### Data-Driven Joint Estimation for Blind Signal Based on GA-PSO Algorithm

2019-12-30 09:44:36 《ZTE Communications》 2019年3期

LIU Shen QIN Yuannian LI Xiaofan ZHAO Yubin XU Chengzhong

Abstract： Without any prior information about related wireless transmitting nodes， joint estimation of the position and power of a blind signal combined with multiple co?frequency radio waves is a challenging task. Measuring the signal related data based on a group distributed sensor is an efficient way to infer the various characteristics of the signal sources. In this paper， we propose a particle swarm optimization to estimate multiple co?frequency “blind” source nodes， which is based on the received power data measured by the sensors. To distract the mix signals precisely， a genetic algorithm is applied， and it further improves the estimation performance of the system. The simulation results show the efficiency of the proposed algorithm.

Keywords： Particle Swarm Optimization （PSO）; Genetic Algorithm （GA）; spatially distributed sensor; blind signal detection

DOI：10.12142/ZTECOM.201903010

http：//kns.cnki.net/kcms/detail/34.1294.TN.201900910.0953.002.html， published online September 10， 2019

Manuscript received： 2019?01?21

1 Introduction

s mobile broadband traffic and end?user demands continue to grow， the radio frequency spectrum has become an expensive and limited resource for wireless communications. Therefore， how to reasonably allocate spectrum resources， avoid conflicts， and detect interference have become an extremely worthwhile research issue. Spatially distributed sensor networks can effectively detect a certain frequency band in a certain area [1]. The power information can be bused in a variety of applications， such as indoor positioning， interference detection， signal recognition， and cognitive radio systems. As a major threat to wireless communications， interference creates significant usage and financial impact on users and operators. Interference is generally processed by several related techniques， such as interference monitoring， interference detection and isolation， interference classification， interference localization， and interference mitigation. Interference localization is what we are concerned about.

General interference signals are blind source signals， with unknown transmission power， which also brings difficulties to interference location [2]. For some communication systems， interference sources can cause very serious consequences if they cannot be located and eliminated in real time [3]. For instance， the signals in the communication based train control system （CBTC） communicate with the base station in the 2.4 GHz public band and are easily interfered by other devices in the same band. Especially when there are non?protocol signals in the environment， the system signals may be interfered by them. Once the same frequency signals are mixed， the signal sources are difficult to locate. Therefore， it is necessary to use appropriate methods to detect blind signals. Currently， common spectrum sensing techniques include matched filter detection， cyclostationary detection， and energy detection， which are mainly based on physical layer signal processing. Several methods were proposed to solve the problem of blind signal detection， by the use of a path loss model. The most used is the theoretical analysis method of using received power measurements at spatially distributed monitors [4]， [5]， [6]. Some scholars have proposed a method to detect the co?frequency blind signal by using the topology of the receiver and the mathematical models [6]. Some methods use k?means clustering algorithm combined with Particle Swarm Optimization （PSO） to estimate the position of nodes [2]. Other methods use SDR equipment for interference detection [7]. From the simulation results， the PSO has better adaptability and performance when dealing with such interference problems [8]， [9]. The PSO has caught great attention and various improved algorithms are continuously proposed， such as the local PSO through changing the topology of the particle population. There are some methods combined with other algorithms such as Genetic Algorithm （GA） and clustering algorithms to improve performance [10]， [11]. The PSO is then extended to use for the multi?objective estimation problem [10]. Genetic algorithms are also widely used in smart applications [12]-[14]. Similarly， improvements to genetic algorithms have never stopped， such as the elite genetic algorithm， adaptive genetic algorithm， multi?objective genetic algorithm， and hybrid genetic algorithm [15]-[18].

Through simulation， we found that the combined performance of PSO has been significantly improved after combining GA. The estimated error is reduced by a maximum of 0.6 m， and the estimation accuracy is improved by nearly 30%. Compared with the PSO with the exhaustive method， the performance gap is about 30%.

The rest of this paper proceeds as follows. Section 2 introduces the system model. The PSO algorithm improved according to system characteristics is proposed in Section 3. Section 4 mainly deals with unique GA and the method combined with PSO. In Section 5， the algorithm combined with the proposed PSO and GA is simulated and verified. Section 6 concludes this paper.

2 System Model

We assume a scenario where there are M transmitters and N sensor nodes within a certain square area. There is no reflective medium in the area， and there will be no multipath effect. In general， spatially distributed sensor networks are placed according to a certain spatial topology. This usually enables the system to have better estimation performance and to preliminarily position the target node. However， in order to make the study without loss of generality， we randomly placed the sensor in the hypothetical area and recorded its coordinates. The locations of the transmitters and sensors are represented in Cartesian coordinates. The uppercase notation denotes the coordination and power of transmitters such as [（X1，Y1）] and [（PT1]， while the lowercase denotes the coordinates and power of sensors such as [（x1，y1）] and [（pr1）]. For example， a diagram of the square region containing M transmitters and N receivers is shown in Fig. 1. Here， we only consider the line?of?sight channels from each transmitter to each sensor.

[pr=PTβda] ， （1）

where [d] denotes the Euclidean distance between the transmitter and the sensor， [pr] denotes the measured power of sensor， [PT] denotes the transmitted power of the blind signal， and [β] is a known constant selected based on the carrier frequency and the antenna structure. In practice， [α∈[2，6]] depending on the environment. Here， we make the value of [α=2] . Since the estimation system only utilizes the received power level of the sensor， we do not consider short? term fading.

2.1 Multiple Transmitter System

Since we chose PSO as the primary tool to solve joint estimation problems， we transform the system model into an objective function that serves as the basis for particle search. We define that the objective function is the sum of the squared difference between the actual measured power of each sensor and the predicted received power based on the estimated transmitter power and coordinates and causes the population of particles to search for its minimum value.

[F=i=1Npr，i-j=1MPT，jβdαi，j2，] （2）

where [pr，i] denotes the measured power of sensor i. [PT，j] denotes the transmitted power of the transmitter j. [dαi，j] denotes the Euclidean distance between the transmitter j and the sensor i. Our objective function is not convex concerning the estimated transmitter locations. Note that there may be many local optimal solutions when the number of sensor nodes is small， and the estimation error does not approach zero endlessly as the number of sensor nodes increases.

3 Particle Swarm Optimization

PSO is a population?based evolutionary algorithm. The classical PSO is used for balancing the weights of a neural network. The basic unit of the PSO population is the particle. The algorithm forms the search behavior through the interaction between each particle. Each particle represents a solution to the objective function and corresponds to a fitness function value. The merits of the fitness function value directly determine the quality of the solution. The target position is considered a global optimal solution.

PSO has two important concepts：

1） Exploration means that particles leave the original search trajectory to a certain extent and search in a new direction， which reflects the ability to develop into unknown regions.

2） Exploitation refers to the fact that particles continue to perform more detailed searches on the original search trajectory to some extent.

Population searches for optimal solutions in exploration and development. To control these two kinds of search better， the inertia weight is introduced. Its value can adjust the global and local search ability of PSO. When α is large， global optimization ability tends to be strong. On the contrary， the local search ability is enhanced. In this paper， we utilize the equation with inertia weights. The topology of the population directly determines the way in which particles interact. The classical PSO is a global topology and the learning samples for each particle are all other particles in the population. Subsequently， scholars proposed a variety of local PSO algorithms with excellent performance， and found that local PSO algorithm has better performance in local search. But what our system needs most is the global search ability of the algorithm. Therefore， it is more appropriate for us to choose a global topology.

We generate a certain number of particle populations， and then initialize the particles and randomly generate their speeds and positions. All particles are initialized， giving them random values in each dimension， as shown in Equ. （3）， where k is the number of the particle and j is the number of the transmitter. Then we calculate the fitness function value of each particle according to Equ. （4）， where Fk denotes the fitness function of particle k. i is the number of the sensor， and update the particles speeds and positions according to Equs. （5） and （6） in each iteration until the end of the algorithm. The equations and pseudo code of the standard PSO （Algorithm 1） are as follows.

[xk=Xk1，Yk1，PkT，1，...，XkM，YkM，PkT，Mvk=Xk1，Yk1，PkT，1，...，XkM，YkM，PkT，M] ， （3）

[Fk=i=1Npr，i-j=1MPkT，jβ（Xkj-xi）2+（Ykj-yi）22，] （4）

[vk（t+1）=ω×vk（t）+c1×r1×（pbestk（t）-xk（t））+c2×]

[r2×（gbest（t）-xk（t）） ，] （5）

[xk（t+1）=xk（t）+vk（t+1） ，] （6）

where [vk（t）] denotes the speed of particle k at iteration time t. [xk] denotes the position of the particle k. The [pbestk] is the optimal position experienced by the particle k. The [pbest] denotes the position of the particle that operates optimally in the population. [c1] and [c2] denote the acceleration constants of the particles. In order to make the particles have stronger self?searching ability in the initial stage， they can converge to the global optimum at the later stage. We linearize [c1] and [c2] so that [c1] has a larger initial weight and gradually decreases. And [c2] is the opposite.

[c1=-tT+2c2=tT+1]. （7）

[r1] and [r2] are two random numbers distributed uniformly in [0，1]. [ω] is generally a constant， and the linearly decreasing weight is currently used more frequently as the value of the inertia weight.

[ω=ωmax-（ωmax-ωmin）×tT，] （8）

where T denotes the total number of iterations and t denotes the number of iterations that have taken place.

The population size of particles affects the performance of the algorithm. Different estimation problems apply to different population sizes， and it is generally proportional to the dimension of the objective function. Some results suggest that using [（2m+1）2] particles work better， where m is the number of dimensions the objective function has. For our simulation， each unknown transmitter needs to estimate three dimensions [（x，y，PT）]. Therefore， for each additional transmitter， there are three dimensions added. We need to change the population of particles according to the different dimensions of the objective function. Otherwise， too few particles may miss the global optimal solution， while too many particles may produce many repeated results， reducing the efficiency of the algorithm. So we use [（2m+1）2] particles， which is enough for most of the estimation problems. Using excess particles within the algorithm can indeed make the estimation more accurate. However， it will cause the algorithm calculation volume to increase， affecting the overall performance of the system. In Section 4， with the help of the exhaustive method， we use a large number of particle population to approximate the estimation error limit of the objective function in this paper.

To evaluate the effectiveness of the proposed joint estimation technique， we attempted to simulate the performance of three to twenty sensors and one to four transmitters based on different systems. As mentioned earlier， each additional transmitter will add 3?dimensions that need to be estimation to the system. For the estimation problem， the number of equations should be more than or equal to the estimated dimensions. In other words， every time an unknown transmitter is added， at least three receivers need to be added. Increasing the number of transmitters and receivers does increase the computational burden of the simulation， but the proposed method has no inherent limits to the dimensionality it can handle. However， as the dimension increases， the performance of the PSO deteriorates. In the standard PSO， the learning object of each particle is a particle in the population that has the best fitness function value. When the dimensions are large， it is difficult to ensure that the global?best particle can search for the optimal solution in every dimension.

After a large number of simulation experiments using only the particle swarm algorithm， we found that the ratio between the powers of multiple transmitters had different effects on the results. The impact can be divided into two situations. In each case， the algorithm falls into a special local minimum. In the first case， when there are two or more transmitters with similar actual power， the particle swarm algorithm may easily match the estimated power of one transmitter with the estimated position of another transmitter with similar power. Because the objective function is a multi?dimensional estimate， when the estimated value of some of the dimensions is close to the actual value， the overall fitness function value is too small. The algorithm tends to converge and falls into a local minimum.

In the second case， the high power transmitter estimates better than the low power transmitter. This situation is caused by the objective function. High?power transmitters have a greater impact on fitness function values than low? power transmitters. Although the dimensions are synchronous estimates， the convergence of various dimensions of the high power transmitter is significantly faster than the dimensions of the low power transmitter. When the various dimensions of the high?power transmitter obtain relatively accurate estimates， the fitness function value is already small and the algorithm tends to converge.

4 Genetic Algorithm

The genetic algorithm is a computational model that simulates the natural evolution of Darwins biological evolution theory and the biological evolution process of the genetic mechanism. It is a method to search for optimal solutions by simulating natural evolutionary processes. The GA begins with a population that represents a potential solution set of problems， while a population consists of a certain number of individuals genetically encoded. Each is an entity with a characteristic chromosome. Chromosomes are the main carrier of genetic material， that is， a collection of multiple genes whose internal manifestation is a combination of genes that determine the external representation of the shape of the individual. Therefore， mapping from phenotype to genotype， that is， coding work， needs to be implemented at the beginning. Since the work of gene encoding is complex， we tend to simplify it. Here， we combine GA and PSO， which share a population. Next， we genetically encode each particle according to the category of information estimated on each dimension of the particle. The specific gene coding method is shown in Fig. 2.

Because the PSO is difficult to distinguish several blind source signals with similar power， it is extremely easy to fall into the local minimum. Therefore， when the genes are crossed， we allow the coordinate loci to be interchanged and the power loci can be interchanged， although this may make the progeny particle gene obtained after the crossover completely different from the paternal particle gene. Because of the existence of elite strategies， we do not need to worry that the PSO will lose the original possible correct estimation results.

We hope that when the PSO particles tend to converge， some particles can still jump out of the existing estimation results. The particles may quickly and accurately estimate the position and power of the high?power transmitter， especially when the power difference between the two transmitters is very large. Therefore， the entire PSO algorithm tends to converge when the low power transmitter does not obtain an accurate estimate. And the estimated result falls into a local minimum. So the design of genetic mutation becomes extremely critical. The mutation may occur on any one or more genes of the particle， and the mutation is completely random in the range of values of the gene. We do not make any human intervention in the values and direction of mutation. The mutation probability is set to increase linearly with the number of iterations， as shown in Equ. （9）， where Pmuta denotes the mutation probability.

[Pmuta=tT×0.1+0.05.] （9）

The specific operation of the particle group gene crossover and mutation is shown in Fig. 3.

Referring to Fig. 3， the first two genes are the coordinate estimate genes， and the last two are the power estimate genes. Each of the two paternal particles that exchange genes takes out a coordinate estimate gene and a power estimate gene. These four random genes are randomly combined to form progeny particles with new gene sequences. Taking two unknown nodes as an example， the genetic composition of the progeny particles is 64 cases. And the genes of the progeny particles are still arranged in the order of the genes of the paternal particles. Genetic mutation may also occur in progeny particles obtained after crossing.

The computational complexity of the GA?PSO algorithm is indeed higher than the PSO algorithm. For the traditional PSO algorithm， the time complexity is [O（N×m×（2m+1）2×T）]. That is the product of the number of receivers， the number of objective function dimensions， the total number of particles， and the number of iterations. In the GA?PSO algorithm， the main computational complexity still comes from the PSO part. And iterations do not run the GA algorithm every time. Instead， every other iteration of h runs the GA algorithm. Through simulation experiments， we found that when the value of h is less than 5， the algorithm works better. In the experimental part that follows， our default h has a value of 5. Therefore， the time complexity of the GA?PSO algorithm in this paper is [O（N×m×（2m+1）2×T+（1+4（（2m+1）2-1））×T/5）].

5 Simulation Results and Discussion

In this work， we set up a Monte?Carlo based simulation. We jointly estimate the power and position of 2 unknown transmitters. We fix the number of spatially distributed receivers to 20 and ensured that each receiver has the same weight and assume that the size of the test area is 10 m×10 m.

Before performing the simulation， we must first make a basic estimate of the power and location of the blind source nodes within the system. Some scholars have proposed to use the received power of spatially distributed receivers for clustering， and use the k?means algorithm to quickly narrow the search range of PSO. However， this proposed method is for known nodes with the same power. The problems we face are obviously much more complicated. When the power difference between two unknown transmitters is too large， we may no longer be able to use clustering to determine the approximate location of the blind source node. Because the blind source node with low power is likely to disappear in the signal strength of the high power blind source node. In this paper， we do not pre?estimate the position of the particle in order to more directly show the improvement of the performance of the PSO in dealing with this kind of problem. But we still make a preliminary estimate of the power of the unknown node. First， we set the lower limit of the estimated power to zero. Then we select the transmitter with the lowest received power， assuming that it is at the maximum distance from the transmitter （according to the estimated area， [dmax=102]）. Substituting the minimum received power and the maximum distance into Equ. （1）， what is obtained is the upper limit of the transmission power. Note that this upper limit is the upper limit of the sum of the powers of multiple transmitters.

In the simulation， we assume that the transmit power of the unknown transmitter 1 is always 100 mw， while the transmit power of the unknown transmitter 2 is from 10 mw to 90 mw. The power of each transmitter is still unknown to the system. We use PT2/PT1 as the independent variable and the average estimation error as the dependent variable. In order to form a comparison， we also add the position estimation error of the GA?PSO algorithm under known power. At the same time， we use the idea of the exhaustive method to maximize the particle population of the PSO （excellent performance）， and test the lower error limit of the objective function.

From Fig. 4， the estimation performance of the PSO algorithm is greatly improved after adding the GA. Especially when the value of PT2/PT1 is in the range of [0.3， 0.7]. The average error is reduced by up to about 0.6 m， and the overall performance is increased by about 30%. However， when the power of the unknown nodes is similar or the difference is large， the system estimates that the performance improvement is slightly reduced. Compared with the results obtained by the exhaustive method， the algorithm proposed in this paper still has a certain gap and there is still room for improvement in the future. However， the difference between the joint estimate and the estimate with known power is not very large.

As shown in Fig. 5， as PT2/PT1 gradually decreases， the difference between the estimation errors of the unknown node 2 and the unknown node 1 gradually increases. Although the genetic PSO algorithm has reduced both， it cannot suppress this trend. Fig. 6 shows the case where the power estimation error varies with the ratio of PT2 and PT1. When the power of two unknown nodes is similar， the power estimation error is only about 10%. And when the power difference between the two is large， the power estimation error is also steady.

The main reason for this trend is the design of the objective function. High power transmitters have a greater impact on the objective function than small power transmitters. Both PSO and GA are algorithms for finding suboptimal solutions. They only care if the fitness function value is small enough. As long as the power and position estimates of a high power transmitter are accurate， the fitness function value can be reduced to a small enough. Therefore， even if the power and position of the small power transmitter are not accurate enough， the algorithm will tend to converge.

We also conduct an artificial observation analysis of the error results and find that there are still cases where the two unknown nodes estimate the coordinate interchange because they fall into the local minimum. Comparing the values of the fitness function of the local minimum and the global optimal solution， it is found that their fitness function values are indeed very close. The introduction of the GA algorithm can make the algorithm jump out of the local minimum and can effectively guide the estimated value to the global optimal solution. However， there is still no guarantee that it will not fall into other local optimal solutions after jumping out. This shows that the objective function as a non?convex function has many non?inferior solutions. In future research， we can extend this problem from single?objective PSO to multi?objective PSO， and new development may be made.

6 Conclusions

Joint estimation of power and positions for blind signals is essential to detect the co?frequency interference signal. We propose a data?driven based PSO algorithm combined with a special GA to estimate multiple co?frequency wireless blind source nodes with different powers. To avoid the local minimum problem， we use GA to help particle population jump out of local minima. The simulation results show that the proposed GA?PSO algorithm has better estimation performance than the classical PSO algorithm and can reduce the error distance by up to 30%.

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Biographies

LIU Shen received his B.S. from Zhengzhou University （ZZU）， China in 2016. He received his M.S. in electronic and communication engineering from Guilin University of Electronic Technology， China in 2019. He studied and worked in Shenzhen Institute of Advanced Technology， Chinese Academy of Sciences and Shenzhen Institute of Radio Testing & Tech， China from 2017 to 2018. He is currently an engineer in Monolithic Power System （MPS）， China. His research interests include indoor localization and software defined radio when he was a student.

QIN Yuannian received his B.S. from University of Electronic Science and Technology， China in 1994. In 2005， he received the title of senior experimental teacher. He is currently employed as a professor. He is the director of the Communication Experimental Center. The Communication Experimental Center has been awarded the title of the Experimental Teaching Demonstration Center of Guangxi Universities. As the main participant， he participated in 6 provincial and ministerial scientific research projects， presided over one Guangxi Natural Fund project， one Guangxi science and technology development project， three horizontal scientific research projects， 14 horizontal scientific research projects as the main personnel， published 22 papers， and participated in the compilation and publication of the textbook Mobile Communications.

LI Xiaofan received her B.S. and Ph.D. degrees from Beijing University of Posts and Telecommunication， China in 2007 and 2012. From 2010 to 2011， she studied in University of Washington， USA as an exchanged Ph.D. student. She joined the State Radio Monitoring Center and Testing Center （SRTC） in 2012 and was transferred to SRTC Shenzhen Lab from 2013. She is now an associate professor in Jinan University， Zhuhai， China. Her research interests include interference analysis among different radio systems， testing and evaluation methods for innovative radio technologies， cooperative communication， cognitive radio， internet of things， radio management strategy， etc.

ZHAO Yubin （zhaoyubin [email protected]） received his B.S. and M.S. from Beijing University of Posts and Telecommunications， China in 2007 and 2010. He received his Ph.D. degree in computer science in 2014 from Freie Universiteat Berlin （FU Berlin）， Germany. He has been an assistant professor in Center for Cloud Computing， Shenzhen Institutes of Advanced Technology， Chinese Academy of Sciences， China， since 2014. He serves as the reviewers for many scientific journals and session chairs for several conferences. He co-organized the workshop in ICCC 2019. His current research interests include indoor localization and target tracking， wireless power transfer and mobile edge computing.

XU Chengzhong received the Ph.D. degree from the University of Hong Kong in 1993. He is a full professor in the Department of Computer and Information Science， Faculty of Science and Technology， State Key Laboratory of IoT for Smart City， University of Macau， China. His research interests include networked computing systems and applications. He is an IEEE Fellow due to contribution in resource management in parallel and distributed computing.

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