The chapter focuses on minimizing the amount of wireless transmission in sensory data gathering for correlated data field monitoring in wireless sensor networks (WSN), which is a major source of power consumption. Compressive sensing (CS) is a new in-node compression technique that is economically used for data gathering in an energy-constrained WSN. Among existing CS-based routing, cluster-based methods offer the most transmission-efficient architecture. Most CS-based clustering methods randomly choose nodes to form clusters, neglecting the topology structure. A novel base station (BS)-assisted cluster, spatially correlated cluster using compressive sensing (SCC_CS), is proposed to reduce number of transmissions in and form the cluster by exploiting spatial correlation based on geographical proximity. The proposed BS-assisted clustering scheme follows hexagonal deployment strategy. In SCC_CS, cluster heads are solely involved in data gathering and transmitting CS measurements to BS, saving intra-cluster communication cost, and thus, network life increases as proved by simulation.
TopIntroduction
Wireless Sensor Network (WSN) is an agglomeration of randomly scattered tiny sensor nodes, whose primary objective is to gather data for the specific application they have been deployed in an Adhoc fashion. This gathered data is wirelessly transmitted to the Base Station (BS)/Sink. Wireless Communication is the main contributor to a sensor’s energy consumption. Hence, even though sensory data gathering is the fundamental task in WSN, it is a major source of power consumption. To reduce the number of data packet transmission required for data gathering usually compression techniques are employed. However, conventional compression techniques introduce excessive in-node computations and control overheads. Compressive Sensing (CS) is a new in-node compression technique that compresses sensory data and accurately recovers it at the BS. It can be very economically used for data gathering in energy constrained WSN. A brief overview of CS is as follows:
Compressive sensing is a new framework developed for single-signal sensing and compression. It exploits the fact that many natural occurring signals are sparse or compressible if represented on a proper basis and represented concisely, then recovery from a small number of projections is guaranteed or traceable (Donoho David L.,2006). Compressive sensing data compression is accomplished in the following three steps.
Consider a signal fd to be a real-valued discrete-time signal with finite length N. Vectorally represented as
(1.1)It is defined as k-sparse if it has a sparse representation in a proper basis
(1.2) Where
fd=𝜓
x and
x has only
k non-zero elements
The k -sparse signal can be under-sampled and be recovered from M≪N random measurements.
(1.3)The random measurements are generated by
(1.4) Where
is called the measurement matrix.
The measurement vector Y for N element is formed by
(1.5)It has been shown that reconstruction of a k-sparse signal with high probability from only 
CS measurements employing l1 Optimization problem is possible. l1-norm minimization is given by
(1.6)CS obeys the rule of Restricted Isometric Property (RIP) or Uncertainty Principle (UUP) i.e. sensing and measurement matrix be incoherent with each other. Fig. 1 shows the CS framework.
Figure 1. Compressive Sensing Framework