China Communications May 201483

potentially make CR devices more energy

consuming. In this sense, issues in energy ef-ficiency could be even more stringent in CR

systems than in conventional wireless commu-nication systems and tremendous efforts have been made to improve the energy-efficiency of

CR systems in terms of spectrum sensing and

resource allocation [1] [2] [3].Recently, energy harvesting draws exten-

sive attention since wireless communication systems powered by renewable energy source can significantly alleviate energy-deficiency with more eco-friendliness [4] [5]. In addi-tion to other commonly used energy sources such as natural and mechanical energy, radio signal can be another viable energy source since radio signal carries energy as well as information. Consequently, wireless energy harvesting becomes appealing since it could take advantages of interference signal which used to be eliminated in conventional wireless communication systems.

Wireless energy harvesting is pioneered in [6], in which the idea of transmitting infor-mation and energy simultaneously as well as a capacity-energy function to characterize the fundamental tradeoffs is proposed. In addi-tion, the authors in [7] investigate the optimal switching rule between information decoding mode and energy harvesting mode. A save-then-transmit protocol is proposed in [8] to optimize the system outage performance via

Abstract: In this paper, we consider a cognitive radio system with energy harvesting, in which the secondary user operates in a saving-sensing-transmitting (SST) fashion.

We investigate the tradeoff between energy harves t ing , channel sens ing and data transmission and focus on the optimal SST structure to maximize the SUs expected achievable throughput. We consider imperfect knowledge of energy harvesting rate, which cannot be exactly known and only its statistical information is available. By formulating the problem of expected achievable throughput optimization as a mixed-integer non-linear programming one, we derive the optimal save-ratio and number of sensed channels with in-depth analysis. Simulation results show that the optimal SST structure outperforms random one and performance gain can be enhanced by increasing the SUs energy harvesting rate.Key words: cognitive radio; spectrum sensing; energy harvesting

I. INTRODUCTION

Considered as a promising solution to improve spectrum efficiency, cognitive radio (CR)

allows efficient spectrum sharing between pri-mary users (PUs) and secondary users (SUs)

by opportunistically utilizing spectrum that is temporarily unused by PUs. However, exclu-sive functionalities such as spectrum sensing

Optimal Spectrum Sensing in Energy Harvesting Cognitive Radio Systems

QU Zhaowei1, SONG Qizhu2, YIN Sixing1

1 Beijing University of Posts and Telecommunications, Beijing 100876, P. R. China2 State Radio Monitoring Center of China, Beijing 100037, P. R. China

COMMUNICATIONS SYSTEM DESIGN

China Communications May 2014 84

SST structure are presented in Section V, fol-

lowing which, simulations are performed in Section VI to validate the optimality of the op-

timal SST structure over random one. Finally we conclude this paper in Section VII.

II. SYSTEM MODEL

We consider a self-powered CR system

comprising one SU and several PUs operating in slotted mode. The SU has no fixed power supplies and extracts energy exclusively via energy harvested from ambient radio signal. In order to avoid collision with PUs, the SU needs to perform channel sensing before data transmission to make sure that PUs are not present. Therefore, we assume that the SU operates in an SST fashion due to the du-plex-constrained hardware [8] [14]. In each

timeslot with duration T, a fraction (referred

to as save-ratio [8], denoted by ) of time is

devoted exclusively to energy harvesting, an-other fraction which depends on the number of sensed channels is dedicated to channel sens-ing, while the remaining one is used for data transmission. The SST structure is shown in Fig.1 and detailed as the following three steps:

(1) Energy harvesting: during interval (0,

T ], the energy harvester collects energy from ambient radio signal and deposits the energy into a storage device.

(2) Channel Sensing: during interval (T, T + nTs], the energy harvester stops working and the sensing receiver is powered on for

fi nding the optimal save-ratio. In [9], the au-

thors investigate the performance limits of self-powered wireless networks and extend the rate-energy region characterization to MIMO

broadcast systems.There have been also several precedential

works on CR systems powered by energy har-

vesting, in most of which optimal policies for either energy harvesting and spectrum sensing are investigated [10] [11] [12]. Moreover, in

[13], spatial spectrum reuse in CR networks

with energy harvesting is investigated based on a stochastic-geometry model. Compared with these works, the salient feature of this paper is that, we investigate the tradeoff be-tween energy harvesting, channel sensing and data transmission and jointly optimize both save-ratio and number of sensed channels to maximize the SUs expected achievable throughput.

In this paper, we consider a slotted CR

system in which the SU has no fixed power supplies and extract energy only via wireless energy harvesting from ambient radio signal. We assume that SUs can only perform either of energy harvesting (also termed saving),

channel sensing or data transmission at one moment due to hardware duplex limitation (e.g., secondary transmission can be started

only when spectrum sensing for all the li-censed channels is fi nished [14]). In this sense,

a timeslot is partitioned into three non-over-lapping fractions and there exists non-trivial tradeoff between the three operations due to their mutual-constraining relationship (as de-

scribed in Section II). To this end, we focus on

optimizing saving sensing-transmitting (SST)

structure (jointly optimizing save-ratio and

number of sensed channels) to maximize the

SUs expected achievable throughput. The remainder of this paper is organized

as follows. The SST structure as well as re-lated assumptions is described in Section II. In Section III, we formulate the SST structure optimization as a mixed-integer non-linear programming (MINLP) problem. In Section

IV, we elaborate derivation for the optimal

solution. Analytical results for the optimal Fig.1 SST structure with wireless energy harvesting.

In this paper, we con-sider a cognitive radio system with energy harvesting, in which the secondary user operates in a sav-ing-sensing-transmit-ting (SST) fashion.

China Communications May 201485

III. PROBLEM FORMULATION

As shown in Fig. 1, achievable throughput of the SU in each timeslot is given by

(1)

where X denotes the energy harvesting rate, namely average energy harvested in unit time (say, one second), h denotes the channel gain, denotes the noise power, Es denotes the energy cost of sensing one channel and M de-notes the number of channels found available after sensing n channels. Assume that licensed channels are independent and identically dis-tributed (i.i.d) and state of each channel is

Bernoulli-distributed with parameter p (e.g. idle probability of a channel), then M is a Binomial-distributed random variable with pa-rameters n and p, and its expectation is given by E[M ] = np, where E[.] refers to expectation operator. Hence, the achievable throughput in

each timeslot is also a random variable. In this sense, we aim at optimizing the long-term ex-pectation of the achievable throughput (E[R]).

In this paper, imperfect knowledge of energy harvesting rate is considered. To be more specific, X cannot be known exactly and only its probability distribution is available. Here notation h and are discarded since they can be merely considered as constant coefficients of energy harvesting rate. In oth-er words, X also represents the equivalent energy harvesting rate at the SUs receiver. With the assumption that number of chan-nels found available and energy harvesting rate are independent with each other, the SUs achievable throughput optimization problem can be formulated as the following:

(2)

where

and

sensing n channels. Here Ts denotes the time cost of sensing one channel.

(3) Data transmission: during interval (T + nTs, T ], the sensing receiver is shut down and the transmitter is powered on for data trans-mission with energy in the storage device.

Obviously, a higher leads to more harvest-ed energy such that instantaneous transmission rate can be improved. Similarly, more avail-able channels can be possibly captured and in-stantaneous transmission rate can be improved by sensing more channels (in either random or

sequential manner) in spite of time and energy

cost. However, with more time and energy

spent on energy harvesting and channel sens-ing, less remains for data transmission, which downgrades the effective transmission quality (e.g., achievable throughput). Therefore, we

focus on the tradeoff between energy harvest-ing, spectrum sensing and data transmission in this paper. Several other assumptions are made for the scenario in this paper as follows:

(1) The SU operates in a saturated model

and always has plenty of data in buffer such that it wishes to exploit as many licensed channels as possible to gain higher through-put. In this sense, we specify that the SU will exhaust all the harvested energy for data trans-mission without considering the SU can pre-serve some of its harvested energy for future use. Thus, the SUs energy storage is always empty at the beginning of each timeslot.

(2) Results of channel sensing are accurate

and will not incur any false-alarms or miss-de-tections, which might be impractical due to the imperfectness of current channel sensing techniques (e.g., energy detection and signal

feature recognition). Discussion on false-

alarm and miss-detection of channel sensing is beyond the scope of this paper.

(3) We assume that PUs also operate in

slotted mode (such as GSM systems) and the

state of a licensed channel stays unchanged within one timeslot. Thus, each licensed chan-nel needs to be sensed at most once in each timeslot.

China Communications May 2014 86

(4)

while or otherwise.Since X is Gamma-distributed, we have

for the probability of , where (.,.) refers to upper incomplete Gamma func-tion. Then (4) can be rewritten as

(5)

Following (5), the objective function in (2)

can be equivalently expressed as

(6)

Since it is too difficult to either make judg-ment for the concavity or analytically derive the closed-form optimal solution, we employ the heuristic algorithm proposed in an existing work on solving MINLP problems [17], which

extended the different evolution (DE) algo-rithm to MINLP problems and demonstrated

preferable solution quality and robustness property. Although the global optimality of any heuristic algorithm cannot be guaranteed, one can still derived the optimal solution by setting proper parameters (e.g., number of

population, stop criterion).

We first replace the problem in (6) with an

unconstrained one, which is given by

(7)

where refers to the penalty coefficient. Then (7) is solved in compliance with the algorithm

which represents the SUs expected instan-taneous throughput. It is noteworthy that the second constraint condition in (2) is only to

avoid energy overflow (available energy is less

than that to be consumed) in the sense of sta-tistical average since energy overflow is inev-itable while the energy harvesting rate cannot be known in advance. From (1) and (2) we can

see that the SUs expected achievable through-put highly depends on save-ratio and number of sensed channels. Hence, in the next section,

we will investigate joint optimization for both save-ratio and number of sensed channels in the two cases.

IV. THROUGHPUT OPTIMIZATION

Due to the imperfect knowledge on energy

harvesting rate, we assume that X is Gam-ma-distributed. Gamma distribution can model many positive random variables is very general, including exponential, Rayleigh, and

Chi-Square as special cases. Furthermore, the probability density function (PDF) of any

positive continuous random variable can be properly approximated by the sum of Gamma PDFs [15] [8]. The PDF of X is given by

where k, > 0 and (.) refer to the shape pa-rameter, scale parameter and gamma function, respectively. Then we have E[X] = k and D[X] = k2 for the expectation and variance of energy harvesting rate. Since deriving the closed form expression of Ri is mathematically difficult, we solve the problem in (2) by ap-proximation with Taylor expansions.

In probability theory, it is possible to ap-proximate the expectation (first-order moment)

of a function f of a random variable V using Taylor expansions (also referred to as delta

method [16]), which is given by

(3)

Following (3), we have

China Communications May 201487

are set to 10 5 and 50, respectively.In each iteration, (7) is solved with the

modified DE algorithm, which is detailed in

Algorithm 2. Here we defi ne

( ) ( )( ), , INTx y x y= where INT(y) refers to the nearest integer to y. The population size (Np), mutation factor (F) and crossover constant (Cr) are set to 20, 0.85 and 0.7, respectively. In addition, the maxi-mum generation (Gmax) in stopping criterion is set to 50.

V. NUMERICAL RESULTS

The optimal save-ratio and number of sensed channels with different time and energy cost of channel sensing are shown in Fig. 2 and 3 (with k = 5 and = 2), respectively.

It can be shown that, as time cost ()

grows, a higher fraction of time for energy harvesting is preferred such that higher en-ergy cost of channel sensing can be afforded with suffi cient harvested energy to maximize

the expected achievable throughput. On the contrary, as energy cost () grows, a lower

fraction of time for energy harvesting is pre-ferred such that more time remains for channel sensing and data transmission. Moreover, Fig.

2 and 3 also show that sensing less channels is preferred with higher time and energy cost of channel sensing such that enough time for data transmission can be conserved and the SUs expected achievable throughput can be improved.

The optimal save-ratio and number of sensed channels with different scale and shape parameters of energy harvesting rate are shown in Fig. 4 and 5 (with T = 1, Ts = 0.02 and Es = 1), respectively. It can be shown that, with higher expected energy harvesting rate (higher k or ), a smaller fraction of time for energy harvesting is preferred such that more time remains for channel sensing and data transmission. Meanwhile, as scale or shape pa-

rameter of energy harvesting rate grows, more channels are preferably sensed such that more available channels could possibly be detected.

of exterior-point sequential unconstrained minimization technique (SUMT), which is

detailed in Algorithm 1. The normalized initial value of and n are set to 0.5 and 1, respec-tively. The initial penalty coeffi cient (1) and

iterative multiplier (C) are set to 1 and 5, re-spectively. The improvement threshold () and

maximum iteration number in stop criterion

Algorithm 1 Exterior-point SUMT

1: Initialization: i = i +1;2: while true do3: Solve (7) and derive the optimal solution ;

4: if < then5: break;

6: else7: i = i + 1, i +1 = Ci;8: end if9: end while10: return ;

Fig.3 Optimal number of sensed channels versus time and energy cost.

Fig.2 Optimal save-ratio versus time and energy cost

China Communications May 2014 88

Moreover, in spite of the unsmoothness in

Fig. 2 and 4 made by the non-zero improve-

ment threshold () in SUMT algorithm, it

can still be made out in Fig. 2 and 4, that the

optimal save-ratio also presents a zigzag re-

lation to either the time and energy cost or the scale and shape parameters of energy harvest-ing rate.

VI. PERFORMANCE EVALUATION

We perform simulation of 50 timeslots by gen-erating 50 state samples of 20 channels with idle probability of each channel 0.5. Both the optimal SST structure and a random one in which save-ratio and number of sensed chan-nels are randomly selected are applied for the purpose of performance comparison.

Since the energy harvesting rate is consid-ered as a random variable, we defi ne X (5, 2) and other parameters remain unchanged.

Fig. 6 shows that the optimal structure outper-forms the random one for most of the timeslots with only a small portion of timeslots in the opposite case.

We also investigate the average achievable throughput with different expected energy har-vesting rates by altering the scale parameter of X. As is shown in Fig. 7, the average achiev-able throughput over the entire 50 timeslots with fi ve different settings of scale parameter

of X, namely 5, 7.5, 10, 12.5 and 15 (or equiv-alently 10, 15, 20, 25 and 30 for the expected energy harvesting rate), and other parameters

remain unchanged. It can be shown that higher expected energy harvesting rate brings higher average achievable throughput and the perfor-mance gap between the random structure and the optimal one is enlarged as energy harvest-ing rate increases.

VII. CONCLUSION

In this paper, we consider a CR system oper-

ating in slotted mode, in which the SU has no fi xed power supplies and extracts energy only

via wireless energy harvesting from ambient radio signal. It is assumed that the SU operates

Fig.5 Optimal number of sensed channels versus energy harvesting rate.

Fig.4 Optimal save-ratio versus energy harvesting rate.

Algorithm 2 Hybrid Differential Evolution Algorithm

Require: Set Opt=0; Set G=0 Randomly select Np vectors of (i, ni)(i = 1,2,3,....,Np) from and

with uniform probability distribution;

Ensure:1: While G < Gmax do2: ;3: for all i {1,2,..., Np } do4: Randomly pick a, b and c {1,2,... Np}{i};5: 6: Randomly pick k1 and k2[0,1]7: if k1 >Cr then ;8: else ;9: endif10: if k2 >Cr then ;11: else ;12: endif13: if then 14: endif 15: end for16: ;17:endwhile

China Communications May 201489

Science Foundation of China (NO. 61372109).

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in an SST fashion, which partitions a timeslot into non-overlapping fractions for energy harvesting, channel sensing and data transmis-sion. We focus on optimizing SST structure to maximize the SUs expected with imperfect knowledge on energy harvesting rate, name-ly, energy harvesting rate cannot be exactly known and only its statistical information is available. By formulating the expected achiev-able throughput optimization as an MINLP

problem, we separately derive the optimal SST structure in the two cases. The simulation re-sults show that the optimal SST structure out-performs the random one (in which save-ratio

and number of sensed channels are randomly selected) and the performance gain can be en-

hanced by increasing the SUs energy harvest-ing rate.

ACKNOWLEDGEMENTS

This work was supported by National Nature

Fig.6 Performance comparison between the optimal structure and random struc-ture.

Fig.7 Average achievable throughput with different expected energy harvesting rate.

China Communications May 2014 90

2006, respectively. He is currently a reseach fellow in School of Network Technology, Bejiing University of Posts and Telecommunications. His research interests include cognitive radios, spectrum management and wireless networks.

SONG Qizhu, received his Ph.D. degree in Beijing University of Posts and Telecommunications, Beijing, China, in 2010. His research interests include wireless devices testing and economics in spectrum manage-ment.

YIN Sixing, received his B.S., M.S., and Ph.D. degrees from Department of Information and Communica-tion Engineering in Bejiing University of Posts and Telecommunications, China, in 2003, 2006, and 2010, respectively. He was a visiting scholar in Hong Kong University of Science and Technology from 2008-2009 and worked as a Post Doctoral Fellow in Bejiing University of Posts and Telecommunications from 2010 to 2012. He is currently an assistant professor in School of Information and Communication En-gineering, Bejiing University of Posts and Telecom-munications. His research interests include cognitive radio networks, spectrum measurement data analysis and energy-efficient wireless communications. *The corresponding author. Email: yinsixing@bupt.edu.cn

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BiographiesQU Zhaowei, received his M.S. degree in Depart-ment of Computer Engineering from Kyung Hee University, Seoul, Korea in 2002 and received his B.S. and Ph.D degree from Beijing University of Posts and Telecommunications, Beijing, China in 2002 and