Spectrum Sharing Between Radar and Communication Systems Based on Overlapped Virtual Subarrays

In this paper, we propose a new technique for spectrum sharing between radar and communication systems. The new technique enjoys the advantages of null-space projecting which can be used to mitigate the interference between radar and communication systems. In order to reduce the number of radar antennas and reduce the requirement of manufacture, deployment, and implementation, we also introduce virtual subarray architecture to reap a more effective transmit array aperture. The essence is to partition the multiple-input multiple-output (MIMO) antenna array into multiple overlapped subarrays to reap a compromise between coherent gain and diversity gain. We show that the configuration with overlapped subarrays can be used to form narrower beams with lower sidelobes, which is good for reaping higher performance in target detection. In order to evaluate the impact on the performance of radar systems with the implementation of spectrum sharing, the generalized likelihood ratio test for target detection is derived. It is shown that, although the implementation of the proposed spectrum sharing method would lose the radar system’s target detection performance, we can reap the benefits of spectrum sharing. That is to say, we achieve a good tradeoff between spectrum sharing and target detecting.

Federal Communications Commission (FCC) has shown that 23 some frequency bands are heavily used by licensed systems in 24 The associate editor coordinating the review of this manuscript and approving it for publication was Olutayo O. Oyerinde . particular locations and at particular times, but that there are 25 also many frequency bands which are only partly occupied or 26 largely unoccupied [1]. So, it is an emergency to design new 27 paradigms to enhance the utilization of the radio frequency 28 spectrum. 29 In a conventional spectrum licensing scheme, spectrum 30 allocation is based on the command-and-control model, 31 where the radio spectrum allocated to license users is not 32 used, it cannot be utilized by unlicensed users and applica-33 tions [2]. It is this static and inflexible allocation that leads to 34 the problem of spectrum scarce problem. To solve the prob-35 lem, cognitive radio is introduced to reuse the underutilized 36 the spectrum resources for automotive radars to minimize 93 interference. Reference [20] provides a signal processing 94 perspective of mm-wave JRC systems with an emphasis on 95 waveform design. 96 Besides the above studies, another line of work resorts 97 to beamforming [21] and waveform-shaping [22] based 98 schemes to mitigate radar interference in the communication 99 system. In [22], the authors study the target detection per-100 formance of spectrum sharing multiple-input multiple-output 101 (MIMO) radars. However, the number of transmit antennas in 102 the radar system grows linearly with the number of users in 103 the communication system. The requirement of manufacture 104 and deployment for radar systems will become more rigorous 105 when the communication system has a large scale. 106 In this paper, we consider a coexistence scenario where 107 the MIMO radar system and communication system work at 108 the same time with the same frequency. We propose a null-109 space-based method to mitigate the interference caused by 110 radar systems to the communication system. Besides, with the 111 help of using virtual subarrays of overlapped-MIMO archi-112 tecture, we partition the MIMO antenna array into multiple 113 overlapped subarrays to increase diversity gain and reduce 114 the requirement of the number of antennas. In this work, 115 we analyze the problem of target detection when sharing radar 116 spectrum with cellular systems and show the advantages of 117 using overlapped MIMO to alleviate interference. We study 118 the performance of the considered method and show different 119 measurements to be taken when the number of the radar 120 antennas is different.

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The main contributions of this paper can be summarized as 122 follows:

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• We analyze the advantage of overlapped virtual subar-124 rays in restraining sidelobe and increasing diversity gain. 125 Based on that, we construct a spectrum-sharing archi-126 tecture between MIMO radar and the

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where T 0 is the radar pulse width, (·) H stands for the Hermi- where θ s is the target direction, β s is the complex-valued are the actual transmit and actual receive steering vectors 179 associated with the direction θ.

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Let s UE j (t) be the signal transmitted from the j th UE in the 181 i th cell. If there is no interference from the radar system, the 182 received signal at the i th BS receiver can be written as T channel between the j th UE 185 transmitter and the i th BS receiver. n(t) is the additive white 186 Gaussian noise with zero mean and variance σ 2 n .

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In this section, we describe the architecture of the spectrum 189 sharing problem, including the overlapped MIMO radar and 190 the spectrum sharing algorithm we used.

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A. OVERLAPPED MIMO RADAR 192 Considering that the overlapped MIMO architecture can 193 increase the effective number of transmitting arrays, 194 we implement it to reap more coherent processing gain and 195 overall suppressed sidelobes [23]. The key idea behind this 196 approach is to partition the transmit arrays into K subarrays 197 where 1 ≤ K ≤ M T , which are allowed to overlap. The 198 overlapped MIMO radar formulation is shown in Fig.2.   The signal reflected by a target located at the direction θ in 215 the far field can be expressed as where a k (θ ) is the steering vector of the k th subarray, and 218 τ k (θ) is the time required for the wave to travel from the first 219 element to the k th element.

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The received complex vector of the array observation can 221 be written as 222

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where D is the number of interfering signals.

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By matched-filtering x(t) to each of the waveforms, we can 225 obtain the virtual data vector as [23] 226 230 and the diversity vector

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In the case of non-adaptive beamforming, the correspond-233 ing beamformer weight vectors are given as At the receive array, the receive beamformer weight vector 236 is given by 238 Let G(θ) be the normalized overall beam pattern, that is

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For the case of a uniform linear array (ULA), we have Then, the beam pattern of the overlapped MIMO radar for 243 a ULA with overlapped partitioning of transmitting subarrays 244 can be expressed as In the spectrum sharing scenario, the radar system is sharing 249 N BS interference channels with the communication system. 250 The received signal at the i th BS receiver can be written as where the first part is the interference from the radar system 253 , and M is the number 254 of the transmit antennas, which is equal to M T or M κ = 255 (M T − K + 1)K for the traditional MIMO and the overlapped 256 MIMO architecture, respectively. s(t) is the transmitted com-257 plex vector of the array. The second part is the received 258 communication signal. The third part is the noise.

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In order to avoid interference to the i th BS, we map s(t) onto 260 the null-space of H N BS ×M i , then the first part of (18) will equal 261 0, and we will have (4) instead of (18). In this circumstance, 262 the two systems will coexist in the same spectrum. And the 263 aim of spectrum sharing will be achieved.

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In the traditional MIMO architecture, when M T is less than 265 N BS R , it is impossible to map the radar signal to the null-space 266 of the interference channel because there is no sufficient 267 degree of freedom (DoF). Whereas, with the advantage of 268 using overlapped architecture, we can reap more DoF to 269 mitigate interference to the communication system.

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Because the DoF available at the radar is associated with 271 the effective transmit array aperture. We consider two spec-272 trum sharing scenarios which are discussed as follows.
Consider a scenario in which the effective transmit array 275 aperture is very large as compared to the combined antenna 276 array of N BS BSs. In this scenario, the available DoF is 277 sufficient enough for the overlapped MIMO radar to simulta-278 neously mitigate interference to all the N BS BSs.

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The combined interference channel that the radar shares 280 with the communication system can be written as In order to implement spectrum sharing, we need to find 283 the projection matrix to project the radar signal onto the null 284 space of the combined interference channel H. 285 At first, based on the singular value decomposition (SVD) 286 theorem, we find SVD of H as of singular values, which can be written as 298 Based on that, we can define the projection matrix as

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The radar signal projected onto the null space of the inter-301 ference channel will become 302 s (t) = Ps(t).

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And the first part of (18) can be expressed as 304 It is obvious that the interference from the radar system is 308 eliminated, and the two systems coexist in the same spectrum.  The other N BS − 1 BSs in the communication system can 320 be moved to non-radar frequency bands to avoid interference 321 from the radar system through spectrum sensing and access 322 in cognitive radio techniques [25], [26], [27].

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If spectrum sharing is implemented with the i th BS, 324 we need to find the projection matrix to project the radar 325 signal onto the null space of the interference channel.

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At first, based on the singular value decomposition (SVD) 327 theorem, we find SVD of H i as   where l = min(N BS R , M κ ), in this case l = N BS R and σ i,1 > 333 σ i,2 > · · · > σ i,n > σ i,n+1 = σ i,n+2 = · · · = σ i,l = 0 are the 334 singular values. 335 Now, we define Based on that, we can define the projection matrix as The radar signal projected onto the null space of the inter-342 ference channel will become 343 s (t) = P i s(t).
(32) 344 VOLUME 10, 2022 It is obvious that the interference from the radar system is 349 eliminated, and the radar system coexists with the i th BS in 350 the same spectrum.

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In order to select the interference channel with the least 352 degradation of radar waveform, the projection matrix can be 353 set as

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In this paper, we project the radar signal onto the null space 359 of the interference channel to avoid interference to the com-  Then, the GLRT can be written as where f y (y, θ, β; H 1 ) and f y (y; H 0 ) are the probability density 393 functions of the received signal under hypotheses H 1 and H 0 , 394 respectively. δ is the threshold required for a decision between 395 the two hypotheses. Hence, the GLRT can be written as According to [29], [30], [31], the asymptotic statistic 398 of L(θ ML ) under the two hypotheses has the following 399 distribution where χ 2 2 and χ 2 2 (ρ) are central and non-central chi-square 402 distributions respectively, each with two degrees of freedom 403 and a non-centrality parameter of ρ for the latter one, which 404 is equal to Based on the distribution, the probability of false alarm can 407 be expressed as where (·) is the gamma function, (·, ·) is the incomplete 410 gamma function.

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Given the target false alarm probability P f , the thresholdδ 412 can be determined as where −1 (·, ·) denotes the inverse of the incomplete gamma 415 function.

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Then, the probability of detection can be given as where Q 2 (·, ·) is the generalized Marcum Q-function. In this case, the GLRT can be expressed as For the spectrum sharing scenario considered in this paper, 428 we have Therefore, the GLRT can be expressed as and the asymptotic statistics of L(θ ML ) in this case is

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In this section, in order to study the performance of the spec-   4 shows the overall beam pattern for the three different 466 radar formulations with the implementation of null-space 467 projecting. We can observe that, although the implementation 468 of projecting has reduced sidelobe suppression, the beam pat-469 tern of the overlapped MIMO radar still provides encouraging 470 suppression compared to the other two radars. Meanwhile, 471 we can reap the benefits of spectrum sharing because the 472 implementation of null-space projecting minimizes interfer-473 ence from the radar system to the communications system.

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In order to evaluate the detection performance of the 475 radar system with the implementation of spectrum sharing, 476 in Fig. 5, we consider the case when the effective transmit 477 array aperture of the overlapped MIMO radar is very large as 478 compared to the combined antenna array of N BS BSs. In this 479 VOLUME 10, 2022 FIGURE 6. Detection performance when the radar system simultaneously share spectrum with one of the 5 BSs in the case that the effective transmit array aperture of the overlapped MIMO radar is not large enough to simultaneously share spectrum with all the communication BSs but large enough to share spectrum with one of them. in order to get a desired P d for a fixed P f , we need more SNR 494 for spectrum sharing. For example, according to Fig. 5 (a), 495 with P f = 10 −3 , if we desire P d = 0.9, then we need 2 to 496 10 dB more gain in SNR for spectrum sharing when N BS R is 4, 497 6, 8, 10, and 12, respectively, to get the same result produced 498 by the orthogonal waveforms. According to Fig. 5 (b), with 499 P f = 10 −5 , if we desire P d = 0.9, then we need 3 to 11 dB 500 more gain in SNR for spectrum sharing when N BS R is 4, 6, 8, 501 10, and 12, respectively, to get the same result produced by 502 the orthogonal waveforms.

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In order to illustrate the necessity of selecting the best 504 sharing channel when the available DoF of the radar system 505 is not very large, in Fig. 6, we consider the case when the 506 effective transmit array aperture is not large enough to simul-507 taneously share spectrum with all the communication BSs 508 but large enough to share spectrum with one of them. In this 509 scenario, we assume a ULA with 8 antenna elements at the 510 transmitter. In overlapped radar, the number of the subarrays 511 is K = 3, and each subarray has 6 antenna elements. In a 512 communications system, there are N BS = 5 BSs, each BS 513 is equipped with N BS R = 8 receive antennas. It can be noted 514 R is satisfied. 515 In this case, the radar system tries to share the spectrum with 516 one of the BSs. And it is important to find the optimal BS 517 to minimize the degradation of radar waveform. In Fig. 6, 518 detection performance for orthogonal waveform signal and 519 five different spectrum sharing signals with the implemen-520 tation of null space projecting onto five different BSs is 521 illustrated, where the probability of. We can observe that, 522 with P f = 10 −3 , in order to achieve a detection probability of 523 90%, we need 6 dB to 9 dB more gain in SNR as compared 524 to the orthogonal waveform. With P f = 10 −5 , in order to 525 achieve a detection probability of 90%, we need 5 dB to 7 dB 526 more gain in SNR as compared to the orthogonal waveform. 527 Using the method shown in (35), we ''principle'' can select 528 the interference channel with the least degradation of radar 529 waveform. In this scenario, the first BS and the fourth BS 530 will be selected to coexist with the radar system when the 531 probability of false alarm is set as P f = 10 −3 , and P f = 10 −5 , 532 respectively.

534
In this paper, we considered a scenario where a MIMO 535 radar shares a spectrum with an LTE communication system. 536 A spectrum-sharing architecture was designed to realize the 537 coexistence of the two systems and mitigate the interference 538 between them. Based on null-space theory, we proposed to 539 project the radar signal to the null-space of the interference 540 channel, so as to avoid interference to the communication 541 system. Additionally, the virtual subarray architecture was 542 used to reap a more effective transmit array aperture. This 543 configuration increased diversity gain and formed narrower 544 beams. We enjoyed this advantage to ensure the performance 545 in target detection and reduce the requirement of the number 546 of antennas and naturally reduce the requirement of manufac-547 ture, deployment, and implementation. 548 the overlapped MIMO radar is very large as compared to 550 the combined antenna array of all BSs, the available DoF 551 is sufficient enough to mitigate interference to all the BSs. 552 We proposed to simultaneously share the spectrum with all 553 the BSs. In the case that the effective transmit array aperture 554 of the overlapped MIMO radar is not very large, we proposed 555 to select the optimal BS to minimize the degradation of radar