A wireless sensor network (WSN) is made of tiny sensor nodes usually deployed in high density within a targeted area to monitor a phenomenon of interest such as temperature, vibration or humidity. The WSNs can be employed in various applications (e.g., Structural monitoring, agriculture, environment monitoring, machine health monitoring, military, and health). For each application area there are different technical issues and remedies. Various challenges need to be considered while setting up a WSN, including limited computing, memory and energy resources, wireless channel errors and network scalability. One way of addressing these problems is by implementing a routing protocol that efficiently uses these limited resources and hence reduces errors, improves scalability and increases the network lifetime. The topology of any network is important and wireless sensor networks (WSNs) are no exception. In order to effectively model an energy-efficient routing algorithm, the topology of the WSN must be factored in. However, little work has been done on routing for WSNs with regular patterned topologies, except for the shortest path first (SPF) routing algorithms. The issue with the SPF algorithm is that it requires global location information of the nodes from the sensor network, which proves to be a drain on the network resources. In this thesis a novel algorithm namely, BRALB (Biased Random Algorithm for Load Balancing) is proposed to overcome the issues faced in routing data within WSNs with regular topologies such as square-base topology and triangle-based topology. It is based on random walk and probability. The proposed algorithm uses probability theory to build a repository of information containing the estimate of energy resources in each node, in order to route packets based on the energy resources in each node and thus does not require any global information from the network. It is shown in this thesis by statistical analysis and simulations that BRALB uses the same energy as the shortest path first routing as long as the data packets are comparable in size to the inquiry packets used between neighbours. It is also shown to balance the load (i.e. the packets to be sent) efficiently among the nodes in the network. In most of the WSN applications the messages sent to the base station are very small in size. Therefore BRALB is viable and can be used in sensor networks employed in such applications. However, one of the constraints of BRALB is that it is not very scalable; this is a genuine concern as most WSNs deployment is large scale. In order to remedy this problem, C-BRALB (Clustered Biased Random Algorithm for Load Balancing) has been proposed as an extension of BRALB with clustering mechanism. The same clustering technique used in Improved Directed Diffusion (IDD) has been adopted for C-BRALB. The routing mechanism in C-BRALB is based on energy biased random walk. This algorithm also does not require any global information apart from the initial flooding initiated by the sink to create the clusters. It uses probability theory to acquire all the information it needs to route packets based on energy resources in each cluster head node. It is shown in this thesis by using both simulations and statistical analysis that C-BRALB is an efficient routing algorithm in applications where the message to be sent is comparable to the inquiry message among the neighbours. It is also shown to balance the load (i.e. the packets to be sent) among the neighbouring cluster head nodes.

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Biological signal processing can help us gain knowledge about biological complexity, as well as using this knowledge to engineer better systems. Three areas are identified as critical to understanding biology: 1) understanding DNA, 2) examining the overall biological function and 3) evaluating these systems in environmental (ie: turbulent) conditions. DNA is investigated for coding structure and redundancy, and a new tandem repeat region, an indicator of a neurodegenerative disease, is discovered. The linear algebraic framework can be used for further analysis and techniques. The work illustrates how signal processing is a tool to reverse engineer biological systems, and how our better understanding of biology can improve engineering designs. Then, the way a single-cell mobilizes in response to a chemical gradient, known as chemotaxis, is examined. Inspiration from receptor clustering in chemotaxis combined with a Hebbian learning method is shown to improve a gradient-source (chemical/thermal) localization algorithm. The algorithm is implemented, and its performance is evaluated in diffusive and turbulent environments. We then show that sensor cross-correlation can be used in solving chemical localization in difficult turbulent scenarios. This leads into future techniques which can be designed for gradient source tracking. These techniques pave the way for use of biologically-inspired sensor networks in chemical localization.