4-d arrays as enabling technology for cognitive radio systems.pdf

1102 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 3, MARCH 2014

4-D Arrays as Enabling Technologyfor Cognitive Radio Systems

Paolo Rocca, Senior Member, IEEE, Quanjiang Zhu, Student Member, IEEE, Ephrem T. Bekele,Shiwen Yang, Senior Member, IEEE, and Andrea Massa, Member, IEEE

AbstractTime-modulation (TM) in four-dimensional (4-D)arrays is implemented by using a set of radio-frequency switchesin the beam forming network to modulate, by means of periodicpulse sequences, the static excitations and thus control the antennaradiation features. The onoff reconfiguration of the switches, thatcan be easily implemented via software, unavoidably generatesharmonic radiations that can be suitably exploited for multiplechannel communication purposes. As a matter of fact, harmonicbeams can be synthesized having different spatial distribution andshapes in order to receive signals arriving on the antenna fromdifferent directions. Similarly, the capability to generate a fieldhaving different frequency and spatial distribution implies that thesignal transmitted by time-modulated 4-D arrays is direction-de-pendent. Accordingly, such a feature is also exploited to implementa secure communication scheme directly at the physical layer.Thanks to the easy software-based reconfigurability, the multipleharmonic beamforming, and the security capability, 4-D arrayscan be considered as an enabling technology for future cognitiveradio systems. In this paper, these potentialities of time-modulated4-D arrays are presented and their effectiveness is supported by aset of representative numerical simulation results.

Index Terms4-D arrays, cognitive radio, harmonic beam-forming, multiple-input multiple-output (MIMO), reconfigura-bility, secure communications, time-modulated arrays.

I. INTRODUCTION

N OWADAYS, the growing request of information and mo-bility has had an unavoidable impact on the prolifera-tion of wireless systems and services with a consequent con-gestion of the wireless medium. Accordingly, issues regardingan efficient and smart utilization of the limited radio resourcehave been raised. To address these problems, a possible solu-tion considers the use of antenna systems able to first sensethe external electromagnetic environment and second recon-figure the radiation characteristics of the generated field (forexample in terms of shape, carrier-frequency, and modulationstrategy) to guarantee reliable communications. In this frame-work, the cognitive radio (CR) paradigm has recently received

Manuscript received October 03, 2012; revised August 07, 2013; acceptedSeptember 29, 2013. Date of publication November 01, 2013; date of currentversion February 27, 2014. This work was supported by the Natural ScienceFoundation of Chinaunder Grant 61125104.P. Rocca, E. T. Bekele, and A. Massa are with the ELEDIA Research

Center@DISI, University of Trento, Povo 38123 Trento, Italy (e-mail: [email protected]; [email protected]; [email protected]).Q. Zhu and S. Yang are with School of Electronic Engineering, University

of Electronic Science and Technology of China (UESTC), Chengdu 611731,China (e-mail: [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TAP.2013.2288109

great attention [1][4]. Indeed, the primary objectives of CRare the efficient use of the available spectrum and the relia-bility of the wireless communications. To achieve these goals,the antenna has to rapidly adapt to the changing electromag-netic scenario by reconfiguring, possibly via software (SW),the radiation pattern in order to suppress the interfering signals,to transmit/receive information in the free/less-disturbed bands,and to properly modulate the signals to obtain secure commu-nication links.In the last decades, several solutions have been proposed in

the scientific literature to the design and synthesis of adaptive/smart antennas [5][8], SW-defined radio system [9], [10], anddirectional modulation techniques [11][13] as suitable ways toimplement CR. In this framework, there has been recently a re-newed interest towards the use of time as an additional degree offreedom (DoF) for the antenna synthesis to obtain performancenot achievable with conventional antennas. The use of the fourthdimension for array design has a long history dating back to thepioneering work by Shanks and Bickmore in the late 1950s [14].They proposed to use a set of radio-frequency (RF) switches tomodulate one or more antenna parameters (e.g., element exci-tations, aperture size, etc.) through periodic time sequences toobtain radiation characteristics which cannot be easily achievedby conventional phased arrays. Afterwards, Kummer et al. [15]gave a more detailed treatment of the effects of time-modula-tion on the received/transmitted signals and proposed an ex-perimental prototype to obtain an ultra-low sidelobe antenna.In [15], the slots of an eight-element linear array have been pro-gressively switched-off starting from the tails of the array whilemaintaining only the two central elements always active to en-force an average tapering in the time domain for sidelobe re-duction. Ever since then, a lot of effort has been made in theresearch community to use time-domain parameters to designantennas with enhanced performance [16]. This research topichas then received a great boost with the introduction of effectiveoptimization strategies, the computational resources allowed bymodern computers as well as the demand of highly reconfig-urable antennas with simplified control. Accordingly, severaldesign problems have been effectively addressed and innovativesolutions have been proposed based on the use of time-modula-tion in 4-D arrays [17][20].In 4-D arrays, because of the introduction of the periodic time

modulation, multiple harmonic signals are generated [21]. In thepast, most researches have been focused on synthesizing a de-sired pattern shape at the antenna central frequency and simul-taneously minimizing the power in the harmonics [22][25]. Asa matter of fact, these power losses unavoidably reduce the an-tenna directivity [15], [26] since they have to be filtered out to

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ROCCA et al.: 4-D ARRAYS AS ENABLING TECHNOLOGY FOR CR SYSTEMS 1103

correctly receive the desired signal. More recently, the researchinterest in time-modulated 4-D arrays has been redirected to-wards making use of these harmonic radiations. The synthesisof simultaneous and multiple harmonic beams for applicationslike direction finding and beam steering has been already inves-tigated [27][30] to improve the reliability of the communica-tion system. Indeed, the individual harmonic patterns, each as-sociated with a characteristic frequency, can be utilized as inde-pendent information channels [14], [16] whichmay be separatedat the receiver and each one utilized in a conventional manner.This key feature of 4-D arrays enables their use for simulta-neous operations and potentially to harvest multiple replicasof a signal thus leading to their applications in multiple-inputmultiple-output (MIMO) systems as preliminary investigatedin [31], [32]. The same antenna structure can also be used to re-ceive multiple independent signals which carry different infor-mation. As amatter of fact, it is widely recognized that the use ofMIMO antennas can be profitably adopted to increase both thespectral and spatial efficiency of wireless communications [33]as well as the system throughput as requested in CR systems.Unlike conventional MIMO, an innovative approach to the de-sign of 4-D arrays able to generate multiple and simultaneousharmonic beam patterns pointing towards different directions ispresented in order to exploit the angular diversity. More specif-ically, the parameters controlling the on-off behavior of the RFswitches in the 4-D array are properly optimized by means of aglobal evolutionary technique to direct the harmonic beams to-wards the directions of arrival (DoAs) of the signal arriving onthe antenna. Unlike [30] where the objective was only to syn-thesize desired harmonic beam shapes, in the present paper theoptimization approach is aimed to directly enhance the qualityof the received signal and suppress potential interferences to-gether with the background noise such to improve the overallsystem capacity and reliability.On the basis of the same modulation principles used in 4-D

arrays to generate multiple harmonic beams, it is possible to ob-serve that, when the antenna is used in the transmitting mode,the frequency spectrum distributions of the transmitted signalsin different directions are different. It means that the radiatedsignal, which is produced at the antenna level by time-modula-tion, is direction-dependent and can be regarded as a kind of di-rectional modulation technique that can be exploited for securecommunication purposes [34], [35]. Therefore, unlike conven-tional 4-D arrays where the center frequency and sideband sig-nals are usually separated from each other to avoid the aliasingeffects (i.e., overlapping of themodulated signal spectrum) [21],the aliasing effects are utilized, for the first time to the best of theauthors knowledge, for the purpose of distorting the radiatedsignals in some directions where sideband signals exist. Thisallows to implement a secure communication system with 4-Darrays [36], useful for CR applications.In this paper, 4-D arrays are presented as an enabling tech-

nology for the realization of the CR at the physical layer. Theuse of 4-D arrays as MIMO antennas as well as systems imple-menting secure communications are presented and discussed.The remainder of the paper is organized as follows. The basicmathematical formulation of 4-D arrays is given in Section II.Then, the description of the design and use of 4-D arrays assystems able to simultaneously receive multiple signals thus

Fig. 1. Sketch of the (a) receiving and (b) transmitting 4-D linear arraystructure.

enabling MIMO applications (Section III-A) as well as securecommunications (Section III-B) is reported where a set of repre-sentative examples are shown and discussed. Eventually, someconclusions are drawn in Section IV.

II. MATHEMATICAL FORMULATION

Let us consider a 4-D linear array made of isotropic ra-diators uniformly spaced of along the array axis as shown inFig. 1. The corresponding array factor, with the term ex-plicitly included [15], is mathematically expressed as

(1)


Fig. 2. Example of pulse controlling one RF switch and available control pa-rameters in the time-domain: switch-on instant and pulse duration .

where is the antenna central frequency,is the set of static phase weights, is the free-space wave-number, being the speed of light in vacuum, andis the observation angle. Moreover,

is the set of periodic pulses of perioddescribing the onoff behavior of the RF switches (Fig. 2) andused for the time-modulation of the static excitation weights.By virtue of the periodicity of the pulse sequence,

can be expanded in terms of the corresponding Fourier serieswhere and the

Fourier coefficients

(2)

are descriptive of the harmonic content of the modu-lating sequence. In (2), and

are the normalized (with respect to) switch-on instants and pulse durations (Fig. 2). Assuming

[15], [21], where , the array factor (1) atthe th harmonic can be written as

(3)

which is shifted by with respect to the carrier frequency .Accordingly, the contribution at the antenna central frequency

is

(4)

and the so-called sideband radiation (SR ), namely thesummation of all harmonic terms without the one at , turnsout being [21]

(5)

Fig. 3. Multiple Harmonic BeamformingSketch of the reference scenarioand expected antenna behavior.

In (2), it is easy to prove that for the correspondingFourier coefficients are only real and equal to the duration of themodulation pulses (i.e., .Although ideal rectangular pulses are considered in this work,the use of real RF switches with non-null transition between theon and off state and the impact on the radiation features has beeninvestigated [37].

III. CR APPLICATIONS USING 4-D ARRAYS

In this section, two innovative examples of use of 4-D arraysfor future communication systems are presented and discussed.In the first example, the synthesis of the pulse sequence control-ling the RF switches is performed by means of a Particle SwarmOptimizer (PSO) [38] to generate multiple harmonic beams ableto simultaneously receive multiple signals arriving on the an-tenna from different directions. Towards this aim and in order toindependently receive a signal on each harmonic channel gener-ated by the receiving 4-D array [Fig. 1(a)], each harmonic beamhas to be optimized such to have a maximum towards the DoAof one arriving signal and deep sidelobes or nulls along the di-rections of other signals. The second example is instead devotedto show how 4-D arrays can provide secure communications atthe physical layer. Unlike the previous example, the pulse con-figuration is analytically determined in this case and the 4-Darray is used in the transmitting mode [Fig. 1(b)].

A. Multiple Harmonic Beam Reconfiguration

1) Basic Idea of the MIMO Receiver Using 4-D Arrays: Letus consider the 4-D array used as a receiver [Fig. 1(a)] and sup-pose that a set of narrowband plane waveswith carrier frequency impinges on the array from direc-tions (Fig. 3). In order to simultaneously re-ceive the signals arriving on the antenna, the first terms in(3) of lower order, namely having small values,1 are con-sidered to create different harmonic beams. Towards this aimand in order to minimize the mutual interferences, the avail-able DoFs, namely the sets of time domain parameters and1The lower order terms are used since they are characterized by the higher

power content. As a matter of fact, the amplitude of the Fourier coefficientsdecreases as the absolute value of increases (2).


, and the phase weights , are properly optimized such that foreach th signal, the corresponding th harmonic pattern is max-imum in the signal direction (i.e., )and minimum along the DoAs of all other signals (i.e.,

). Hence, it is pos-sible to distinguish the different signals [39] after the filteringprocess [Fig. 1(a)] and to improve the quality of the communi-cation and the system throughput. Accordingly, a signal-to-in-terference-plus-noise ratio (SINR) term to be maximized is as-sociated to each harmonic channel. For example, supposing thatthe th harmonic is assigned to the reception of the th signal,all other signals are considered as unde-sired. Consequently, the problem can be cast to the simultane-ously optimization of the SINR on harmonics generated bythe receiving 4-D array.It is important to point out that, although the signals are sup-

posed to be monochromatic [15], they can be characterized bya maximum base-band angular frequency [i.e., the signalcan vary in time: ] until the condition issatisfied. In such a case, the aliasing is avoided and the orig-inal signal can be correctly recovered [21] by using an antennastructure as shown in Fig. 1(a).Since the SINR is a quantity that can not be directly measured

at the receiver because is not possible to distinguish the powergathered from the individual signals, the following functional isconsidered in the optimization process [40]

(6)

where , and and are the total powerreceived on the th harmonic channel and the background noisepower, respectively. The value of (6) can be computed for a trialonce is known. It is also important to observe that the reasonof choosing (6) is related to the fact that the configuration ofunknown parameters providing its maximum value is the samethat maximizes the SINR [40]. In order to maximize (6) for theharmonics, the following strategy has been implemented. Step 0Problem Setup: For a known scenario and agiven array structure, the number of signals arriving onthe antenna as well as their DoAs aresupposed estimated or a priori determined.

Step 1PSO InitializationAt the beginning of the op-timization, the particles of the swarm are randomly gener-ated. However, the values and , for at least one particleof the swarm, can be analytically set to steer the beam at

in the direction of one signal and the beam atin the direction of another signal since the DoAs of the ar-riving signals are known. This allows to improve the effi-ciency of the approach and enables the antenna to quicklyreconfigure also in time varying scenarios. Accordingly,the maximum of is oriented along by choosing

. In addition, thevalues of the switch-on instants are setto

(7)

Fig. 4. Multiple Harmonic BeamformingFitness Function Definition Ex-pected radiation performances and representation of the constraints adopted inthe fitness function.

to steer the th harmonic beam towards , where mod isthe modulo operation and . It can be shown thatthere is a strict relationship between the directions of thepeaks of symmetric harmonic beams (see the Appendix).Hence, there is a limit in the capability of independentlycontrolling and steering multiple harmonic beams. More-over, since only two harmonic beams can be a priori di-rected along desired directions and the analytically definedsolution is not optimal in terms of SINR, the following op-timization is performed.

Step 2Pulse Sequence Optimization: The main ob-jective of the synthesis is the maximization of the SINRin each harmonic channel through the maximization ofterms like (6), . Moreover, two addi-tional constraints have been imposed (Fig. 4) in the designproblem with the aim of reducing the sidelobe levels andof increasing the strength of each harmonic beam in the di-rection of the corresponding signal. Accordingly, the fol-lowing term to be minimized has been introduced

(8)

where is the reference level of the side-lobes for the th space factor,

,being , and theangular region of the beam directed along the th signal.Moreover, is the Heaviside function and is the PSOiteration index. Together with (8), the following term (tobe minimized) has been also added

(9)

to generate harmonic beams with peak values close asmuch as possible thus uniforming the antenna sensitivity at


the different harmonics. Accordingly, the total functionalto be maximized in the PSO-based optimization turns outbeing

(10)

where , and are real weighting coefficients.2) Numerical Results: To validate the proposed approach,

the results from a set of numerical simulations are reported in thefollowing. In all test cases, the signals arriving on the antennaare assumed being replicas of the same signal, having uniformstrength and carrier frequency , andmodulation according to abinary phase-shift keying (BPSK) strategy. The receiving arrayis composed of elements and . Moreover,the environmental background noise is modeled as an additivewhite Gaussian noise (AWGN) with uncorrelated contributionsat each element of the array and dB with respectto the strength of the impinging signals. To quantify the effec-tiveness of the achieved results, the bit error rate obtained withthe proposed approach is computed and compared with that ofa 4-D array aimed at receiving a single replica where all SR arefiltered out.In the first experiment, a scenario with signals is taken

into account with DoAs equal to and .According to the proposed strategy, the harmonic isdedicated to receive signal and the first positive harmonic

is instead used for the reception of signal . In theoptimization, the target level of the sidelobes has been set to

dB, and uniform weighting coeffi-cients (i.e., ) have been considered in (10).The particle of the swarm which is analytically defined has

since andset according to (7). Moreover, the pulse durations have beenchosen equal to [Fig. 5(a)] since in thiscase the Fourier coefficients for are zero (2) (i.e.,

). The power of the harmonic patterns atand for the analytical solution are reported in Fig. 5(b).In this case, the depths of the sidelobes at the carrier frequency

along and at the first harmonic along areequal to 27.2 dB and dB, respectively (Table I). Theresulting SINR turns out being equal to dBand dB.The PSO-based procedure has been then used by considering

a swarm of 40 particles, cognitive and social acceleration co-efficients set to , and inertial weight coefficientto [41]. The termination criterion is based on a max-imum number of iterations (set to ) or on a sta-tionary condition on the best fitness value [38]. The pulse se-quence and the corresponding beam patterns for the best solu-tion achieved at the end of the optimization process are shown inFigs. 6(a) and (b), respectively. As can be observed in Fig. 6(b),deeper nulls with respect to those achieved for the analyticalsolution [Fig. 5(b)] have been synthesized. More precisely, thelevel of the sidelobes has been reduced to 38.6 dB

Fig. 5. Multiple Harmonic BeamformingTwo Signals, Static Scenario)Plot of (a) the pulse

sequence analytically defined at the initialization of the PSO-based optimiza-tion and (b) corresponding power patterns generated at the central frequency

and at the fundamental frequency .

TABLE IMULTIPLE HARMONIC BEAMFORMINGTWO SIGNALS, STATIC SCENARIO

)PATTERN FEATURES

and 52.1 dB as reported in Table I. This means animprovement of more than 10 dB and 20 dB, respectively, alongthe DoAs of the undesired signals. The values of the SINR forthe best solution of the swarm throughout the PSO optimizationis shown in Fig. 7(a) while Fig. 7(b) reports the evolution of thefitness function and of each term of (10). As shown in Fig. 7(a),the values dB and dBare achieved at the end of the optimization step. The improve-ments with respect to the performance obtained with the analyt-ical solution are non-negligible.


Fig. 6. Multiple Harmonic BeamformingTwo Signals, Static ScenarioPlot of (a) the pulse sequence and of

(b) the corresponding power patterns generated at the central frequencyand at the fundamental frequency for the best solution achieved at theend of the PSO-based optimization.

In order to quantify such improvement, let us consider thefollowing definition of bit error rate [42]

(11)

where the signals are affected by an independently distributedRayleigh flat-fading channel gains that are supposed estimatedat the receiver, and being theaverage signal to noise ratio. Fig. 8 shows the values of the BERversus the for a BPSK communication scheme in the idealconditions (i.e., AWGN channel) as compared to that achievablein a Rayleigh flat-fading channel when replicas of the signalare received and combined by means of a maximum ratio di-versity combiner (MRC). By referring to Fig. 8 and supposing

, since the undesired signals can be consideredhaving a marginal contribution after the optimization step, theBER turns to be with an improvementof a factor with respect to the single channel case

Fig. 7. Multiple Harmonic BeamformingTwo Signals, Static ScenarioPlot of (a) the SINR behavior

on each harmonic channel at the receiver for the best solution synthesized bymeans of the PSO at each iteration of the optimization process and (b) values ofthe corresponding fitness function.

when all the available DoFs are ex-ploited for the optimization of a single harmonic . Thisresult clearly highlights the advantages offered by the smart useof the angular diversity enabled by 4-D arrays.In order to show the effectiveness of the approach when

dealing with time varying scenarios and DoAs, in the secondexperiment the direction of arrival of signal changes ateach time-interval ) in the range

with being the main lobe regionof dedicated to receive signal . The DoA of is sup-posed fixed to . In the simulation,different scenarios have been taken into account. The DoAs

are shown in Fig. 9(a). Fig. 9(b) shows therunning mean value of the SINR achieved for the two signalson the harmonic channel and at the receiver whenconsidering a average moving window. For the sakeof completeness, the statistics of the SINR values among all thetime varying scenarios is reported in Table II. It is worth notingthat the SINR is always kept above 21 dB. In addition, the lowstandard deviation dBTable II) implies that


Fig. 8. Multiple Harmonic BeamformingBehavior of the BER versus SNRfor a Rayleigh fading channel [33] when considering signals arrivingon the antenna characterized by a BPSK modulation and for the ideal AWGNchannel.

the majority of the results is concentrated around the averagedB and dB) which

are close to the maximum value (dB and dB). In

terms of BER, the improvement is comparable to that achievedin the previous case ( versus

). In the simulations, the averagecomputational burden is lower than one second when usinga standard processing unit (i.e., 2.4 GHz PC with 2 GB ofRAM) and a non-optimized code. Of course, the reconfigura-tion time can be further reduced by using dedicated hardwareprogrammable devices as well as considering improved opti-mization techniques exploiting a memory mechanism about thepreviously addressed scenarios [43].In the next example, a more challenging scenario is consid-

ered with . By virtue of the fact that only two beamscan be analytically steered towards desired DoAs, two differentexamples are considered in the following. In one case, alsothe third harmonic beam obtained with the analytical solutionhas peak value in the direction of the third incident signal[Fig. 10(a)]. Differently, in the other case the peak of one har-monic pattern is not already in the direction of one impingingsignal [Fig. 10(b)]. The actual DoAs are ,and [Fig. 10(a)] and , and

[Fig. 10(b)]. The corresponding pulse sequencesare given in Figs. 10(c) and (d), respectively, and

. The switch-on instants and the pulse durationsare then optimized and the best solution achieved at the end

of the PSO-based optimization are shown in Fig. 11.It is noticeable the improvement achieved in Fig. 11(a) with

respect to the analytical solution [Fig. 10(a)] as confirmed bythe indexes reported in Table III. As a matter of fact, the depthof the nulls has been reduced on average of more than 17 dB.Moreover, all dB, and the dif-ference between the peaks is lower than 1 dB. The optimizedSINR for all the harmonic channels converges in this case toalmost 31 dB as shown in Fig. 12(a). In the other case, it issimple to observe in Fig. 11(b) how the peak of the beam in

Fig. 9. Multiple Harmonic BeamformingTwo Signals, Time-Varying Sce-nario Graph of(a) the distribution of the DoA of the signal as a function of the temporalsnapshot and (b) running average of the resulting SINR for the two harmonicchannels used at the receiver ( ).

TABLE IIMULTIPLE HARMONIC BEAMFORMINGTWO SIGNALS, TIME-VARYING

SCENARIO STATISTICSOF THE SINR ACHIEVED AT THE END OF EACH ANTENNA

RECONFIGURATION BY MEANS OF THE PSO-BASED OPTIMIZATIONFOR DIFFERENT SCENARIOS

the direction is increased with respect to the resultof Fig. 10(b) thus determining an important improvement of thecorresponding SINR as shown in Fig. 12(b). In terms of BER,it reduces from to

[Fig. 11(a)] and [Fig. 11(c)]. Inthis example, the reduction of the BER due to the exploitationof the angular diversity offered by the harmonic beams furtherhighlights the effectiveness of 4-D arrays for multiple signal re-ception and the development of MIMO receivers exploiting an-gular diversity.


Fig. 10. Multiple Harmonic BeamformingThree Signals, Static Scenario Plot of (a) (b) the power patterns generated at the centralfrequency ) and at the two first harmonics through the (c) (d) pulse sequence analytically defined at the initialization of the PSO-basedoptimization when the DoAs are (a) (c) and (b) (d) .

Finally and unlike the previous experiments, the impact of awrong estimation of the signal DoAs and of the number of sig-nals is assessed in order to evaluate the practical robustnessof the proposed approach. In order to analyze the effects whenerrors on the signal DoAs are present, the optimized solution ofFig. 6 is taken into account and it is supposed that the directionof signal has not been correctly estimated. Accordingly, itis expected to receive the signal from but the actualDoA is different. The behavior of the SINR of the two harmonicchannels versus the DoA estimation error is given in Fig. 13. Itis possible to observe that the value of decreasesalmost symmetrically with respect to the estimation error dueto the presence of the mainlobe of [Fig. 6(b)]. More-over, also the values of reduce because of the nullis no more located in along the direction of signal. Nevertheless, the average SINR is still high

dB and dB) because low sidelobeshave been obtained on the harmonic patterns thanks to the PSO-based optimization. The last experiment is devoted to analyzethe robustness of the approach when an additional replica ofthe signal is present in the scenario but it was not previouslydetected. In this case, the optimized solutions of Figs. 11(a)and (b) are taken into account. Fig. 14 shows the behavior ofthe SINR for the three harmonic channel whenthe DoA of the fourth signal varies among the whole angularrange. As expected, a strong reduction of the SINR performance

is obtained when the unexpected signal enters the mainlobeof each harmonic channel. However, the average SINR valuesachieved in Fig. 14(a) dB,

dB, and dB) are higher than those ofFig. 14(b) dB, dB,and dB) since the optimized solution ofFig. 11(a) has lower sidelobes than those achieved in Fig. 11(b).In a similar fashion, the performance of the 4-D array can be af-fected by the non-calibration or calibration error of the antennacontrol points since the maximization of (10) depends on thearray factor. To cope with such problems, more complex arraymodels or compensation method can be considered as that pro-posed in [44] where the problem of the mutual coupling betweenthe array elements has been effectively addressed.

B. Secure Communications

1) Basic Idea for Secure Communication Using 4-D Arrays:One characteristic of cognitive radio is to provide secure andreliable communication using spread spectrum modulation andencryption techniques [45]. However, it is still possible in theoryfor a receiver at an undesired direction to eavesdrop the infor-mation. To avoid this drawback, techniques based on the useof variable directional antenna (e.g., electrically steerable para-sitic array radiatorESPAR) and channel estimation for secret


Fig. 11. Multiple Harmonic BeamformingThree Signals, Static Scenario Plot of (a) (b) the power patterns generated at the centralfrequency and at the two first harmonics through the (c) (d) pulse sequence of the best solution achieved at the end of the PSO-basedoptimization when the DoAs are (a) (c) and (b) (d) .

key generation [46] and near-field antenna modulation strate-gies have been presented [47]. More recently, directional mod-ulation techniques have been proposed to provide secure com-munication link [11][13], [34], [35]. They have a common ca-pability that they can transmit a direction-modulated signal andprevent eavesdroppers from properly demodulating the signalsradiated through the sidelobes of the antenna. In this framework,time modulation technique in 4-D arrays can be regarded asanother directional modulation technique. The frequency spec-trum distributions of the signals transmitted by 4-D arrays in dif-ferent directions are usually different from each other. It meansthat the radiated signal, which is produced at the antenna levelby time modulation, is direction-dependent and will be an ad-vantage for secure communication.In previous studies on signal-processing of 4-D arrays, the

center frequency and sideband signals are usually separatedfrom each other to avoid the aliasing effects (overlapping of themodulated signal spectrum) [21]. Thus, the signal bandwidthis usually set less than the time modulation frequency

such that the original signal can be recovered using a band-passfilter, whose bandwidth is a little greater than and less than, as shown in Fig. 15(a). In secure communications based

on 4-D arrays, the aliasing effects are utilized for the purposeof distorting the radiated signals in some directions wheresideband signals exist. Accordingly, suppose that a signal witha bandwidth is to be transmitted by the 4-D

array [Fig. 1(b)]. If the radiated signal in a specific directionof the array is not time-modulated, the frequency spectrumof the signal is the same as that of original signal. However,the radiated signals in other sidelobe directions have distortedfrequency spectrum, as shown in Fig. 15(b). Obviously, thesignals cannot be recovered fully by using any bandwidth filter,and their time-domain waveforms will become distorted. As anexample, a broadside 4-D array of isotropic elementswith at the operating frequency is considered.The array is excited with uniform amplitude and phase, oper-ating as a transmitting antenna. The time modulation periodof the array is supposed to be , implying a time modulationfrequency . In [48], a 4-D array with constantinstantaneous directivity has been obtained by switching-on anelement while switching-off another element. Following themethod, a typical time modulation function is designedin this paper, given as

others

others

(12)


Fig. 12. Multiple Harmonic BeamformingThree Signals, Static ScenarioPlot of the SINR behavior on each harmonic

channel at the receiver for the best solution synthesized by means of thePSO at each iteration of the optimization process when the DoAs are (a) (c)

and (b) (d) .

The radiation patterns of the 4-D array at the center frequencyas well as the first two harmonics are shown in Fig. 16. It is seenthat a null of sideband patterns appears at broadside ,implying that the signal at this angle is not modulated (no side-band signals). However, the transmitted signals in the other di-rections except for nulls are time-modulated. Since there are sixactive elements all the time, the array has a constant instan-taneous directivity of 7.78 dB (i.e., ). Accordingto Fig. 16, the sideband signals exist in any direction exceptfor the broadside and nulls. It can be anticipated in theory thatthe transmitted signal in any direction except for the broadsidewill be distorted. Thus, this characteristic is suitable for securecommunication.2) Numerical Results Based on AM Signal Transmission: To

validate the proposed approach, the amplitudemodulation (AM)signal transmission through the 4-D array is studied. The expres-sion of a double-sideband AM signal can be modeled as

(13)

Fig. 13. Multiple Harmonic BeamformingTwo Signals, Static ScenarioPlot of the SINR behavior

on the two harmonic channels related to the power patterns ofFig. 6(b) when errors are committed on the DoA estimation of signal .

where represents the amplitude modulation frequency. Afterthe AM signal is fed into the 4-D array, it will be time-modulatedin a periodic manner and then transmitted. As the 4-D arrayis excited with uniform amplitude and phase, the transmittedsignal can be simply expressed as [49]

(14)

In the numerical simulation, it is assumed that kHz,GHz. The time-modulation frequency is set as

kHz, which is less than the AM signal bandwidth (kHz). The signal-to-noise ratio at broadside is set

as 20 dB, which is high enough that the noise can hardly af-fect the waveforms of the transmitted signals at 0 , 25 , and60 . Fig. 17 illustrates the simulated frequency spectrum forthe original signal and transmitted signals at 0 and 60 . It isobserved in Figs. 17(a) and (b) that the shape of the simulatedspectrum at broadside (i.e., 0 ) is the same as that of the orig-inal AM signal, implying that the radiated signal at broadside isnot time-modulated and correct. However, the spectrum for thesignal at 60 becomes overlapped due to time modulation, asshown in Fig. 17(c). Even if a band-pass filter with a bandwidthis used to filter out the unwanted sideband signals, the filtered

spectrum shown in Fig. 17(d) is still distorted as compared tothat of the original signal. It should be noted that if ,the spectrum will be overlapped as long as there are sidebandsignals caused by time modulation.To observe the transmitted signals directly, the time-domain

waveforms of the transmitted signals are also simulated. Fig. 18illustrates the waveform of the original AM signal [Fig. 18(a)]as well as that of the transmitted signals at 0 [Fig. 18(b)], 25[Fig. 18(c)], and 60 [Fig. 18(e)]. As can be seen, the signalenvelope shown in Fig. 18(b) is almost the same as that inFig. 18(a). This means that the signal transmitted at 0 (broad-side) is correct. At the same time, the waveforms of transmittedsignals at 25 and 60 have been time-modulated and becomedistorted due to the spectrum aliasing effects. Even if theyare filtered, the waveforms still can not be fully recovered, as


TABLE IIIMULTIPLE HARMONIC BEAMFORMINGTHREE SIGNALS, STATIC SCENARIO AND

PATTERN FEATURES

Fig. 14. Multiple Harmonic BeamformingThree Signals, Static ScenarioPlot of the SINR behavior at the central frequency

and at the two first harmonics related to the power patternsof (a) Fig. 11(a) and (b) Fig. 11(b) when an additional signal arrived on the 4-Darray with direction .

Fig. 15. Secure CommunicationsFrequency spectrum of the transmitted sig-nals in 4-D arrays when (a) and (b) .

shown in Fig. 18(d) and (f). This is a consequence of the factthat the center frequency and sideband signals are overlappedtogether and cannot be separated from each other.In order to quantify how secure the proposed directional mod-

ulation technique is the distortion level of the time-modulatedAM signal is analyzed by computing the similarity factor (SF)[50] defined as

(15)

where is the original AM signal and is thetime-modulated signal that has been received after the filtering


Fig. 16. Secure Communications Power patternsgenerated at the central frequency and at the two first harmonics

.

Fig. 17. Secure Communications Frequency spec-trum of (a) the original AM signal and transmitted signals from the 4-D array at(b) 0 and (c) (d) 60 .

as a function of the azimuthal angle . Fig. 19 shows the be-havior of when the signal in Fig. 18(a) is radiated by the4-D array. It is possible to observe that the values of the sim-ilarity factor drastically decrease outside the mainlobe regionwhen kHz. Accordingly, the signal turns out beingseverely distorted. Differently, when the Nyquist condition isrespected (i.e., kHz), the aliasing effect is avoidedand the time-modulated signal can be correctly demodulated inall directions since .

IV. CONCLUSION

The suitability of 4-D arrays as enabling technology for theantenna front-end of CR systems has been discussed in thispaper. Towards this aim, two innovative applications of 4-D

Fig. 18. Secure Communications Simulated AMsignal waveform: (a) original AM signal; transmitted AM signal at (b) 0(c) 25 (e) 60 ; filtered AM signal at (d) 25 and (f) 60 .

Fig. 19. Secure Communications Simulated simi-larity factor versus azimuth angle when (i.e., kHz)and (i.e., kHz).

arrays have been presented and assessed. It has been shownthat a proper definition of the pulse sequence controlling theon-off behavior of the RF switches enables the possibility


i) to simultaneously receive multiple signals impinging on theantenna from different directions such to increase the wirelesssystem throughput and ii) to modulate the signal in order totransmit the correct information in a desired direction and makethe signal unintelligible for eavesdroppers receiving the signalin other directions. The DoFs available in the time domain havebeen set by using either a PSO-based optimization algorithmor have been analytically determined. The reported resultshave shown the effectiveness of the proposed approaches, thusdemonstrating that 4-D arrays based on time modulation can beconsidered for CR applications.More specifically, the analysis has pointed out the following

features of the proposed technique: when dealing with the reception of two-signals ,the analytic initialization guarantee to start the optimiza-tion from a good starting point and to obtain high values ofSINR on each harmonic channel in an efficient way;

in case , whatever the directions of arrival of the twosignals, the antenna is able to reconfigure the modulationsequence and consequently the radiation diagram to guar-antee reliable communication links;

the degradation of the SINR that unavoidably occurs whenis balanced by the increased spatial diversity offered

by the antenna thus maintaining improved performance interms of BER as compared to the reception of a singlereplica;

as long as the transmitted signal bandwidth is much greaterthan the timemodulation frequency, the signals transmittedthrough the sidelobes are distorted due to aliasing effect,while the signal at broadside is correct. Consequently, asecure communication can be achieved by using the 4-Darrays.

APPENDIX

In the following, it will be demonstrated that when the beamsat the central frequency and at a superior harmonic

are directed along and , respectively, thedirection of the peak of the th harmonic beam is univocallydetermined. Towards this aim, let us start from the general def-inition of harmonic space factor

(16)

By substituting (2) into (16), it results that

(17)

which is maximum along for

(18)

Since and

to steer the maximum for and along and ,in case is considered (18), it follows that

(19)

After simple mathematical steps it turns out that

(20)

and therefore

(21)

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Paolo Rocca (M09SM13) received the M.S. de-gree (summa cum laude) in telecommunications en-gineering and the Ph.D. degree in information andcommunication technologies from the University ofTrento, Trento, Italy, in 2005 and 2008, respectively.He is currently an Assistant Professor in the De-

partment of Information Engineering and ComputerScience, University of Trento, and a member of theELEDIA Research Center. He is the author/coauthorof over 180 peer reviewed papers on internationaljournals and conferences. He has been a visiting stu-

dent at the Pennsylvania State University and at the University Mediterraneaof Reggio Calabria. His main interests are in the framework of antenna arraysynthesis and design, electromagnetic inverse scattering, and optimization tech-niques for electromagnetics.Dr. Rocca has been awarded from the IEEE Geoscience and Remote Sensing

Society and the Italy Sectionwith the best Ph.D. thesis award IEEE-GRSCentralItaly Chapter. He serves as an Associate Editor of the IEEE ANTENNAS ANDWIRELESS PROPAGATION LETTERS.

Quanjiang Zhu (S12) was born in Hubei Province,China, in 1987. He received the B.S. degree inelectronic engineering from the University of Elec-tronic Science and Technology of China (UESTC),Chengdu, in 2009, where he is currently workingtoward the Ph.D. degree.From March 2013 to August 2013, he was a Vis-

iting Ph.D. Student at the ELEDIA Research Centerof the University of Trento, Italy. His current researchinterests include antennas, antenna arrays, and arraysignal processing.

Mr. Zhu won an Intel Fellowship from Intel Products (Chengdu) Co., Ltd. anda Scholarship Award for Excellent Doctoral Student granted by the Ministry ofEducation in China in 2012.

Ephrem T. Bekele received the B.Sc. degree in elec-trical engineering from Bahir Dar University, BahirDar, Ethiopia, in 2007. He received the M.Sc. de-gree in telecommunications engineering from Uni-versity of Trento, Trento, Italy, in 2011. He is cur-rently a Ph.D. student at the ICT International Doc-toral School of Trento.He was an Assistant Lecturer at Bahir Dar Univer-

sity from 2007 to 2009. He is conducting researchin the ELEDIA Research Center. His main researchinterests are antenna arrays, electromagnetic inverse

scattering, and metamaterials optimization.


Shiwen Yang (M00SM04) was born in SichuanProvince, China, in 1967. He received the B.S. de-gree in electronic science and technology from EastChina Normal University, Shanghai, the M.S. degreein electromagnetics and microwave technology andthe Ph.D. degree in physical electronics from theUniversity of Electronic Science and Technology ofChina (UESTC), Chengdu, in 1989, 1992 and 1998,respectively.From 1994 to 1998, he was a Lecturer at the Insti-

tute of High Energy Electronics, UESTC. From 1998to 2001, he was a Research Fellow at the School of Electrical and Electronic En-gineering, Nanyang Technological University, Singapore. From 2002 to 2004,he was a Research Scientist with Temasek Laboratories, National University ofSingapore. He is currently a Full Professor at the School of Electronic Engi-neering, UESTC. His research interests include antennas, antennas arrays, op-timization techniques, and computational electromagnetics.

Andrea Massa (M96) received the laurea degreein electronic engineering and the Ph.D. degree inelectronics and computer science from the Uni-versity of Genoa, Genoa, Italy, in 1992 and 1996,respectively.From 1997 to 1999, he was an Assistant Professor

of electromagnetic fields in the Department ofBiophysical and Electronic Engineering, Universityof Genoa, teaching the university course of elec-tromagnetic fields 1. From 2001 to 2004, he wasan Associate Professor at the University of Trento.

Since 2005, he has been a Full Professor of electromagnetic fields at theUniversity of Trento, where he currently teaches electromagnetic fields, inversescattering techniques, antennas and wireless communications, and optimizationtechniques. Currently, he is the director of the ELEDIA Research Center at theUniversity of Trento. Moreover, he is Adjunct Professor at Pennsylvania StateUniversity, State College, PA, USA, and Visiting Professor at the MissouriUniversity of Science and Technology, Rolla, MO, USA, at the NagasakiUniversity, Nagasaki, Japan, at the University of Paris Sud, Paris, France, andat the Kumamoto University, Kumamoto, Japan.Prof. Massa is a member of the IEEE Society, of the PIERS Technical

Committee, of the Inter-University Research Center for Interactions BetweenElectromagnetic Fields and Biological Systems (ICEmB), and he has servedas Italian representative in the general assembly of the European MicrowaveAssociation (EuMA). His research work since 1992 has been principally onelectromagnetic direct and inverse scattering, microwave imaging, optimiza-tion techniques, wave propagation in presence of nonlinear media, wirelesscommunications and applications of electromagnetic fields to telecommuni-cations, medicine and biology. He serves as an Associate Editor of the IEEETRANSACTIONS ON ANTENNAS AND PROPAGATION.

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