Abstract-This paper studies selective relaying schemes based on signal-to-noise-ratio (SNR) to minimize the end-to-end (e2e) bit error rate (BER) in cooperative digital relaying systems using BPSK modulation. In the SNR-based selective relaying, the relay either retransmits or remains silent depending on the SNRs of the source-relay, relay-destination, and source-destination links. Different models assuming the availability of different sets of instantaneous and average SNR information at the relay are studied. For each model, the optimal strategy to minimize the e2e BER is a different threshold rule on the source-relay SNR, if the link SNRs are uncorrelated in time and space. Approximations for the optimal threshold values that minimize the e2e BER and the resulting performance are derived analytically for BPSK modulation. Using the derived threshold the e2e BER can be reduced significantly compared to simple digital relaying. By studying the performance under different models, it is shown that knowledge of the instantaneous source-destination SNR at the relay can be exploited. The gain from this knowledge is higher when the average source-destination SNR is large. However, knowledge of the instantaneous relay-destination SNR at the relay does not change performance significantly.Index Terms-Multihop communication, cooperative diversity, threshold based digital relaying, selective digital relaying, SNR based selective relaying.

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Abstract-We study selective digital relaying schemes where the relay may choose to retransmit or to remain silent based on the qualities of the links between the source, relay and the destination. We first analyze a baseline scheme, called static relaying, where the relaying decisions are based only on the average signal-to-noise ratio (SNR) values of all the links. The second scheme, dynamic relaying, allows the relay to make decisions based on the instantaneous SNR of the source-relay link and average SNRs of the relay-destination and source-destination links. We show that, in dynamic relaying the optimal strategy to minimize the average end-to-end bit error rate is a threshold rule on the instantaneous SNR of the source-relay channel. In this case, the optimal threshold value is a function of average SNR of relay-destination and source-destination channels. We derive closed-form expressions for the optimal threshold and the bit error performance achieved by this threshold. We show that dynamic relaying can provide significant performance advantage over static relaying.

Abstract-Threshold relaying is an effective technique to achieve cooperative diversity in uncoded cooperative wireless networks, which suffer from error propagation due to detection errors at the relays. This paper analyzes the asymptotic end-toend (e2e) bit error rate (BER) of threshold digital relaying. A three node network with a source, destination and relay and with links experiencing independent Rayleigh fading is considered. It is shown that, as the average link signal-to-noise ratios (SNR) are increased simultaneously, the optimal threshold that minimizes the e2e BER increases as log(SNR). The resulting e2e BER decreases as log(SNR)/SNR 2 . Moreover, any threshold of the form log(c SNR), where c is a positive constant, achieves the same order of e2e BER as the one achieved by the optimal threshold and provides dual diversity. A value of c that performs very close to the optimal threshold is also proposed.Index Terms-Cooperative diversity relaying, threshold maximum ratio combining, diversity order, selective digital relaying, SNR based selective relaying, multihop communication.

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Abstract-This paper considers two-hop cooperative relaying using multiple relays and proposes a threshold based relay selection protocol. In this protocol the relays are selected among those having received SNR higher than a threshold value. The relay selection is performed by the destination based on the received SNRs at the destination during the last hop. The exact bit error rate of this protocol is derived and it is shown that it achieves full diversity order. Unlike some other full diversity achieving protocols in the literature, the requirement that the exact/average SNRs of the source-relay links be known at the destination is eliminated using an appropriate SNR threshold. I. INTRODUCTIONCooperative relaying can induce spatial diversity in wireless networks without any reliance on multiple antennas. Various decode-and-forward protocols have been proposed based on selective relaying, distributed space-time coding and relay selection, and have been shown to achieve full diversity [1]- [3]. Recently, detection aspects of cooperative relaying have been analyzed [4]-[8]. These works study digital (or demodulate-and-forward) cooperative relaying protocols, in which the relaying does not rely on any error correction or detection codes. Such protocols are particularly attractive for wireless sensor networks, for which coded transmission can be costly due to severe energy limitations.Unlike ideal decode-and-forward relaying, in digital relaying the relays can forward erroneous information, and with a conventional combining scheme such as Maximal Ratio Combining (MRC), these errors propagate to the destination, causing end-to-end (e2e) detection errors. Existing techniques for mitigating error propagation can be classified into two groups. The first of these comprises selective and adaptive relaying techniques, which include link adaptive relaying (LAR) [4], [5] and threshold digital relaying (TDR) [9]-[11]. Both techniques use link SNRs to evaluate the reliability of the data received by the relay. In TDR a relay forwards the received data only when its received SNR is above a threshold value. In LAR the relay transmits with a fraction α of its maximum transmit power, where α depends on the source-relay and relay-destination SNRs. In [4], a function for calculating α

Abstract-Threshold relaying is an effective technique to achieve cooperative diversity in uncoded cooperative wireless networks, which suffer from error propagation due to detection errors at the relays. This paper analyzes the asymptotic end-toend (e2e) bit error rate (BER) of threshold digital relaying. A three node network with a source, destination and relay and with links experiencing independent Rayleigh fading is considered. It is shown that, as the average link signal-to-noise ratios (SNR) are increased simultaneously, the optimal threshold that minimizes the e2e BER increases as log(SNR). The resulting e2e BER decreases as log(SNR)/SNR 2 . Moreover, any threshold of the form log(c SNR), where c is a positive constant, achieves the same order of e2e BER as the one achieved by the optimal threshold and provides dual diversity. A value of c that performs very close to the optimal threshold is also proposed.Index Terms-Cooperative diversity relaying, threshold maximum ratio combining, diversity order, selective digital relaying, SNR based selective relaying, multihop communication.

In this paper, we consider graphs created by actu-The maximum distance to which a node can transmit directly ators (people, robots, vehicles etc.) in sensor-actuator networks. is called the node's transmission range. It is usually assumed Most simulation studies for wireless ad hoc and sensor networks that all nodes have a common transmission range. Unit disk use connected random unit disk graphs generated by placing nodes randomly and independently from each other. However, rnido graphis aetenmused toreprse this topologyx.d in real life networks are created by actuators in a cooperative unit disk graph is determined by node positions and a fixed manner. Usually certain restrictions are imposed during the communication range, R, for all nodes. Any two nodes whose placement of a new node in order to improve network con-distance does not exceed R are connected by a bidirectional nectivity and functionality. This article is an initial study on edge. In simulation studies, it is desirable to generate conhow connected actuator graphs (CAG) can be generated by fast . .u algorithms and what kind of desirable characteristics can be n e end nit disk graphs to evaluate the performance achieved compared to completely random graphs, especially for of different network protocols. These graphs are normally sparse node densities. generated by placing nodes randomly and independently fromWe describe several CAG generation schemes where the next each other, and testing connectivity at the end. Sparse random node (actuator) position is selected based on the distribution of unit disk graphs have high probability of being partitioned, the nodes already placed. In our Minimum Degree Proximity which increases the generation time.algorithm (MIN-DPA), a new node is placed to be a neighbor of Assuming thepenerahon f a n s y an existing node with the lowest degree (number of neighbors). In Assuming independent positions for all nodes may be our Maximum Degree Proximity algorithm (MAX-DPA), a new appropriate for sensors dropped from air or thrown manually.node cannot be placed to increase the degree of any existing node However, in SANs, actuators create their own communication over a pre-specified parameter limit. We show that these new graph to enhance their coordination, data communication and algorithms are significantly faster than the well-known random . . ' unit graph generation scheme for sparse graphs. The graphs abiity os the nework etter. Simposes in generated by these new schemes are not necessarily drawn from restrictions on their location with each other. Similarly, in real the same distribution as those generated by the independent node life, we usually tend to choose our own locations depending placement. Thus, we explore their properties by studying their on the locations of other users. For instance, in a conference average node degree and partition patterns. We show that our with attendants forming a multihop ad hoc network with new schemes produce random unit disk graphs with reduced g degree (average number of neighbor...