Design Of Structured Sensing Matrix And The Applications Of Compressive Sensing In Wireless Sensor Networks

Taking advantages of the good environmental adaptability,high data accuracy,flexible coverage area,low-power communications ability,good concealment and strong survivability of Wireless Sensor Networks(WSN),WSN has been widely applied in a plurality of areas like environment monitoring,precision farming,health care,and battlefield surveillance.But WSN is still faced with many problems like complex deploy environments,unstable network topology,limited power and computational resources.Therefore,that's a challenge problem to design an efficient data fusion method,which can reduce the power consuming of sensor node and decrease the communication transmissions under the promise of acceptable recover accuracy.The emergence of signal processing system of compressive sensing(CS)has provided a new approach to solve above problems.The properties of non-adaptive measuring,sub-sampled linear projection,equal importance of samples,and non-linear reconstruction of CS exactly satisfies the requirements of the system of WSN by the simple encoding and complex decoding property.On the other hand,the high correlated characteristics of the data of WSN just satisfy the needs of the appliance of CS.Therefore,applying CS in WSN can solve many problems during the data fusion procedure.It can reduce the power consuming of sensor node and decrease the communication transmissions under the promise of acceptable recover accuracy.Thus,it has important significance to realize high precision,high efficiency and longtime information detection in wireless sensor networks.In order to reduce the energy consumption and to improve the efficiency of information fusion in WSN,this dissertation carries out the research of the applications of CS at the sensor node level and at the network level.And the following aspects are studied.The general steps to state a Toeplitz matrix satisfied the Restricted Isometry Property(RIP)and a circulant shifted diagonal block Toeplitz sensing matrix are proposed.Based on the signal acquiring and processing of time invariant system in wireless sensor nodes,this dissertation studied the design of the Toeplitz structured sensing matrix of CS.The distribution of the entries of the gram matrix of Toeplitz matrix is discussed.We proved that every element of the gram matrix can be divided into at most 3 independent components sum and the general steps to state a Toeplitz matrix satisfied RIP.And to overcome the shortage of conventional Toeplitz matrices like dense,hard to implement and need a lot of random variables,this dissertation constructed a circulant shifted diagonal block Toeplitz sensing matrix,the reference blocks is generated by random shift a diagonal matrix which is constructed by the sequence of alternating +1 and-1.The proposed matrix is well structured and is highly sparse,thus the corresponding sensing procedure is simple.Meanwhile,the experimental results show that the performances of proposed matrix are much superior to that of blocked Gaussian random matrix,which turns out to have better performances than dense Gaussian random matrix.A semi-deterministic structured sensing matrix and the corresponding fast sensing method are proposed.Based on the signal acquiring and processing of compressive signal in wireless sensor nodes,in order to solve the problem that conventional sensing matrix is hard for software and hardware implementation and needs lots of random variables during matrix construction,this dissertation take the deterministic unit matrix and the kronecker product matrix of Hadamard matrix as reference matrix,constructed a semi-deterministic structured sensing matrix and proved that the proposed matrix satisfies RIP.Moreover,taking advantages of the structure characteristics of the proposed matrix,the corresponding fast sensing method is developed for processing large signals.Simulation results illustrate that the proposed sensing matrix maintains almost the same performance with the popular sampling matrices with at least 50%less random variables.Meanwhile,it saved roughly 15%-35%processing time in comparison to that of the structured random matrices.An m sequence based fast and low complexity sensing method is proposed.In terms of the system implementation of compressive sensing in wireless sensor nodes,the random sensing algorithms are hard for hardware implementation while the deterministic sensing algorithms have difficult in acquiring large signals in the sensing systems of compressive sensing.This dissertation proposed a fast sensing method for compressive sensing with low complexity.The input signal is firstly permuted by an m-sequence controlled interleaving device.Then the permuted signal is transformed by the fast Walsh-Hadamard transform and down sampled to generate the measurements.Theoretical analysis indicates that the entries of the corresponding sensing matrices are asymptotically normally distributed.The simulation results show that the sensing performance of the corresponding matrices is almost the same with that of completely random sensing operators with shorter computational time cost.The proposed method has good sensing performance and is easier for hardware implementation,which is meaningful in practice.A Neighbor-Aided Compressive Sensing(NACS)scheme is proposed for efficient data gathering in spatial and temporal correlated WSNs.Based on the simplifying of the design complexity and reducing the power cost of wireless sensor nodes,we further considered the spatial-temporal correlations of the information data in the WSN.Single-dimensional CS approaches are inapplicable in spatial and temporal correlated WSNs while the Kronecker Compressive Sensing(KCS)model suffers performance degradation along with the increasing data dimensions.In this dissertation,NACS scheme is proposed for efficient data gathering in spatial and temporal correlated WSNs.During every sensing period,the sensor node just sends the raw readings within the sensing period to a randomly and uniquely selected neighbor.Then,the CS measurements created by the neighbor are sent to the sink node directly.The equivalent sensing matrix is proved to satisfy both Structured Random Matrix(SRM)and generalized KCS models.And,by introducing the idea of SRM to KCS,the recovery performance of KCS is significantly improved.Simulation results demonstrate that compared with the conventional KCS models,the proposed NACS model can achieve vastly superior recovery performance and receptions with much fewer transmissions.