Research Letter | Open Access

Ghasem Naddafzadeh Shirazi, Peng-Yong Kong, Chen-Khong Tham, "A Low-Overhead Cooperative Retransmission Scheme for IR-UWB Networks", *Journal of Electrical and Computer Engineering*, vol. 2008, Article ID 291858, 3 pages, 2008. https://doi.org/10.1155/2008/291858

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

**Academic Editor:**Luca De Nardis

#### 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.

#### 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 an
*U*WB-based *Co*operative
*R*etransmission *S*cheme (*UCoRS*) [1].

Most of the existing distributed relay selection
schemes, such as [2β4] 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

Figure 1 shows the system model.
As can be seen, there are a source and a destination ,
and relays , ,
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 *i*th relay, ,
decides to cooperate (i.e., retransmit the data) with probability .

**(a) Network model**

**(b) Time slot model**

Since accurate ranging information is available
through UWB physical layer, we also presume that when finds its distance to and ,
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 by and , as can be seen in Figure 1. The success probability of the link is denoted by . To calculate these values, we note that in time-hopping pulse position modulation, TH-PPM, the transmitted signal by node is given by , where is the transmission energy per pulse, and are the frame and chip durations, is the information bit to be sent, is the monocycle pulse, and determines the time shift in the chip when the data bit is . Each frame consists of chips, that is, . Moreover, each bit is repeated in frames with different time hopping codes, , which results in additional (random) time shifts and hence increases the pulse immunity to interference.

The received signal from user at node is given by [7] , where is AWGN with the power spectral density , and denotes the 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 [7], where is the autocorrelation function of the monocycle pulse, . From the above-mentioned model, the probability that a packet with length bits is successfully transmitted can be represented as follows:This equation can be used to determine the values of and as a function of the relays' distances to and . Having obtained and from (1), the next problem is to find the cooperation probabilities in order to maximize the 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, successfully receives a useful data packet if either the 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 in *UCoRS*, a relay is unable to find out the set of relays which
have successfully decoded the packet from at time slot ,
denoted by .
In fact, the global optimum of the relay selection problem would be obtained if were available to the nodes.

In the proactive case, the expected success probability in a time slot is given byIn 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 one pair and relays. The optimal cooperation strategy to
maximize the throughput ( in (2)) is ,
where satisfies: ,
and ,
where relays are sorted in descending order according to the values of (i.e., ); and denotes a binary vector whose first Kth elements are .
(Proof is straightforward from Lemma 1.)*

Here, we mention that if , then , and only 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

Figure 2 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 3(a) shows the effect of increasing the number
of relays on the achieved PDR in *UCoRS* for different 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 ,
regardless of number of available relays.

**(a) Effect of increasing number of relays on PDR**

**(b) Asymptotic throughput achievable by UCoRS and PBT as π β β**

Figure 3(b) shows the asymptotic achievable throughput
of *UCoRS*, *PBT*, and noncooperative schemes as a function of when .
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 introduced *UCoRS*,
a simple *U*WB-based *Co*operative *R*etransmission *S*cheme,
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.

#### Appendix

Lemma 1. *Assume a set
of variables ,
that can take on real values between and ,
respectively. Then, the maximum value of is obtained when , , and , ,
where satisfies ,
and .*

*Proof. *Taking the
partial derivative of ,
we have

Therefore, ,
and .
According to these two results, in order to maximize ,
the βbestβ variables (with looser bounds) should
be set to their maximum values and other variables should be set to .
The required conditions on are also clearly
observed from the above-mentioned equations. Note that if ,
then .

#### Acknowledgments

An earlier version of paper [1] has won the Best Student Paper award in the IEEE International
Conference on Ultra-Wideband (ICUWB), 10-12 September 2008, Germany. This work is done under the USCAM-CQ project which is a part of the Ultra Wide
Band-enabled Sentient Computing (UWB-SC) Research Program funded by Science and Engineering Research Council (SERC), A^{*}STAR, Singapore.

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#### Copyright

Copyright © 2008 Ghasem Naddafzadeh Shirazi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.