# Exploiting Outage and Error Probability
## 1 Introduction  
In addition to a wide range of applications, Underwater Wireless Sensor Networks (UWSNs) have gained attention due to significance in emerging paradigms. These networks consist of sensors and vehicles that are deployed in aqueous environment to perform collaborative monitoring tasks. These networks offer variety of applications like assisted navigation, environmental monitoring, resource investigation, tactical surveillance, disaster prevention, etc. [1]. Instead of radio and light waves, UWSNs use acoustic waves due to favourable propagation characteristics in water. Unlike terrestrial WSNs, which use radio and light waves, UWSNs pose some design challenges; long propagation delay, energy constrained sensor nodes, dynamic network topology, huge monitoring area and lowbandwidth [1; 2; 3]. Channel impairments like path loss, multi-path fading, reflection, refraction and aquatic noises introduce high Bit Error Rate (BER) in acoustic transmission and thus lead to lower quality of the received signal [4]. Data critical applications require reliable communication and higher throughput efficiency. Authors in [4; 5] suggest that Automatic Repeat reQuest (ARQ) and cooperative diversity schemes efficiently improve the BER. The basic idea of ARQ is to retransmit data in case of failure [4]. On the other hand, Cooperation means sharing each others's resources to achieve a common goal. Consider a system with a source-destination pair and a relay. Source node broadcasts its data to destination and relay node. As a second replica of the original signal, the relay node forwards the received signal to the destination where both independently received copies are combined to improve quality of the received signal [6]. Cooperative diversity relaying techniques are divided into two categories; fixed relaying and incremental relaying [5]. In fixed relaying, two commonly used techniques are Amplify and Forward (AF) and Decode and Forward (DF). In AF, relay node only amplifies the received signal and forwards it to destination, whereas, in DF, data at relay is decoded, corrected, recorded and forwarded to destination [7]. In incremental relaying, source broadcasts data to destination and relay in a way that feedback is generated from destination about success or failure of the data. In case of negative acknowledgement, relay retransmits data to destination using AF or DF relaying technique, otherwise, source continues with the next packet. Incremental relaying is an on-demand cooperative ARQ scheme and is also termed as Hybrid-ARQ (H-ARQ) scheme [5]. In [8], [PERSON] et al. present end-to-end performance analysis of incremental relaying cooperative diversity over Rayleigh fading channels, in which the best relay among multiple available relays retransmits the source signal. Similarly, [PERSON] et al. [9] exploit multiple relays and select one of the relays to retransmit signal. However, the aforementioned works only focus on single retransmission (increase of direct transmission failure). In aqueous environment, poor link quality due to severe fading, path-loss and noise may lead to loss of transmitted data. If, somehow, the data reaches its destination, quality is so poor that makes it useless. Therefore, we exploit more number of retransmissions to achieve the desired signal quality at the receiver and require more number of retransmissions. In this regard, we presented closed-form expressions for outage and error probability of incremental relaying with cooperative retransmissions. Our main contributions in this work are as follows:  
1. We proposed incremental relaying cooperative diversity scheme based on multiple number of relays. In our proposed scheme, source broadcasts data to destination and relays. If destination receives an erroneous signal, then relay is responsible to retransmit the signal. Both direct and relayed signals are combined at destination using a diversity combining technique. If signal quality is still not sufficient, second relay is held responsible to retransmit the data.