This paper addresses the optimization of collaborative wireless network detectors with limited resources in the presence of energy storages and massive MIMO antennas for the fusion center (FC). The amount of harvested and stored energy as well as positioning the location of each sensor is effective in achieving collaboration of sensor nodes. Therefore, the energy harvesting and storage capabilities of sensor nodes with the objective of keeping the network more active has been considered. In the current paper, a flexible, structural optimization for network maintenance and sending data is considered using collaborative function and the amount of energy stored. In the suggested optimization problem, maximizing the probability function detector is done based on collaborative function and storage variables by the capability of energy harvesting and using massive MIMO antennas in FCs. In this paper, there are an optimization problem of non-convex objective function which has linear limitations, so an optimum solution is considered. The main function of this problem is converted to a convex function using a relaxation; therefore, an optimum solution is obtained for this problem using local optimum results.The numerical results obtained by simulation are presented for problem validation.
Keywords: Collaborative Improve Detection, Collaborative Wireless Networks, Multiple Antennas, Energy Harvesting Capability, Convex Optimization.
1. Introduction
The main purpose of this study is to achieve the detection objective of the wireless sensor network. In summary, this is meant to get the contribution rates at the fusion center. These coefficients must be applied at each sensor node for the amount of contribution and transmission of data and energy to other sensors in order to optimize the network in the detection of the target. It should be noted that these coefficients are sent to each sensor via a link to each of the sensors, and failure to get these coefficients to each of the sensors means that the sensor is not sent to the fusion center. In this case, each sensor node needs only to perform energy sensing and data transmission to other sensors, and constant power should be available to them. The main focus of most studies has been on uniquely sensing and detecting targets, with less focus on resources and constraints[1], [2] .
In this paper, the allocation of resources took into account the distribution of wireless sensor networks and their limitations in order to improve the detection target,
Assuming that the fusion center has access to each of the sensor nodes to apply the computing coefficients. The recently research is on the distribution of adaptable power resources in each sensor networks for transforming to multi-antenna receivers. It is assumed that all sensor nodes are capable of energy harvesting.
The authors of [3] considered the optimal power allocation strategy for sensor networks in complete communication with each other. The connection between the sensors ensure that all sensors work, communicate with each other and share with each other the measured values.
In [4], the authors obtained optimal participatory strategies for the structure of the proposed network. In this reference, the performance of the connected network was nearly perfect in the complete network. In [5], the cost of participation is also considered for each connection. The simulation provides for optimal configuration, collaborative structure and energy allocation methodology.
However, due to the small size of the batteries used to power the sensor nodes, power consumption in sensor networks is an important limitation. So, in order to increase the duration of a sensor network, it is necessary to have a sensor capable of harvesting energy. Although this raises complexity and cost, the energy harvest in different modes will lead to a more durable network [6].
On the other hand, the concept of justice in the use of energy resources is such that when the sensor is transmitted from a sensor over a period of time in each sensor of the network, then other sensors must be used for the subsequent periods until the resource of sensors be fairly consumed. However, since the sensor distribution network is not homogeneous, the lack of an appropriate sensor would decrease the network performance. However, due to the optimal use of each sensor as well as its position, if there is a possibility of harvesting and storage, then network performance would be closer to optimal mode and would be longer over the network.
Normally, local sensors are powered by small batteries, and their replacement is challenging or non-economic.
Therefore, power management is an important principle in the detection application[7].
In [8], a single-sensor equipped with energy harvesting equipment is used to estimate the objective parameter. In this reference, the design to optimize energy allocation strategy is based on energy harvesting done in the past and the future.
In [9] the design of the network’s energy allocation is based on the assumption of orthogonal multiple channel access. In this reference, energy limitation was the best linear unbiased estimator for the minimum error. In [10],
relationships were obtained for the power allocation in unlimited and limited energy harvesting times using random control.
The ideal state of antennas is the use of wide array antennas. Each additional antenna increases the freedom degree of data transmission; therefore, it has recently been applied in communication base stations equipped with arrays of antennas, called massive MIMO antennas.
The structure of these equipment is that a large number of connected antennas are placed on the same surface [11].
The authors of [12] have shown that if the number of fusion center antennas is much larger than the number of sensor antennas, in other words, if the ratio of the number of antenna receivers to the number of transmitter antennas is much larger than one, then the deployment of that number of antennas further improves the transmission efficiency. In this case, the effects of fast fading and the correlated noise are both zero. This feature is established even in low-noise environments. In addition, this reference showed that using simple signal processing can increase link capacity in massive MIMO antenna.
In [13], both energy harvesting and collaboration between the sensors were investigated.
In this reference, it was shown that energy harvesting can increase the stability of the network. However, in this reference, the receiver antenna in the fusion center is a single antenna. The probability of detection and signal to noise ratio (SNR) effects was not studied. The objective function can be used to optimize a simpler way to proceed. For sensor nodes whose links were not available, they were assumed not to transmit any noise.
This is possible only for specific nodes and is not for the general public. In addition, the collaboration function in this reference is a nonlinear function that could handle with the relaxation to the zero norm function. It is possible to solve a proposed linear collaboration function.
In addition, the optimization of energy efficiency for designing the translator in the simultaneous wireless information and power transfer (SWIPT) system has been less emphasized in wireless sensor networks from the perspective of recyclable energies and green telecommunications. SWIPT technique have been recently considered as a hopeful approach for improving the performance of wireless sensor networ ks with limited
energy supply. However, the optimization of energy efficiency for designing the SWIPT in rechargeable sensor networks was not studied from a green communication perspective.
In most studies involving the allocation of network resources, the focus is on the allocation of one of the network’s most important resources, which is the transformation power. In most cases, there are inadequate and inefficient in approach energy efficiency and power consumption, resource allocation, computational size, required signaling work and problem solution.
To resolve this issue, assuming that the feedback is on the network, all of these are considered at the FC, then the proportional collaboration coefficients are transmitted from the fusion center to each of the nodes. In this paper, we employed sufficient energy in the nodes' collaboration, which affects the amount of energy consumed and stored in each sensing node, to achieve optimal detection.
1.1. Motivation and major contributions
A set of digital devices (e.g., digital watch, sensor shoes, etc.) Always transfer the data with different power values to seniors in different distance.
The sensors share the received data to other sensors and then transfer them to the massive MIMO antenna of fusion center.
In order to solve the problem, the following steps were considered:
• Novel system model: In the first stage, the problem is modeled by using probability function of detection and false alarm and other constrains, then, in the second step, the relaxation was performed to convex in the main function. Then, the simulation result suggestion were presented for probability detection and false alarm in terms of change in the number of fusion center (FC) antenna for the different ratio of SNRs, variety of energy harvesting, battery charging and discharging threshold of different sensors. Figure 1 illustrates the general diagram of the suggested system.
• Energy harvesting for obviating limited battery size: In this study, it was assumed that the problem constraints include the limitations of storage resources (batteries) in energy harvesting, limitations on keeping on the network, and prevent network failure. However, the non-convex function is a relaxation using a function to convert convex function. Therefore, using assumed relaxations, the objective is an optimization problem with the above constraints, which allows for an optimal solution. Simulation results show the advantage of the proposed scheme for energy allocation and energy harvesting as well as the collaboration between sensors. The table Table 1 illustrates the applied parameters in this paper.
• Used optimization parameter: In this paper, in order to use diversity features in FCs, it is suggested that massive MIMO antennas are used in the receiver; the Neyman-Pearson detector is an optimal convex function. The main focus of our discussion is on integrating the target detection improvement into a wireless sensor network with massive MIMO antennas. Here, the FC obtain collaboration coefficients that must be applied to each sensor node for transfer to other sensors in order to optimize our network for detection. We know that these coefficients are transmitted to each of the sensors through the feedback link from the FC, and failure to get these coefficients for each of the sensors means that there is no access to the FC, in which case each sensor node should only have a sensing specific power and sharing of data.
1.2. Paper organization
The suggested system model is introduced in the section 2, and section 3 presents the partitioning of the problem definition step. In section 4, we consider the conversion and relaxations of the non-convex function to the convex optimization problem, and in section 5 and 6 numerical simulations, discussion and conclusions are described.
2. System Model
Please In this paper, it is considered that the task of the sensor network is to estimate a time-varying parameter such as the main variable over a time horizon of . A specific state of the participant detector system is examined, since the sensors have the ability to collaborate and share their observations and energy with other adjacent sensors. The sensor results are then transmitted to the FC through the coherent multiple access channel (MAC), which estimates the total for each time In the wireless sensor network, each sensor is equipped with an energy harvesting device and a limited capacity battery for energy storage; the former harvests the renewable energy from the environment, allowing any sensor to perform charging/discharging actions during state sensing/sharing
data transmission. An overview of the collaborative estimation system with respect to energy harvesting and
Table 1. The Applied Parameters
Notation Definitions
Number of Sensor
Number of Time Period
Fundamental Data
Number of Antenna in FC
Measurement Noise
Channel Observation Coefficients
Vector of Measurements
Collaboration Function Matrix
Vector of Collaborative Signals
Channel Gain Vector
Receiver Noise
Fading Channel Gain Vector
the average distance between each sensor node and the kth antenna of FC
Channel Fading Factor between the sensor nodes and the antenna of FC
Vector of Received Signals in FC
Covariance is
Covariance is
The Amount of Energy Harvesting
Average of Energy Harvesting Rate
Charging and Discharging sensor
Limitation of Battery Capacity
Keeping Limitation Minimum of Network Energy
Cost Collaboration Link
Location of Sensor
storage is shown in Figure 1. The measurement vector for each sensor at time is as follows [14]:
(1)
where is measurements vector, is the vector of observation coefficients, is the interest parameter with the distribution is the
Figure 2 Vectorization example of
noise vector with i.i.d. with for and
In relation to the above, each complex vector measurement data is normally distributed, and each complex numerical coefficient data vector is under observation.
After sensing, each sensor may pass its observation and energy harvesting to other sensors for collaboration prior to transmission to the FC.
With a relabeling of sensors, we assume that the all sensors communicate with the FC.
Collaboration among sensors is represented by a known matrix with zero-one entries, namely, for and .
There they call ; a topology matrix, where signifies that the nth sensor shares its observation with the th sensor, and indicates the absence of a collaboration link from the th sensor to the th sensor. Note that is essentially a truncated adjacency matrix. The bidirectional communication link between two sensors indicates that the underlying graph of the network is directed but not necessarily connected. In particular, the network given by for corresponds to the amplify-and-forward transmission strategy considered in [13].
Based on the topology matrix, It is assumed that all sensor nodes are associated with the FC; The collaboration process of sensors at time is given by [13]:
(2)
where is the collaborative signals at sensor th and time th, is the collaboration function matrix which includes the collaborative weights that are used to combine sensing signals based on energy used to combine sensor measurements at time th, denotes the elementwise product, is the vector of all ones, and is the matrix of all zeroes.
In what follows, while referring to vectors of all ones and all zeroes.
The author [14] simplify equation (2)by exploiting the sparsity structure of the topology matrix and concatenating the nonzero entries of a collaboration matrix into a collaboration vector. Two benefits to using matrix vectorization can be eliminated without loss of performance, and the structure of non-convexities is more easily revealed via such a reformulation.
In equation (2), the one of the optimization variables is the nonzero entries of collaboration matrices. We concatenate these nonzero entries (columnwise) into a collaboration vector
(3)
where denotes the th entry of and L is the number of nonzero entries of the topology matrix . Figure 2 illustrate the vectorization of through an example, where we consider the number of sensor are , the nodes of communicated are , and the links of collaboration are .
In (2), In the case of transmission weights, it is assumed that an antenna that receives information shares information and energy at this state. The proposed ideal collaboration model enables theirs to obtain explicit expressions for transmission cost and estimation distortion[13].
It transmits information over a period of time and shares it in the next period according to the conditions of other network sensors. It is necessary to explain that in the same period of time, if energy is extracted and possessed by other sensors, they share the energy according to the collaboration weights.
After sensor collaboration in data and energy, the message is transmitted through a coherent MAC to the FC so that the each of the sum of received signal of equation (2) is as follows [15]:
(4)
where is the channel gain vector at th sensor , received antenna th and time th of FC. complex white Gaussian noise with zero mean and the variance for fading channel at th antenna at FC.
Obviously, each of the element of is defined for a fading channel as follows [16]:
(5)
where is a distribution complex fading channel gain vector and of the vector is the average distance between each sensor node and the th antenna of FC.
Remark 1. although sensor collaboration is performed with respect to a time-invariant (fixed) topology matrix energy allocation in terms of the magnitude of nonzero entries in is time varying in the presence of temporal dynamics of the sensor network. As will be evident later, the proposed sensor collaboration approach is also applicable to the problem with time-varying topologies.