Performance Analysis of Distributed Spatial Multiplexing with Multi-hop Amplify and Forward Relaying in Cellular Networks

International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.1, No.6, December 2011
DOI : 10.5121/ijcsea.2011.1607 85
Performance Analysis of Distributed Spatial
Multiplexing with Multi-hop Amplify and Forward
Relaying in Cellular Networks
M.Sushanth Babu1
and Prof.K.Kishan Rao2
1
Associate Professor, Department of Electronics & Communication Engineering
Vaagdevi College of Engineering, Warangal, A.P., INDIA
sushanth_6@yahoo.com
2
Director, Vaagdevi College of Engineering, Warangal, A.P., INDIA
prof_kkr@rediffmail.com
ABSTRACT
This paper describes a frame work investigating the performance of distributed spatial multiplexing (DSM)
in cooperative multi-hop cellular networks. The cooperative communication in cellular networks gives us
leverage to get the inherent advantages of its random relay locations and the direction of the data flow.
However, traditional centralized relay selection needs considerable overhead and signaling. In our
proposed work, threshold based relay selection is adopted based on the received signal strength (RSS) and
Signal to Noise Ratio (SNR). The best relay chosen will transmit jointly with source using Amplify and
forward (AF) protocol. The evaluation is performed with bit error rate (BER) and energy per bit for
distributed spatial multiplexing scheme with multi-hop networking.
KEYWORDS
Amplify and Forward relaying, Received signal strength, Energy per bit, Distributed Spatial Multiplexing,
Cooperative multi-hop networking, Cellular networks.
1. INTRODUCTION
Cooperative communication has recently emerged as a promising technique to combat fading in
wireless networks. It leverages the broadcast nature of wireless channel and enables multiple
wireless terminals to assist each other for high quality transmission [1]. Although the advantages
of Multiple-input-multiple-output (MIMO) systems are well known, it may be impractical to
equip very small mobile equipments with multiple antennas. This is primarily due to the size and
power limitations of these nodes. To overcome these issues and embrace the benefits offered by
the MIMO systems, the concept of cooperative relaying can be successfully implemented in
cellular communications [2].
Several cooperation strategies with different relaying techniques, including amplify-and-forward
(AF), decode-and-forward (DF), and selective relaying (SR), have been proposed and
investigated in terms of outage probability and bit error probability [4]. Next generation multi-
hop cellular networks, especially in the infrastructure based relay networks, multiple concurrent
transmission from users are expected and should be well supported by relay stations. The
selection of subset relays according to the performance metric can further enhance the

86
performance of the cooperative networks [3]. However, how to select the best relays for
cooperative diversity in a dynamic network environment is still an open challenge. In particular
the work in [5] evaluates the cooperative diversity performance when the best relays are chosen
according to the average SNR, and the outage probability. Some researchers have proposed a
centralized solution where a fixed node decides which relay will be selected to help the source to
forward its information based on perfect knowledge of channel information. In [6], centralized
power allocation schemes are presented by assuming all the relay nodes to minimize the system
outage behavior and improve the average throughput. In [7], the problem of power allocation has
been considered for multiple relay systems. The power allocation schemes in [8] divide the
transmit power among the source and the relay(s) to maximize the channel capacity or the
instantaneous SNR and thus minimizing the system outage probability. Those schemes have high
computation and feedback requirements and cannot be applied for cellular system. However,
most existing work focuses on relay selection in a centralized fashion. There is already a lot of
works related to cluster formation [4],[7], capacity improvement [9] and energy efficient
cooperative communication [3],[10], but little attention has been given to cooperative relay
selection on the basis of their location in clusters to improve the energy efficiency and reliability.
In this paper, we propose a completely distributed relay selection scheme for multi-hop cellular
networks using Amplify and Forward (AF) protocol based only on the source-relay channel and
threshold based optimization. Further this paper describes the idea of distributed spatial
multiplexing in wireless multi-hop networks.
The remainder of this paper is organized as follows: In Section II, we describe the system model
with threshold based relay selection algorithm for multi-hop cellular networks. The
implementation of distributed spatial multiplexing and the evaluation of energy consumption are
described in Section III. In Section IV, numerical results are presented and in Section V, we
conclude.
2. SYSTEM MODEL
Fig. 1, represents a cooperative multi-hop cellular network with Amplify and Forward relaying
protocol. The system model considered in this paper is High Speed Uplink Packet access
(HSUPA), Release-6. All nodes are assumed to be equipped with single antennas, operating in
half duplex mode and each transmission link between any two nodes are modeled as Ricean
fading channel. In the general cooperative phenomenon, source broadcasts the information to
selected relays and Base station [BS] in phase 1and from phase 2 relays retransmit the amplified
version of information to next selected best relays in neighboring cluster. This process continues
in multiple phases until relays retransmit the information to BS with minimum acceptable bit
error rate [BER].
2.1. Threshold based relay selection
Energy efficiency of cooperative communication in a clustered network has been investigated in
[11]. In [11], nodes collaborate on signal transmission and/ or reception in a deterministic way. It
is shown that if the long haul transmission distance between clusters is large enough, cooperative
transmissions can dramatically reduce the total energy consumption. Energy allocation can
further improve the performance of cooperative communication. Optimal energy distribution
among cooperative nodes is studied in [12] to minimize the link outage probability. In amplify
and forward cooperation protocol, considerable energy saving can be obtained even if source
contain few channel information bits [6].

87
Cooperative communications in wireless networks can be more beneficial if transmit cooperative
relays are at equal distance from the intended receiver. Propagation measurements in a mobile
radio channel indicate that the average received signal strength at any point decays as a power
law of the distance of separation between a transmitter and receiver.
Figure 1. Cooperative Multi-hop Distributed spatial multiplexing cellular network
The average received signal strength (RSS) at a distance d from the transmitting antenna is
approximated by
n
iD
d
PRSS
−








= 0 (1)
where 0P is the power received at a close in reference point, n is the path loss exponent. iD is the
distance of the i th
interferer from the mobile, the received power at a mobile due to the ith
interfering cell will be proportional to ( ) n
iD − .
Based on these distance estimates source allocates an equal-power group identity (Cluster) to
those nodes which lies within a certain range, K= min( (i)
x_s
d ) ⊆ X(i), where K represents
number of nodes in each cluster. In addition to this the cooperative nodes should be at minimum
distance from each other to save energy in local communication within the cooperative relays
cluster. We propose Threshold based relay selection algorithm, which generalizes threshold
digital relaying to multiple relays. The relay who’s SNR larger than Threshold (T) are allowed to
retransmit.
The PDF of the SNR is given as








−=
lk
x
lk
x
lkSNRf
,
exp
,
1
)(
, λλ
(2)
where SNRk,l is the signal to noise ratio on the link between two nodes k and l, λk,l = E(SNRk,l) and
E(.) is the expectation operator. Assume that A is the number of relays having an SNR greater
than the threshold T. The probability that A equal to two, means that only two relays are
participating in cooperative transmission.

88
{ } ∏
≠=






<∑
=






≥==
N
iKK
T
KRSSNRP
N
i
T
iRSSNRPAP
,1
,
1
,2 (3)
3. EVALUATION OF ENERGY CONSUPTION
In order to achieve high throughput and spectral efficiency we split the data stream into several
sub-streams and transmit the sub-streams simultaneously over spatial sub-channels. These sub-
channels are created in a distributed fashion by the network itself.
3.1. Distributed Spatial Multiplexing
Consider a wireless network as shown in fig. 1, where a single-antenna source wants to send a
data packet of length PT to a single-antenna destination over 1+L hops, whereas L denotes the
number of clusters containing K intermediate nodes that act as single-antenna amplify-and-
forward (AF) relays. The nodes
)1(
1r and
)1(
2r cooperate such, that
)1(
1r forwards the first half of
the data packet and
)1(
2r the second half. As a result the packet duration at intermediate hops is
2/PT . Intermediate nodes simply store and forward the received packets simultaneously without
further cooperation. Note that the sub-packets forwarded by
)2(
1r and
)2(
2r are linear superposition
of the sub-packets forwarded by
)1(
1r and
)1(
2r . In the last hop the nodes
)4(
1r and
)4(
2r cooperate
such, that the destination receives two sub-packets sequentially in time. With suitable space-time
signal processing at the source, the destination is able to decode the information bits. As the
packet length reduces to 2/PT , the multi-hop delay drops accordingly. Neglecting the time for
signal propagation, the multi-hop delay τ is in general given by 




 −
+=
K
L
PT
1
2τ , where K is the
number of forwarding relays in a cluster.
3.1.1. Signal and Channel Model
All signal arrivals and departures are perfectly synchronized. The nodes cannot transmit and
receive simultaneously and transmitted signals only reach the next cluster. The equivalent
complex baseband signals received by the relays in the first cluster are stacked into a vector
111 wxHy += where ( )T
K,....,xxx= 1 is the data vector sent by the source with average power
constraint [ ] KPixE /
2
= . Note that
i
x is the symbol which will be forwarded from relay i in the
first cluster. ( )1,.....,11diag1H Khh= is a KxK diagonal matrix with ( )1,01 CNih ≈ the complex path
gain from source to relay i in the first forwarding cluster and ( )T)1(
,....,
)1(
11w Kww= with
( )2
,0
)(
RCN
l
iw σ≈ describes the additive white Gaussian noise at the relays. The symbols
K
xx ,.....,
1
are launched into the network via orthogonal channels that are described by 1H . The
signals received in the l th cluster are given as
lllll
w
1
ygHy +
−
= , with
T
,.....,
)(
1
y 



= l
K
y
l
y
l
.
l
H ,

89
where Ll ,........,2= is a KKx channel matrix with elements ( )1,0
)(
CN
l
ij
h ≈ describing the complex
path gain from the j th relay in cluster 1−l to the i th relay in cluster l . The scaling factor
l
g is
chosen such that the average transmits power of every relay equals KP / . The vector received by
the destination is then given by
444 3444 2144 344 21
n
1
ww1Hg
H
1
xHg1H=y ∑
=
∏
=
+++∏
=
+
L
m
L
mn
mnn
L
l
llL (4)
With







≤≤
+
=
+
=
.2;
2
/
,1;
2/
/
2
g
Ll
R
P
KP
l
R
KP
KP
l
σ
σ
( )Khh 1,.....,11diag1LH =+ is again a KKx diagonal matrix with ( )1,01 CNih ≈ the complex path gain
from relayi in the last forwarding cluster to the destination. The covariance matrix R is given as
KK
L
m
L
mn
L
mn
nnn I
2
I
2
R
H
1
1H1H
2
g=R σσ +∑
=
∏
=
∏
=
++ 







(5)
Where 2
σ denotes the noise power at the destination.
3.2. Evaluation for Energy per Bit
We have modeled the cellular network with Ricean fading channel model. In the particular
arrangement of cooperative multi-hop network shown in Fig. 1, where all relays are at same
distance from the intended receivers, following equation (6) represents the total energy required
per bit per hop,
( )
( )
Rn
bR
electrxP
Tn
bR
electtxP
fNlM
rGtG
iSXd
ibitLEibitLE
__
2
2
)(_4
1)(_)(_1
++
++=+
λ
π
α
(6)
Where ,....1,0=L and 0)(
_0
=i
bit
E
where α is depends upon the drain efficiency of power amplifier in transmitter circuitry, ρ is the
signal power to noise ratio at each of the receive node, N0 is AWGN power spectral density,
dX_S(i) is the average distance between transmitter and receiver, λ is the carrier wavelength, , G t
G r are antenna gains of transmitter and receiver respectively, M l is the link margin compensating
hardware process variations and other noise or interference, Nf is the receiver noise figure, Rb is
transmission rate and Ptx_elect (180mW), Prx_ elect (200mW) are power dissipated in transmitter and
receiver circuits, respectively. The transmitted power depends on ρ and bit error

90
probability, ( )ρρ aerfc
b
P ≈)( , where a,b>0 and SNRs of the
BSiKandiKSBSS −−− )()(, links are denoted by BSS−ρ , )(iKS−ρ , BSiK −)(ρ respectively.
Note that typically b depends on the minimum distance in the consolation and depends on the
number of neighbors with minimum distance. The bit error probability of most popular schemes
can approximated as, for BPSK (b,a) = (0.5,1) and for MPSK
( ) ( ) ( ) ( )( )MMMab /
2
sin2log,2log/1, π= . Based on this general Pb expression, the average bit
error probability under Ricean fading is expressed as
( ) ( )[ ] 





+
−==
ρ
ρ
ρρρ
a
a
baerfcEbP
1
1 (7)
( )
( )
Rn
bR
electrxP
Tn
bR
electtxP
fNlM
rGtG
iSXd
FLH
NbPTn
ibitLEibitLE
__
2
2)(_4
2
14
0/1ln
1)(_)(_1
++
+
++=+
λ
π
α
(8)
Therefore, the bit error rate probability and energy per bit will eventually converge to a value
solely determined by the distance between the neighboring relays, modulation schemes and the
respective SNRs.
4. NUMERICAL RESULTS
To demonstrate the efficiency of the proposed framework, we assume the proposed network is
High Speed Up-link Packet Access (HSUPA), Release-6 (category 6). BW=2000MHz,
Transmitted power of UE = 21dBm (Class 4 UE), number of multi-hops (Phases) = 3. Data
rate=5.8Mbps, Radius of cell site=600m, and the number of data bits in a packet=1024bits.
Fig.2 depicts the computational experiments carried out on a set of moderately sized network
with 50 random nodes, distributed in 600X600 grid.
Xloc= 8.95 114.25 233.45 232.15 436.5 515.26 514.23 218.2 319.0 216.2 23.25 24.6 296.5
328.5 429.4 217.56 325.26 38.45 336.24 314.21 312.45 452.2 419.2 471.5 462.2 412.3 562.2
582.6 512.2 593.2 66 462 64 563 74 375 372 578 82 486 84 93 96 98 95 91 77 98 84 33.3 120
111 136 145 156 166 171 183 194 164 200 210 221 234 241 253 264 275 283 294 299.12 301
310 320 330 349 358 362 372 383 387 399 402 419 423 438 447 455 465 476 487 498 503 512
523 533 544 566 577 588 599 600.
Yloc= 599.5 165.32 287.25 129.63 545.25 569.25 415.25 515.63 134 126 222 123.6 120.5 150
316 335 425 226 428 306 340 45 460 48 422 511 533 518 64 65 62 69 71 375 273 179 84 85 86
91 95 96 98 12 16 19 47 53.9 23 82 590 560 555 456 432 345 456 234 345 456 567 243 354 576
262 363 474 575 233 244 255 266 277 245 455 466 477 488 499 453 452 451 354 356 357 358
328 421 487 365 376 385 393 330 350 337 358 390 590 570 560 520.
Fig. 3, represents threshold based selected nodes in each cluster. The number of clusters are
confined to L=3 for simplicity. The cluster and best two relays are selected based on distance and
threshold criteria. Fig. 4, provides an analysis of Distributed Spatial Multiplexing (DSM) bit error
rate at selected multi phases. Because of the Amplify and Forward relay protocol implementation

91
in DSM, it is observed from various iterations that BER increases with number of multi phases.
Fig 5 and 6, demonstrates the energy consumption per bit for multiple phases, selected at
different locations.
Figure 2. Illustrating randomly spaced cellular nodes
Figure 3. Selected Clusters and best relays based on proposed Algorithm

92
Figure 4. Performance of Distributed Spatial Multiplexing in multi-hop AF relaying protocol
Figure 5. Evaluation of Energy per bit versus SNR

93
Figure 6. Evaluation of Energy per bit with multi-hop distance metric
5. CONCLUSION
In this paper, we provided a frame work on multi-hop cooperative cellular network, in which the
evaluation of the system is carried out in two phases. Threshold based relay selection Algorithm
is proposed with less complexity and fairness for cellular networks. Furthermore, Distributed
Spatial Multiplexing (DSM) with Amplify and Forward relaying is analyzed for multi-hop
networks. The numerical results demonstrated the energy consumption per bit for both schemes
under distance and diversity metrics.
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Authors
M.SUSHANTH BABU received his B.E. in Electronics and Communication
Engineering in 2002 from North Maharastra University and his M.Tech. degree from
Jawaharlal Nehru Technological University, Hyderabad in 2008. He has been working
towards his Ph.D. degree in Wireless Communications at Jawaharlal Nehru
Technological University, Hyderabad since 2009. He is presently working as Associate
Professor in Department of Electronics and Communication Engineering. He guided 18
Masters and 30 UG projects. He is a member of professional bodies like, IEEE, ISTE
and IETE. He is technical program committee member of 09 IEEE International Conferences. His research
interests are in the areas of Wireless Mobile Communication, Cellular Networking, Distributed Cooperative
Communication, MIMO and Signal Processing Applications.
Prof.K.KISHAN RAO is currently a Professor in Electronics and Communication
Engineering and working as Director in Viswambhara Educational Society. He received
his B.E. and M.E. degrees from Osmania University in 1965 and 1967.He is awarded
with Ph.D. degree from Indian Institute of Technology, Kanpur [IIT] in 1973.He worked
as Principal for National Institute of Technology and Kakathiya Institute of Technology
and Science, Warangal. He a senior member of professional bodies like IEEE [comsoc],
ISTE, and IETE. He has published over 78 International articles. He currently serves as
Editor for International Journal of Wireless Personal communication, Springer and International Journal
of Wireless Networks, Springer. He guided 03 Ph.D scholars and guided 62 Master Projects. His research
interests are in the areas of Wireless Communications, Signal Processing Applications and Cooperative
Mobile Communications.

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