Cooperative spectrum sensing and data transmission optimization for multichannel cognitive sonar communication network
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Abstract
The natural acoustic system used by marine mammals and the artificial sonar system used by humans coexist in the underwater cognitive sonar communication networks (CSCN). They share the spectrum when they are in the same waters. The CSCN detects the natural acoustic signal depending on cooperative spectrum sensing of sonar nodes. In order to improve spectrum sensing performance of CSCN, the optimization of cooperative spectrum sensing and data transmission is investigated. We seek to obtain spectrum efficiency maximization (SEM) and energy efficiency maximization (EEM) of CSCN through jointly optimizing sensing time, subchannel allocation, and transmission power. We have formulated a class of optimization problems and obtained the optimal solutions by alternating direction optimization and Dinkelbach’s optimization. The simulation results have indicated that SEM can achieve higher spectrum efficiency while EEM may get higher energy efficiency.
Keywords
Cognitive radio Cooperative spectrum sensing Spectrum efficiency Energy efficiency1 Introduction
Cognitive radio (CR) can improve spectrum utilization greatly through letting secondary user (SU) to access the idle spectrum licensed to the primary user (PU) [1]. However, the SU has to detect the absence of the PU through performing spectrum sensing, in order to guarantee the normal communications of the PU [2]. Energy detection is widely used as an effective spectrum sensing method due to the unnecessary prior information of the detected signal [3]. But the performance of energy detection will decrease if the PU is in fading or shadowing path, which is called “hidden terminal problem.” Cooperative spectrum sensing has been proposed to cope with this problem through letting multiple SUs detect the PU and exchange the sensing information collaboratively [4].
Recently, underwater communication network has attracted the attention, which can be used in underwater environment monitoring and submarine resource exploration. The underwater communication network transmits data using the underwater acoustic channel [5]. However, there are often multiple different underwater acoustic systems in the same water area, which may cause the interference to each other. In order to improve the spectrum utilization, CR has been introduced in the underwater communication network, called as cognitive sonar communication networks (CSCN) [6]. CSCN can use the sonar nodes to detect the presence of the other underwater acoustic systems in the surrounding water environment and transmit data on the premise of detecting the idle underwater acoustic channel. The underwater acoustic environment in the ocean is very complex, and usually, multiple acoustic systems coexist in the same water area, such as artificial echolocation systems, monitoring systems, and the nature acoustic systems of marine mammals [7]. The spectrum sharing of artificial acoustic network system and natural acoustic system will affect the transmission efficiency and the survival of marine mammals. The CSCN can realize the coexistence of a variety of artificial underwater acoustic systems in the protection of marine animals [8]. Thus, in the CSCN, the sonar node and the nature acoustic system can be seen as a SU and a PU, respectively.
Spectrum efficiency is an important index to evaluate the transmission performance of CSCN. Most of the previous works focused on optimizing either cooperative sensing or data transmission to maximize the spectrum efficiency of the CSCN. For instance, the listeningbeforetransmitting spectrum access is proposed, which can maximize the spectrum efficiency through optimizing sensing time [9]; both [10] and [11] assumed that each SU had a fixed transmission power, which ignored the potential gain of dynamic resource optimization. The water filling algorithm could maximize the spectrum efficiency of multichannel CSCN through optimizing subchannel power [12]. Recently, green communications have attracted the attentions of the scholars. Energy efficiency has been proposed to measure the effectiveness of energy utilization [13].

We seek to maximize spectrum efficiency and energy efficiency of CSCN, respectively, while considering both spectrum sensing performance for detecting the nature acoustic system and the power constraint of each sonar node.

We have formulated the cooperative spectrum sensing and data transmission optimization as a class of optimization problems about sensing time, subchannel allocation, and transmission power. In the optimization problem, the nature acoustic system is fully protected, while the transmission performance of the CSCN is improved as much as possible.

The joint optimization algorithm is proposed to obtain the solutions to the optimization problems, which is based on the alternating direction optimization and the Dinkelbach optimization.
2 System modeling
Then, in the cooperative interaction slot, each SU uses one common channel to report the local sensing information to the fusion center, which makes a final decision on the activation of the PU by the softdecisional combination of the local sensing information. To avoid the mutual interference, the SUs cannot report from the common channel simultaneously at the same time. Hence, in order to save the bandwidth of the common channel, the SU adopts time division multiple access (TDMA) to report the local sensing information. Finally, in the data transmission slot, the SUs access the licensed spectrum to communicate according to the decision result of the fusion center.
2.1 Underwater acoustic channel model
where \(\bar {h}_{n,l}\) is the statistical average of h _{ n,l }.
2.2 Cooperative spectrum sensing
where \(\bar {\gamma }_{l}=\frac {1}{N} {\sum _{n=1}^{N} {\frac {p^{s}_{l} h_{n,l}^{2}}{\sigma _{l}^{2}}}}\) is the average sensing SNR of N SUs in subchannel l, and the function \(Q(x)=\frac {1}{\sqrt {2\pi }}\int _{x}^{+\infty }\exp \left (\frac {z^{2}}{2}\right) \ \mathbf{d} z\).
In underwater, since the channel between the signal source and the sonar is often in severe fading, the received signal by one sonar may be too weak to be detected accurately. However, with cooperative spectrum sensing, the same signal can be received by multiple sonars from different paths. If the received signal by one sonar is too weak, the detection performance cannot be decreased through sharing the sensing information with the other sonars. Thus, the sensing diversity gain can be achieved to improve the final detection performance through cooperative spectrum sensing.
2.3 Spectrum efficiency maximization (SEM)
where \(\kappa =Q^{1}(Q_{d}^{\text {min}})(\bar {\gamma }_{l}+1)\) and \(\hat {p}^{\text {max}}_{n}=p^{\text {max}}_{n}p_{c}\). Then, we will give the following theorem.
Theorem 1
Problem (11) is a convex optimization problem.
Proof
which indicates that η _{SE} is convex in τ. Moreover, R _{ n,l } is obviously convex in (a _{ n,l },ω _{ n,l }). Since η _{SE} is the nonnegative linear combination of R _{ n,l }, η _{SE} is also convex in ({a _{ n,l }},{ω _{ n,l }}). Hence, η _{SE} is a convex optimization problem about (τ,{a _{ n,l }},{ω _{ n,l }}). □
where k≥0 is the iteration index. As mentioned above, we use ADO to optimize (a _{ n,l },ω _{ n,l }) and τ alternatively until a _{ n,l }, ω _{ n,l }, and τ are all convergent, as shown in Algorithm 1. Then, if a _{ n,l }=0, the transmission power p _{ n,l }=0; otherwise, \(p_{n,l}=\frac {\omega _{n,l}}{a_{n,l}}\). Since η _{SE} is convex in τ, a and ω, η _{SE} is nondecreasing during each iteration, which is described as follows:
Hence, the convergence of η _{SE} can be obtained after some iterations.
Supposing the estimation error is δ, η _{SE} will be convergent when τ ^{(k)},{a _{ n,l }}^{(k)}, and {ω _{ n,l }}^{(k)} are all convergent. Thus, the iterative complexity of the joint optimization algorithm is given by \(O\left (\frac {1}{\delta ^{3}}\right)\).
2.4 Energy efficiency maximization (EEM)
We have proven η _{SE}(τ,{a _{ n,l }},{p _{ n,l }}) to be a continuous positive convex function. As E _{ T }(τ,{a _{ n,l }},{p _{ n,l }}) is a linear positive function, we can solve the optimization problem (21) by the Dinkelbach optimization [14].
Supposing the feasible region of the solutions to (21) is denoted as S, the joint optimization algorithm based on the Dinkelbach optimization is described in Algorithm 2.
3 Simulations and discussions
In the simulations, the number of SUs is N=10, the number of subchannels is L=32, the channels obey the Rayleigh distribution with the mean −10 dB, the absence probability of the PU is P _{ r }(θ _{ l }=0)=0.5, the frame duration is T=100 ms, the length of cooperative interaction slot is ε=1 ms, the sampling frequency is f _{ s }=100 KHz, the maximal power of each SU is \(p_{n}^{\text {max}}=10\) mW, the sensing power p _{ c }=1 mW, and the noise power is \(\sigma _{l}^{2}=0.01\) mW.
4 Conclusions
In this paper, we have maximized spectrum efficiency and energy efficiency of periodic cooperative spectrum sensing for multichannel CSCN, respectively, through formulating optimization problems and jointly optimizing sensing time, subchannel allocation, and transmission power. We have got the following conclusions: (1) there is a tradeoff between spectrum sensing and data transmission; (2) SEM can obtain higher spectrum efficiency while EEM may achieve higher energy efficiency.
Notes
Acknowledgements
This work was supported by the National Natural Science Foundations of China under Grant Nos. 61601221, 91438205, and 61671183; the Natural Science Foundations of Jiangsu Province under Grant No. BK20140828; the China Postdoctoral Science Foundations under Grant No. 2015M580425; the Fundamental Research Funds for the Central Universities under Grant No. DUT16RC(3)045; and the Open Research Fund of State Key Laboratory of SpaceGround Integrated Information Technology under Grant No. 2015_SGIIT_KFJJ_TX_02.
Authors’ contributions
XL conceived and designed the study. MJ performed the simulation experiments. XL wrote the paper. MJ reviewed and edited the manuscript. Both authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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