Coexistence Analysis between Radar and Cellular System in LoS Channel
aa r X i v : . [ c s . N I] A p r Coexistence Analysis between Radar and CellularSystem in LoS Channel
Awais Khawar, Ahmed Abdelhadi, and T. Charles Clancy { awais, aabdelhadi, tcc } @vt.eduDepartment of Electrical and Computer Engineering, Virginia Tech, VA, USA Abstract —Sharing spectrum with incumbents such as radarsystems is an attractive solution for cellular operators in orderto meet the ever growing bandwidth requirements and ease thespectrum crunch problem. In order to realize efficient spectrumsharing, interference mitigation techniques are required. In thisletter we address techniques to mitigate MIMO radar interfer-ence at MIMO cellular base stations (BSs). We specifically lookat the amount of power received at BSs when radar uses nullspace projection (NSP)-based interference mitigation method.NSP reduces the amount of projected power at targets that arein-close vicinity to BSs. We study this issue and show that this canbe avoided if radar employs a larger transmit array. In addition,we compute the coherence time of channel between radar andBSs and show that the coherence time of channel is much largerthan the pulse repetition interval of radars. Therefore, NSP-basedinterference mitigation techniques which depends on accuratechannel state information (CSI) can be effective as the problemof CSI being outdated does not occur for most practical scenarios.
I. I
NTRODUCTION
The ubiquitous use of smart phones and tablets has re-sulted in tremendous growth in wireless data traffic. Currentspectrum allocations are making it hard for operators tosupport the growth in broadband demand. In order to solve thespectrum congestion problem innovative solutions have beenproposed that include design of spectrally efficient air-waves,bandwidth-rich millimeter wave communication systems, andsharing of spectrum across government agencies and com-mercial services. Spectrum sharing is a promising solution asit does not involve expensive and time consuming efforts torelocate incumbents for spectrum reallocation. A proposal toallow small cells to share the 3.5 GHz radar band is underconsideration by the Federal Communications Commission(FCC) [1]. This is a promising initiative but considerableresearch is required to address the interference concerns thatwill arise due to the co-channel spectrum sharing of radar andsmall cells.Opportunistic spectrum access schemes have been con-sidered in past to share spectrum with traditional rotatingradar systems [2], [3]. However, modern military ships areequipped with phased array radar systems that do not rotate.Furthermore, in near-future, these systems are to be replaced
This work was supported by DARPA under the SSPARC program. ContractAward Number: HR0011-14-C-0027. The views, opinions, and/or findingscontained in this article are those of the authors and should not be interpretedas representing the official views or policies of the Department of Defense orthe U.S. Government.Approved for Public Release, Distribution Unlimited by MIMO radars as they promise waveform diversity, tar-get localization, and interference mitigation capabilities thatare superior than phased array radar systems [4]. Therefore,in this paper we consider shipborne MIMO radar architec-ture, because of its potential near-future field deployment,for our coexistence analysis. Recently, beamforming [5] andwaveform-shaping [6] based schemes have been proposed tomitigate MIMO radar interference at communication system.In this letter, we focus on the waveform-shaping approach [6]that mitigates radar interference at communication systems byshaping radar waveform in a way that it falls in null spaceof channel between radar and communication system. NSP-based technique preserves radar mission objectives, with minordegradation [6], while allowing spectral coexistence and thusincreasing available spectrum for commercial communicationsystems without needing to relocate radars to new frequencybands.In this letter, we extend the previous work in [6] –which is limited to studying target detection performance ofspectrum sharing MIMO radars in Rayleigh channels – topower received at communication system, degradation in radartransmitted power, and calculation of coherence time of radar-communication system in LoS channels. The NSP techniquedepends on accurate CSI for effective interference mitigation.CSI is valid as long as radar’s pulse repetition interval (PRI) isshorter than the channel’s coherence time. CSI is acquired byradar by aiding communication systems in channel estimation,with the help of a low-power reference signal (see Sec II. I in[6]). These CSI estimates are fed back by the communicationsystem to radar. We compute the channel coherence time for aspectrum sharing scenario in which a moving seaborne radaris sharing spectrum with an onshore communication systemand show that PRI of many practical radars are much shorterthan the coherence time of the channel. Thus, NSP techniquescan be applied without any fear of CSI being outdated.The rest of this letter is organized as follows. Section IIbriefly presents MIMO radar architecture, spectrum sharingscenario, and LoS channel model. Section III provides adiscussion on interference power received at communicationsystems and loss in projected radar power at target. SectionIV computes the coherence time of channel and discusses anumerical example. Section V concludes the letter.I. S YSTEM M ODELS
In this section, we briefly introduce the fundamentals ofMIMO radar, LoS channel model, and spectrum sharing sce-nario between radar and communication systems.
A. MIMO Radar
We consider M antenna elements and denote samples ofbaseband equivalent transmitted waveform as { x ( n ) } Ln =1 . InMIMO radar literature orthogonal waveforms are shown tooutperform other waveforms [4], therefore, we design orthog-onal waveforms whose signal correlation matrix is R = 1 L L X n =1 x ( n ) x H ( n ) = I (1)where L is the total number of time samples and n is thetime index. The signal received from a single point target atan angle θ can be written as [4] y ( n ) = α A ( θ ) x ( n ) + w ( n ) (2)where α represents the complex path loss including thepropagation loss and the coefficient of reflection, w ( n ) is thewhite Gaussian noise, and A ( θ ) is the transmit-receive steeringmatrix defined as A ( θ ) , a ( θ ) a T ( θ ) . The transmit/receivesteering vector a ( θ ) is given as a ( θ ) , (cid:2) e − jω c τ t, ( θ ) e − jω c τ t, ( θ ) · · · e − jω c τ t,M ( θ ) (cid:3) T . (3) B. Spectral Coexistence Scenario
We consider a practical scenario where radar (incumbent)is operating in the 3550-3650 MHz band which FCC hasproposed to share with commercial cellular systems on aco-primary basis [1]. Thus, opportunistic spectrum accesstechniques proposed – for e.g., as in [2] – are no longer valid.For the prevailing cellular standard i.e., long term evolution(LTE), 3GPP has defined Band 22 for Frequency DivisionDuplex (FDD) LTE (Uplink:3410-3490 MHz/Downlink:3510-3590 MHz) and Bands 42 (3400-3600 MHz) and 43 (3600-3800 MHz) for Time Division Duplex (TDD). Since, FCC’sproposed frequency range is not fully aligned with the current3GPP band definition there is a need for a new 3GPP fre-quency band. So, we assume a FDD LTE deployment in whichuplink is in the 3550-3650 MHz band, or radar band, andBSs get interfered by radar operations. We device a schemefor interference mitigation from radar in the uplink. Notethat since downlink is assumed to be in a higher non-radarband there will be no interference to cellular users from radarsystems. Without loss of generality, we consider a single cellor a BS that receives the following signal on the uplink r = K X i =1 G i s i + Hx + n (4)where K is the number of users in the cell, G i is the channelgain between the BS and the i th user, H is the channelgain between the BS and the radar, x is the interfering signal from the MIMO radar, and n is the white Gaussiannoise component. The interfering signal x from radar can bemitigated by projecting radar waveform onto null space ofinterference channel such that Hx = , please see [6]–[19]and reference therein for a discussion on this approach. C. LoS Channel Model
We consider a spectrum sharing scenario between a ship-borne radar and a BS mounted on the top of a building or itssidewalls such that it has a LoS component with the radar. Thisis typical of littoral areas. Since littoral area is assumed, thearea is free of reflectors or scatterers or they are very weak ascompared to the LoS component and do not contribute towardsthe channel model. We model the LoS channel by assumingthe inter-element spacing between antennas at the BS is ∆ N and at radar is ∆ M , the channel matrix can be written as H = a √ N M exp (cid:18) − j π dλ c (cid:19) e N (Ω N ) e ∗ M (Ω M ) (5)where a is the attenuation along the line-of-sight path whichis assumed to be equal for all antenna pairs, d is the distancebetween radar transmit antenna 1 and BS receive antenna 1, λ c is the carrier wavelength, e N and e M are defined to be e l (Ω l ) = 1 √ l − j π ∆ l Ω l )exp ( − j π l Ω l ) ... exp ( − j π ( l −
1) ∆ l Ω l ) (6)where l = { N, M } , Ω M , cos φ M and Ω N , cos φ N are theangles of incidence of the line-of-sight path on the radar andBS antenna arrays, respectively.III. R ECEIVED P OWER A NALYSIS
In this section, we look at the amount of power receivedat BSs and the target. We are interested in knowing aboutthe power received at BSs and target for effective interferencemitigation and target detection purposes, respectively. The gainof the radar transmit array in a direction θ when the beam issteered digitally to a direction θ D is given by [4] G ( θ, θ D ) = Γ | a H ( θ ) R T a ( θ D ) | a H ( θ D ) R T a ( θ D ) (7)where Γ is the normalization constant. We are interested inplacing nulls or having minimum gain towards the directionof BSs, by using NSP-based interference mitigation scheme,and maximum gain in the direction of target. In the followingsections we cover both the scenarios in detail along withexamples. A. Power Received at Cellular System
In this section we study the received power at locationsnulled by radar system using null space projection algorithm.These nulled locations are occupied by cellular BSs and aresubject to interference protection from radar system. In Figure1 we show this scenario when the target is located at ◦ and
40 −30 −20 −10 0 10 20 30 40−200−180−160−140−120−100−80−60−40−200 θ (degree) P o w e r ( d B ) Orthogonal WaveformNSP Waveform
Fig. 1. Radar’s transmit beampattern. NSP-based interference mitigationscheme places accurate and deep nulls in the location of BSs ( ◦ to ◦ )for effective interference mitigation. BSs are located at an azimuth of ◦ to ◦ . Note that thereceived power at BS locations is much below the powerprojected at target and other azimuthal locations. The NSPplaces accurate and deep nulls at locations that are occupiedby cellular BSs. The received power level is much below thenoise floor of most practical BSs. For example, LTE eNodeB has a noise floor of -120 dBm (-150 dB) [20]. Thus, radarinterference can be effectively mitigated by using the proposedNSP-based algorithm. B. Reduction in Power Projected at Target
In this section, we evaluate the power reduction in the mainbeam due to NSP. As an example, we consider the case whereBSs are present at an azimuth angle of ◦ to ◦ and thetarget first appears at an azimuth angle of ◦ , with respectto (w.r.t.) radar. Thus, there is a angular separation of ◦ between the communication systems and the target. We furtherincrease this angular separation to ◦ , ◦ , ◦ , ◦ , ◦ , ◦ ,and ◦ and study reduction in mainlobe power. So thereduction in mainlobe power is presented as a function ofangular difference between the communication systems andthe target. Moreover, we analyze this power reduction byemploying M = 10 , , , and 100 antenna elements atMIMO radar while the antennas elements at communicationsystem are fixed at N = 5 . The results are reported in Figure2. It can be noted that for a small radar array and a targetimmediately next to the nulled zone, i.e when N = 10 andtarget is at ◦ relative to BSs, the loss in projected poweris much more severe than all the other cases. As the targetmoves away from the communication systems the loss inpower projected becomes smaller and smaller. Moreover, whenthe radar employs a larger antenna array, for example with 70or 100 elements, the power reduction in mainlobe, due to NSP,is negligible.IV. C OHERENCE T IME O F A S
HIPBORNE R ADAR
Null-space based projection scheme requires CSI estima-tion. However, it has not been investigated that for how longthe CSI is valid and after what time period the CSI becomes
12 5 10 15 20 30 5005101520 Target far from nulled ares ( θ ) P o w e r r edu c t i on ( d B ) M=10M=30M=50M=70M=100
Fig. 2. Power reduction in mainlobe due to NSP as a function of angularseparation between communication system and target. outdated. Specifically, knowledge about the coherence timeof the channel between shipborne radar and cellular systemis not available. In this letter, we investigate this issue andderive coherence time of channel between shipborne radarand stationary communication system. The movement of aship, and hence radar, is affected by factors such as windspeed, length of time the wind blows, distance of open waterover which the wind blows (i.e. fetch), see Table I; becausethese factors gives rise to waves which affect the motion ofa ship. Thus, this work is different from the classical workdone on finding coherence time of channel between BS andstatic/mobile user [21] in a way that in addition to ship’shorizontal motion (speed) we consider ship’s vertical motion(bob) induced by sea.Consider a ship-borne radar, as shown in Figure 3, movingwith a constant horizontal velocity v s to point a . Rough seasgive rise to waves that are steep, where steepness of a wave isthe ratio of wave height to the length of wave, which in turnintroduces bobbing velocity v bob . Assume the ship is movingat speed v R which is the resultant of v s and v bob . So, v R isgiven by, v R = v s cos ( θ ) + v bob cos (cid:16) π − θ (cid:17) (8)where θ = tan − ( v bob /v s ) and using values in Table I, v bob is given by v bob = 2 v s Height of waveLength of wave (9)At speed v R , the ship-borne radar moves along a path segment D while it illuminates its search space which also contains aremote communication system. The difference in path lengthtraveled by the waves between the two points along D to thecommunication system can be written as: ∆ l = D cos ( π − ϕ ) = v R ∆ t cos ( ϕ ) (10)where ∆ t is the time required for the ship to travel the pathsegment D . Since, the communication system is assumed tobe far away, φ is assumed to be the same at the two ends of D .The phase change of the signal received at the communication ig. 3. Coherence time analysis of a moving shipborne radar. system corresponding to this difference in path lengths istherefore ∆ α = 2 π ∆ lλ = 2 πv R ∆ tλ cos ( φ ) . (11)So, the apparent change in frequency, or Doppler shift, is givenby f d = 12 π · ∆ α ∆ t = v R λ cos ( φ ) . (12)Consequently, coherence time, which is the time domain dualof Doppler spread, is given by [21], T c = s πf m = 0 . λv R (13)where f m is the maximum Doppler shift. Example: Coherence time analysis of a moving ship-borneradar and a static BS –
In this example, we study therelationship between coherence time of channel and NSP andseek to answer the question about the applicability of NSP fora moving radar. Consider an AN/SPN-43C air traffic control(ATC) radar, used by navy in the 3.5 GHz band, with a pulserepetition rate (PRR) of 1000 Hz or pulse repetition interval(PRI) of 1 millisecond (ms) [22]. Such radars are mountedon ships that typically move with a top speed of 32 knots.Also consider radars that transmit fixed-frequency carrier wavepulse modulated waveform and swept-frequency carrier wavepulse modulated waveform. These are referred to as P0Nand Q3N, respectively, in the National Telecommunicationsand Information Administration (NTIA) report [20]. Usually,PRI, speed, and other parameters of a military radar or shipare confidential. Therefore, we use the sample informationprovided by NTIA in its assessment reports [20], [23]. Usingthis information the coherence time of channel is calculatedand shown in Figure 4 for various operating conditions byvarying ship’s speed and considering different values of windspeed, wave height, wave length, for a 200 nautical mile fetchof wave. These calculations are reported in Table I. It can beobserved that since the PRI of radar is much smaller than thecoherence time, therefore, NSP will be working perfectly evenwith a moving shipborne radar.
20 22 24 26 28 30 3200.511.522.533.54
Speed of seaborne radar (knots) T i m e ( m s ) Coherence time T c AN/SPN−43C ATC radar PRR = 1 KHzP0N−2 PRR = 3 KHzQ3N−3 PRR = 30 KHz
Fig. 4. The problem of CSI being outdated for the application of NSP doesnot occur as the coherence time of radar-BS channel is much larger than PRIof most practical radars. TABLE IV
ALUES OF v bob FOR VARIOUS OPERATING SPEEDS AND ENVIRONMENTALCONDITIONS . V. C
ONCLUSION
In this letter, we evaluated a spectrum sharing scenariobetween seaborne radar and an onshore cellular systems. Weshowed that the nulls placed in the direction of BSs resultedin received power well below the noise floor of commercialBSs thus mitigating radar interference. However, the interfer-ence mitigation scheme employed resulted in loss of radar’sprojected power at targets that were immediately next to BSlocations in the azimuth. We showed that this problem can becompensated by using a large radar antenna array. In addition,we showed that the coherence time of radar-BS channel waslarge enough for the application of NSP-based interferencemitigation scheme which relied on CSI estimation. Thus, theissue of CSI being outdated did not arise in the radar-cellularsystem spectrum sharing scenario.R
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