SELECTION AND DATA TRANSMISSION IN COOPERATIVE … · SELECTION AND DATA TRANSMISSION IN...
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SELECTION AND DATA TRANSMISSION IN COOPERATIVE SYSTEMS K.Sakthivel
1, S.Anitha
2
Assistant Professor 1 2
Department of EEE, BIST, BIHER, Bharath University, Chennai.
Abstract—A common and practical paradigm in
cooperativecommunications is the use of a dynamically selected
‘best’ relay to decode and forward information from a source to a
destination. Such a system consists of two core phases: a relay
selection phase, in which the system expends resources to select the
best relay, and a data transmission phase, in which it uses the
selected relay to forward data to the destination. In this paper, we
study and optimize the trade-off between the selection and data
transmission phase durations. We derive closed-form expressions for
the overall throughput of a non-adaptive system that includes the
selection phase overhead, and then optimize the selection and data
transmission phase durations. Corresponding results are also
derived for an adaptive system in which the relays can vary their
transmission rates. Our results show that the optimal selection phase
overhead can be significant even for fast selection algorithms.
I. INTRODUCTION
Relay-based multi-hop cooperation, in which a source node
transfers information to the destination with the help of a relay
selected from the available nodes has attracted considerable
at-tension in the literature [1]–[4]. The relay is selected
depending on its instantaneous channel gains on the basis of a
real-valued locally known metric that is a function of the
relay-destination (RD) channel gain or the source-relay (SR)
channel gain or both, depending on the cooperation protocol.
Relay selection has been shown to help the system exploit the
spatial diversity afforded by having geographically spaced
multiple relays. It improves the symbol error probability [3] or
increases the data transmission rate [5]. In general, the extent
and nature of the benefits from selection depends on both the
selection criteria and the cooperation scheme [6]–[11]. After the source broadcasts its data, these systems typically use
two phases to complete the transmission to the destination: (i) a relay selection phase, in which the ‘best’ relay with the
highest metric is chosen by a selection mechanism, and (ii) a data
transmission phase, in which data is transmitted to thedestination
by the selected relay. The selection phase is needed because the
source does not know a priori which relay is the best one.
Furthermore, since the metric is a function of local
The work of the first two authors was partially supported by a research project sponsored by Boeing-ANRC.
Channel gains, each relay knows only its metric, and not that of the others.
In most papers, the selection is assumed to be perfect and
instantaneous. In effect, it is assumed to incur no time or
energy overhead. However, in practice, the system does need
to expend time and energy during the selection phase to find
the best relay. The simulations in [12], [13], which modeled
several practical aspects of a contention-based se-lection
process, indicate that the relative time and energy spent in the
relay selection phase can be considerable. This overhead
clearly depends on the selection mechanism. For example, in a
centralized polling mechanism, the overhead for selection
increases linearly with the number of available relays. In [12],
a source uses overhead handshaking messages to exhaustively
track the rate that each candidate relay can support. The
selection phase overhead can be reduced by using distributed
mechanisms based on back-off timers [14] or time-slotted
splitting algorithms [15]–[17]. The selection phase cannot always be perfect. For example,
a practical system may terminate the selection phase after
some time even when the best relay has not been selected.
This leads to an outage during the subsequent data
transmission phase. While increasing the selection phase
duration reduces this outage probability, it does so at the
expense of the overall throughput due to the less time
available for data transmission. Thus, the two phases affect
each other, and cannot be optimized in isolation. This paper conducts a comprehensive system-level analysis
and optimization that considers the trade-offs between the two
phases. Such a modeling and joint optimization has received
limited attention in the literature [11]–[13], [18]. For example,
[18] considers outage and throughput, but not the selection
phase overhead. We consider a generic system-level model
that explicitly models the two phases and develop analytical
expressions for the overall system throughput. We first
analyze a non-adaptive system in which the data rates and
time intervals for the phases are fixed, and then an adaptive
system in which the selected relay adapts its transmission rate
to improve overall throughput. The optimal trade-off between
the two phases is different for these two systems. To be able to make precise system-level quantitative state-
ments, a choice needs to be made about the mechanism used
International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 5101-5110ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu
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for selection. To this end, we consider the splitting algorithm for
relay selection [19-23] given its remarkable speed and scalability.
While the time taken by the splitting algorithm to select the best
node depends on the specific realizations of their metrics, on
average it can find the best node within 2.47 slots even when an
asymptotically large number of nodes contend. Even for such an
efficient algorithm, the time overhead of the selection phase often
turns out to be considerable. Our analysis shows that the optimal
selection phase duration is often at least a factor of two or more
than the above average in order to ensure a sufficiently large
probability of success in selecting the best relay[24-29]. Thus,
our analysis shows that a joint design is also desirable in systems
that use other selection mechanisms. The paper is organized as follows. The system model is set
up in Sec. II. The analysis is developed in Sec. III. The design
implications are brought out in Sec. IV, and are followed by
our conclusions in Sec. V.
II. SYSTEM MODEL
Figure 1 shows a schematic of the cooperative relay network that we consider. It contains one source node, one
destination node, and n decode-and-forward relays. The channels from the source to the relays as well as from the relays to the destination are assumed to be frequency flat
channels that undergo independent fading. Thus, for relay i,
the source to relay (SR) channel power gain, hsi, and the relay
to destination (RD) channel power gain, hid, are independent and identical exponentially distributed random variables with the same mean[30-35].
We focus on the identically distributed case in this paper
due to space constraints. The analysis can be generalized to
handle the case of non-identical SR and RD channels [19]. We
assume, without loss of generality (w.l.o.g.), the fading
powers means are all normalized to 1. We assume a block
fading channel model in which the channel gains remain
constant over the selection and data transmission phases
(described below). In practice[36-39], the system can operate
over time-varying channels and thus have to live with partially
(though not fully) outdated metrics after selection. Modeling
the time-varying nature of the channels and its impact on the
overall system performance, and then optimizing the selection
mechanism’s parameters is an interesting avenue for future
work. The noise at each receiving node is additive white
Gaussian with zero mean and unit variance[40-45]. For
analytical tractability, we shall assume that the direct source
to destination link is weak, as is typically the case [6], [20].1
We now describe the cooperation protocol for the baseline non-adaptive system. The adaptive system is discussed next.
1) SR Data Transmission Phase: The source broadcastsBbits in Td time units and all the relays listen. The fading-averaged SNR at a relay’s receiver is ρs. To relate B, hsi, and ρs, we use the ideal Shannon capacity formula,and assume that a relay i can decode the source’s
1The reader is referred to [21] for an analysis that
includes the S-D link. The papers discusses why doing so makes the analysis more involved.
hs1 R1
h1d
S R2 D
hsn hnd
Rn
Fig. 1. A cooperative system consisting of a source (S), a destination (D), and n relays, from which the best relay is selected chosen.
transmission only if
2 B
− 1
B ≤ W Tdlog2(1 + hsiρs), i.e., hsi> W Td
γsr ,
ρs
(1)
where W is bandwidth in Hz. Practical coding ineffi-ciencies can also be easily incorporated along the lines of [22], [23].
2) Relay Selection Phase: The relays contend for a
durationof Tc slots, each of duration tslot. The selection criterion and algorithm is explained below in Sections II-A and II-B.
3) RD Data Transmission Phase: At the end of the relayselection phase, the selected relay, if any, transmits
data to the destination for Td time units (using the same modulation and coding as the source). The destination decodes the message if hjd>2
B
1 /ρr γrd,
W Td
where j is the selected relay_and ρr
−is
_the fading-
averaged SNR at the destination. We say an outage occurs if the destination cannot receive
source’s message successfully. All time durations such as Td – and consequently B itself – are normalized w.l.o.g. with respect to a
contention slot’s duration tslot. A. Relay Selection Criterion
The goal of the selection algorithm is to select the relay with the highest RD channel gain [20]. Each relay knows its RD channel gain but not that of others. Furthermore, only those relays that decode the source’s message and have an RD channel gain large enough to support transmission to the destination participate in the selection process. Other relays settheir metrics to 0 and do not contend, as this wastes energywithout improving throughput. Formally, the local
metric, μi, based on which a relay i contends is
μi=_
0, h
si < γ
sr or hid< γrd
. (2)
hid
, otherwise
The complementary cumulative distribution function (CCDF)
of the metric μi is denoted by Fc(μ) = Pr (μi≥μ). B. Relay Selection Algorithm
The splitting-based selection algorithm only requires that the
CCDF and n is known to all relays. It proceeds as follows [15],
[17]. At the beginning of a slot k, each relay
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locally computes two thresholds HL(k) and HH(k), and the destination. One implication of this is that no relay
transmits if its metric μ satisfies HL(k)< μ < HH(k). At the will get selected after _nFc(γrd)_ initial idle slots.
end of each slot, the source broadcasts one of three outcomes • The slot duration of the splitting algorithm depends on
to all the relays: (i) idle when no relay transmitted, (ii) success the transmission protocol. Each slot needs to allow for
when exactly one relay transmitted, or (iii) collision when two transmissions – one by the nodes and the other by
multiple relays transmitted and collided.2 The relays update the sink – and necessary gaps, as required, between these
their thresholds for the next slot accordingly. two transmissions. For example, in 802.11 systems, each
Formally, the algorithm is specified as follows. Let Hmin(k) slot’s duration can easily exceed 100 μsec [24].
denote the largest value of the metric known up to slot k C. Adaptive System
above which the best metric surely lies. And, let split (a, b)
F −1 Fc(a)+Fc(b) . This split function ensures that, on aver- Since the relay knows its channel gain to the destination, it
2
c
can reduce its transmission duration by adapting its transmit
only half the relays involved in the last collision transmit
age, _ _
rate to log2(1 +ρrhid). The relay’s transmit SNR, ρr , is
in the next slot. It can be easily shown that
e−(γsr+
μ),
μ ≥ γrd
kept the same as for the non-adaptive system. In addition, the
system wastes no time in the RD phase in case the selection
Fc(μ) = e−(γsr+γrd), 0 < μ < γrd. (3) phase results in an outage.
1, μ = 0 It must be noted that other forms of adaptation are certainly
In the first slot, the variables are initialized as follows: possible if the system design allows it. For example, the relay
HL(1) = max(γrd, F −1 (1/n)),HH (1) =
∞ , and Hmin(1) = can adjust its transmit power instead of rate to minimize energy
consumed. Furthermore, in some systems, even the selection
th c
0. In the (k + 1) slot, the variables are updated based on the phase can terminated as soon as a success is fed back by
outcome as follows:
the source or when it becomes obvious (after _nFc(γrd)_ idle
1) If feedback (of the kth
slot) is an idle and no col-
lisions have occurred thus far, then HH(k+ 1) = slots) that no success is possible. These adaptations and others
are not analyzed in this paper due to space constraints, and
HL(k), Hmin(k + 1) = 0, and HL(k + 1) =
are addressed in detail in [19].
max(γrd, F
−1(
i+1 )).
c n
HH(k + 1) =
2) If feedback is a collision, then III. ANALYSIS
HH(k), Hmin(k + 1) = HL(k), andHL(k + 1) = We first analyze the throughput of the non-adaptive system
3) split (HL(k), HH(k)). and then that of the adaptive system.
If feedback is an idle and a collision has occurred in the A. Non-Adaptive System
past, then HH(k+1) =HL(k), Hmin(k+1) =Hmin(k),
and HL(k+ 1) = split (Hmin(k), HH(k)). The destination can successfully decode only when all the
The reader is referred to [15], [17] for a detailed explanation following three conditions are satisfied: (i) There is at least
of the above steps. We shall call the durations of the algorithm one relay that has decoded the message from the source,
before and after the first non-idle slot as the idle and collision (ii) Among the relays that have decoded the source message,
phases, respectively. During idle phase, the algorithm ensures at least one of them has a good enough link to the destination,
that only one node, on average, transmits in each slot. Once and (iii) The selection phase can select the best relay within
collision happens, the nodes are split in subsequent slots until Tcslots. In our set up, the above conditions together are
success happens. equivalent to the condition that the selection phase terminates
The splitting algorithm is fast because it ensures that one successfully withinTcslots.
node, on average, transmits in each of the idle slots, regardless The throughput, η, for the non-adaptive system is therefore
of the number of nodes in the system. Furthermore, in the η = BPs(Tc)
(4)
event of a collision, it is very likely that only two nodes have ,
collided. These are then separated quickly by successively 2Td + Tc
where Ps(Tc) is the probability that the selection phase
splitting the interval.
Comments: terminates successfully. The denominator in (4) is the total
time, including selection phase, taken by the source and relays
• Note that the formulation above differs slightly from the
to transmit B bits (normalized with respect to tslot).
original algorithm proposed in [15]. During idle phase,
To determine Ps(Tc), we first state an intermediate result
we introduce the max(.) function to prevent relays with
about the selection algorithm’s behavior.
metrics below γrd from transmitting. This is done, since
Lemma 1:The probability,p(a, b), that exactlybslots are transmission from such relays only results in wastage
required to resolve a collision involving a relays is
of energy without increasing throughput as they have
either not decoded the source’s message or do not have 1 a a
a strong enough RD channel to forward the message to p(a, b) =
_
p(a, b − 1) + i=2 i_
p(i, b −1)_
, ∀ a, b >1,
2a
2The sink can determine these outcomes based, for example, on the strength
where p(a,1) =a/2a, ∀a >1, and p(1, b) = 0.
(5)
of the received power, which is measurable by many receivers today [16].
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.
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Proof: The proof is given in Appendix A.
The main result on the probability of success now follows.
Theorem 1:The probability of successful data transfer is min(Tc,r)
i
_
n−1
r
1
Ps(Tc) =
−
+I{Tc>r}n_
α−
_
(1−α)n−1
i=1 n n
min(Tc −1,r)n n 1 k i n−k Tc−i
_
_
+ i=1k=2k_
1 −
j=1 p(k, j)
n n
n n
_
_α
r k Tc−r −1
+I{T
c
>r+1} k=2k −
_
(1−α)n−k
p(k, j),
j=1
where, T(x, y;k), 0≤x < y, is the average time required for data transmission when the relay with the highest metric is selected
from among k relays all of whose metrics lie in the interval
(Fc−1
(y), Fc−1
(x)). It is given by
T (x, y; k) = B ke−kγ
sr k−1 (
−
1)j k −1 log(2)
W (y − x)k
j=0
j _
×(yeγsr )
k−1 −j_
ψ1 j+ 1, log(1 +
ρrF
c−1(y
) )
ρr _
− ψ
1j+ 1,log(1 +
ρrF
c−1
(x))
_, (9)
ρr _
and ψ1(a, u) = u t exp _ t +
1 −
a _ dt.
∞ 1 et
Proof: The proof is given in Appendix C.
We specify the intervals limits in T(., .;k) in terms of Fc−1
(.)
as it helps simplify the notation. This is valid as Fc−1
(.) is a
one-to-one monotonic mapping for continuous distributions.
IV. RESULTS AND SYSTEM DESIGN IMPLICATIONS
We study the system-level tradeoffs using both the analytical
B. Adaptive System results derived in Sec. III and Monte Carlo simulations with
105samples. The parameter values chosen are:ρs = ρr =
In this system, a relay can now adapt its transmission rate.
6 dB, andB = W Td log2(1 + 100.6
), which implies that a
Equivalently, it adapts its transmission duration – subject to a relay or destination can decode successfully if its instantaneous
cap of Tmax, which is a system parameter. A relay contends
received SNR is at least 6 dB.
only if it can transmit the information to the destination within For the non-adaptive system, Figure 2 shows that the prob- Tmax,i.e., it contends when its RD channel gain exceeds the
ability of successful selection, Ps(Tc), increases as the total
adp
B
2 W T
max −1.
number of available relays (n), or the selection phase duration
threshold γrd ρr
The new throughput (normalized with respect to tslot ) then ( Tc ) increases. For large T , P s (T c ) saturates at 1 − (1 − α)
n.
nc
equals BPs(Tc)
This is because (1−α) is the probability that an outage
η =
,
(7) occurs because none of the n available relays contend in the
Td+ Tc+ Tadp selection phase. Notice also that the analytical and simulation
where Tadp is the average RD transmission phase duration. results match very well.
While increasing Tc improves the probability of successful
The probability of successful selection, Ps(Tc), above is again
given by (6) with γrd simply replaced by γ adp 3 Finally, the selection, it also increases the overall time of the three phases.
.
rd
This important trade-off between the overall system through-
average RD transmission phase duration, Tadp, is then given
put and Tc is shown in Figure 3. For small Tc, increasing Tc
by the following result.
improves throughput since the probability of outage decreases.
Theorem 2:When the RD data transmission duration is
However, for larger Tc, the throughput starts decreasing as
adapted, its average equals
Ps(Tc)saturates. The results show that the optimal value for
min(Tc,r) i
_
n−1 i − 1
i
the selection phase duration depends on both n and Td. For
Tadp =
1
; 1
T ,
example, for Td= 13, Tc= 4 and 5 are optimal for n= 6 and
− n
i=1 n n _ 15, respectively. Whereas, forTd = 100, the optimal values
min(Tc−1,r) n 1
k n k Tc
− i of Tc increase to 7 and 8 for n= 6 and 15, respectively.
+ n 1 i
_
− T
i − 1 , i ; k p(k, j) Furthermore, the throughput increases as the number of relays
− n
i=1 k=2k_
n_ n n
_j=1 increases or as the data transmission duration increases. The
where I{x} is an indicator function that equals 1 if condition x is true and is 0 otherwise, α = Fc(γrd),
and r =_nα_−1.
Proof: The proof is given in Appendix B.
The above result can be understood as follows. Its first two terms correspond to the first non-idle slot being a success. The third and the
fourth term correspond to the first non-idle slot (ith
slot) being a
collision among k >1 relays that is resolved in the remaining Tc−i slots.
(6)
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transm
issio
n
1
0.9
0.8
data
0.7
in
success
0.6
0.5
Analysis: n=6
of
Pro
ba
bili
ty
Simulation: n=6
0.4 Analysis: n=15
Simulation: n=15
1 2 3 4 5 6 7 8 9 10
Tc
Fig. 2. Probability of successful data transfer as a function of selection phase
duration (Tc) and number of relays (n) for the non-adaptive system.
1
n=15, Analysis
0.9
Td=100 n=15,
Simulation
Td=13
0.8
Th
rou
gh
pu
t
0.7 n=6,
Td=100
0.6
0.5 n=6,
Td=13
0.4 2 3 4 5 6 7 8 9 10 1
Tc
Fig. 3. Non-adaptive system: Trade-off between overall throughput, normal-ized with respect to W , and selection phase duration for different numbers of
relays (n) and for different source data transmission durations, Td, normalized
with respect to tslot. n = 15and Td= 100, the maximum throughput of 1.202of the adaptive system is 22% more than its non-adaptive counterpart. The optimal selection duration shrinks for the adaptive case. For
example, at Td= 13, Tc= 3 and 4 are throughput optimal for n= 6 and 15, respectively. As in the non-adaptive system, the optimum
selection duration increases as Td increases. As Figures 3 and 4
suggest, the throughput is a concave function of Tc. Thus, fast convex optimization techniques can be used to determine
optimum Tc. The optimal Tctypically lies between2and9(slots),
with the exact valuedepending on Td.
V. CONCLUSIONS
We analyzed the system-level interactions and trade-off
between the relay selection and data transmission phases of a
cooperative relay system. To this end, we developed analytical
expressions for the probability of successful selection and the
average system throughput. We saw that even with a fast
splitting-based selection algorithm, the relative overhead
1.3
n=15,
1.2 Td=100
1.1 n=15, Analysis
Simulation
Thro
ugh
put
Td=13
1
0.9 n=6,
0.8 Td=100 n=6,
0.7 Td=13
0.6
0.5 5 T
1 2 3 4 6 7 8 9 10
c
Fig. 4. Adaptive system: Trade-off between overall throughput, normalized with respect to W , and selection phase duration for different numbers of
relays (n) and different source data transmission durations, Td, normalized
with respect to tslot, for Tmax=Td. of the selection phase was non-negligible. In general, the relative
overhead of the selection phase decreased as the source
transmission duration increased. Also, the overhead increased as
the number of available relays increased. We also saw that the
optimal system parameter settings for the adaptive and non-
adaptive systems are different. The optimum selection phase
duration value was lower for the rate adaptive system. The results
in this paper show that the time devoted to the selection phase
must be carefully chosen in order to maximize the overall system
throughput. Future work includes optimizing the energy-
efficiency of the systems as well.
APPENDIX A. Proof of Lemma 1
The probability that i relays, among the a that collided, transmit in
the next slot equals _a
i
_/2
a. Thus p(a, b) =a/2
a for b= 1. When b >1,
the following three cases arise: (i) The next slot is idle: The
probability that the collision among a relays is resolved in b −1slots is
p(a, b −1); (ii) i (i >1)relays collide in the next slot: The probability that
it is resolved in exactly b−1 remaining slots is p(i, b−1); (iii) The next
slot is a success: Since the collision is already resolved, the
probability that it is resolved in exactly b slots is 0. B. Proof of Theorem 1
For i ≤ r
, the probability that the first non-idle slot is the ith
n 1 k 1 −
i n−k
slot and k≥1 relays transmit in it is
. k n n
The i= (r+ 1) case is slightly different. From (2), relays
_ _ _ _ _ _
whose RD channel gains are below ar set their metrics to be 0. This occurs
with probability 1−α, where α=Fc(ar). Now, the probability that the first non-
idle slot is (r+ 1)th
slot with k relays involved in it is the probability that k relays have their metric between F
−1 r and ar , and the remaining
c n
n − k relayskhave metric Therefore, this probability equals 0. _ _
_ n _ _ r _ (1 −α)
n−k . No non-idle slot can occur after the
k α−th n
(r + 1) slot. If k relays are involved in the collision in the
International Journal of Pure and Applied Mathematics Special Issue
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ith
slot, the probability that the collision is resolved in the
remaining Tc−i slots is Tc−i p(k, j).
j=1
Depending on Tc and r_,the following two cases occur:
1) Tc ≤ r: Successfulthdata transfer a
occurs if in the
first non-idle slot (i slot): (i) success occurs,
which happens with probability n 1 1 − i , or 1 n n
(ii) k 2 relays collide, which happens with probability
n ≥k 1 − i n − k _ _ _ _ _ _
1
_ _ _
, and are resolved in Tc−i slots. k n n
Thus ,
_ _ _
Tc
1 −
i
_
n−1
Ps(
Tc) =i=1
n
Tc−1 n n 1 k i n−k Tc−i
+ i=1 k=2 k _
_
1 −
_
j=1 p(k, j).
n n
2) Tc> r: Successful data transfer occurs if during the firstnon-idle slot (i≤r+ 1):
(i) a success occurs, or (ii) if resolved in
Tc− i s lots .
k ≥2relays collide and this isth
If a collision occurs in the (r+1) slot, the interval that
needs to be split has a probability mass α−nr since only
relays with non-zero metrics contend. The expression for
Ps(Tc)becomes n−1
r i r
_
Ps(
Tc) =i=11−
+n_
α−
_
(1−α)n−1
n n
rn n 1 k i n−k Tc−i
+ i=1 k=2 k _
_
1 −
_
j=1 p(k, j)
n n
n k_ _
α −n_ k (1 −α)
n−k Tc−r −1 p(k, j).
+ k=2 j=1
n r
Equation (6) compactly expresses the above two results using
the indicator function I{.}. C. Proof of Theorem 2
First, we derive the expression for T(x, y;k). Given that a metric lies in (Fc−1
(y), Fc−1
(x)), its
probability distribution function (PDF) isf1(t) =
e−γsre−tand its cumulative
y−x distribution function is F
1(t) =
e−γsr(e
γsry−e−t
). Using y−x
order statistics [25], the average total transmit time required
when k relays have their metrics in the above interval and the one with the highest metric is selected is B Fc
−1(x)
1
T (x, y; k) = _
Fc−1(y) kf1(t)F1(t)k−1
dt,
W log2(1 + ρrt)
B F −1(x)
ke−kγ
sre−t(e
γsry e−
t)
k−1
c
=
_
−
dt.
W Fc−1
(y) log2(1 + ρrt)(y−x)k
Expanding the integrand as a binomial series and further simplifying yields (9).
Given that the first non-idle slot is the ith
slot and k relays are involved
in it, the average time required is T_i−
n1
,ni;k
_, if i≤r, and T
_n
r, α;k
_, if i=r+
1. The probability of this event can be derived from the proof of Theorem
1. Combining the above results leads to the desired expression.
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116, I-17 Special Issue, PP-113-116, 2017
2. Parameswari, D., Khanaa, V., Deploying
lamport clocks and linked lists, International
Journal of Pharmacy and Technology, V-8, I-3,
PP-17039-17044, 2016
3. Parameswari, D., Khanaa, V., Case for massive
multiplayer online role-playing games,
International Journal of Pharmacy and
Technology, V-8, I-3, PP-17404-17409, 2016
4. Parameswari, D., Khanaa, V., Deconstructing
model checking with hueddot, International
Journal of Pharmacy and Technology, V-8, I-3,
PP-17370-17375, 2016
5. Parameswari, D., Khanaa, V., The effect of self-
learning epistemologies on theory, International
Journal of Pharmacy and Technology, V-8, I-3,
PP-17314-17320, 2016
6. Pavithra, J., Peter, M., GowthamAashirwad, K.,
A study on business process in IT and systems
through extranet, International Journal of Pure
and Applied Mathematics, V-116, I-19 Special
Issue, PP-571-576, 2017
7. Pavithra, J., Ramamoorthy, R., Satyapira Das,
S., A report on evaluating the effectiveness of
working capital management in googolsoft
technologies, Chennai, International Journal of
Pure and Applied Mathematics, V-116, I-14
Special Issue, PP-129-132, 2017
8. Pavithra, J., Thooyamani, K.P., A cram on
consumer behaviour on Mahindra two wheelers
in Chennai, International Journal of Pure and
Applied Mathematics, V-116, I-18 Special
Issue, PP-55-57, 2017
9. Pavithra, J., Thooyamani, K.P., Dkhar, K., A
study on the air freight customer satisfaction,
International Journal of Pure and Applied
Mathematics, V-116, I-14 Special Issue, PP-
179-184, 2017
10. Pavithra, J., Thooyamani, K.P., Dkhar, K., A
study on the working capital management of
TVS credit services limited, International
Journal of Pure and Applied Mathematics, V-
116, I-14 Special Issue, PP-185-187, 2017
11. Pavithra, J., Thooyamani, K.P., Dkhar, K., A
study on the analysis of financial performance
with reference to Jeppiaar Cements Pvt Ltd,
International Journal of Pure and Applied Mathematics Special Issue
5107
International Journal of Pure and Applied
Mathematics, V-116, I-14 Special Issue, PP-
189-194, 2017
12. Peter, M., Dayakar, P., Gupta, C., A study on
employee motivation at Banalari World Cars
Pvt Ltd Shillong, International Journal of Pure
and Applied Mathematics, V-116, I-18 Special
Issue, PP-291-294, 2017
13. Peter, M., Kausalya, R., A study on capital
budgeting with reference to signware
technologies, International Journal of Pure and
Applied Mathematics, V-116, I-18 Special
Issue, PP-71-74, 2017
14. Peter, M., Kausalya, R., Akash, R., A study on
career development with reference to
premheerasurgicals, International Journal of
Pure and Applied Mathematics, V-116, I-14
Special Issue, PP-415-420, 2017
15. Peter, M., Kausalya, R., Mohanta, S., A study
on awareness about the cost reduction and
elimination of waste among employees in life
line multispeciality hospital, International
Journal of Pure and Applied Mathematics, V-
116, I-14 Special Issue, PP-287-293, 2017
16. Peter, M., Srinivasan, V., Vignesh, A., A study
on working capital management at deccan
Finance Pvt Limited Chennai, International
Journal of Pure and Applied Mathematics, V-
116, I-14 Special Issue, PP-255-260, 2017
17. Peter, M., Thooyamani, K.P., Srinivasan, V., A
study on performance of the commodity market
based on technicalanalysis, International Journal
of Pure and Applied Mathematics, V-116, I-18
Special Issue, PP-99-103, 2017
18. Philomina, S., Karthik, B., Wi-Fi energy meter
implementation using embedded linux in ARM
9, Middle - East Journal of Scientific Research,
V-20, I-12, PP-2434-2438, 2014
19. Philomina, S., Subbulakshmi, K., Efficient
wireless message transfer system, International
Journal of Pure and Applied Mathematics, V-
116, I-20 Special Issue, PP-289-293, 2017
20. Philomina, S., Subbulakshmi, K., Ignition
system for vechiles on the basis of GSM,
International Journal of Pure and Applied
Mathematics, V-116, I-20 Special Issue, PP-
283-286, 2017
21. Philomina, S., Subbulakshmi, K., Avoidance of
fire accident by wireless sensor network,
International Journal of Pure and Applied
Mathematics, V-116, I-20 Special Issue, PP-
295-299, 2017
22. Pothumani, S., Anuradha, C., Monitoring
android mobiles in an industry, International
Journal of Pure and Applied Mathematics, V-
116, I-20 Special Issue, PP-537-540, 2017
23. Pothumani, S., Anuradha, C., Decoy method on
various environments - A survey, International
Journal of Pure and Applied Mathematics, V-
116, I-10 Special Issue, PP-197-199, 2017
24. Pothumani, S., Anuradha, C., Priya, N., Study
on apple iCloud, International Journal of Pure
and Applied Mathematics, V-116, I-8 Special
Issue, PP-389-391, 2017
25. Pothumani, S., Hameed Hussain, J., A novel
economic framework for cloud and grid
computing, International Journal of Pure and
Applied Mathematics, V-116, I-13 Special
Issue, PP-5-8, 2017
26. Pothumani, S., Hameed Hussain, J., A novel
method to manage network requirements,
International Journal of Pure and Applied
Mathematics, V-116, I-13 Special Issue, PP-9-
15, 2017
27. Pradeep, R., Vikram, C.J., Naveenchandra, P.,
Experimental evaluation and finite element
analysis of composite leaf spring for automotive
vehicle, Middle - East Journal of Scientific
Research, V-12, I-12, PP-1750-1753, 2012
28. Prakash, S., Jayalakshmi, V., Power quality
improvement using matrix converter,
International Journal of Pure and Applied
Mathematics, V-116, I-19 Special Issue, PP-95-
98, 2017
29. Prakash, S., Jayalakshmi, V., Power quality
analysis & power system study in high
voltage systems, International Journal of Pure
and Applied Mathematics, V-116, I-19 Special
Issue, PP-47-52, 2017
30. Prakash, S., Sherine, S., Control of BLDC motor
powered electric vehicle using indirect vector
control and sliding mode observer, International
Journal of Pure and Applied Mathematics, V-
116, I-19 Special Issue, PP-295-299, 2017
31. Prakesh, S., Sherine, S., Forecasting
methodologies of solar resource and PV power
for smart grid energy management, International
Journal of Pure and Applied Mathematics, V-
116, I-18 Special Issue, PP-313-317, 2017
32. Prasanna, D., Arulselvi, S., Decoupling
smalltalk from rpcs in access points,
International Journal of Pure and Applied Mathematics Special Issue
5108
International Journal of Pure and Applied
Mathematics, V-116, I-16 Special Issue, PP-1-4,
2017
33. Prasanna, D., Arulselvi, S., Exploring gigabit
switches and journaling file systems,
International Journal of Pure and Applied
Mathematics, V-116, I-16 Special Issue, PP-13-
17, 2017
34. Prasanna, D., Arulselvi, S., Collaborative
configurations for wireless sensor networks
systems, International Journal of Pure and
Applied Mathematics, V-116, I-15 Special
Issue, PP-577-581, 2017
35. Priya, N., Anuradha, C., Kavitha, R., Li-Fi
science transmission of knowledge by way of
light, International Journal of Pure and Applied
Mathematics, V-116, I-9 Special Issue, PP-285-
290, 2017
36. Priya, N., Pothumani, S., Kavitha, R., Merging
of e-commerce and e-market-a novel approach,
International Journal of Pure and Applied
Mathematics, V-116, I-9 Special Issue, PP-313-
316, 2017
37. Raj, R.M., Karthik, B., Effective demining
based on statistical modeling for detecting
thermal infrared, International Journal of Pure
and Applied Mathematics, V-116, I-20 Special
Issue, PP-273-276, 2017
38. Raj, R.M., Karthik, B., Energy sag mitigation
for chopper, International Journal of Pure and
Applied Mathematics, V-116, I-20 Special
Issue, PP-267-270, 2017
39. Raj, R.M., Karthik, B., Efficient survey in
CDMA system on the basis of error revealing,
International Journal of Pure and Applied
Mathematics, V-116, I-20 Special Issue, PP-
279-281, 2017
40. Rajasulochana, P., Krishnamoorthy, P., Ramesh
Babu, P., Datta, R., Innovative business
modeling towards sustainable E-Health
applications, International Journal of Pharmacy
and Technology, V-4, I-4, PP-4898-4904, 2012
41. Rama, A., Nalini, C., Shanthi, E., An iris based
authentication system by eye localization,
International Journal of Pharmacy and
Technology, V-8, I-4, PP-23973-23980, 2016
42. Rama, A., Nalini, C., Shanthi, E., Effective
collaborative target tracking in wireless sensor
networks, International Journal of Pharmacy and
Technology, V-8, I-4, PP-23981-23986, 2016
43. Ramamoorthy, R., Kanagasabai, V., Irshad
Khan, S., Budget and budgetary control,
International Journal of Pure and Applied
Mathematics, V-116, I-20 Special Issue, PP-
189-191, 2017
44. Ramamoorthy, R., Kanagasabai, V., Jivandan,
S., A study on training and development process
at Vantec Logistics India Pvt Ltd, International
Journal of Pure and Applied Mathematics, V-
116, I-14 Special Issue, PP-201-207, 2017.
45. Pradeep, R., Vikram, C.J., Naveenchandran, P.,
Experimental evaluation and finite element
analysis of composite leaf spring for automotive
vehicle, Middle - East Journal of Scientific
Research, V-17, I-12, PP-1760-1763, 2013
International Journal of Pure and Applied Mathematics Special Issue
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