Relay Search Algorithms for Coded Cooperative
Systems
Zinan Lin and Elza Erkip
Polytechnic University, ECE Department, Brooklyn, NY 11201
[email protected] and [email protected]
Abstract— Cooperation provides an efficient form of diversity in wireless communications. In this paper we consider a
coded cooperative system where the source and the relays may
have multiple antennas. We describe two simple algorithms for
choosing a good relay: Blind-Selection-Algorithm and InformedSelection-Algorithm. These algorithms only require the knowledge of average received signal to noise ratios at the destination.
Simulation results, carried out for a cellular system, show that
both algorithms result in substantial improvement over direct
transmission and random choice of relay in the cell and provide
error rates close to best relay performance.
I. I NTRODUCTION
Cooperative communication uses partners to create spatial
diversity and robustness against channel fading. Most of the
existing work on cooperation [1]–[5] assumes that a partner is
already chosen and investigates the details of how cooperation
should be carried out. The emphasis is on diversity and system
performance in terms of outage probability or frame error rate
(FER). In [6], we derived geometric conditions for the source
and the relay under which coded cooperation [5] improves
FER. We defined cooperation gain as the ratio of direct
transmission FER to cooperative FER and studied cooperative
region (relay locations for which cooperation gain is at least
1) assuming source and destination locations are fixed. We
also provided simple analytical guidelines that enable us to
choose the best relay among available relays that are all inside
cooperative region. Using our analytical guidelines, which are
based on an exact pairwise error probability (PEP) formulation, one can avoid extensive FER simulations to find the
best relay. However, we need to know source-to-destination,
source-to-relay and relay-to-destination distances, or alternatively respective average signal to noise ratios (SNR’s). For
uplink cellular or WLAN, while it is reasonable to assume
that the base station (BS) or access point (AP) can measure the
average received SNR of all the users, estimating the average
SNR between a source and all possible relays will bring extra
complexity to the system. Furthermore this estimated SNR has
to be communicated to the BS or AP, which then can assign
the best relay to the source.
In this paper, we describe simple relay search algorithms
that only utilize the knowledge of average received SNR’s
at the destination. Our methods apply to both single antenna
(SISO) terminals [5] and multi-antenna (MIMO) terminals
using cooperative space-time coding [7]. We extend the notion
of cooperative region to compute relay locations which guarantee a cooperation gain of at least g with g ≥ 1. Extending
the analytical approximation in [6] to MIMO terminals, these
higher cooperation gain regions can easily be computed. Using
a CDMA2000 cellular system as an example, we illustrate that
our algorithms perform much better than choosing a random
relay in the cell and provide FER performance close to the
ones obtained by selecting the best relay.
Related work [8] and [9] also discuss relay search for
cooperation. In [8], two approaches for selecting a best relay
are provided: Best-Select in the Neighbor Set and Best-Select
in the Decoded Set. The former is based on the average
received SNR’s, while the latter is based on the instantaneous
SNR’s. Distributed user cooperation protocols proposed in
[9] are also based on instantaneous channel realizations. This
means that the relay should be updated every time the fading
changes, which can bring extra overhead to the network.
The paper is organized as follows. In the next section,
we present the system model. Section III introduces PEPbased guidelines to compute cooperation gain for MIMO
terminals. Section IV describes the details of the proposed
algorithms. In Section V, we simulate the FER performance
for CDMA2000 systems and provide comparisons. We also
investigate the effect of the number of relay antennas on the
selection algorithms and performance. Section VI concludes
our work.
II. S YSTEM M ODEL
We consider a wireless network with N +1 terminals. In the
context of a cellular system, the cell is approximated as a circle
and the common destination, BS, is located at the center of the
circle. As shown in Fig. 1, we let B be the destination, S be the
source (or terminal 1) and Ri , i = 2, 3, . . . , N + 1 be the relay
candidates for the source. We assume the relays are randomly
placed in the cell. The source has M1 antennas, relay i has
Mi antennas and the destination has V antennas. We denote γi
as the average received SNR at the destination from terminal
i, γ1i as the average received SNR between the source and
Ri , Di as the distance between the destination and terminal
i and D1i as the inter-user distance between the source and
Ri . Only one of the N available relays cooperates with the
source. We adapt the framework of [5] and [7] for coded
cooperation: S transmits half of coded bits which are overhead
by the selected relay, Ri , and the destination. If Ri decodes the
information bit correctly (which can be checked using CRC),
it encodes the information and sends the remaining coded bits.
The destination combines signals from S and Ri , thus creating
Fig. 1.
System model for one source and N available relays
spatial diversity. If the inter-user channel is not reliable, S
continues transmission by sending the remaining coded bits.
Our relay choice is based on average SNR’s, once Ri is picked
up as the relay for S, S does not change its relay even when the
instantaneous inter-user channel between them is not reliable.
We assume all nodes have the same transmit energy E per
coded bit and the Gaussian noise power spectral density is N20 .
We consider a complex Gaussian, flat fading channel with zero
mean and unit variance and also include the path loss effect.
Hence, the average received SNR per coded bit is proportional
to NE0 D−α , where α is the path loss component which is determined by the environment and D represents the normalized
distance between the transmitter and the receiver. Typically
the path loss exponent α is between 2 and 4 [11]. We assume
that within the course of transmission, each user observes only
one fading level towards the destination. These fading values
are independent. Hence user-to-destination channel is quasistatic, but cooperative transmission results in a block fading
environment. The inter-user channel is also assumed to be
quasi-static and independent of user-to-destination links.
the quasi-static fading channel of S to destination in the noncooperative (direct transmission) case, PfBF the FER for the
block fading channel when cooperation takes place between
S and Ri . We argued in [10] that Gf ≥ 1 if and only if
Θf ≤ 1. Hence, whether cooperative coding improves the
FER or not is independent of the FER of the source-relay
channel, Pfin . Therefore, we name Θf as cooperation decision
parameter (CDP). We also defined the cooperative region as
relay locations for which Gf ≥ 1 [6].
It is difficult to obtain an analytical expression for the FER,
so one has to rely on simulations to calculate the cooperative
region. In [10], we showed that when each terminal has one
BF
antenna, PEP based CDP, i.e, Θp = PP EP
, calculated for
EP QS
the minimum distance error event is parallel to Θf with a
certain SNR offset. We call this offset as the correction factor
(CF). Using this CF and exact PEP formula [12], we were
able to characterize the cooperative region quite accurately. We
showed that cooperative region boundary is a circle around the
destination whose radius is related to the path loss component
α, the transmitted energy E per coded bit, the channel code
and D1 . Whenever the relay is inside the cooperative region,
cooperation improves the FER of the source terminal.
In this paper, we characterize higher cooperation gain regions, Gf ≥ g again using PEP for both SISO and MIMO
terminals. For this, we first extend our SISO results to incorporate MIMO terminals. In [12], we computed the exact PEP
for a MIMO block fading channel with L blocks, Mi transmit
antennas in block i and V antennas at the receiver:
Z π2 Y
Mi
L Y
1
1
P EP =
(2)
´V dθ.
³
π 0 i=1 m=1
ai
1 + sinm2 θ
where
aim =
Ψ(ξ) =
In [10] we defined user cooperation gain, Gf to quantify
the FER benefits of coded cooperation:
F ER(no − coop)
1
´
Gf =
=³
F ER(coop)
1 − Pfin Θf + Pfin
(1)
where Pfin denotes the FER of the chosen channel code for
the inter-user channel and Θf =
PfBF
PfQS
with PfQS the FER for
1
QL QMi ³
i=1
m=1
ξ+
1
aim
´V .
(4)
with ξ = sin12 θ . Applying partial fraction expansion to Ψ(ξ),
we get a closed form of the exact PEP for the MIMO block
fading channel:
Pk
A. Cooperation Gain
(3)
λim ’s are the eigenvalues of the codeword difference matrix
[12], m = 1, 2, . . . , Mi . Define
III. C OOPERATION G AIN AND “G AIN - G ” C IRCLE FOR
MIMO TERMINALS
In this section, we first present an analytical guideline, based
on the exact PEP, to quantify cooperation gain for MIMO
systems. We next define “Gain-g” circle which simplifies
selection of a good relay among many candidates.
γi λim
,
4Mi
P EP =
Ã
1−
Pnp Pp
(p)
j
Aq,j (a(p)
q )
2j
³
´
p
Qk
Qnp
(p)
q=1 aq
p=Lr
p=V
1
(p)
uq
q=1
!j j−1
X
j=1
·
!l
µ
¶Ã
j−1+l
1
2
1 + (p) ,
l
uq
l=0
−l
(5)
PL
where k ≤ V ( i=1 Mi ) is maximum number of repeated
poles of Ψ(ξ), np is the number of distinct poles, p is the
S1: Source with 1 Tx, S2: Relay with 2 Txs, SNR1 = 0dB
1
[5 7] Convolutional Code for 1 Tx2 and 2 Rxs
0
10
10
FER
PEP
ΘMIMO
f
ΘpMIMO
−1
10
0
10
−2
10
Probability of Error
−1
Theta
10
−2
10
−3
10
−4
10
−3
10
−5
10
−6
−4
10
−15
−10
−5
0
5
10
15
10
20
0
2
4
6
SNR2(dB)
IM O and ΘM IM O for space-time coded cooperative systems.
Fig. 2. ΘM
p
f
We assume [5, 7, 5, 7, 5, 7] channel code.
(p)
p-repeated pole, uq
=
q
1+
1
(p)
aq
8
SNR (dB)
10
14
16
Fig. 3. PEP and FER for the inter-user channel. The source has one antenna
and the relay has two antennas. We assume [5, 7] channel code.
SNR1 = 10dB
(p)
, Aq,j is the jth residue
Gf=1
(p)
associated with the qth p-repeated pole aq of Eqn. (4).
Using this we define the PEP-based-CDP for cooperative
space-time coding with MIMO terminals as
IM O
=
ΘM
p
12
P EP BF
,
P EP QS
Gf=5
(6)
where P EP1BF and P EP1QS can be obtained from Eqn. (5)
by substituting L = 2 and L = 1 respectively.
Similar to the SISO case, when terminals have multiple
IM O
IM O
and ΘM
are parallel with an SNR
antennas, ΘM
p
f
MIMO
offset of CF
for the SNR range of interest as shown
in Fig. 2. Even though we only illustrate one value of γ1 , the
offset remains the same for different values of γ1 as in [10].
The correction factor CFMIMO only requires FER calculation
at one set of average received SNR values from the source
and the relay. It solely depends on the channel code, so it
has to be calculated only once for a given cooperative code.
Therefore, similar to SISO, MIMO cooperative region can also
be analytically estimated accurately.
While cooperative region guarantees that cooperation is
desirable, we characterize higher cooperation gain regions
to help us in our choice of the best relay. However, unlike
Gf = 1, Gf = g, g > 1, is not independent of the inter-user
FER Pfin . For the same Θf , relay which is closer to the source
(lower Pfin ) results in higher cooperation gain. We use the fact
that PEP for the minimum distance error event is parallel to
FER at medium to high SNR with an SNR offset we call offset
factor (OF) [6]. Similar to CF, OF only requires one FER
calculation. This observation, made for SISO terminals in [6],
can easily be extended to MIMO. In Fig. 3, we illustrate this
for the inter-user channel, where the source has one antenna
IM O
and the relay has two antennas. Combining ΘM
, P EPin ,
p
MIMO
MIMO
CF
and OF
, the cooperation gain Gf in Eqn. (1)
can be analytically approximated for cooperative coding of
MIMO terminals.
As an example, the cooperative region (Gf = 1) and
Gf = 5 region boundaries, calculated using this analytical
approximation, for [5, 7, 5, 7] code with one antenna terminals
S
B
C51
Fig. 4. Estimated cooperation gain regions. The destination (B) and the
source (S) are located at (0,0) and (1,0) respectively. We assume one antenna
terminals, [5, 7, 5, 7] channel code.
and SN R = 10dB are illustrated in Fig. 4. The destination
(B) is located at (0, 0) and the source is at (1, 0). The path
loss exponent is assumed to be α = 2.0.
B. “Gain-g Circle”
As discussed in Section III-A, to guarantee a cooperation
gain, Gf = g > 1, one leads to know the average SNR
between the source and the relay as well as source-destination,
relay-destination average SNR’s. Geometrically, this corresponds to Gf = g boundaries no longer being represented
as circles around the destination for fixed B and S locations.
To arrive at a simpler region which only utilizes relay-todestination distance, we consider the largest circle centered
around the destination that falls inside Gf = g region as shown
g
in Fig. 4. We call this circle as “Gain-g” circle, CM
, where
M is number of relay antennas.
To find the radius of this circle, we need the “worst” relay
location that guarantees a cooperation gain Gf = g. This
happens when the relay is on the line joining the source
and the destination, but behind the destination, i.e., D12 =
D1 + D2 . Using the analytical approximation of Gf described
g
in Section III-A, the radius of CM
and corresponding relay-todestination average SNR can be easily computed numerically.
For example, for the parameters in Figure 4 the radius of C15
g
can be calculated as 0.81. Note that radius of CM
depends on
D1 , the path loss exponent, the transmitted energy E and the
channel code.
g
g
The advantages of CM
are: (i) all relays inside CM
result
in at least a cooperation gain of g; (ii) only relay-destination
average SNR (or distance) has to be measured. Also, it is easy
to observe that following properties hold:
g
increases with M for a required g.
1) The radius of CM
g
2) The radius of CM
decreases with g for a fixed M .
Note that when g is very large, Gf = g region does not contain
g
the destination any more and CM
cannot be used. However,
we observe in Section V that our relay selection algorithms
g
based on CM
for a g lower than this threshold guarantees a
good system performance.
IV. R ELAY S ELECTION A LGORITHMS
In order to utilize PEP based formulas as an analytical
guideline for choosing the best relay as done in [6], we need
to know all average link SNR’s, i.e. source-to-destination (γ1 ),
relay-to-destination (γi ) and source-to-relay (γ1i ) or corresponding distances for all relays. The algorithms we propose
only utilize γ1 and γi , i = 2, · · · , N + 1, or alternatively D1
and Di to arrive at a suboptimal but (as we will show later)
quite reasonable relay assignment.
In the case of WLAN or uplink cellular, the destination
already needs the knowledge of average and instantaneous
SNR’s for coherent communication, so there is no additional
overhead. The relay choice is made by the destination and
does not change based on instantaneous channel conditions.
This allows few updates on the relay assignment.
We allow the source and the relays to have arbitrary number
of antennas. We illustrate the algorithms in terms of user
geometry, but alternatively knowledge of γi0 s would be sufficient. We present two algorithms: Blind-Selection-Algorithm
(BSA) which does not utilize the information on the number of
relay antennas and Informed-Selection-Algorithm (ISA) which
uses the antenna information to arrive at a better relay.
Blind-Selection-Algorithm (BSA):
We consider a target cooperation gain g, that is we would
like to have F ER(coop) = g1 F ERno−coop . We will utilize
g
Gain-g circle around the destination, CM
described in Section III-B. Since this algorithm does not differentiate relays
g
with different number of antennas, and the radius of CM
increases with the relay antennas M , we will consider the
g
smallest gain circle CM
for a given g, where Mmin =
min
min {M2 , · · · , MN +1 }. This guarantees a cooperation gain g
no matter how many antennas the relay has. The radius of
this circle can be approximated analytically as described in
Section III-B. For simplicity, we will consider integer g in
the following algorithm, but it can easily be used with noninteger g as well. We assume that the destination has already
measured all average relay SNR’s or knows the locations.
Step 1 : Based on an initial desired cooperation gain g for
the FER, the destination randomly chooses a relay
g
inside Gain-g circle, CM
.
min
g
Step 2 : If no relay inside CMmin , decrease g by 1. If g−1 ≥
1, go back to step 1. Otherwise, no relay is assigned
and the source transmits in non-cooperative fashion
to the destination.
Note that g = 1 corresponds to the cooperative region. We
already know that if there are no relays inside the cooperative
region, cooperation would not improve FER.
Informed-Selection-Algorithm (ISA):
This algorithm is a modified version of BSA that takes
into account the number of antennas each relay candidate
has: We assume the relay indices are assigned such that
Mmax = M2 ≥ M3 ≥ . . . ≥ MN +1 = Mmin and set the
initial k to be 2.
Step1a: Based on an initial desired cooperation gain g,
the destination randomly chooses a relay with Mk
antennas in Gain-g circle for the Mk relay antennas,
g
CM
.
k
g
Step1b: If no relay is inside CM
and k < N + 1, set
k
k = k + 1 and go back to step 1(a). If k = N + 1,
go to step 2.
Step 2 : Set g = g − 1. If g − 1 ≥ 1, go back to step
1(a). Otherwise no relay is assigned and the source
transmits directly to the destination.
In both BSA and ISA, if no relay that can guarantee a
cooperation gain of g can be found, we decrease the desired
gain g and hence increase the search region. Compared with
BSA, ISA adapts the search region to the number of relay
g
antennas. Since CM
is larger for higher M , the initial search
region for ISA is larger. However, if BSA is able to find a relay
g
, then it is likely that the cooperation gain will be
in CM
min
higher than g since the chosen relay may have more antennas
than Mmin .
V. S IMULATION R ESULTS
In this section, we use parameter settings from CDMA2000
system to simulate FER performances by using two random
relay selection methods proposed in the previous section.
We use the path loss model in CDMA2000 systems as
P L(dB) = 25.6 + 35 ∗ log10 (D) (D is in meters), where
the path loss component α = 3.5 [13]. Given that the noise
figure is −204dB/hz and the bandwidth is 1.25Mhz, the noise
variance in the channel is N0 = −143dB. We assume there is
no shadowing and ignore inter-cell and intra-cell interferences
in this study. The average received SNR at the destination is
γi (dB) = 10 ∗ log10 E − N0 (dB) − PL(dB). We consider a
cell radius of 1.2Km in our simulation. BS is at the center
of the cell and the source location is fixed at D1 = 300m.
We use BPSK modulation in all simulations. For simplicity,
we consider the case when the source has one antenna and
the relay candidates inside the cell have one or two antennas.
Not all terminals in the cell will be available for relaying, so
we assume that there are 10 possible relays in the cell. We
Source: 1 Tx, Relays: 1 Tx
0
10
relay selection performances are close to best relay and are
able to capture the increased diversity of cooperation. We also
observe that as expected two antenna relays result in better
performance than one antenna relays.
Overall Minimum
Random Selection in C15
Random Selection in Cooperative Region
Random Selection in Cell Size
No Cooperation
−1
FER
10
Source: 1 Tx, p% Relays: 2 Txs and (1−p%) Relays: 1 Tx, p =20
0
10
Overall Minimum
Random Selection in C51
−2
10
Random Selection in Cooperative Region
Random Selection in Cell Size
No Cooperation
−1
10
−3
10
2
4
6
8
10
12
14
16
FER
SNR1(dB)
−2
10
Fig. 5.
FER performances for different relay search regions when all
candidates have 1 antenna inside the cell.
Source: 1 Tx, Relays: 2 Txs
0
−3
10
10
Overall Minimum
Random Selection in C52
Random Selection in Cooperative Region
Random Selection in Cell Size
No Cooperation
−1
−4
10
10
2
4
6
8
10
12
14
16
FER
SNR1(dB)
Fig. 7. FER performances for different relay search regions when 20% of
candidates have 2 antennas, 80% have 1 antenna. BSA is used for the relay
search.
−2
10
Source: 1 Tx, p% Relays: 2 Txs and (1−p%) Relays: 1 Tx, p =80
0
10
Overall Minimum
Random Selection in C51
−3
10
Random Selection in Cooperative Region
Random Selection in Cell Size
No Cooperation
−1
10
−4
10
2
4
6
8
10
12
14
16
Fig. 6.
FER performances for different relay search regions when all
candidates have 2 antennas inside the cell.
FER
SNR1(dB)
−2
10
−3
10
use [5, 7, 5, 7] or [5, 7, 5, 7, 5, 7] convolutional code as
the cooperative channel code [7]. Given the source has one
antenna, if the relay has one antenna as well, [5, 7, 5, 7]
channel code is used for cooperation; if the relay has two
antennas, the source utilizes [5, 7] code and the relay uses [5,
7, 5, 7] code over its two antennas for cooperation.
In Figs. 5 and 6, we first consider the case when all relays
have one or two antennas respectively. Since Mmin = Mmax ,
the BSA and ISA algorithms are equivalent. We start the
relay selection algorithm from gain g = 5. This is denoted
5
as “Random Selection in CM
” in the figures, where M = 1, 2
respectively. For one antenna relays, at γ1 = 9.7dB, C15 has
a radius of 168m and the radius of the cooperative region is
722m. For two antenna relays, at the same SNR, the radius of
C25 becomes 328m and the cooperative region’s radius is 840m.
For comparison, we also consider no cooperation, random
relay selection in the cell, random selection in cooperative
region and the best relay. We observe that random selection
in the cell provides small improvement over no cooperation
for small SNR’s, while the improvement is more pronounced
as SNR increases. Random selection in cooperative region
is better than random selection in the cell, but eventually
converges to the latter as the cooperative region increases
to include the whole cell for high SNR [6]. Our proposed
−4
10
2
4
6
8
10
12
14
16
SNR1(dB)
Fig. 8. FER performances for different relay search regions when 80% of
candidates have 2 antennas, 20% have 1 antenna. BSA is used for the relay
search.
We next consider the case when p percentage of relays have
two antennas, the remaining have one antenna. Performance of
BSA algorithm along with no cooperation, random selection
in cell, random selection in cooperative region and best relay
are illustrated in Figs. 7 and 8. As expected, the performance
of BSA is in between the one-antenna and two-antenna cases
of Figs. 5 and 6, and is better when p = 80. The performance
of random selection in cell and in cooperative region is not
very much affected by the composition of relays, p. Figs. 9
and 10 illustrate the performance for p = 20 and 80 for the ISA
algorithm. Since ISA starts its search from 2 antenna relays in
a larger region, performance is better than BSA and is more
pronounced for larger p and smaller SNR’s. We predict that the
performance would depend much more on the composition of
the relays p and on the type of selection algorithm (BSA versus
ISA) if we use a stronger cooperative space-time code [7].
Source: 1 Tx, p% Relays: 2 Txs and (1−p%) Relays: 1 Tx, p =20
0
10
Overall Minimum
Random Selection first in C25 then in C15
Random Selection in Cooperative Region
Random Selection in Cell Size
No Cooperation
−1
FER
10
−2
10
−3
10
−4
10
2
4
6
8
10
12
14
16
SNR1(dB)
Fig. 9. FER performances for different relay search regions when 20% of
candidates have 2 antennas, 80% have 1 antenna. ISA is used for the relay
search.
Source: 1 Tx, p% Relays: 2 Txs and (1−p%) Relays: 1 Tx, p =80
0
10
Overall Minimum
Random Selection first in C52 then in C51
Random Selection in Cooperative Region
Random Selection in Cell Size
No Cooperation
−1
FER
10
−2
10
−3
10
−4
10
2
4
6
8
10
12
14
16
SNR1(dB)
Fig. 10. FER performances for different relay search regions when 80% of
candidates have 2 antennas, 20% have 1 antenna. ISA is used for the relay
search.
VI. C ONCLUSION
In this paper, we examine the problem of relay selection
from a list of candidates for MIMO coded cooperative systems.
We propose simple relay search algorithms: Blind-SelectionAlgorithm (BSA) and Informed-Selection-Algorithm (ISA).
These two algorithms can be easily implemented using our
analytical guidelines and are suitable for a centralized network
as they only require information on the average received SNR
from the available relays to the destination. ISA is a modified
version of BSA, it requires the destination to distinguish
the number of antennas the relay has. We apply these two
algorithms to a cellular system. Simulation results show that
unlike relay random selection in the cell, our algorithm shows
diversity advantage even for medium SNR’s. We also observe
that the FER performances of using BSA and ISA are close
to the best-relay.
R EFERENCES
[1] A. Sendonaris, E. Erkip and B. Aazhang, “User cooperation diversitypart I: System description,” IEEE Trans. Commun., vol. 51, no. 11,
pp. 1927-1938, Nov. 2003.
[2] A. Sendonaris, E. Erkip and B. Aazhang, “User cooperation diversitypart II: Implementation aspects and performance analysis,” IEEE
Trans. Commun., vol.51, no.11, pp. 1939-1948, Nov. 2003.
[3] J. N. Laneman, D. N. C. Tse and G. W. Wornell, “Cooperative diversity in wireless networks: efficient protocols and outage behavior,”
IEEE Trans. Inform. Theory, vol.50, no.12, pp. 3062 - 3080, Dec.
2004.
[4] T. Hunter and A. Nosratinia, “Cooperative diversity through coding,”
in Proc. IEEE International Symposium on Information Theory
(ISIT), Lausanne, Switzerland, June, 2002.
[5] A. Stefanov and E. Erkip, “Cooperative coding for wireless networks,” IEEE Trans. Commun., vol.52, no.9, pp.1470 - 1476, Sept.
2004.
[6] Z. Lin, E. Erkip and A. Stefanov, “Cooperative regions for coded cooperative systems”, in Proc. IEEE Global Telecommucatins (Globecom), vol. 1, pp. 21-25, Dallas, Texas, Nov-Dec. 2004.
[7] A. Stefanov and E. Erkip, “Cooperative Space-Time Coding for
Wireless Networks,” accepted for publication of IEEE Trans on
Commun., 2005.
[8] J. Luo, R. S. Blum, L. J. Greenstein, L. J. Cimini and A. M.
Haimovich, “New approaches for cooperative use of multiple antennas in ad-hoc wireless networks,”Proc. IEEE Vehicular Technology
Conference (VTC)-Fall, Los Angeles, California, Sept. 2004.
[9] T. Hunter and A. Nosratinia, “Distributed Protocols for User Cooperation in Multi-User Wireless Networks,”Proc. IEEE Global Telecommunications (Globecom), vol. 6, pp.3788-3972, Dallas, Texas, Nov.
29-Dec.3, 2004.
[10] Z. Lin, E. Erkip and A. Stefanov, “An asymptotic analysis on the
performance of coded cooperation systems,” Proc. of IEEE Vehicular
Technology Conference(VTC)-Fall, Los Angeles, California, Sept.
2004.
[11] H. L. Bertoni, Radio Propagation for Modern Wireless System, Upper
Saddle River, NJ:Prentice Hall, 2000.
[12] Z. Lin, E. Erkip and A. Stefanov, “The exact pairwise error probability for MIMO block fading channel,” Proc. of 2004 International
Symposium on Information Theory and its Applications, Parma, Italy,
Oct. 2004.
[13] Document TR 25.896, “Uplink enhancements for dedicated transport
channels,” www.3gpp.org.