IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO.

4, APRIL 2010 1255

Joint Power Allocation and Relay Selection for

Multiuser Cooperative Communication
Kanchan Vardhe, Associate Member, IEEE, Daryl Reynolds, Member, IEEE,
and Brian D. Woerner, Senior Member, IEEE

Abstract—User cooperation, whereby multiple users share [7] optimally allocated relay powers in DF multi-hop wireless
their antennas and transmit to a common destination in a networks. The power control algorithm, which attempts to
collaborative manner, has been shown to be an effective way minimize the outage probability under short-term and long-
to achieve spatial diversity. We propose in this paper, a strategy
to minimize the total transmit power in a decode-and-forward term total power constraints, was studied in [8] for two-
(DF) multi-user, multi-relay cooperative uplink, such that each user cooperation scheme, while [9] considered optimization of
user satisfies its quality-of-service (QoS) data rate. Each user high-SNR approximations of outage probability for the multi-
in the proposed system transmits its own data towards the base user space-time coded DF protocol. In [10], an opportunistic
station and also serves as a relay for other users. The base station DF protocol was developed where a relay terminal is utilized
assigns one or more relays to each user in order to minimize
total power in the uplink. The relay selection is based upon the depending on the overall network state with dynamic allo-
instantaneous user to base station channels, inter-user channels cation of time and power. The above work demonstrated a
and also the target rates of the users. The simulation results significant performance improvement due to optimal power al-
indicate significant power savings over a non-cooperative uplink, location over equal power allocation in cooperative networks.
under proposed joint relay selection and power minimization The partner choice problem in a DF cooperative network
algorithm in a DF cooperative uplink when using a space-time
coded cooperative diversity. was investigated in [11], where authors devised a method to
choose a single partner among available partners to increase
Index Terms—Cooperative diversity, mutual information,
the user cooperation gain. Grouping schemes for regenerative
power allocation.
cooperative network of 𝑁 nodes, based on both centralized
and distributed control strategies were presented in [12].
I. I NTRODUCTION Bletsas et el., [13] proposed the best relay selection method

I N those wireless applications where it is impractical to

implement multiple antennas at the mobile units, user
cooperation seems to be a viable option to achieve spatial
that takes into account the instantaneous channel conditions
of both source to relay and relay to destination channels.
Most previous work on cooperative diversity either 1)
diversity [1]. User cooperation provides diversity gains using makes no attempt to optimize power, or 2) optimizes power,
antennas of neighboring users in the network. We present in assuming a cooperating group has been assigned a priori.
this paper, an algorithm that performs relay selection while There has been very little work on joint relay selection and
minimizing the total transmit power and satisfying certain power allocation in multi-user cooperative networks. Power
quality-of-service (QoS) requirement in multi-user decode- allocation for space-time coded DF cooperative diversity was
and-forward (DF) cooperative networks. studied in [14], where the authors presented a suboptimal
Recently, references [2], [3] indicated performance im- solution to minimizing the outage probability where the source
provements due to use of cooperative diversity over point-to- power is fixed (perhaps fixing the decoding set in effect) and
point links in wireless networks when using single antenna the remaining power is equally distributed among the relays.
at mobile nodes and equal power allocation. Later, efforts The sub-optimal source power is obtained numerically through
were made to further improve the performance of cooperative exhaustive search. Relative to [14], the novelty of our approach
diversity by optimal power allocation and optimal group is the non-suboptimal solution for the source and relay powers
assignment. For example, considering a three terminal DF and joint relay selection as explained in the sequel.
relay terminal network, optimal power allocation was studied We consider a user-cooperative uplink where users have
when optimizing either achievable rates [4], outage events been allocated orthogonal channels for transmission (using,
[5], or outage probability [6]. Using outage probability as an for example, orthogonal CDMA spreading codes1 ). Each user
optimization criterion and total power constraint, the authors in has its own data to send to the base station. We develop in
Manuscript received February 5, 2008; revised July 9, 2008 and July 28,
this paper, a strategy to minimize the total transmit power
2009; accepted November 11, 2009. The associate editor coordinating the in a decode-and-forward (DF) user cooperative uplink, such
review of this letter and approving it for publication was K. B. Lee. that each user satisfies its quality-of-service (QoS), data rate.
This work was supported in part by the National Science Foundation under
CAREER Grant Number ECCS-0747801 and the Lane Graduate Fellowship
We model the total power minimization problem as an opti-
award at West Virginia University. mization problem where the objective function (total network
K. Vardhe was with West Virginia University, Morgntown, WV (e-mail: power) is a convex function of user powers and the constraints
kanchan.vardhe@ieee.org).
D. Reynolds and B. D. Woerner are with the Lane Department of Comp.
are target rates of users which are concave functions. We
Sci. and Elec. Engg., West Virginia University, Morgantown, WV 26506 USA
(e-mail: {Daryl.Reynolds, Brian.Woerner}@mail.wvu.edu). 1 Non-orthogonal channels can be dealt with using decorrelating multiuser
Digital Object Identifier 10.1109/TWC.2010.04.080175 detection and an additional noise variance factor [15].
1536-1276/10$25.00 ⃝
c 2010 IEEE

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1256 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 4, APRIL 2010

then solve the optimization problem by Lagrange multiplier without shadowing. The channel (distance) between the 𝑘-th
method. The solution to the optimization problem in DF user and the base station is denoted by ℎ𝑘,𝑑 (𝑑𝑘,𝑑 ) while ℎ𝑖,𝑗
cooperative uplink leads to an iterative algorithm that jointly (𝑑𝑖,𝑗 ) denotes the inter-user channel (distance) between users
performs relay selection for cooperation and optimally allo- 𝑖 and 𝑗. Let 𝑔𝑖,𝑗 denote the channel gain for the link between
cates source and the relay powers. users 𝑖 and 𝑗 where 𝑔𝑖,𝑗 = ∣ℎ𝑖,𝑗 ∣2 /𝑑𝛼
𝑖,𝑗 , 𝛼 being the path loss
The remainder of the paper is organized as follows. Section coefficient.
II introduces the uplink system model, channel model, and also
describes the user cooperation protocol. Section III considers III. P OWER C ONSUMPTION IN A N ON -C OOPERATIVE
power consumption under non-cooperative uplink as a baseline U PLINK
for the proposed power minimization algorithm. Section IV For certain traffic types, e.g., real-time video, it is necessary
describes the proposed joint relay and power allocation al- that the transmission meets certain QoS requirement, e.g.,
gorithm under both diversity combining and code combining. data rate. The total network power consumption under a non-
Simulation results are presented in Section V and Section VI cooperative scenario, where users expend power to achieve
concludes. target rates, can be found in a straightforward manner as
follows.
II. S YSTEM M ODEL The signal received by the base station, 𝑑 due to the 𝑘-th
The uplink consists of 𝐾 users that have been allocated user’s transmission is
orthogonal channels. Each user has its own data to transmit √ ℎ𝑘,𝑑
to the base station, potentially using other users as relays. 𝑟𝑑 [𝑛] = 𝑝𝑘 𝛼 𝑥𝑘 [𝑛] + 𝑣[𝑛] (1)
𝑑𝑘,𝑑
We consider a decode-and-forward (DF) protocol that consists
of two transmission phases. During the first phase, each user where 𝑝𝑘 is the power used by the 𝑘-th source and 𝑣[𝑛] is
𝑘 broadcasts its message to the base station with power 𝑝𝑘 . the receiver noise and is distributed as 𝑣[𝑛] ∼ 𝒩𝑐 (0, 1). The
In the second phase, other users that can decode the 𝑘-th mutual information for the channel between the 𝑘-th user and
user’s transmission form a decoding set 𝒟(𝑘) and may serve the base station is
as relays. Based on our proposed relay selection criterion, log (1 + 𝑝𝑘 𝑔𝑘,𝑑 ) . (2)
some relays from the decoding set would, however, remain
silent even if they can decode the 𝑘-th user’s transmission The minimum transmit power required at the source 𝑘 to
in order to reduce the power consumption in the network. achieve the target rate 𝑅, under no cooperation, is
Since each user acts as a source during the first time phase 2𝑅 − 1
and may serve as relay during second time phase, we use 𝑝𝑘,nc = . (3)
𝑔𝑘,𝑑
the terms user, source and relay interchangeably. We consider
two practical scenarios. In the first case, selected relays could The total uplink power under no cooperation scenario is
transmit using incremental redundancy which leads to code 𝐾
∑
combining of the relayed information. As an alternative, the 𝑝nc = 𝑝𝑘,nc . (4)
selected relays may use a distributed space-time code for 𝑘=1
the source’s transmission that leads to diversity combining of
the relayed transmissions [3]. Incremental redundancy type of IV. P OWER M INIMIZATION IN A U SER -C OOPERATIVE
cooperation protocol enjoys full spatial diversity gains but at U PLINK
the expense of bandwidth inefficiency since each user requires In wireless networks, at any given time instant, users might
a separate orthogonal channel for its own transmission and for experience very different fading channel conditions. Users
relaying other user’s data. More bandwidth efficient space- experiencing deep fades will then have to expend large amount
time coded cooperation provides full spatial diversity gains, of power in order to meet the QoS constraints as can be seen
however, requires symbol level inter-user synchronization. from (3). Spatial diversity created due to user cooperation
The base station is assumed to have the knowledge of might reduce the probability of deep fades, thus reducing the
all instantaneous channel conditions including user to base total transmit power. To further enhance the performance of
station channels as well as inter-user channels and makes all user-cooperative uplink, it is imperative to devise algorithms
assignment decisions2 . It then conveys the relay assignment for optimal relay selection and power allocation across source
and the optimized powers to users through a low rate feedback and relay terminals. Optimal power allocation in a DF uplink
channel. The user-to-base station channels and the inter-user is complicated by the fact that decoding set is a function
channels undergo independent quasi-static Rayleigh fading of both inter-user channels as well as the source power in
and path loss. The inter-user channels are non-symmetric, i.e., the first phase. Given all instantaneous channel conditions,
the channel between user 𝑖 and 𝑗 is, in general, different from one of the naive approaches to the relay selection would be
the channel between user 𝑗 and 𝑖. All channels are statistically to perform exhaustive search over all possible decoding sets
modeled as zero-mean, circularly symmetric complex Gaus- for a particular source by appropriately setting source power
sian random variables. We model distance dependent path loss in the first phase and then deciding upon the decoding set
that minimizes the total uplink transmit power after optimal
2 The assumption on the knowledge of all instantaneous channel gains at
power allocation.
∑𝐾−1 ( This ) relay selection process would alone
the base station is not practical. However, the results provide baseline for
comparison with practical systems and also provide guidance in the design require 𝑖=1 𝐾−1 𝑖 iterations per user, which is impractical
of practical systems. for larger number of uplink users.

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 4, APRIL 2010 1257

We develop an iterative algorithm that jointly performs codebook for its own data and for each potential source’s
relay selection for the purposes of cooperation and optimally data. As an example, each relay could transmit a different
allocates source and the relay powers. This iterative method part of the codeword which results in a code combining at the
requires only up to 𝐾 iterations. In this section, we state base station. Similar to the non-cooperative case, the mutual
the proposed power minimization problem with respect to information due to the 𝑘-th user’s transmission during the first
general mutual information expressions. In the later sections, phase is
we consider specific cooperative diversity protocols along 1
with corresponding mutual information expressions and then log (1 + 𝑝𝑘 𝑔𝑘,𝑑 ) . (6)
𝐾
provide solution to the joint relay selection and power mini-
mization problem. The proposed power minimization problem The factor 1/𝐾 is due to the fact that each source transmits
can be formulated as follows. during 1/𝐾 of total time slots in incremental redundancy-
⎧ ⎫ based coded cooperative diversity [3]. A potential relay will

 

∑𝐾 ⎨ ∑𝐾 ⎬ be able to decode 𝑘-th user’s message if the realized mutual
minimize 𝑝𝑘 + 𝑝𝑘,𝑟 (5) information between user 𝑘 and the relay 𝑟 is greater than the
 
𝑘=1 
⎩ 𝑟=1 
⎭ fixed target spectral efficiency 𝑅. Therefore, the relay will be
𝑟∕=𝑘
in the decoding set of user 𝑘 if
subject to
1
𝐼1 = 𝑅1 log (1 + 𝑝𝑘 𝑔𝑘,𝑟 ) ≥ 𝑅, (7)
𝐾
𝐼2 = 𝑅2
.. i.e.,
.
2𝐾𝑅 − 1
𝐼𝐾 = 𝑅𝐾 𝑝𝑘 ≥ . (8)
𝑔𝑘,𝑟
𝑝𝑘 ≥ 𝑝𝑘,min ; 𝑘 = 1, 2, ⋅ ⋅ ⋅ , 𝐾
We denote by 𝑝𝑘,𝑟,min , the minimum power source 𝑘 should
𝑝𝑘,𝑟 ≥ 0; 𝑘 = 1, ⋅ ⋅ ⋅ , 𝐾; transmit with that will guarantee successful decoding at the
𝑟 = 1, ⋅ ⋅ ⋅ , 𝐾, 𝑟 ∕= 𝑘 relay 𝑟. Hence
where 𝑝𝑘 is the 𝑘-th user’s transmit power during phase I, 2𝐾𝑅 − 1
𝑝𝑘,𝑟 is the transmit power by relay 𝑟 when forwarding 𝑘-th 𝑝𝑘,𝑟,min = . (9)
𝑔𝑘,𝑟
user’s message, 𝐼𝑘 is the mutual information for the channel
between user 𝑘 and the base station which will be defined in The overall average mutual information between user 𝑘 and
subsequent sections, 𝑅𝑘 is the target rate of user 𝑘, and 𝑝𝑘,min the base station under code combining is 3
is the minimum power that source 𝑘 transmits with during the
first time phase that helps choose relays. The power 𝑝𝑘,min 1
𝐼𝑘,𝑐𝑐 = log (1 + 𝑝𝑘 𝑔𝑘,𝑑 )
is updated in each iteration of the proposed iterative power 𝐾
𝐾
minimization algorithm in order to select the most efficient 1∑
(optimal) set of relays from the decoding set for source’s + 1 log (1 + 𝑝𝑘,𝑟 𝑔𝑟,𝑑 ) (10)
𝐾 𝑟=1 ¯𝑝𝑘 >𝑝𝑘,𝑟min
transmission. The role of 𝑝𝑘,min will be clarified further in
𝑟∕=𝑘
the next Section. In the discussion to follow, we assume for
the sake of exposition that the target rates of all users are the where 1𝑥>𝑦 is a indicator function
¯
same, i.e., 𝑅1 = 𝑅2 = ⋅ ⋅ ⋅ 𝑅. {
In the above optimization problem, the minimization is done 1, if 𝑥 > 𝑦;
1𝑥>𝑦 = (11)
over source and the relay powers. The objective function here ¯ 0, otherwise.
is a affine function of source and relay powers and hence is a
convex function. Each constraint function, i.e., the target rate Now with mutual information 𝐼𝑘 ’s defined for the special
is a concave function. The convex optimization problem can case of code combining, we return to the optimization problem
now be solved by Lagrange multiplier technique [17]. The in (5). The Lagrangian equation for the optimization problem
solution to the above problem when selecting the optimal set in (5) is
⎧ ⎫
of relays from a decoding set leads to an iterative algorithm  
𝐾 ⎨ 𝐾 
⎬ ∑ 𝐾
as will be explained in the sequel. ∑ ∑
𝑝𝑘 + 𝑝𝑘,𝑟 − 𝜆𝑖 (𝐼𝑖,𝑐𝑐 − 𝑅𝑖 ) = 0. (12)
 
𝑘=1 
⎩ 𝑟=1 
⎭ 𝑖=1
A. Power Minimization under Code Combining 𝑟∕=𝑘

In this section, we develop a power optimization proto- By taking the derivative of (12) with respect to the source
col for the incremental redundancy type coded cooperation and relay powers, applying the Kuhn-Tucker conditions, and
protocol discussed in [3]. During the first time phase, each taking into account the non-negativity constraints,
user 𝑘 transmits to the base station. During the second time
3 Although it appears that spectral efficiency under incremental redundancy
phase, each relay selected after executing the proposed power
cooperative diversity goes to zero as 𝐾 goes to infinity, following the
minimization algorithm transmits the source’s information technique in [16] it can be easily shown that it approaches a fixed non-zero
over orthogonal subchannels. Each relay has it’s own unique value.

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1258 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 4, APRIL 2010

The factor 1/2 is due to the time phase orthogonality in

( )
𝜆𝑘 1 space-time coded protocol. A potential relay will be able to
𝑝𝑘 = max − , 𝑝𝑘,min ; 𝑘 = 1, ⋅ ⋅ ⋅ , 𝐾 (13) decode 𝑘-th users message if the realized mutual information
log 2 𝑔𝑘,𝑑
between user 𝑘 and the relay 𝑟 is greater than the fixed spectral
( )
𝜆𝑘 1 efficiency 𝑅. Therefore, relay will be in the decoding set of
𝑝𝑘,𝑟 = 1𝑝𝑘 >𝑝𝑘,𝑟min × max − ,0 user 𝑘 if
¯ log 2 𝑔𝑟,𝑑
1
log (1 + 𝑝𝑘 𝑔𝑘,𝑟 ) ≥ 𝑅, (17)
for 𝑘 = 1, ⋅ ⋅ ⋅ , 𝐾; 𝑟 = 1, ⋅ ⋅ ⋅ , 𝐾; 𝑟 ∕= 𝑘 (14) 2
where the powers 𝑝𝑘,min in the first iteration are set according i.e.,
to the following rule: 22𝑅 − 1
{ 𝑝𝑘 ≥ . (18)
𝑝𝑘,nc , if 𝑝𝑘,𝑟,min ≥ 𝑝𝑘,nc , ∀ 𝑟; 𝑔𝑘,𝑟
𝑝𝑘,min = (15)
arg max Ω, otherwise Hence
𝑟
where Ω = {𝑝𝑘,𝑟,min ∣ 𝑝𝑘,𝑟,min ≤ 𝑝𝑘,nc }. Equation (15) has 22𝑅 − 1
𝑝𝑘,𝑟,min = . (19)
the following interpretation. During the first iteration, if the 𝑔𝑘,𝑟
source to destination channel is stronger than any of the source The overall average mutual information between user 𝑘 and
to (potential) relay channels, then only direct transmission is the base station under diversity combining is
preferred, else the source transmits with a minimum power that
guarantees largest possible decoding set for its transmission.
1
Hence, at the start of the first iteration of the algorithm, all 𝐼𝑘,𝑠𝑐 = log (1 + 𝑝𝑘 𝑔𝑘,𝑑 )
2 ⎛ ⎞
potential relays for the source 𝑘 for which 𝑝𝑘,min ≥ 𝑝𝑘,𝑟,min
are the decoding relays. 𝜆𝑘 is found by substituting source ⎜ 𝐾
∑ ⎟
1
powers 𝑝𝑘 and the relay powers 𝑝𝑘,𝑟 from (13) and (14) in the + log ⎜
⎝ 1+ 1𝑝𝑘 >𝑝𝑘,𝑟min 𝑝𝑘,𝑟 𝑔𝑟,𝑑 ⎟
⎠ . (20)
𝑘-th constraint of (5) and solving the transcendental equation 2 𝑟=1
¯
𝑟∕=𝑘
in 𝜆𝑘 . The source and relay powers are then obtained by
substituting for 𝜆𝑘 in (13) and (14). From the set of decoding The diversity combining case with space-time coded proto-
relays considered during the previous iteration, the relays that col thus differs from the code combining case in the bandwidth
resulted in corresponding 𝑝𝑘,𝑟 = 0 after power minimization, utilization factor in front of the log terms which is 1/𝐾 for the
are excluded from a set of decoding relays. This is because incremental redundancy based coded cooperative diversity and
for any 𝑝𝑘,𝑟 = 0, the resulting power minimization suggests 1/2 for the space-time coded cooperative diversity. It also dif-
not selecting that particular relay for cooperation purposes. fers in the mutual information expressions in that incremental
The corresponding minimum source power to have second redundancy based cooperative diversity with code combining
largest possible decoding set is then updated using equation involves sum-log expression while space-time coded diversity
(15) as also the source and relay powers. A total of up to 𝐾 with diversity combining involves log-sum expressions for the
iterations are needed to find the most efficient set of relays second phase of transmission. The Lagrangian equation for the
and the corresponding relay powers for each source. If the optimization problem in (5) is
computed transmit powers do not change between successive ⎧ ⎫

 

iterations, the iterative procedure described in the proposed ∑𝐾 ⎨ ∑𝐾 ⎬ ∑ 𝐾
algorithm can be stopped. In a conventional DF protocol 𝑝𝑘 + 𝑝𝑘,𝑟 − 𝜆𝑖 (𝐼𝑖,𝑠𝑐 − 𝑅𝑖 ) = 0. (21)
 
using constant power allocation, the relays remain silent if 𝑘=1 
⎩ 𝑟=1 
⎭ 𝑖=1
𝑟∕=𝑘
they cannot decode the source’s transmission. However, in the
proposed setup, whenever it is advantageous for the source to By taking the derivative of (21) with respect to the source
utilize a relay, it transmits with a sufficient power level that and relay powers, applying the Kuhn-Tucker conditions and
guarantees successful decoding at the relay. This also helps taking into account the non-negativity constraints,
in finding the optimal source power for the first phase of
( )
transmission. 𝜆𝑘 1
𝑝𝑘 = max − , 𝑝𝑘,min ; 𝑘 = 1, ⋅ ⋅ ⋅ , 𝐾 (22)
log 2 𝑔𝑘,𝑑
B. Power Minimization under Diversity Combining
We consider here a space-time coded protocol where during ⎛ ⎞
the second time phase of cooperation, the selected relays from ⎜ 𝜆𝑘 𝐾
∑
1 𝑝𝑘,𝑖 𝑔𝑘,𝑖 ⎟
the decoding set of a particular user use an ideal space- 𝑝𝑘,𝑟 = max ⎜
⎝ log 2 − 𝑔𝑟,𝑑 − 1𝑝𝑘 >𝑝𝑘,𝑖min × , 0⎟
⎠
time code and hence can transmit simultaneously on the 𝑖=1
¯ 𝑔𝑟,𝑑
𝑖∕=𝑟
same subchannel [3]. We develop a iterative relay selection
and power minimization algorithm very similar to the code for 𝑘 = 1, ⋅ ⋅ ⋅ , 𝐾; 𝑟 = 1, ⋅ ⋅ ⋅ , 𝐾; 𝑟 ∕= 𝑘. (23)
combining case discussed earlier. The mutual information due
to 𝑘-th user’s transmission during the first phase is As seen from (23), the relay powers are now interdependent.
1 The relay powers 𝑝𝑘,𝑟 are found sequentially and in an iterative
log(1 + 𝑝𝑘 𝑔𝑘,𝑑 ). (16) fashion, where sequence order is not crucial to finding the
2

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 4, APRIL 2010 1259

4
optimum solution. The relay powers are initially set to zero
and are updated as the sequence of relay power equations in 3.5
(23) is traced, for a particular value of 𝜆𝑘 . By varying the no cooperation

value of 𝜆𝑘 , a transcendental equation in 𝜆𝑘 is solved. The

incremental redundancy based cooperation − code combining
3 space−time coded cooperation − diversity combining

remaining iterative steps of the underlined joint relay selection

log ( E[Total uplink power] )

and power allocation algorithm remain the same as the code 2.5

combining case.
2

V. S IMULATION R ESULTS
We assume for the simulation purposes that the users are 1.5

distributed uniformly over a grid of 1 × 1 units with the base

1
station located at position (1,1). All channels including the
inter-user channels and the user-to-base station channels are 0.5
independent. The channel coefficients are complex Gaussian
with zero mean and unit variance. The path loss coefficient 𝛼 0
is set to 3.
3 4 5 10
Total number of users
Fig. 1 indicates the average power consumption in a uplink
with respect to total number of users under direct transmission Fig. 1. Average power consumption in a uplink as a function of total
number of users. The target rate is 𝑅 = 1 bit/sec/Hz. We see that
and two different user cooperation scenarios. The target rate incremental redundancy based cooperation improves performance up to about
is 𝑅 = 1 bit/sec/Hz. It is seen that for a fixed rate, as we 5 users, while space-time cooperation uniformly outperforms no cooperation
increase the total number of uplink users, the average total or incremental redundancy based cooperation for all users.
uplink power consumption under incremental redundancy-
based cooperative diversity with code combining exceeds that 12
2 user nc
of direct transmission. We see that incremental redundancy- 2 user cc
based cooperation improves performance up to about 5 users. 10 3 user nc
The space-time coded protocol with diversity combining per- 3 user cc
log ( E [ Total Uplink Power ] )

3 user dc
forms uniformly better than no cooperation and incremental 4 user nc
redundancy-based cooperation with code combining. This is 8
4 user cc
because, with an increase in the total number of users, each 4 user dc
potential relay requires a separate orthogonal subchannel in 6
incremental redundancy-based cooperative diversity, hence,
making the system bandwidth inefficient. This loss in the
4
spectral efficiency in case of incremental redundancy based
cooperation dominates any gain due to cooperation. The
system utilizing a space-time coded protocol, however, re- 2
quires all relays to transmit over the same subchannel and
is hence bandwidth efficient when compared to incremental 0
redundancy-based protocol. Therefore, the space-time coded 0.5 1 1.5 2 2.5 3 3.5 4
Target Rate ( bits/sec/Hz )
protocol offers significant power savings over no cooperation
(direct transmission) under the proposed relay selection and Fig. 2. Average power consumption in a uplink as a function of target rate
power minimization algorithm. for no cooperation (nc), incremental redundancy-based cooperative diversity
Fig. 2 illustrates the average power consumption in a user under code combining (cc), and space-time coded cooperative diversity under
diversity combining (dc). The figure indicates that for fewer number of users
cooperative uplink and under direct transmission, as a function and target rates of interests, the average total power consumption under both
of target rate on a logarithmic scale. It is observed that incremental redundancy-based and space-time coded cooperative diversity is
incremental redundancy-based cooperative diversity with code significantly less than no cooperation.
combining is better than no cooperation up to target rate of 2
bit/Hz/sec for 3 users and up to target rate of 1 bit/sec/Hz for
5 users. The figure indicates that for fewer number of users cooperative uplink such that each user satisfies its target data
and target rates of interest, the average total power consump- rate. The proposed iterative algorithm for minimizing the
tion under both incremental redundancy-based and space-time total uplink power jointly performs relay selection for the
coded cooperative diversity is significantly less than the direct purposes of cooperation and optimally allocates source and
transmission. For higher target rates and more total users in the the relay powers. We develop a power minimization scheme
uplink, the space-time coded protocol outperforms both direct for incremental redundancy-based cooperative diversity with
transmission and incremental redundancy-based cooperative code combining (of relayed information) and space-time coded
diversity, in terms of power consumption. protocol with diversity combining. With respect to incremental
redundancy-based cooperative diversity, we find that the co-
VI. C ONCLUSION operation is beneficial in terms of minimizing the total uplink
In this paper, we propose a strategy to minimize the total power at lower target rates and less number of cooperating
uplink transmit power in a decode-and-forward (DF) user users. Significant cooperation gains could be obtained using a

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1260 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 4, APRIL 2010

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