# A Low-Overhead Cooperative Retransmission Scheme for IR-UWB Networks

Authors: Ghasem Naddafzadeh Shirazi; Peng-Yong Kong; Chen-Khong Tham
Journal: Research Letters in Communications
 (2008)

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## Abstract

The UWB unique properties such as fine ranging and immunity to small scale fading are utilized in order to exploit the multiuser diversity in UWB networks. The optimal
cooperation strategies in the absence of control packet overhead
are analyzed in the proactive and reactive settings. It is shown
that the proposed method achieves a considerable diversity gain
while minimizing the overhead of control packet exchange that
is required for coordination among the relays.


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## Body

## 1. Introduction

Due to the
large bandwidth occupied by pulses, UWB signals are considered robust to small
scale fading effects. In addition, UWB enables high accuracy ranging which can
be used for the design of location-aware MAC and routing mechanisms. We exploit
these properties of UWB, that is, availability of ranging information and
immunity to small scale fading, in the design of anUWB-based Cooperative
Retransmission Scheme (UCoRS) [1].Most of the existing distributed relay selection
schemes, such as [2–4] rely on the Priority-Based Backoff Timer (PBT)
mechanism to discover which relay is the best one at a time instance by sending
a flag message. We note that like PBT, the other existing mechanisms
such as CMAC [5] also require the exchange of the RTS/CTS and other
control messages for every transmission. These cooperative methods may be
inefficient for UWB networks. This is because the standard IR-UWB MAC protocol
is ALOHA [6] and the
exchange of RTS/CTS packets is not required prior to the data transmission in
UWB. Furthermore, it is preferred to exchange fewer control packets due to the
complex and costly UWB receiving procedure.


## 2. System Model

Figure1 shows the system model.
As can be seen, there are a source S and a destination D,
and N relays Ri, i=1,2,…,N,
in a slotted time domain, and each time slot
consists of 2 subslots. At the transmission subslot
(Tx), the source node sends data to its destination. At the Cx subslot, the
relays retransmit the source data. In particular, the ith relay, Ri,
decides to cooperate (i.e., retransmit the data) with probability ai.System model.
(a)
Network model(b)
Time slot modelSince accurate ranging information is available
through UWB physical layer, we also presume that whenRi finds its distance to S and D,
it broadcasts a packet to inform other nodes about these ranging information.
Note that as long as the nodes do not move, the process of ranging and
informing other nodes should be performed only once, which incurs much less
overhead compared to sending control packets for every transmission.The link success probabilities are denoted byPi and Qi,
as can be seen in Figure 1. The success probability of the S−D link is denoted by P0.
To calculate these values, we note that in time-hopping pulse position modulation,
TH-PPM, the transmitted signal by node i is given by si(t)=∑j=−∞∞Epω(t−jTf−cjiTc−δb⌊j/NS⌋i), where Ep is the transmission energy per pulse, Tf and Tc are the frame and chip durations, b⌊j/NS⌋i∈{0,1} is the information bit to be sent, ω(t) is the monocycle pulse, and δ determines the time shift in the chip when the
data bit is 1.
Each frame consists of Nh chips, that is, Tf=NhTc.
Moreover, each bit is repeated in NS frames with different time hopping codes, cji∈{0,1,…,Nh−1},
which results in additional (random) time shifts and hence increases the pulse
immunity to interference.The received signal from useri at node j is given by [7] rij(t)=αij∑c=1C∑l=1Lβclsi(t−τcl)+n(t),
where n(t) is AWGN with the power spectral density N0/2,
and αij denotes the i−j link gain. Since UWB pulses are robust to
small scale fading effects, we consider only the channel pathloss, as defined
in [1, 6]. Then, the bit error
probability (BEP) in the absence of interference can be approximated by Pbe(dij)=(1/2)erfc((αijEpNS/2N0)(1−ρ(δ))) [7], where ρ(δ) is the autocorrelation function of the
monocycle pulse, ω(t).
From the above-mentioned model, the probability that a packet with length L bits is successfully transmitted can be
represented as follows:(1)Ps(d)=1−(1−Pbe(d))L.This equation can be used to
determine the values of Pi and Qi as a function of the relays' distances to S and D.
Having obtained Pi and Qis from (1), the next problem is to find the
cooperation probabilities ai in order to maximize the S−D throughput.


## 3. Analysis

We assume that
the packet level collision occurs if the signal strength of more than one
packet is above the threshold at the receiver. Therefore,D successfully receives a useful data packet if
either the S−D transmission in the Tx subslot is successful,
or the transmission from one and only one of the relays in the Cx subslot is successful.We consider two different settings, namely, the
proactive and reactive modes. In the proactive mode, the decision is made prior
to the source transmission. In the reactive mode, all relays listen for the
data first and then decide to cooperate. Note that since message exchange
between relays is not performed inUCoRS, a relay Ri is unable to find out the set of relays which
have successfully decoded the packet from S at time slot t,
denoted by F(t).
In fact, the global optimum of the relay selection problem would be obtained if F(t) were available to the nodes.In the proactive case, the expected success
probability in a time slot is given by(2)U(A)=P0+(1−P0)∑i=1N[aiPiQi∏j=1,j≠iN(1−ajPjQj)].In order to find the optimal
solution of (2), we use Lemma 1 in the Appendix. The following theorem gives
the optimal solution.Theorem 1.
Consider a cooperative network with oneS−D pair and N relays. The optimal cooperation strategy to
maximize the S−D throughput (U(A) in (2)) is A(K)={ai=1,i≤K;ai=0,i>K},
where K satisfies: ∑i=1K−1(PiQi/(1−PiQi))<1,
and ∑i=1K(PiQi/(1−PiQi))≥1,
where relays are sorted in descending order according to the values of PiQi (i.e., i≤j⇔PiQi≥PjQj); and A(K) denotes a binary vector whose first Kth elements are 1.
(Proof is straightforward from Lemma 1.)Here, we
mention that ifP1Q1≥0.5,
then K=1,
and only R1 will be active. In this special case, the result
is in agreement with [3]. The reactive and global optimum cooperation
strategies can be derived using the same reasoning as Theorem 1, as discussed
in detail in [1].


## 4. Performance Evaluation

Figure2
compares the packet delivery ratio (PDR) for different scenarios. As can be
seen, the proactive performance is near to the maximum achievable throughput.
Furthermore, as expected, both reactive and proactive methods outperform the
noncooperative case.Figure 2
Comparison of packet delivery ratio (PDR) for different schemes.Figure3(a) shows the effect of increasing the number
of relays on the achieved PDR in UCoRS for different S−D link qualities. As can be seen, adding one
relay can significantly increase the PDR of the direct link. However, the
achieved PDR in UCoRS is upper bounded by a function of dSD,
regardless of number of available relays.Simulation results.
(a)
Effect of increasing number of relays on PDR(b)
Asymptotic throughput achievable byUCoRS and PBT as N→∞Figure3(b) shows the asymptotic achievable throughput
of UCoRS, PBT, and noncooperative schemes as a function of P0 when N→∞.
As stated previously, the throughput advantage of PBT over UCoRS is at the expense of control packet exchange for every data transmission, which
may not be efficient in UWB. More details can be found in [1].


## 5. Conclusion

We introducedUCoRS,
a simple UWB-based Cooperative Retransmission Scheme,
that utilizes the unique properties of IR-UWB technology for achieving
multiuser diversity in UWB in the proactive and reactive settings. The amount
of control packet overhead is minimized in UCoRS in order to eliminate
the corresponding energy cost at the UWB receivers.



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*Source: 291858-2008-12-31.xml*