Journal of Electrical and Computer Engineering

Journal of Electrical and Computer Engineering / 2008 / Article

Research Letter | Open Access

Volume 2008 |Article ID 291858 |

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.

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

Academic Editor: Luca De Nardis
Received29 Sep 2008
Accepted03 Dec 2008
Published31 Dec 2008


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 UWB-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

Figure 1 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 π‘Žπ‘–.

Since accurate ranging information is available through UWB physical layer, we also presume that when 𝑅𝑖 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 by 𝑃𝑖 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 π‘ π‘–βˆ‘(𝑑)=βˆžπ‘—=βˆ’βˆžβˆšπΈπ‘πœ”(π‘‘βˆ’π‘—π‘‡π‘“βˆ’π‘π‘–π‘—π‘‡π‘βˆ’π›Ώπ‘π‘–βŒŠπ‘—/π‘π‘†βŒ‹), where 𝐸𝑝 is the transmission energy per pulse, 𝑇𝑓 and 𝑇𝑐 are the frame and chip durations, π‘π‘–βŒŠπ‘—/π‘π‘†βŒ‹βˆˆ{0,1} is the information bit to be sent, πœ”(𝑑) is the monocycle pulse, and 𝛿 determines the time shift in the chip when the data bit is 1. Each frame consists of π‘β„Ž chips, that is, 𝑇𝑓=π‘β„Žπ‘‡π‘. Moreover, each bit is repeated in 𝑁𝑆 frames with different time hopping codes, π‘π‘–π‘—βˆˆ{0,1,…,π‘β„Žβˆ’1}, which results in additional (random) time shifts and hence increases the pulse immunity to interference.

The received signal from user 𝑖 at node 𝑗 is given by [7] π‘Ÿπ‘–π‘—(𝑑)=π›Όπ‘–π‘—βˆ‘πΆπ‘=1βˆ‘πΏπ‘™=1𝛽𝑐𝑙𝑠𝑖(π‘‘βˆ’πœπ‘π‘™)+𝑛(𝑑), where 𝑛(𝑑) 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(π‘‘π‘–π‘—βˆš)=(1/2)erfc((𝛼𝑖𝑗𝐸𝑝𝑁𝑆/2𝑁0)(1βˆ’πœŒ(𝛿))) [7], where 𝜌(𝛿) is the autocorrelation function of the monocycle pulse, πœ”(𝑑). From the above-mentioned model, the probability that a packet with length 𝐿 bits is successfully transmitted can be represented as follows:𝑃𝑠(𝑑)=1βˆ’1βˆ’π‘ƒbe(𝑑)𝐿.(1)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 π‘Žπ‘– 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 in UCoRS, a relay 𝑅𝑖 is unable to find out the set of relays which have successfully decoded the packet from 𝑆 at time slot 𝑑, denoted by 𝐹(𝑑). In fact, the global optimum of the relay selection problem would be obtained if 𝐹(𝑑) were available to the nodes.

In the proactive case, the expected success probability in a time slot is given byπ‘ˆ(𝐴)=𝑃0+ξ‚€1βˆ’π‘ƒ0𝑁𝑖=1[π‘Žπ‘–π‘ƒπ‘–π‘„π‘–π‘ξ‘π‘—=1,𝑗≠𝑖1βˆ’π‘Žπ‘—π‘ƒπ‘—π‘„π‘—ξ‚].(2)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 one 𝑆-𝐷 pair and 𝑁 relays. The optimal cooperation strategy to maximize the 𝑆-𝐷 throughput (π‘ˆ(𝐴) in (2)) is 𝐴(𝐾)={π‘Žπ‘–=1,𝑖≀𝐾;π‘Žπ‘–=0,𝑖>𝐾}, where 𝐾 satisfies: βˆ‘πΎβˆ’1𝑖=1(𝑃𝑖𝑄𝑖/(1βˆ’π‘ƒπ‘–π‘„π‘–))<1, and βˆ‘πΎπ‘–=1(𝑃𝑖𝑄𝑖/(1βˆ’π‘ƒπ‘–π‘„π‘–))β‰₯1, where relays are sorted in descending order according to the values of 𝑃𝑖𝑄𝑖 (i.e., 𝑖≀𝑗⇔𝑃𝑖𝑄𝑖β‰₯𝑃𝑗𝑄𝑗); and 𝐴(𝐾) denotes a binary vector whose first Kth elements are 1. (Proof is straightforward from Lemma 1.)

Here, we mention that if 𝑃1𝑄1β‰₯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

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 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.

Figure 3(b) shows the asymptotic achievable throughput of UCoRS, PBT, and noncooperative schemes as a function of 𝑃0 when π‘β†’βˆž. 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 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.


Lemma 1. Assume a set of variables 𝑍={𝑧𝑖},𝑖=1,2,…,𝑛, that can take on real values between 0 and 1>π‘š1β‰₯π‘š2β‰₯β‹―β‰₯π‘šπ‘›, respectively. Then, the maximum value of βˆ‘π‘‹(𝑍)=𝑛𝑖=1(𝑧𝑖)βˆπ‘—β‰ π‘–(1βˆ’π‘§π‘—) is obtained when 𝑧𝑖=π‘šπ‘–, 𝑖≀𝐾, and 𝑧𝑖=0, 𝑖>𝐾, where 𝐾 satisfies βˆ‘πΎπ‘–=1(π‘šπ‘–/(1βˆ’π‘šπ‘–))β‰₯1, and βˆ‘πΎβˆ’1𝑖=1(π‘šπ‘–/(1βˆ’π‘šπ‘–))<1.

Proof. Taking the partial derivative of 𝑋(𝑍), we haveπœ•π‘‹(𝑍)πœ•π‘§π‘–=𝑗≠𝑖1βˆ’π‘§π‘—ξ‚βˆ’ξ“π‘—β‰ π‘–(π‘§π‘—ξ‘π‘˜β‰ π‘–,𝑗1βˆ’π‘§π‘˜ξ‚)=𝑗≠𝑖1βˆ’π‘§π‘—ξ‚ξ“(1βˆ’π‘—β‰ π‘–π‘§π‘—1βˆ’π‘§π‘—).(A.1)
Therefore, πœ•π‘‹(𝑍)/πœ•π‘§π‘–βˆ‘>0⇔𝑛𝑗=1,𝑗≠𝑖(𝑧𝑗/(1βˆ’π‘§π‘—))<1, and πœ•π‘‹(𝑍)/πœ•π‘§π‘–>πœ•π‘‹(𝑍)/πœ•π‘§π‘—β‡”π‘§π‘–>𝑧𝑗. According to these two results, in order to maximize 𝑋(𝑍), the 𝐾 β€œbest” variables (with looser bounds) should be set to their maximum values and other variables should be set to 0. The required conditions on 𝐾 are also clearly observed from the above-mentioned equations. Note that if π‘š1β‰₯0.5, then 𝐾=1.


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 © 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.

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