Cooperative Multiple Input Multiple Output Communication in Wireless Sensor Network: An Error Correcting Code approach using LDPC Code Goutham Kumar Kandukuri

Introduction Energy efficient data transmission is one of the key factors for energy constrained wireless sensor network (WSN). Wireless Sensor Nodes are developed to enable technology advancement in WSN. Here the battery capacity of each node is limited, we try to maximize the lifetime of the network, by following some energy consumption constraints. LDPC codes are more reliable than the block and conventional codes. Cooperative communication is compared with SISO communication considering LDPC code as an error correcting code.

Wireless Sensor Network Consists of spatially distributed autonomous Sensor to monitor physical or environmental conditions, to cooperatively pass their data through the network to a main location. Wireless sensor networks consist of a large number of tiny sensors that have only limited energy supply. Maintain long network lifetime as well as sufficient sensing area.

MIMO(Multiple Input Multiple Output) A signal is transmitted from one terminal to multiple users in same bandwidth Simultaneously. y = Hx + n y - Receive Vector x - Transmit Vector H - Channel Matrix n - Noise Vector MIMO can be divided into 3 main categories they are 1) Precoding 2) Spatial Multiplexing 3) Diversity Coding

System Model The system model is a centralized wireless sensor network, where there is a data gathering node (DGN) and several clusters with several sensors in each cluster. Sensors in one cluster transmit the data to the sensors in adjacent cluster and in step by step the data reach the DGN. The system considers N number of sensors in one cluster and the transmitted antennas are each placed at a sensor. In this model, a sensor with high residual energy is deployed as a cluster head and it remains the cluster head until the network dies. The cluster head broadcasts its status to the other sensors in the network. Each sensor node determines to which cluster it wants to belong by choosing the cluster head that requires the minimum communication energy.

System Model

Low Density Parity Check Codes(LDPC) LDPC codes are specified by a matrix containing mostly 0’s & relatively few 1‘s. LDPC codes are decoded by means of iterative belief propagation using the Sum-Product (SP) algorithm. The code length is designed by n, & Number of constraints by m. Which gives n variable nodes and m check nodes. Edges in the graph connect the variable nodes inorder to check nodes and then represents the nonzero entries in H matrix. The term “low density” conveys the fact that the fraction of nonzero entries in H is small, in particular it is linear in block length n, compared to random linear codes.(expected fraction n^2).

Richardson Scheme as the encoding Technique H can be converted to an approximate lower triangular matrix Considering m x n parity check matrix H over F, n – number of variable nodes m – number of check nodes Parity check matrix H is transformed in the form of where A is (m − g) × (n − m) B is (m − g) × g, T is (m− g) × (m− g) C is g × (n −m) D is g × g, and E is g × (m − g) g is gap T is lower triangular with ones along the diagonal

Richardson Scheme as the encoding Technique This matrix is multiplied left by And H Matrix is found as The code word is broken as x = (s, p1, p2) s – systematic part p1,p2 – parity part p1 has length g p2 has length (m-g)

Richardson Scheme as the encoding Technique This equation used to follow two equations. Taking as non singular, it is included that And using step by step procedure, it is shown that complexity of calculating p1 is p2 is

Energy Model PT = PPA + PC PT - Total power consumption PPA - Power amplifiers PC - Power consumption of all other circuit blocks PPA = (1+α)Pout α = (ξ/η− 1), η - drain efficiency, ξ - peak to average ratio Nf = Nr/N0 When the channel only experiences a kth power path loss. - average energy per bit Rb is the transmission bit rate

Simulation Results & Discussion Total Energy consumption over Distance Energy Efficiency Over Distance

Simulation Results & Discussion

Conclusion Energy efficient data transmission is one of the key factors for energy constraint wireless sensor network. The energy efficiency remains almost unchanged in different encoding rates. Data with smaller encoding rate shows better BER results than larger encoding rate for a fixed SNR The results show that the cooperative communication outperforms SISO transmission at the presence of error correction code.

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