## 1 Introduction  
The transmission medium in Wireless Sensor Networks (WSNs) is under-utilized due to the bursty traffic resulting from the network's event-driven communication [1]. The scarce, yet underutilized resources must therefore be efficiently allocated for better utilization. Unlike WSNs, cognitive radio sensor nodes are intelligent and can access multiple redundant channels. This enables them address some challenges of WSNs that traditionally employ fixed spectrum allocation and are constrained in communication resources and processing capacity. Transmission is made more reliable since they reduce congestion and excessive packet loss [2]. \"Cognitive Radio Sensor Networks (CRSNs) are the state-of-the-art communication paradigm for power constrained short range data communication\" [3]. To practically realize CRSNs, the optimum packet size must be addressed since most of the optimum packet sizes available are meant for WSNs and/or CRNs and are not optimal for CRSNs [4]. CRSNs are one of the possible technologies implemented for the Internet of Things (IoT) and other future machine-to-machine-based applications most of which are delay sensitive and power constrained [3]. The optimal packet size of CRSNs for maximizing energy efficiency is studied in [4]. The conditions of maintaining allowable licensed primary user (PU) interference level while achieving reliable event detection, are also enforced. In variable conditions of the channel, shorter packets are more optimal and reduce the PU interference though there's energy wastage due to wide overhead caused by headers and trailers. Conversely, the increase in packet size enhances the throughput and spectrum usage for secondary users (SUs), while enhancing packet loss probability in similar channel conditions [4]. According to [5], data packet size and transmission power level are very important factors in improving energy efficiency and network lifetime for WSNs. To decrease the total effect of Bit Error Rate (BER) on loss of packets, the packets should be of small sizes although this is achieved with fragmentation into more data packets leading to increase in energy dissipation. Therefore, data packet size is a very important parameter of power and energy efficiency for improving the lifetime of a Cognitive Radio (CR)-WSN. In addition, to reduce the packet loss probability, there is need to increase the transmission power. There are also a number of applications that are delay intolerant [5]. We aim at minimizing the transmission delay as one of the objectives in our optimization problem. An increase in throughput is realized when the packet size is fixed compared to the exponential distribution of packet size in Cognitive Radio Networks [6]. These do not look at power and energy efficiency and reliability in event detection, yet these are key challenges in sensor networks. In terms of delay and energy efficiency, transmitting data with varying packet sizes rather than fixed data packet length dependent network conditions is advantageous to some extent. When network conditions are bad, re-transmission energy overhead is increased by the big size of packets due to the likely packet collisions. Very small packet size enhances delay overhead emanating from transmission of overhead header, trailer and additional redundant bits save for information bits [3]. Whereas power and energy efficiency are very important in resource-constrained sensor devices, it is not addressed by Cognitive Radio Networks (CRNs). Many currently available protocols from physical layer to upper layers run short of addressing the joint CRN and WSN software and hardware needs and thus may not be applicable in CR-WSNs [1]. We thus need to design power saving, energy-efficient CR-WSN algorithms that are sensitive to the resource limitations of the CR-WSNs to enhance Quality of Service (QoS) in the context of the Internet of Things (IoT), while saving power during transmission.