to-noise ratio requested by substream M Nn

i of user m, and the inequality in Eq. 6 implies that the minimize E [ P ] = ∑ ∑ β k, n x k, n such that (13)
expected value of the SNR achieved at the receiver must n = 1k = 1
equal or exceed the desired SNR.
G m x i, m
Eq. 5 - Eq. 7 constitute a linear programming problem ∀i, m , -----------------------------------------------------------------------------------
N
- ≥ SNR i, m , (14)
M n
and can be solved numerically via the Simplex algorithm
∑ ∑ β k, n x k, n
2
[20], but we can obtain a closed-form solution. In the Ap- σ m + E [ f m ]G m
pendix, we derive that the necessary and sufficient condi- n = 1k = 1
n≠m
tion for feasibility is

γ < 1, (8) x i, m ≥ 0 , SNR i, m > 0 . (15)

M The downlink solution is derived along the same line of

where γ = ∑ γm, (9) reasoning as the uplink. The necessary and sufficient condi-
m=1 tion for downlink feasibility is identical to the uplink case,
provided we substitute E [ f m ] for E [ f ] in the expressions
Nm
for γ m and α i, m (Eq. 10 and Eq. 11). If feasible, the unique,
γ m = E[ f ] ∑ α k, m , (10)
k=1 optimal solution is

SNR i, m β i, m 2
x i, m = SNR i, m ( σ m ⁄ G m + E [ f m ] ( E [ P ] – E [ P m ] ) ) ,
and α i, m = ----------------------------------------------------------------
Nm
- , (11)
1 + E[ f ] ∑ βk, m SNR k, m  σm
2

k=1 with E [ P m ] = γ m  ------------------------ + E [ P ]
 Gm E [ f m ] 
i = 1, …, N m , m = 1, …, M .
–1 γn M
2
and E [ P ] = ( 1 – γ )  ∑ ----------------------σ n . (16)
Further, if the system is feasible, it has a unique, optimal  n = 1 Gn E [ f n ] 
solution given by
3 DISCUSSION
SNR i, m 1 – γ m 2
x i, m = ------------------- --------------- σ . (12) Looking at (11), α i, m is a monotonically increasing
Gm  1 – γ 
function of SNR i, m ; thus, the power assigned to a sub-
2.2 Downlink Power Control stream is monotonic in the substream’s desired reliability
On the downlink, all intracell substreams arrive at mo- requirement. We can interpret (8), the feasibility criterion,
bile receiver m via the same multipath channel and thus are as a measure of the QOS capacity for an interference-limit-
attenuated by the same amount, G m . In contrast, the inter- ed CDMA system. The closer γ is to unity, the closer such a
system is to operating at capacity in terms of being able to
cell interference is different for each mobile. Since trans- meet QOS requirements for all users and substreams. If the
mission is synchronous, the downlink code correlation QOS requirements of the substreams in a cell are too strin-
coefficient f m will be directly proportional to the fraction of gent, then the intracell interference will be too great and no
the received power which is scattered due to the multipath solution exists, regardless of how much power is pumped
in user m’s channel [11]. For a practical CDMA system em- into the cell. In addition to a fundamental rate capacity, we
ploying time diversity [18], this information is available at have shown for interference-limited CDMA that there is a
the RAKE receiver. In absence of time diversity, we consid- signal-to interference, or QOS, capacity as well.
er the worst case, namely when no line-of-sight power com- Secondly, the feasibility criterion points to a simple way
ponent exists. In this event, the crosscorrelation can be to perform call admission. To determine if we can add a new
modelled by f, as in the uplink. substream without violating the QOS guarantees for sub-
The downlink formulation is then streams in-progress, we simply check whether
 γ current system + E [ f ]α new substream < 1 . (17) ity mass function

Pr [ P m = x k, m ] = β k, m , k = 1, …, N m ,
If Eq. 17 holds, we can admit the new substream; other-
wise, we will have to renegotiate the QOS contracts of the Nm
existing substreams to make room for the new substream. Pr [ P m = 0 ] = 1– ∑ β k, m
To better understand what can be gained by using power k=1
control, we simulated the system in Fig. 1 for 50 users. Hy-
and variance
brid PN-Walsh codes from the IS-95 standard [24] were 2
σ P =  ∑ β k, m x k, m – ∑ β k, m x k, m .
2 2
chosen to perform the spreading. The channel consisted of (18)
m
an FIR filter followed by an additive Gaussian noise source, k k
to simulate background noise, intercell interference and
multipath. The intercell interference noise power that each Assuming independence of different user traffic, the stan-
user experiences is random, uniformly distributed between dard deviation in the total received power is
0 to 20 dB. So that results can be readily interpreted, we
M
consider the case where each user has only one substream, 2
∑
2
and all substreams request the same QOS. Plotted in Fig. 2 σ P_received = Gm σ Pm (19)
is a histogram of the number of users versus the bit error rate m=1
experienced for 2 cases, power control and no power con- If we now consider the ratio of the standard deviation to
trol. For fairness of comparison, the total transmit power is the mean for the total received power, it can be shown [22]
the same for both. In the case of no power control, power is that this ratio approaches zero as the number of users tends
divided evenly between all 50 users. to infinity. Hence, as the number of users grow large, the to-
tal received power becomes increasingly deterministic. By
applying a statistical guarantee when the system is heavily
loaded, the instantaneous intracell interference power will
power be close to the expected interference power, with the degree
control of variability in the achieved SNRs becoming ever smaller
as the number of users increases. Likewise, the quantity we
are minimizing - the expected total transmit power - will
closely reflect the instantaneous total power. Thus, a statis-
tical criterion and high system utilization work together to
no power each other’s mutual advantage.
no power control allo-
control
cates higher reliability
than needed
In conclusion, we have described how power control
can be used simultaneously to provide variable QOS and to
combat intracell and intercell interference in a cellular sys-
tem. UEP by power modulation can be applied at all levels,
not just the bit level, and the degree of protection can be var-
ied with fine granularity. The scheme does not require band-
Figure 2. Histogram of the number of users vs. the bit error width expansion and the computations are relatively simple,
rate each user receives, with and without power making it suitable for time-varying error protection on a
control. bandlimited channel.
In the absence of power control, higher reliability than
4 APPENDIX
needed is allocated to roughly half of the users, at the ex-
pense of unacceptable QOS for the rest of the users. By con- We now derive the closed-form solution to the uplink
trast, power control permits the network to utilize the same optimization problem; the downlink is symmetric. The
amount of power resource to satisfy the QOS contracts of all proof is similar in spirit to [21]. Map substream i of user m
users. m–1

Finally, we consider the variability incurred in the to an index u by u ( i, m ) = i + ∑ N n , and likewise let
achieved SNRs through usage of a statistical bound. From n=1
the solution, we note that the transmit power of user channel v ( j, n ) be a (substream, user) index. Let K be the total
m at any instant is a discrete random variable with probabil-
number of substreams, and define the K × K matrix moreover it will be unique and therefore optimal for system
(22).
A = [ a u, v ] by
We next prove that solving system (22) is equivalent to
solving system (21). We show if a solution to (22) exists,
a u ( i, m ), v ( j, n ) = G m ⁄ SNR i, m , u = v, (20) then it is optimal for (21); we then demonstrate if (22) has
no solution, neither does (21).
= – G n E [ f ]β j, n, u ≠ v.
Suppose x is optimal for (22) for { SNR i, m } ,
Define the K × 1 vectors c, b, x by c u ( i, m ) = β i, m ,
i = 1, …, N m , m = 1, …, M . Clearly x is also feasible
2
b u ( i, m ) = σ , and x u ( i, m ) = x i, m respectively. The
for (21). Let x′ be any feasible solution to (21). Then x′ will
uplink formulation (Eq. 5 - Eq. 7) can then be expressed as
satisfy system (22) for some set { SNR′ i, m } where, from
t
minimize c x (21)
Eq. 6,
such that Ax ≥ b, x ≥ 0 .
SNR′ i, m ≥ SNR i, m , i = 1, …, N m , m = 1, …, N .(26)
We will solve system (21) by first finding the optimal
solution to the system of equalities Noting that the function f ( t ) = t ⁄ ( 1 + t ) is monotonic
in t, we have
t
minimize c x (22)
Nm
such that Ax = b, x ≥ 0 . ′
E[ f ] ∑ β j, m SNR j, m
In general, the solution set for system (22) is a subset of the γ m ′ = ---------------------------------------------------------------
j=1 - ≥ γ m, (27)
N m
solution set for system (21). However, we will prove that ′
(21) and (22) have equal solution spaces for the problem of 1 + E[ f ] ∑ β j, m SNR j, m
interest. j=1

Eq. 9 - Eq. 12 can be verified to form a solution to m = 1, …, M ,

Ax = b. Moreover, if Eq. 8 holds then x ≥ 0 and Eq. 9 - Eq.
12 represent a finite, feasible solution to our problem; oth- and γ ′ ≥ γ . (28)
erwise, a finite, feasible solution does not exist. It remains Rewriting Eq. 12 as
to show that this solution is optimal. From basic algebra, A  
is nonsingular if and only if x = 0 is the unique solution to 2  M  
SNR i, m σ    
x u ( i, m ) = -------------------------- 1 +  ∑ γ n ⁄ ( 1 – γ ) 
Ax = 0. To use this fact, we manipulate the system Ax = 0
into the following form: Gm  n = 1  
 n≠m  
–1  
x u ( i, m ) = SNR i, m G m ( 1 – γ m )I , u = 1, …, K , (23)
and applying Eq. 26 - Eq. 28 yields
I(1 – γ ) = 0 , (24)
x′ u ( i, m ) ≥ x u ( i, m ) . (29)
M Nn
with I defined as I = E [ f ] ∑ G n ∑ β k, n x k, n . It follows that any feasible solution x′ to (21) will have an
objective value greater than or equal to that of the solution
n=1 k=1
x. Thus, the solution to (22) is optimal for (21).
From Eq. 23 and Eq. 24,
Finally, suppose no solution to (22) exists for
γ≠1⇒x≡0 . (25)
{ SNR i, m } , i = 1, …, N m , m = 1, …, M . We then
We have the result that matrix A will be non-singular if
γ ≠ 1 . Hence, if γ < 1, a positive solution will exist, and have γ ≥ 1 . Suppose a feasible solution x′ to (21) exists.
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