Relaying in CDMA Networks:
Pathloss Reduction and Transmit Power Savings
Patrick Herhold, Wolfgang Rave, Gerhard Fettweis
Technische Universität Dresden, Vodafone Chair Mobile Communications Systems, D-01062 Dresden, Germany
Email: herhold@ifn.et.tu-dresden.de, Phone: +49 351 463 32739, Fax: +49 351 463 37255
Abstract— Relaying has recently emerged as a field of growing
interest for wireless systems. The use of intermediate nodes for
relaying information from a source to its destination promises
improvements on various levels, ranging from increased connectivity and reduced transmit powers to diversity gains. We examine
various propagation models and network parameters and show
to which extent the pathloss in cellular wireless systems can be
reduced by the use of relay nodes in a two-hop scenario. Having
highlighted these potentials, we discuss by means of numerical
analysis and system-level simulation under which conditions these
savings can be turned into a transmit power reduction for CDMA
FDD systems. It becomes evident that the overall performance
of the relay system depends on the node density and the relative
load.
I. I NTRODUCTION
Compared to conventional wireless cellular systems, in
which all terminals are directly connected to the backbone
infrastructure via a single hop, the use of intermediate nodes
to help transmit information from one node to another facilitates numerous improvements. For example, the connectivity
of nodes can be improved, a network-level advantage often
referred to as enhancing coverage in cellular systems. With
respect to the physical layer, the inherent diversity of the
relaying channel enables to benefit from these diversity gains
[1].
Moreover, relaying splits longer paths into shorter segments,
thus reducing the resulting total pathloss by exploiting the nonlinear relation of pathloss vs. distance. At system level (MAC),
this potentially allows for a reduction of transmit powers, and,
consequently, lower electromagnetic immission. It is this very
topic – decreasing the exposure to electromagnetic radiation –
that increasingly becomes relevant for system design, partially
for reasons of interference reduction, partially due to pressure
from public opinion.
The idea of relaying in wireless networks has long been
attracting attention [2], yet it was only until recently that
relaying is considered for practical systems.
Various works addressed a variety of different relaying approaches for existing systems. For example, a detailed concept
for incorporating relay functionality into contemporary GSM
networks is presented in [3]; another contribution for relaying
in F/TDMA networks is provided in [4]. A different approach
This work has been supported by the German Federal Ministry for Education and Research under grant 01 BU 053. The authors take on responsibility
for the contents.
is taken in [5], where an additional air interface is used for
the relaying operation, thus inherently enhancing the overall
bandwidth used.
For 3G CDMA networks, the idea of Opportunity Driven
Multiple Access (ODMA) to enhance TDD system capacity and coverage was investigated [6]. Zadeh and Jabbari
considered a FDD system in which digital repeaters relay
data packets in a time-division manner, suggesting that power
savings are feasible [7].
In this paper, we further discuss the possibility of relaying in
CDMA systems. To this end, we enhance the work presented
in [8]. Following a presentation of our CDMA FDD system
model in section II, we demonstrate the achievable pathloss
savings that provide the potential for a reduction of transmit
power savings in Section III. Section IV first analytically
analyzes the achievable transmit power reduction, showing
that transmit power savings and interference levels depend on
system load. Using different carriers for the relay reception and
transmission, respectively, we then investigate more complex
scenarios by means of system-level simulation. The paper
concludes in section V.
II. S YSTEM M ODEL AND A SSUMPTIONS
We investigate a cellular CDMA system, in which all users
simultaneously share the same radio resource. Uplink (UL) and
downlink (DL) are separated from each other in the frequency
domain. Our system assumptions are as follows.
a) Node types: Four types of nodes are present: base
stations (BS), relay stations (RS, these are user terminals that
serve other nodes while simultaneously performing their own
communication with the BS), target stations (TS, served by
the RS), and direct stations (DS, conventionally connected to
the BS); see Fig. 1.
b) Parameters: The total number of mobile nodes is K.
The probability of a mobile station having relay capability is
p(R), so that in average there are p(R) · K relays to serve
the potential TSs. Note that p(R) = 0 corresponds to the
conventional case in which all mobiles directly communicate
with the BS, while for p(R) = 1 all mobiles can potentially act
as relays for other terminals. The number of hops towards a BS
is limited to two (”single-relay”, or ”two-hop” operation). At
most Mmax target stations can be served by a RS. Various
propagation models are examined, each superpositioned by
1
Pathloss model
Relative total pathloss β
BS
DS
RS
TS
0.8
WI LOS
0.6
HATA
0.4
0.2
BS height=20m
Roof top height=25m
K=20
σ =10 dB
WI NLOS
0
0
0.2
0.4
0.6
0.8
Fraction of # relays w.r.t. total # terminals
Fig. 1. An example system snapshot. The plotted antenna characteristics
of the BS reflect the employed three-sectorization. While this plot shows a
single BS only, multiple BS were simulated in order to reduce border effects.
a log-normally distributed random shadowing with standard
deviation σ.
c) Routing: We assume the pathlosses between all
nodes to be known. The routing scheme is a sub-optimum
min-pathloss algorithm [8]: based on the knowledge of all
pathlosses between the network elements, the scheme routes a
potential target station via a relay if this results in a reduction
of the pathloss with respect to the direct link to the “nearest”
BS.
d) Orthogonality Constraint: Relaying requires a relay
node to receive information from a source and to forward
this information to the intended destination. With respect to
capacity considerations, it would be beneficial to retransmit
the relayed signal at the same resource, i.e. at the same time
and frequency, at which it has been received. For the purpose
of a simple analysis, we initially assume the relay nodes to
be capable of performing this operation. However, as this fullduplex mode is technically not feasible in a small-size radio,
it is necessary to allocate orthogonal resources to the relays’
receive- and transmit paths. This is later considered in the
simulations and will then be explained in more detail.
In the following section, we investigate to which extent the
pathloss can be lowered by introducing relay stations.
III. PATHLOSS R EDUCTION
Our aim is to estimate the achievable pathloss reduction
for typical wide-area cellular configurations. To this end, we
denote the total pathloss in the relay case, normalized to the
total pathloss in the direct case, by β. Total pathloss refers
to the sum of all individual link’s pathlosses in the system.
For the employed min-pathloss routing algorithm, we always
achieve pathloss savings, i.e. 0 ≤ β ≤ 1.
Figure 2 shows this relative pathloss reduction β as a
function of the relaying probability p(R) for various propagation models. Assuming that each mobile in a network has
the ability to act as a relay (p(R) = 1.0), the total relay
pathloss amounts to approximately 30% of the pathloss in the
direct case. This strong potential for reduced transmit powers
motivates to investigate the actual effects that relaying has on
the transmit powers in a power-controlled system.
1
p(R)
Fig. 2. Relative pathloss reduction β as a function of the relay density p(R).
Parameter is the pathloss model (WI=COST Walfish Ikegami, HATA=COSTHATA 259, LOS=line of sight, NLOS=non line of sight). BS antennas are
installed below roof top. As the relative number of available relays increases,
the pathloss in the relaying case reduces with respect to the direct case
(p(R) = 0.0). Antenna gains at the BS have not been taken into account.
IV. T RANSMIT P OWERS
We now focus on the actual transmit power savings of
power-controlled CDMA systems. Transmit powers in such
a system are primarily determined by two measures. First, the
received power should match the receivers sensitivity, which
requires that transmit powers be set such that the propagation
loss is overcome. We denote this fraction of the transmit power
as pathloss-determined. Second, the interference level due to
multiple access interference (MAI) may require an additional
increase of the power to ensure a sufficient SINR at the
detector. As interference in a CDMA system is influenced by
the network load, we describe this part of the transmit power
as the load-determined fraction. Power control autonomously
adapts the transmission power to the interference conditions.
The previous section has demonstrated the potential for reducing the pathloss-determined fraction of the transmit power,
and it remains to discuss the relation of relaying and network
load and its influence on the load-determined power fraction.
A. Analysis
1) General Analysis of CDMA Transmit Powers: The system consists of a set of point-to-point links; each link i is
characterized by its required SINR γi at the intended receiver.
In a perfectly power controlled system, the transmit power Pi
is set such that this SINR is achieved exactly. Assuming that
interfering signals can be regarded as white noise, this SINR
relation is expressed as
γi = X
αi,i gi Pi
αi,k Pk + Ni
.
(1)
k6=i
In this equation, αi,k is the path gain that relates the transmit
power of link k to the power level at the receiver of link i by
capturing the effects of path loss and shadowing (0 < αi,k ≤
1). Moreover, gi is the processing gain of link i, and Ni is the
thermal noise power at the receiver of link i. We now aim at
computing the transmit powers Pi . Reordering (1) yields
X γi αi,k
γ i Ni
Pk .
(2)
= Pi −
αi,i gi
αi,i gi
k6=i | {z }
| {z }
ni
Ψi,k
Defining ni = γi Ni /(αi,i gi ) and
0
γi αi,k
Ψi,k =
αi,i gi
i=k
,
i 6= k
equation (2) can be rewritten as
X
ni = P i −
Ψi,k Pk
∀i .
(3)
(4)
i6=k
This set of linear equations can be expressed in matrix form
with the introduction of a noise vector nT = (n1 , .., ni , .., nL )
and a transmit power vector PT = (P1 , .., Pi , .., PL ), so that
we have n = P − Ψ · P. The matrix Ψ consists of the mutual
interferences Ψi,k . Thus, we obtain
P = (I − Ψ)−1 · n .
(5)
Note that equation (5) defines a unique set of transmit powers
given the links’ path gains, required SINRs, noise powers,
and processing gains. A valid set of transmit powers is
characterized by Pi > 0 ∀ i.
2) Pole Capacity, Processing Gain and Data Rate: Our
baseline system for comparison of relaying performance is the
conventional system in which all mobiles directly transmit to
a BS. For such a system, the concept of pole capacity can be
readily applied [9]. To this end, and in order to further simplify
our analysis, we assume in the sequel that the system-level
parameters of all mobile stations are equal, i.e., γi = γ0 , Ni =
N and gi = g0 for all i. Note that choosing equal processing
gains (gi = g0 ) implies that all mobile stations operate at the
same data rate. For the purpose of a pole capacity analysis,
we assume furthermore that the path gains between all mobiles
and the central BS are equal: αi,i = αi,k = α0 . This yields
ni = γ0 N/α0 g0 and Ψi,k = γ0 /g0 . We study an isolated cell,
i.e. intercell interference is neglected. For K users, equation
(4) then reads
γ0
γ0 N
= P0 − (K − 1) P0 .
α0 g 0
g0
(6)
Solving for K and allowing unlimited transmit powers
(P0 → ∞) yields the well-known pole capacity for an isolated
cell of the conventional, direct system Kpole = (g0 /γ0 ) + 1
for P0 → ∞. Equivalently, we can solve for the minimum
required processing gain gpole (K) necessary for serving K
users:
gpole (K) = γ0 · (K − 1)
for P0 → ∞ .
(7)
Hence, gpole (K) is the minimum processing gain that is
required to serve K users with SINR requirement γ0 if an
unlimited transmit power budget was available. In terms of
data rate, gpole (K) is the spreading gain that corresponds to
the maximum data rate per user that is theoretically achievable
given K users with a SINR requirement γ0 . Using (7) in (6)
and solving for P0 yields
P0 =
γ0 N
α
| {z0 }
·
1
,
g0 − gpole (K)
|
{z
}
(8)
pathloss-determined load-determined
where we have separated the parameters into two factors that
reflect the pathloss-dependency and the load-dependency of
the transmit powers.
To see how data rate affects the transmit powers, consider
a fixed number K of users. For low data rates, i.e., for
large processing gains (g0 gpole (K)), the transmit powers
in (8) are primarily pathloss-determined. As the rates and
hence the load increases, i.e. as g0 → gpole (K), the mutual
interferences cause the transmit powers to become dominantly
load-determined. The powers grow unboundedly as the data
rate per user approaches the limit; that is, P0 → ∞ as
g0 → gpole (K).
For the purpose of further exposition, consider the ratio of
the pole processing gain to the actually used processing gain,
0 ≤ gpole (K)/g0 < 1. This ratio represents the normalized
load with respect to the pole capacity, and is for a fixed number
of users solely determined by the employed processing gain
g0 . In the following example we will see how this system load
affects the transmit powers of direct and relaying systems.
B. Relay Case and Numerical Example
Consider the simple single-cell configuration in Figure 3.
An inner tier of mobiles serves as relay stations (RSs) for
distantly located terminals. The pathlosses αi,k reduce with
the introduction of relay hops. This reduction of pathlosses,
however, comes at the cost of an increased total data rate
as relay stations retransmit information that has already been
emitted by the base station or target stations, respectively.
Recalling that RSs transmit their own data in addition to the
relayed information, it is obvious that the links between BS
and RSs carry the total data rate of the cell. Parts of this data
is then additionally relayed to/from the targets.
In order for the links between BS and RSs to be able to
transport this increased rate, the spreading factor of these links
needs to be reduced appropriately. That is, the processing gains
gi need to be lowered for the inner links.
For the example placement of nodes depicted in Fig. 3, we
can easily determine the transmit powers using equation (5).
Towards this end, we assume a log-distance pathloss model
in which αi,k = d−a
, where di,k is the distance between
i,k
transmitter and receiver, and a is the pathloss exponent. For
the numerical examples in this section a pathloss exponent
of a = 3 is used. The nominal processing gain is g0 ; the
links between BS and RS operate with a processing gain of
g0 /2 as double data rates are required for these connections.
For K = 20 mobiles and γ0 = 1 the pole processing gain
becomes gpole (K)
P = 19. The resulting average UL transmit
1
power P̄ = K
i Pi is plotted in Fig. 4 as a function of the
relative load gpole (K)/g0 of the cell.
1.5
1
0.5
y
0
BS
RS
TS
−0.5
−1
−1.5
−2 −1.5 −1 −0.5
0
x
0.5
1
1.5
2
Fig. 3. Example analysis system. Many of the effects of complex relay
networks can be qualitatively described using this simple configuration.
Avg. UL transmit power [dBm]
10
5
Relay case (Mmax=1)
0
−5
−10
Direct case
Break−even
load
−15
−20
0.7
0.75
0.8
0.85
0.9
0.95
gpole/ g0 (Relative load)
1
Fig. 4. UL transmit power (P̄ ) for the example system depicted in Fig. 3 as
a function of the relative load, expressed in terms of the ratio of processing
gains. As the data rate per link increases, i.e. as gpole (K)/g0 → 1, the power
advantage of relaying reduces. Eventually, the transmit powers in the relay
case exceed those of the direct case for loads greater than 0.96.
Clearly, it depends on the load of the system whether
relaying yields transmit power savings with respect to the
direct case. For the considered example, the break-even load
is 0.96: for relative loads stronger than this break-even load,
relaying requires stronger powers than conventional direct
communication. Furthermore, the results in Table I suggest
that the break-even load depends on the node density, a fact
that becomes intuitively clear considering the stronger mutual
interferences that arise from the smaller distances between
receiving and interfering nodes.
Moreover, it becomes obvious that the capacity of the relay
system is smaller than the that of the direct system for high
TABLE I
T HE BREAK - EVEN LOAD , I . E . THE
SYSTEM LOAD FOR WHICH DIRECT
SYSTEM AND RELAY SYSTEM REQUIRE THE SAME TOTAL TRANSMIT
POWER ( FOR THE STAR - CONFIGURATION OF
F IG . 4). F OR LOADS
SMALLER THAN THE BREAK - EVEN LOAD , RELAYING YIELDS TRANSMIT
POWER SAVINGS .
K
Break-even load
10
>1
20
0.96
30
0.83
40
0.69
node densities. An analytical analysis for the case of K = 20
users shows that the transmit powers diverge for a relative load
of 0.98 (see also Fig. 4). In other words, the pole capacity of
the relay system is smaller than that of the direct system.
We see that there are two major system-level drawbacks of
the relaying system. First, the total data rate to be transported
in the relay case increases with the introduction of (additional)
relay hops. Second, the power control must ensure a sufficient
SINR at the relays, thus increasing the number of points at
which signals need to be detected from one (BS in the direct
case) to many (BS and relays in the relay case).
To summarize, two converse trends affect the actual transmit
powers: on one hand, relaying reduces the average pathloss, on
the other hand the network load increases due to the immission
of additional signal copies, thus requiring stronger powers to
overcome enhanced interferences. It hence depends on the load
of the network whether or not relaying results in transmit
power savings, with the load being determined by both the
number of nodes and their individual data rates to be carried.
Note that up to this point we have not made any constraint
on the technical capabilities of the relay nodes. In particular, we disobeyed the orthogonality constraint by assuming
that a relay station is capable of transmitting and receiving
simultaneously at the same resource. This justified a direct
comparison of the direct and the ideal relay system as both
techniques require a single carrier for continuous operation. It
was shown that even under these idealized circumstances relaying may exhibit stronger transmit powers for high network
loads.
In order to study these general trends for more realistic
assumptions, the next subsection discusses a realistic relaying
strategy for a CDMA FDD system and details the simulation
model that is used in this more complex study.
C. Simulation Model
1) Frequency Assignment: As discussed previously, one
needs to assign orthogonal resources for the receive and
transmit path of a relay node. One approach is to use different
time slots for the two operations. This store- and forward
option is especially suitable for data packet communication
and other services that exhibit low delay sensitivity, and is
frequently considered in the literature; see, for example, [7].
Another possibility is to assign different frequencies for the
receive- and transmit paths, an option desirable for the investigated CDMA FDD system for it allows to retain continuous
transmission. However, it requires that different frequencies
be used for reception and transmission at the relay. These
resources can be made available through the use of a second
carrier. Since each carrier provides two frequencies, a total of
four frequencies is then available.
In the framework of a German national project, an algorithm
was developed that assigns carriers such that (i) relay stations
receive and transmit at different frequencies, (ii) mutual interferences are avoided to the best possible extent, and (iii) both
carriers are loaded equally in order to avoid load unbalances.
Similar to the routing scheme, the algorithm takes as input
TABLE II
S IMULATION PARAMETERS .
Parameter
Cell radius (hexagon)
Log-normal shadowing (σ)
Target SINR Eb /N0 (γ0 )
Noise power (N )
Receiver noise figures {BS,DS,RS,TS}
Max. tx powers {BS,DS,RS,TS}
Maximum DCH powers {DL,UL}
DL orthogonality factor
BS antenna height
BS antenna pattern
DS, RS, TS antenna gain
DS, RS, TS antenna (gain)
Pilot & common power fraction
Value
800 m
8.0 dB
var.
-106.7 dBm
{5.0,8.0,5.0,8.0} dB
{43,24,35,24} dBm
{38,24} dBm
0.4
30 m
Realistic sector
18 dBi
Omni (0 dBi)
10%
[dBm]
15
Powers
10
UL
Avg. UL transmit power P
the pathlosses between the links, and then iteratively assigns
frequencies subject to the above mentioned conditions. A
detailed description of this procedure is beyond the scope of
this paper. To permit a fair evaluation, this two-carrier relaying
needs to be compared to a conventional (non-relaying) system
that likewise utilizes two carriers.
2) Simulation Method: A static simulation tool was used
to investigate the effects of relaying on the average transmit
powers for more realistic scenarios. Relevant simulation parameters are summarized in Table II. A perfect power control
(PC) algorithm was implemented [10].
pathloss−
determined
5
load−
determined
0
Direct communication
−5
−10
−15
−20
−25
Relay case
2
N=10 (per cell)
p(R) =1.0
σ (dB)=8.0
4
6
8
10
12
Data rate per mobile [104 kbit/s]
14
Fig. 5. Simulation results. Transmit powers of the conventional system and
the relay system vs. the data rate per mobile. As the data rate per mobile
increases, the load-determined power fraction becomes dominant over the
pathloss-determined fraction, and the rate increase then causes the relaying
system to exhibit stronger transmit powers than the conventional one.
node density. Even for optimistic assumptions (ideal node
placement in a star-scenario, relays have the capability of
transmitting and receiving simultaneously at the same frequency), it was demonstrated that for high system loads the
transmit powers of the relay system exceed those of the direct
system.
For interference-limited power-controlled systems this suggests that direct transmission eventually becomes favorable
with respect to capacity considerations.
R EFERENCES
A simulation consists of numerous snapshots, the results of
which are averaged to obtain reliable statistics. Each snapshot
represents a single realization of a random distribution of users
and log-normal shadowing. At the beginning of a snapshot, the
specified number of mobiles are uniformly distributed over
the area. The subsequent routing procedure then establishes
the connection between the nodes, and finally frequencies are
assigned.
D. Simulation Results
Fig. 5 compares the transmit powers achieved in the direct
case and in the relaying case as a function of the data rate per
mobile station. Clearly, with increasing rate per mobile, i.e.
with higher network loads, relaying becomes less attractive
as predicted by analysis. In this example, relaying does not
provide any power savings for rates greater than eighty kbit/s
per mobile. While a complete discussion of the simulation
results is beyond the scope of this paper, it can be summarized
that power savings ranging from 1 to 8 dB are feasible for low
to medium network loads.
V. S UMMARY
AND
C ONCLUSIONS
We quantified the significant pathloss reductions that are
achievable by relaying in wireless networks. However, due to
the load increase caused by repeated emissions of essentially
the same signal, it was shown that the extent to which transmit
powers can be reduced strongly depends on network load and
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